2023Activity reportProject-TeamAIRSEA

7.1.1 AGRIF

• Name:
  Adaptive Grid Refinement In Fortran
• Keyword:
  Mesh refinement
• Scientific Description:
  AGRIF is a Fortran 90 package for the integration of full adaptive mesh refinement (AMR) features within a multidimensional finite difference model written in Fortran. Its main objective is to simplify the integration of AMR potentialities within an existing model with minimal changes. Capabilities of this package include the management of an arbitrary number of grids, horizontal and/or vertical refinements, dynamic regridding, parallelization of the grids interactions on distributed memory computers. AGRIF requires the model to be discretized on a structured grid, like it is typically done in ocean or atmosphere modelling.
• Functional Description:
  AGRIF is a Fortran 90 package for the integration of full adaptive mesh refinement (AMR) features within a multidimensional finite difference model written in Fortran. Its main objective is to simplify the integration of AMR potentialities within an existing model with minimal changes. Capabilities of this package include the management of an arbitrary number of grids, horizontal and/or vertical refinements, dynamic regridding, parallelization of the grids interactions on distributed memory computers. AGRIF requires the model to be discretized on a structured grid, like it is typically done in ocean or atmosphere modelling.
• News of the Year:
  Within the framework of a European Copernicus contract, improvements have been made to the management of parallelization ( assignment of processors to computational grids).
• URL:
  https://­gitlab.­inria.­fr/­ldebreu/­agrif
• Publications:
  tel-01546328, hal-00387435
• Contact:
  Laurent Debreu
• Participant:
  Laurent Debreu

7.1.2 NEMOVAR

• Name:
  Variational data assimilation for NEMO
• Keywords:
  Oceanography, Data assimilation, Adjoint method, Optimal control
• Functional Description:
  NEMOVAR is a state-of-the-art multi-incremental variational data assimilation system with both 3D and 4D var capabilities, and which is designed to work with NEMO on the native ORCA grids. The background error covariance matrix is modelled using balance operators for the multivariate component and a diffusion operator for the univariate component. It can also be formulated as a linear combination of covariance models to take into account multiple correlation length scales associated with ocean variability on different scales. NEMOVAR has recently been enhanced with the addition of ensemble data assimilation and multi-grid assimilation capabilities. It is used operationnaly in both ECMWF and the Met Office (UK)
• Contact:
  Patrick Vidard
• Partners:
  CERFACS, ECMWF, Met Office

7.1.3 SWEET

• Name:
  Shallow Water Equation Environment for Tests, Awesome!
• Keywords:
  High-Performance Computing, Time integration methods
• Functional Description:

  SWEET supports periodic boundary conditions for * the bi-periodic plane (2D torus) * the sphere

  Space discretization * PLANE: Spectral methods based on Fourier space * PLANE: Finite differences * SPHERE: Spherical Harmonics

  Time discretization * Explicit RK * Implicit RK * Leapfrog * Crank-Nicolson * Semi-Lagrangian * Parallel-in-time ** Parareal ** PFASST ** Rational approximation of exponential Integrators (REXI) ...and many more time steppers...

  Special features * Graphical user interface * Fast Helmholtz solver in spectral space * Easy-to-code in C++ ...

  There’s support for various applications * Shallow-water equations on plane/sphere * Advection * Burgers’ ...

• URL:
  https://­schreiberx.­github.­io/­sweetsite/
• Contact:
  Martin Schreiber
• Partners:
  University of São Paulo, Technical University of Munich (TUM)

8.1.1 Numerical Schemes for Ocean Modelling

Participants: Eric Blayo, Laurent Debreu, Florian Lemarié, Gurvan Madec, Antoine Nasser, Pierre Lozano.

Beyond the hydrostatic assumption

With the increase of resolution, the hydrostatic assumption becomes less valid and the AIRSEA group also works on the development of non-hydrostatic ocean models. The treatment of non-hydrostatic incompressible flows leads to a 3D elliptic system for pressure that can be ill-conditioned, in particular with non geopotential vertical coordinates. That is why we favor the use of the non-hydrostatic compressible equations, that remove the need for a 3D resolution at the price of reincluding acoustic waves. For that purposes a detailed analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean was carried out 37 in part in the PhD of E. Duval. The proposed numerical approach has been implemented in the CROCO ocean model and tested in various flow configurations 56, 66.

Most large scale ocean models are based on the so-called “primitive equations”, which use the hydrostatic and incompressibility assumptions. However, with the increase of resolution, a systematic use of the hydrostatic assumption becomes less valid. The French regional oceanic modeling system CROCO (Coastal and Regional Ocean COmmunity model) developed these last years allows for the use of either the hydrostatic incompressible (HI) equations and the non-hydrostatic compressible (NHC) equations, the latter being much more computationally expensive. A natural idea is thus to limit the use of the NHC version to some particular regions of interest where the hydrostatic assumption is not relevant, and to nest such local NHC zooms within a larger model using the HI version. However such a coupling is quite delicate from a mathematical point of view, due to the different nature of hydrostatic and nonhydrostatic equations (where the vertical velocity is either a diagnostic or a prognostic variable). Following E. Duval's first work during her PhD, P. Lozano is working on the design of methods to couple local nonhydrostatic models to larger scale hydrostatic ones. An interesting lead consists in exploiting a decomposition of the solutions into vertical modes, possibly in association with Perfectly Matched Layers techniques. These first ideas are currently being tested in a prototype which allows for analytical solutions in simplified configurations.

	$1/4^{\circ }$	$1/8^{\circ }$	$1/{12}^{\circ }$
$\sigma$
$\sigma$ penalized
AVISO

Mean sea surface height in CROCO simulations at different resolutions for the standard case with terrain-following ($\sigma$) coordinates (top) and penalization (below). The third row shows the AVISO product for comparison

8.1.2 Coupling Methods for Oceanic and Atmospheric Models and representation of the Air-Sea Interface

Participants: Eric Blayo, Simon Clément, Hugues Lascombes De Laroussilhe, Florian Lemarié, Valentina Schüller.

The Airsea team is involved in the modeling and algorithmic aspects of ocean-atmosphere (OA) coupling. We have been actively working on the analysis of such coupling both in terms of continuous and numerical formulations. Particular attention is paid to the inclusion of physical parameterizations in our theoretical framework. Our activities have recently led to practical implementations in state-of-the-art oceanic and Earth system models. Our focus during the last few years has been on the following topics :

1. Continuous and discrete analysis of Schwarz algorithms for OA coupling    Members of the Airsea team have been developing coupling approaches for several years, based on so-called Schwarz algorithms. Schwarz-like domain decomposition methods are very popular in mathematics, computational sciences and engineering notably for the implementation of coupling strategies. However, for complex applications (like in OA coupling) it is challenging to have an a priori knowledge of the convergence properties of such methods. Indeed coupled problems arising in Earth system modeling often exhibit sharp turbulent boundary layers whose parameterizations lead to peculiar transmission conditions and diffusion coefficients 78. In the framework of S. Clément PhD 43, the well-posedness of the non-linear coupling problem including parameterizations has been addressed and a detailed continuous and discrete analysis of the convergence properties of the Schwarz methods has been pursued to entangle the impact of the different parameters at play in such coupling problem 42, 11. A general framework has been proposed to study the convergence properties at a (semi)-discrete level to allow a systematic comparison with the results obtained from the continuous problem. Such a framework allows to study more complex coupling problems whose formulation is representative of the discretization used in realistic coupled models.
2. A simplified atmospheric boundary layer model for oceanic purposes    Part of our activities within the ongoing SHOM 19CP07 project is dedicated to the development of a simplified model of the marine atmospheric boundary layer (called ABL1d) of intermediate complexity between a bulk parameterization and a full three-dimensional atmospheric model and to its integration to the NEMO general circulation model 64. A constraint in the conception of such a simplified model is to allow an apt representation of the downward momentum mixing mechanism and partial re-energization of the ocean by the atmosphere while keeping the computational efficiency and flexibility inherent to ocean only modeling. Realistic applications of the coupled NEMO-ABL1d modeling system have been carried out and the methodology is being integrated into the operational forecasting system operated by Mercator-Ocean. Over the last year the approach has also been implemented in the CROCO ocean model. A focus has been to find adequate ways to fill some gaps in the 1D approach using multiple scales asymptotic techniques to cast the equations in terms of perturbations around an ambient state given by a large-scale datasets. Such simplified model called ABL3d leads to clear improvements over ABL1d for academic semi-idealized cases. The objective is now to extend the analysis to realistic cases. In parallel, in the framework of the AIRSEA/ATOS collaboration, an objective is to design a surrogate via learning strategies of the response of the atmospheric boundary layer to anomalies in ocean surface temperatures and currents (work of H. Lascombes De Laroussilhe).
3. Impact of the coupling formulation in a realistic context    A Schwarz-like iterative method has been applied in a state-of-the-art Earth-System model (IPSL-CM6) to evaluate the consequences of inaccuracies in the usual ad-hoc ocean-atmosphere coupling algorithms used in realistic models 67, 68. Numerical results obtained with an iterative process show large differences at sunrise and sunset compared to usual ad-hoc algorithms, thus showing that synchrony errors inherent to ad-hoc coupling methods can be large. However, such an iterative coupling method is too costly to be implemented operationally in climate models. In order to keep the computational cost almost constant w.r.t. the usual non iterative approach, the iterative algorithm would need to be provided with a first guess close to the optimum, so as to achieve quasi-convergence in a single iteration. We aim to obtain such an approximation of the optimal state by learning techniques (work of A. Monsimer as part of the programme national de recherche en intelligence artificielle - PNRIA). A learning network based on a test dataset restricted to a few fixed regions has been set up, and is indeed able to provide a first iteration of good quality. The remaining step is to scale up to a global scale, with a view to making the method operationally applicable to a climate model. An other point is that for the simulations with IPSL-CM6 the iterative process was only applied over the ocean as it converges very slowly over sea-ice. We started to study the specific convergence problem occurring over sea-ice during the internship of P. Lozano. It allowed to explain the slow convergence and proposed ways around it. The next step is to use the single column version of EC-Earth climate model to make the link between our theoretical work and practical applications. On these last point, a collaboration has been set up with the University of Lund (Sweden) as part of V. Schüller's thesis.

These topics are addressed through strong collaborations between the applied mathematicians and the climate and operational community (Meteo-France, Ifremer, SHOM, Mercator-Ocean, LMD, and LOCEAN). Airsea team members play a major role in the structuration of a multi-disciplinary scientific community working on ocean-atmosphere coupling spanning a broad range from mathematical theory to practical implementations in climate and operational models.

8.1.3 Physics-Dynamics coupling: Consistent subgrid-scale modeling

Participants: Eric Blayo, Simon Clément, Florian Lemarié, Manolis Perrot.

The AIRSEA team works on topics around physics-dynamics coupling 52. Schematically, numerical models consist of two blocks generally identified as “physics” and “dynamics” which are often developed separately. The “Physics” represents unresolved or under-resolved processes with typical scales below model resolution while the “dynamics” corresponds to a discrete representation in space and time of resolved processes. Unresolved processes cannot be ignored because they directly influence the resolved part of the flow since energy is continuously transferred between scales. The interplay between resolved and unresolved scales is a large, incomplete and complex topic for which there is still much to do within the Earth system modeling community 63. During the last year we worked on the following topics :

1. Representation of the air-sea interface in coupled models    In the PhD work of S. Clément 43 a finite-volume discretization consistent with our knowledge of the underlying physical principles (e.g. the Monin-Obukhov theory in the surface layer) has been derived 12. This work will be taken up again as part of a Master's internship to solidify the theoretical basis and move on to practical assessments.
2. Representation of penetrative convection in oceanic models    Accounting for the mean effect of subgrid scale intermittent coherent structures like convective plumes is very challenging. Currently this is done very crudely in ocean models (vertical diffusion is locally increased to “mix” unstable density profiles). A difficulty is that in convective conditions, turbulent fluxes are dominated by processes unrelated to local gradients, thus invalidating the usual downgradient (a.k.a. eddy-diffusion) approach. In the framework of the PhD of M. Perrot, a first step is to study the derivation of mass-flux convection schemes arising from a multi-fluid decomposition to extend them specifically to the oceanic context. This extension is done under certain “consistency" constraints: energetic considerations and scale-awareness of the resulting model. Reference LES simulations have been developed to guide the formulation of unknown/uncertain free parameters (coefficients or functions) in the proposed extended mass-flux scheme. The Bayesian calibration of such free parameters will be undertaken.
3. Partially Lagrangian implementation of location uncertainty    Recent oceanic parameterizations "under Location Uncertainty" are based on the hypothesis that the small-scale processes are uncorrelated in time. The implementation of such parameterizations can be done in a Lagrangian manner, with rapidly moving grid points. The possibility of keeping the grid close to its original disposition is studied by S. Clement to understand how the time correlation induced by this constraint can be compensated by an Eulerian term.

Those topics are addressed through collaborations with the climate and operational community (Meteo-France, SHOM, Mercator-Ocean, and IGE). Two projects are currently funded, one on the energetically consistent discretization aspect (SHOM 19CP07, 2020-2024, PI: F. Lemarié) and one on the convection parameterization (Institut des Mathématiques pour la Planète Terre, 2021-2024, PIs: F. Lemarié and G. Madec). Furthermore, an ANR project, in which the Airsea team is involved, entitled PLUME was selected for funding in the latest ANR call. One of the objectives of this project is to use LES numerical simulations and laboratory experiments of deep convection to calibrate and evaluate physical parameterizations.

8.1.4 Machine learning for reconstruction of model parameters.

Participants: Laurent Debreu, Eugene Kazantsev, Arthur Vidard, Olivier Zahm.

Artificial intelligence and machine learning may be considered as a potential way to address unresolved model scales and to approximate poorly known processes such as dissipation that occurs essentially at small scales. In order to understand the possibility to combine numerical model and neural network learned with the aid of external data, we develop a network generation and learning algorithm and use it to approximate nonlinear model operators.

A potential way to reconstruct subgrid scales consists in application of the Image Super-Resolution methods that refer to the process of recovering high-resolution images from low-resolution image in computer vision and image processing. Recent years have shown remarkable progress of image super-resolution using machine learning techniques 79. We try to use this methodology in order to identify fine structure of the chaotic turbulent solution of a simple barotropic ocean model. After the learning the flow patterns obtained by the high resolution model, the neuron net can identify fine structure in the low-resolution model solution with better precision than bicubic interpolation.

Different techniques of neuron net construction have been analyzed. Full-connected networks, basic convolutional and encoder-decoder processes 61 as well as mixed architectures were compared with each other and with the classical interpolation of model solution on a low-resolution grid.

8.2.1 Model order reduction

Participants: Clémentine Prieur, Olivier Zahm, Romain Verdière.

In 32 we propose a gradient-enhanced algorithm for high-dimensional function approximation. The algorithm proceeds in two steps: firstly, we reduce the input dimension by learning the relevant input features from gradient evaluations, and secondly, we regress the function output against the pre-learned features. To ensure theoretical guarantees, we construct the feature map as the first components of a diffeomorphism, which we learn by minimizing an error bound obtained using Poincaré Inequality applied either in the input space or in the feature space. This leads to two different strategies, which we compare both theoretically and numerically and relate to existing methods in the literature. In addition, we propose a dimension augmentation trick to increase the approximation power of feature detection. A generalization to vector-valued functions demonstrate that our methodology directly applies to learning autoencoders. Here, we approximate the identity function over a given dataset by a composition of feature map (encoder) with the regression function (decoder). In practice, we construct the diffeomorphism using coupling flows, a particular class of invertible neural networks. Numerical experiments on various high-dimensional functions show that the proposed algorithm outperforms state-of-the-art competitors, especially with small datasets.

In a joint work 69 with Didier Georges (GIPSA Lab, Grenoble) and Mathieu Oliver (internship student), we proposed a spatialized extension of a SIR model that accounts for undetected infections and recoveries as well as the load on hospital services. The spatialized compartmental model we introduced is governed by a set of partial differential equations (PDEs) defined on a spatial domain with complex boundary. We proposed to solve the set of PDEs defining our model by using a meshless numerical method based on a finite difference scheme in which the spatial operators were approximated by using radial basis functions. Then we calibrated our model on the French department of Isère during the first period of lockdown, using daily reports of hospital occupancy in France. Our methodology allowed to simulate the spread of Covid-19 pandemic at a departmental level, and for each compartment. However, the simulation cost prevented from online short-term forecast. Therefore, we proposed to rely on reduced order modeling tools to compute short-term forecasts of infection number. The strategy consisted in learning a time-dependent reduced order model with few compartments from a collection of evaluations of our spatialized detailed model, varying initial conditions and parameter values. A set of reduced bases was learnt in an offline phase while the projection on each reduced basis and the selection of the best projection was performed online, allowing short-term forecast of the global number of infected individuals in the department. This work is going on in the framework of Robin Vaudry's PhD (co-supervised with Didier Georges). We are investigating the more complex setting of spatialized models taking into account the vaccination and the loss of immunity.

In the framework of Arthur Macherey's PhD (defended in June 2021), in collaboration with Anthony Nouy and Marie Billaud-Friess (Ecole Centrale Nantes), we have proposed algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation 40. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Then we turned to parametrized PDE and proposed stochastic algorithms in the framework of potentially high dimensional parameter space 23. A preliminary step was the development of a PAC algorithm in relative precision for bandit problem with costly sampling 41.

External collaborators: Arthur Macherey, Didier Georges and Matthieu Oliver

8.2.2 Design of experiments, climate scenarios and ocean simulation

Participants: Elise Arnaud, Eric Blayo, Angélique Saillet.

In the current context of rapid climate change, numerical models are important tools for predicting climate change and assisting decision making by policy makers (e.g. in terms of protection of marine areas, land use or definition of fishing quotas). The huge complexity of the models and the generally very high cost of numerical simulations make an exhaustive exploration of the parameter space, corresponding to all possible scenarios and all model internal options, completely illusory. The idea is therefore to exploit statistical tools for the design of experiments. These tools make it possible to identify specific combinations that provide maximum information on a given quantity of interest (for example an indicator of ecosystem health) calculated from the simulation performed. The design of experiments also has the advantage that it can be built adaptively, with the aim of taking into account the results of pre-existing simulations, performed with various models, under various scenarios. In Angelique Saillet's PhD, we aim at developing methodologies to address this open research domain, exploiting theoretical tools such as sequential design of experiments, enrichment strategies, and multi-fidelity Gaussian process regression.

8.2.3 Multifidelity Variational Data assimilation

Participants: Arthur Vidard, Hélène Hénon.

Incremental Variational Data Assimilation addresses the non-linear least-square optimization challenge inherent in variational data assimilation by iteratively minimizing a sequence of linear least-squares cost functions. In the context of Hélène Hénon's PhD research, we explore the potential application of a multifidelity approach to tackle these linear least-square problems. This involves considering varying levels of fidelity or accuracy in the computational models, offering a nuanced strategy to enhance the efficiency and effectiveness of the iterative optimization process.

8.3.1 Transport-based density estimation for inverse problems

Participants: Olivier Zahm.

Transport map methods offer a powerful statistical learning tool that can couple a target high-dimensional random variable with some reference random variable using invertible transformations. The paper 24 presents new computational techniques for building the Knothe–Rosenblatt (KR) rearrangement based on general separable functions. We first introduce a new construction of the KR rearrangement—with guaranteed invertibility in its numerical implementation—based on approximating the density of the target random variable using tensor-product spectral polynomials and downward closed sparse index sets. Compared to other constructions of KR arrangements based on either multi-linear approximations or nonlinear optimizations, our new construction only relies on a weighted least square approximation procedure. Then, inspired by the recently developed deep tensor trains (Cui and Dolgov, Found. Comput. Math. 22:1863–1922, 2022), we enhance the approximation power of sparse polynomials by preconditioning the density approximation problem using compositions of maps. This is particularly suitable for high-dimensional and concentrated probability densities commonly seen in many applications. We approximate the complicated target density by a composition of self-reinforced KR rearrangements, in which previously constructed KR rearrangements—based on the same approximation ansatz—are used to precondition the density approximation problem for building each new KR rearrangement. We demonstrate the efficiency of our proposed methods and the importance of using the composite map on several inverse problems governed by ordinary differential equations (ODEs) and partial differential equations (PDEs).

In the paper 3 we present a novel offline-online method to mitigate the computational burden of the characterization of posterior random variables in statistical learning. In the offline phase, the proposed method learns the joint law of the parameter random variables and the observable random variables in the tensor-train (TT) format. In the online phase, the resulting order-preserving conditional transport can characterize the posterior random variables given newly observed data in real time. Compared with the state-of-the-art normalizing flow techniques, the proposed method relies on function approximation and is equipped with a thorough performance analysis. The function approximation perspective also allows us to further extend the capability of transport maps in challenging problems with high-dimensional observations and high-dimensional parameters. On the one hand, we present novel heuristics to reorder and/or reparametrize the variables to enhance the approximation power of TT. On the other hand, we integrate the TT-based transport maps and the parameter reordering/reparametrization into layered compositions to further improve the performance of the resulting transport maps. We demonstrate the efficiency of the proposed method on various statistical learning tasks in ordinary differential equations (ODEs) and partial differential equations (PDEs).

In the paper 1, we address the problem of the parametrization and the learning of monotone triangular transport maps. Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond. Monotone triangular transport maps—approximations of the Knothe–Rosenblatt (KR) rearrangement are a canonical choice for these tasks. Yet the representation and parameterization of such maps have a significant impact on their generality and expressiveness, and on properties of the optimization problem that arises in learning a map from data (e.g., via maximum likelihood estimation). We present a general framework for representing monotone triangular maps via invertible transformations of smooth functions. We establish conditions on the transformation such that the associated infinite-dimensional minimization problem has no spurious local minima, i.e., all local minima are global minima; and we show for target distributions satisfying certain tail conditions that the unique global minimizer corresponds to the KR map. Given a sample from the target, we then propose an adaptive algorithm that estimates a sparse semi-parametric approximation of the underlying KR map. We demonstrate how this framework can be applied to joint and conditional density estimation, likelihood-free inference, and structure learning of directed graphical models, with stable generalization performance across a range of sample sizes.

External collaborators: Sergey Dolgov, Tiangang Cui, Youssef Marzouk, Ricardo Baptista

8.3.2 Dimension reduction of high-dimensional inference problems

Participants: Olivier Zahm, Rafael Flock, Clément Duhamel, Clémentine Prieur, Qiao Chen, Elise Arnaud.

In the paper 28 we investigate the approximation of high-dimensional target measures as low-dimensional updates of a dominating reference measure. This approximation class replaces the associated density with the composition of: (i) a feature map that identifies the leading principal components or features of the target measure, relative to the reference, and (ii) a low-dimensional profile function. When the reference measure satisfies a subspace $\phi$-Sobolev inequality, we construct a computationally tractable approximation that yields certifiable error guarantees with respect to the Amari $\alpha$-divergences. Our construction proceeds in two stages. First, for any feature map and any $\alpha$-divergence, we obtain an analytical expression for the optimal profile function. Second, for linear feature maps, the principal features are obtained from eigenvectors of a matrix involving gradients of the log-density. Neither step requires explicit access to normalizing constants. Notably, by leveraging the $\phi$-Sobolev inequalities, we demonstrate that these features universally certify approximation errors across the range of $\alpha$-divergences $\alpha \in (0,1]$. We then propose an application to Bayesian inverse problems and provide an analogous construction with approximation guarantees that hold in expectation over the data. We conclude with an extension of the proposed dimension reduction strategy to nonlinear feature maps.

In the paper 26 we consider high-dimensional Bayesian inverse problems with arbitrary likelihood and product-form Laplace prior for which we provide a certified approximation of the posterior density in the Hellinger distance. The approximate posterior density differs from the prior density only in a small number of relevant coordinates that contribute the most to the update from the prior to the posterior. We propose and analyze a gradient-based diagnostic to identify these relevant coordinates. Although this diagnostic requires computing an expectation with respect to the posterior, we propose tractable methods for the classical case of a linear forward model with Gaussian likelihood. Our methods can be employed to estimate the diagnostic before solving the Bayesian inverse problem via, e.g., Markov chain Monte Carlo (MCMC) methods. After selecting the coordinates, the approximate posterior density can be efficiently inferred since most of its coordinates are only informed by the prior. Moreover, specialized MCMC methods, such as the pseudo-marginal MCMC algorithm, can be used to obtain less correlated samples when sampling the exact posterior density. We show the applicability of our method using a 1D signal deblurring problem and a high-dimensional 2D super-resolution problem. In Qiao Chen's PhD project, we propose novel approach to jointly reducing parameter and data dimensions in Bayesian inverse problems, addressing a gap in existing research that typically treats these reductions separately. The proposed method leverages gradient information to ensure controlled posterior approximation errors and enables goal-oriented dimension reduction by specifying a parameter subspace of interest. An efficient "Alternating Eigendecomposition" algorithm is presented for solving both coupled and goal-oriented problems. Demonstrating applicability in Bayesian optimal experimental design, the method connects goal-oriented data dimension reduction to maximizing the expected information gain. This overcomes the limitations of existing approaches by accommodating nonlinear models and non Gaussian posteriors. Additionally, the method offers a relaxed perspective on the NP-hard combinatorial optimization problem in optimal experimental design, paving the way for the identification of optimal subspaces and the use of advanced sampling techniques for sensor placement.

Reduced models are also developed in the framework of robust inversion. In 46, we have combined a new greedy algorithm for functional quantization with a Stepwise Uncertainty Reduction strategy to solve a robust inversion problem under functional uncertainties. In a more recent work, we further reduced the number of simulations required to solve the same robust inversion problem, based on Gaussian process meta-modeling on the joint input space of deterministic control parameters and functional uncertain variable 47. These results are applied to automotive depollution. This research axis was conducted in the framework of the Chair OQUAIDO. This research axis is till active in the team through Clément Duhamel's PhD, in collaboration with Céline Helbert (Ecole Centrale Lyon) and Miguel Munoz Zuniga, Delphine Sinoquet (IFPEN, Rueil Malmaison). In particular in 4 we proposed a SUR version of the Bichon criterion for excursion set estimation.

External collaborators: Youssef Marzouk, Matthew Li, Yiqiu Dong, Felipe Uribe

8.3.3 Machine Learning based preconditioners for variational data assimilation

Participants: Victor Trappler, Arthur Vidard.

In Variational Data Assimilation, the analysis step boils down to solving a high-dimensional nonlinear least-squares problem. In practical terms, this minimization process involves iterative inversions of large matrices, which may be ill-conditioned, formed through linearizations of the forward model. To enhance the convergence rate of these methods and thereby reduce computational demands, preconditioning techniques are commonly employed to obtain better-conditioned matrices. However, these techniques typically rely on either the sparsity pattern of the matrix to be inverted or some spectral information.

In our approach, we propose the utilization of Deep Neural Networks to construct a preconditioner. This preconditioner is trained using properties derived from the singular value decomposition, and the training dataset can be dynamically constructed online as needed. This innovative approach aims to improve the efficiency of the inversion process and address the challenges posed by the high dimensionality and potential ill-conditioning of the matrices involved. This work was presented in two conferences 35, 34.

Scientific context

Forecasting geophysical  systems require complex models, which sometimes need to be coupled, and which make use of data assimilation. The objective of this project is, for a given output of such a system, to identify the most influential parameters, and to evaluate the effect of uncertainty in input parameters on model output. Existing stochastic tools are not well suited for high dimension problems (in particular time-dependent problems), while deterministic tools are fully applicable but only provide limited information. So the challenge is to gather expertise on one hand on numerical approximation and control of Partial Differential Equations, and on the other hand on stochastic methods for sensitivity analysis, in order to develop and design innovative stochastic solutions to study high dimension models and to propose new hybrid approaches combining the stochastic and deterministic methods. We took part to the writing of a position paper on the future of sensitivity analysis 75.

8.4.1 Global sensitivity analysis with dependent inputs

An important challenge for stochastic sensitivity analysis is to develop methodologies which work for dependent inputs. Recently, the Shapley value, from econometrics, was proposed as an alternative to quantify the importance of random input variables to a function. Owen 71 derived Shapley value importance for independent inputs and showed that it is bracketed between two different Sobol' indices. Song et al. 77 recently advocated the use of Shapley value for the case of dependent inputs. In a recent work 70, in collaboration with Art Owen (Standford's University), we showed that Shapley value removes the conceptual problems of functional ANOVA for dependent inputs. We also investigated further the properties of Shapley effects in 60. By the end of 2021, Clémentine Prieur started a collaboration with Elmar Plischke (TU Clausthal, Germany) and Emanuele Borgonovo (Bocconi University, Milan, Italy) to estimate total Sobol' indices as a measure for variable selection even in the framework of dependent inputs. In particular, it allows to estimate total Sobol' indices for inputs defined on a non rectangular domain 2. This setting is of particular interest for applications where the input space is reduced due to physical constraints on the quantity of interest. This last setting was encountered, e.g., in Maria Belén Heredia's PhD thesis (defended in december, 2020), and analyzed by estimating Shapley effects with a nonparametric procedure based on nearest neighbors 38 (see Section 8.4.3 for more details). In October 2021, Ri Wang has started a PhD, cosupervised by Clémentine Prieur and Véronique Maume-Deschamps (ICJ, Lyon 1) on the estimation of quantile oriented sensitivity indices in the framework of dependent inputs, by means of random forests or other machine learning tools. Ri Wang has received a funding from the Chinese Scientific Council.

External collaborators: Maria Belén Heredia, Adrien Hirvoas, Alexandre Janon

8.4.2 Sensitivity analysis in pesticide transfer models

Participants: Arthur Vidard, Emilie Rouzies, Katarina Radisic.

Pesticide transfer models play a crucial role in predicting and preventing water body pollution. However, deploying these models in operational settings demands a thorough understanding of their structure, particularly the influential parameters. The objective of E. Rouziès PhD (defended in march 2023 76)) was to conduct a global sensitivity analysis (GSA) on the PESHMELBA model (pesticide and hydrology: modeling at the catchment scale). The challenge lies in the modular and intricate structure of the model, which couples various physical processes, resulting in a high-dimensional input space and significant computational costs that limit the number of feasible runs. An extensive use of different metamodelling techniques made it feasible for such an application 9.

The complexity is further compounded when considering the temporal dimension. We explore this aspect in K. Radisic's PhD, using polynomial chaos extension to conduct a global sensitivity analysis on the small agricultural catchment of Morcille during a winter rainstorm, as detailed in 8. This study expanded to include a comparison of sensitivity analyses under different rainfall forcings and proposed a global index that considers rainfall stochasticity 17.

These initial steps paved the way for developing a method for robust calibration through stochastic metamodelling of PESHMELBA, utilizing stochastic polynomial chaos expansion. Subsequent enhancements were observed by refining the inference of marginal distributions through a Gaussian mixture.

8.4.3 Green sensitivity for multivariate and functional outputs

Participants: Clémentine Prieur.

Another research direction for global SA algorithm starts with the report that most of the algorithms to compute sensitivity measures require special sampling schemes or additional model evaluations so that available data from previous model runs (e.g., from an uncertainty analysis based on Latin Hypercube Sampling) cannot be reused. One challenging task for estimating global sensitivity measures consists in recycling an available finite set of input/output data. Green sensitivity, by recycling, avoids wasting. These given data have been discussed, e.g., in 72, 73. Most of the given data procedures depend on parameters (number of bins, truncation argument…) not easy to calibrate with a bias-variance compromise perspective. Adaptive selection of these parameters remains a challenging issue for most of these given-data algorithms. In the context of María Belén Heredia's PhD thesis, we have proposed 39 a non-parametric given data estimator for aggregated Sobol' indices, introduced in 62 and further developed in 50 for multivariate or functional outputs. We also introduced aggregated Shapley effects and we have extended a nearest neighbor estimation procedure to estimate these indices 38. We also started a collaboration with Sébastien Da Veiga (Safran Tech), Agnès Lagnoux, Thierry Klein and Fabrice Gamboa (Institut de Mathématiques de Toulouse) on a new nonparametric estimation procedure for closed Sobol' indices of any order based on U-statistics 25.

8.4.4 Global sensitivity analysis for parametrized stochastic differential equations

Participants: Clémentine Prieur.

Many models are stochastic in nature, and some of them may be driven by parametrized stochastic differential equations (SDE). It is important for applications to propose a strategy to perform global sensitivity analysis (GSA) for such models, in presence of uncertainties on the parameters. In collaboration with Pierre Etoré (DATA department in Grenoble), Clémentine Prieur proposed an approach based on Feynman-Kac formulas 48. The research on GSA for stochastic simulators is still ongoing, first in the context of the MATH-AmSud project FANTASTIC (Statistical inFerence and sensitivity ANalysis for models described by sTochASTIC differential equations) with Chile and Uruguay, secondly through the PhD thesis of Henri Mermoz Kouye, co-supervised by Clémentine Prieur, in collaboration with Gildas Mazo and Eliza Vergu (INRAE, département MIA,  Jouy). Note that our recent developments with P. Etoré on GSA for parametrized SDEs and are strongly related to reduced order modeling (see Section 8.2), as GSA requires jose leon intensive computations of the quantity of interest. In collaboration with Pierre Etoré and Joël Andrepont (master internship started in spring 2021), Clémentine Prieur is working on GSA for parametrized SDEs based on Fokker-Planck equation and kernel based sensitivity indices. Note that a joint work between Pierre Etoré, Clémentine Prieur and Jose R. Leon has been published 6, related to exact or approximated computation of Kolmogorov hypoelliptic equations (KHE). Even if not dealing with GSA, it could be a starting point for analyzing sensitivity for models described by a parametrized version of KHE. Concerning Henri Mermoz Kouye's PhD thesis, the approach was different. We are interested in GSA for compartmental stochastic models. Our methodology relies on a deterministic representation of continuous time Markov chains stochastic compartmental models 27.

8.5.1 Bayesian calibration

Participants: Adama Barry, Clémentine Prieur.

Physically-based avalanche propagation models must still be locally calibrated to provide robust predictions, e.g. in long-term forecasting and subsequent risk assessment. Friction parameters cannot be measured directly and need to be estimated from observations. Rich and diverse data is now increasingly available from test-sites, but for measurements made along flow propagation, potential autocorrelation should be explicitly accounted for. In the context of María Belén Heredia's PhD, in collaboration with IRSTEA Grenoble, we have proposed in 55 a comprehensive Bayesian calibration and statistical model selection framework with application to an avalanche sliding block model with the standard Voellmy friction law and high rate photogrammetric images. An avalanche released at the Lautaret test-site and a synthetic data set based on the avalanche were used to test the approach. Results have demonstrated i) the efficiency of the proposed calibration scheme, and ii) that including autocorrelation in the statistical modelling definitely improves the accuracy of both parameter estimation and velocity predictions. In the context of the energy transition, wind power generation is developing rapidly in France and worldwide. Research and innovation on wind resource characterisation, turbin control, coupled mechanical modelling of wind systems or technological development of offshore wind turbines floaters are current research topics. In particular, the monitoring and the maintenance of wind turbine is becoming a major issue. Current solutions do not take full advantage of the large amount of data provided by sensors placed on modern wind turbines in production. These data could be advantageously used in order to refine the predictions of production, the life of the structure, the control strategies and the planning of maintenance. In this context, it is interesting to optimally combine production data and numerical models  in order to obtain highly reliable models of wind turbines. This process is of interest to many industrial and academic groups and is known in many fields of the industry, including the wind industry, as "digital twin”. The objective of Adrien Hirvoas's PhD work was to develop of data assimilation methodology to build the "digital twin" of an onshore wind turbine. Based on measurements, the data assimilation should allow to reduce the uncertainties of the physical parameters of the numerical model developed during the design phase to obtain a highly reliable model. Various ensemble data assimilation approches are currently under consideration to address the problem.  In the context of this work, it is necessary to develop algorithms of identification quantifying and ranking all the uncertainty sources. This work was done in collaboration with IFPEN 58, 57. The work on model calibration is still ongoing in our team, through the PhD thesis of Adama Barry. We are finishing a work on designs for physical and numerical calibration in the framework of calibration of costly to evaluate numerical models.

8.5.2 Simulation & Estimation of EPIdemics with Algorithms

Participants: Clémentine Prieur.

Due to the sanitary context, Clémentine Prieur decided to join a working group, SEEPIA Simulation & Estimation of EPIdemics with Algorithms, animated by Didier Georges (Gipsa-lab). A first work has been published 53. An extension of the classical pandemic SIRD model was considered for the regional spread of COVID-19 in France under lockdown strategies. This compartment model divides the infected and the recovered individuals into undetected and detected compartments respectively. By fitting the extended model to the real detected data during the lockdown, an optimization algorithm was used to derive the optimal parameters, the initial condition and the epidemics start date of regions in France. Considering all the age classes together, a network model of the pandemic transport between regions in France was presented on the basis of the regional extended model and was simulated to reveal the transport effect of COVID-19 pandemic after lockdown. Using the the measured values of displacement of people mobilizing between each city, the pandemic network of all cities in France was simulated by using the same model and method as the pandemic network of regions. Finally, a discussion on an integro-differential equation was given and a new model for the network pandemic model of each age was provided. As already mentioned in Section 8.2, Clémentine Prieur went on working on the pandemic, in collaboration with Didier Georges (GIPSA Lab, Grenoble). Both of them supervised the internship of Matthieu Oliver, submitting a work proposing time-dependent reduced order modeling for short-term forecast from a spatialized SIR model 69. Robin Vaudry started in October 2021 a PhD, funded by the CNR research platform MODCOV19, and cosupervised by Clémentine Prieur and Didier Georges. The objective of this PhD is to solve inverse problems related to spatialized and ages structured commpartmental models of COVID19 pandemic.

8.5.3 Parameter estimation under uncertainties

Participants: Exaucé Luweh Adjim Ngarti, Arthur Vidard, Elise Arnaud, Victor Trappler.

Estimating key parameters in numerical models is a crucial aspect of numerical simulation, particularly when some parameters are not directly observable. Traditional estimation methods infer these parameters indirectly from their effects on observable variables, thus introducing uncertainties. In addition to the parameters to be estimated, there are often uncertain and uncontrollable nuisance parameters in the numerical model. Although variational inference is effective in ideal scenarios, its application in the context of nuisance parameters is less explored. Not accounting for the stochastic nature of these nuisance parameters leads to suboptimal estimation of said parameters due to compensation of errors. These nuisance parameters can be modeled as a random variable, and therefore the numerical model is redefined as a random variable. We formulate the problem in a Bayesian framework where we aim at estimating the posterior distribution minimizing the Kullback Leibler distance over a family of parametrized distributions. To do so, we integrate generative neural networks such as normalizing flows to enhance the expressiveness of this family. We apply these methods to the shallow water model, aiming at estimating the friction coefficient, a key parameter in coastal regions that defines the roughness of the seabed. The nuisance parameters represent the boundary forcing due to tidal frequencies and amplitudes.

8.6.1 Dynamic compute-resource utilization

Participants: Martin Schreiber.

The way how applications are executed on supercomputers still follows a traditional static resource allocation pattern: Computing resources are allocated at the start of a job which executes the application and are only released at the end of the job's runtime. This still follows the way of running jobs since decades where a dynamic resource allocation over the application's runtime would lead to several benefits: higher utilization of the computing resources, ad-hoc allocation of AI accelerator cards, less energy consumption, faster response for interactive jobs, improved data locality and I/O over the full runtime, support of urgent computing without necessarily killing running jobs, etc. Various attempts have been conducted under different terminologies used such as “evolving” jobs (application-driven dynamic resource changes) and “malleability” (system-driven dynamic resource changes) where we see a hybridization of them required for reaching optimal results.

We currently investigate possibilities to extend the MPI parallel programming model (which is the de-facto standard in HPC) and also models beyond MPI with such interfaces. As part of that, we participate in regular MPI Session working group meetings where certain effort has been done to investigate such interfaces. Based on previous work 49, 59 we worked on “A Case Study on PMIx-Usage for Dynamic Resource Management interface to a resource manager” 13.

External collaborators: Daniel Holmes, Dominik Huber, Howard Pritchard, Martin Schulz,

8.6.2 Hardware-aware numerics

Participants: Martin Schreiber.

We made further progress toward a Domain-Specific Language (DSL) for the CROCO ocean simulation model to close the increasing gap between the numerics and HPC with a separation of concerns. Such a DSL would allow applied mathematicians to express their model equations in a high-level language and HPC experts to develop tools to automatically transform this into highly performing code on the target programming model and corresponding architecture. For our DSL, we work with PSyclone, a code generation and transformation system for Fortran-based developments, and we would like to gratefully acknowledge various developments (partly unpublished) of PSyclone developers that accelerated our success. Progress has been made on three pillars:

The first pillar is a proof-of-concept on directly using PSyclone in the support of GPU-based architectures: Using the PSyclone NEMO API and our extensions, we can parse, analyze, and automatically insert OpenACC statements in the dynamical core of the CROCO ocean model. With this, we could reproduce a formerly hand-ported and highly optimized OpenACC version with a similar performance, showing the potential to develop a DSL around this.

As a second pillar, we also started with a proof-of-concept to automatically insert code statements implementing MPI communication. This prototype analyzes deep data dependencies to determine communication dependencies and implements the required halo exchanges using asynchronous MPI operations, including in-depth studies of this (see Master's thesis of Anna Mittermair 2023_MA_anna_mittermair.pdf).

The third pillar is on the data assimilation requiring the computation of adjoints of time steps. Realizing this by hand is a non-trivial process and requires maintenance by an expert every time the numerics are updated. We successfully investigated using PSyclone for automatically generating code for adjoints as a proof-of-concept for simple ODE examples psyclone-autodiff.readthedocs.io.

These three pillars will form the fundament for the next steps in developing a DSL for the Croco ocean model which will be embedded into Fortran.

External collaborators: Rupert Ford, Anna Mittermair, Andrew Porter, Sergi Siso

8.6.3 New time-integration methods

Participants: Martin Schreiber, Rishabh Bhatt, Laurent Debreu, Arthur Vidard.

We investigate new time-integration methods by considering HPC requirements, targeting a better wallclock time vs.  error ratio. These numerical methods include exponential, semi-Lagrangian, and parallel-in-time integration methods. Our team and collaborators have made significant progress over the last years. However, publishable results have not yet been generated or are currently in production.

As part of a collaboration with the University of São Paulo (USP), we investigated exponential integration methods based on Faber polynomials with a recently accepted publication 74. Although this paper mainly focuses on seismic wave propagation, these results can also be applied to the linearized fast modes in atmospheric models, e.g., as part of time-splitting methods.

In previous work, we have been able to show significant speedups using the Parallel Full Approximation Scheme in Space and Time (PFASST) parallel-in-time method for the shallow-water equations on the rotating sphere with an IMEX-SDC scheme using benchmarks which are used for the development of dynamical cores 54. Motivated by this work, we investigated this in collaboration with USP using the MGRIT parallel-in-time method. We developed a novel filtering method specific to each multi-level; see 31. It allows running the shallow-water equations on the rotating sphere without artificial viscosity on the target level and with more than two levels, which was considered a significant challenge.

On a related topic, Rishabh Bhatt successfully defended his PhD in December 2023 20, his research focused on the application of time parallelization algorithms to enhance variational data assimilation techniques. In this framework, each iteration of the optimization algorithm involves the integration of the direct model through a time-parallel method, specifically employing the Parareal algorithm 65. The optimization process utilizes a modified version of the inexact conjugate gradient method 51, where matrix-vector multiplications are facilitated through Parareal, introducing a level of inexactness. The convergence conditions of the inexact conjugate gradient method enable adaptive use of Parareal by monitoring errors in matrix-vector products, maintaining accuracy levels comparable to those achieved with the conventional conjugate gradient method. To ensure practical implementation, computationally challenging norms are replaced with easily calculable approximations. The efficacy of this approach was validated by its application to both one and two-dimensional shallow water models. For the more intricate two-dimensional model, a Krylov-enhanced subspace Parareal version was employed, demonstrating accelerated convergence and reduced iteration counts.

External collaborators: Pedro S. Peixoto, João C. Steinstraesser

10.1.1 Visits of international scientists

10.2.1 Other european programs/initiatives

10.2.2 Collaborations with Major European Organizations

• Partner: SAMO board
• SAMO board is in charge of the organization of the SAMO (sensitivity analysis of model outputs) conferences, every three years. It is strongly supported by the Joint Research Center of the European Commission. Clémentine Prieur is the current chair of SAMO-board Executive Committee and a member of its Scientific Committee.

10.3.1 ANR

• A 4-year contract: ANR MOTIONS (Multiscale Oceanic simulaTIONS based on mesh refinement strategies with local adaptation of dynamics and physics). PI: F. Lemarié (Jan. 2024 - Dec. 2027). Other partners: Laboratoire d’Aérologie, UMR 5560 (LAERO), Service Hydrographique et Océanographique de la Marine (SHOM), Institut Camille Jordan, UMR5208 (ICJ), and Laboratoire d’Etudes en Géophysique et Océanographie Spatiales, UMR5566 (LEGOS). The MOTIONS project aims at delivering robust and efficient numerical algorithms allowing an innovative multiscale modeling strategy based on block-structured mesh refinement with local adaptation of model equations, numerics and physics in selected areas of interest. The target application to evaluate numerical developments is the simulation of important fine-scale non-hydrostatic processes and their feedback to larger scales within the Mediterranean / North-East Atlantic dynamical continuum.
• A 4-year contract: ANR PLUME (Observation and Parameterization of Oceanic Convection). PI: B. Deremble (CNRS), Inria PI : F. Lemarié. The objectives of the project are threefold: (1) build a consistent database of convective events (both in the lab and with a numerical model) in order to calibrate free parameters of parameterizations of deep convection. (2) characterize the structure of the thermal plumes in a well defined parameter space that characterizes the rotating/non rotating state and forced vs free convection (3) use a data driven approach to formulate a model of convection without any preconceived bias about the mathematical formulation.
• A 4-year contract: ANR ADOM (Asynchronous Domain decomposition methods) anr.fr/Projet-ANR-18-CE46-0008
• A 5-year contract: ANR MELODY (Bridging geophysics and MachinE Learning for the modeling, simulation and reconstruction of Ocean DYnamic) anr.fr/Projet-ANR-19-CE46-0011
• A 5-year contract with the French Navy (SHOM) on the improvment of the CROCO ocean model www.croco-ocean.org.
• • Title:
    MEDIATION. Methodological developments for a robust and efficient digital twin of the ocean.
  • Duration:
    2022-2027
  • Funding:
    French priority research program (PPR) ”Ocean and Climate"
  • Partners:
    • Inria (DATAMOVE and ODYSSEY teams)
    • CNRS
    • IFREMER
    • IMT-Atlantique
    • IRD
    • Metéo-France
    • SHOM
    • Univ. Grenoble Alpes
    • Univ. Aix-Marseille.
  • Inria contact:
    Laurent Debreu
  • Coordinator:
    Laurent Debreu
  • Summary:
    The MEDIATION project targets two questions: how will global change impact the functioning of regional marine ecosystems, and how to evaluate the effect of measures to preserve the environment? With two main demonstrators on the French coasts (Atlantic and Mediterranean), MEDIATION combines methodological developments in numerical sciences (taking into account uncertainties, high performance computing and artificial intelligence) with advances in the modeling of physical, biogeochemical and biological processes in the ocean. It aims at setting up a modeling chain, integrating data and allowing to significantly increase the number of scenarios (climate change, human activities) evaluated. The digital tools developed will also contribute to a better science-society-policy interaction

10.3.2 Inria Challenge

• Sea Uncertainty Representation and Forecast (SURF),
• Coord : Airsea (A. Vidard),
• Partenaires Inria : Ange, Cardamom, Fluminance, Lemon, Mingus, Defi
• Partenaires extérieurs: BRGM, Ifremer, SHOM

10.3.3 Other Initiatives

• A 3-year contract (started in Sept 2021) funded by the Institut des Mathématiques pour la Planète Terre (IMPT) on the topic "Modélisation cohérente des échelles sous-maille pour les modèles océaniques de climat" (PI: F. Lemarié).
• E. Blayo is co-advising the PhD thesis of Valentin Bellemin-Laponnaz with IGE Lab, in the framework of the NASA-CNES working group on the SWOT satellite.
• Clémentine Prieur is currently a member of the Executive Committee of GdR MASCOT NUM (GDR3179, funded by INSMI @ CNRS) which she chaired during the period 2010-2017.

11.1.1 Scientific events: organisation

• Martin Schreiber organized the “1st EuroHPC Workshop on Malleability in HPC”
• Martin Schreiber organized the “1st EuroHPC malleability hackathon” in Grenoble
• The AIRSEA team organized the PDEs on the sphere workshop in Grenoble.
• Martin Schreiber organized with others the Minisymposium on “Performance and Real-World Applications” at the SIAM CSE 23 in Amsterdam, NL
• E. Blayo organized a one-week school Traitement des Données Massives et Apprentissage in Grenoble, June 5-9.
• Clémentine Prieur is the general chair of next SAMO conference (to be held in Genoble in 2025).

11.1.2 Scientific events: selection

11.1.3 Journal

11.1.4 Invited talks

• E. Blayo was invited as plenary speaker for the “Journées Scientifiques Inria 2023”, Bordeaux, August 30 - September 1.
• Clémentine Prieur was invited to give a talk at Workshop Prévisibilité dans les sciences de l'atmosphère, les océans ou le climat of GdR défis théoriques pour les sciences du climat, October 2-3, 2023, IHP Paris.
• Clémentine Prieur was invited to give a series of talks at virtual seminar on sensitivity analysis (co-organized by H. Moore, Univ. of Florida and R. Smith, North Carolina State Univ.). Her first talk was given in Dec. 2023 and the next one is already planed for February, 2024.
• Clémentine Prieur was invited to give a talk at Bocconi University (Milano, Italy) in November, 2023.
• Martin Schreiber: “Time integration methods of climate and weather simulations: Of fairy tales and co-design”, University of Colorado Boulder, Computer Science Seminar
• Martin Schreiber: “Updates on MPI sessions & new dynamic processes”, International Supercomputing (ISC) 2023, Hambourg, GER (talk in BoF)

11.1.5 Leadership within the scientific community

• L. Debreu is the chair of the CNRS-INSU research program LEFE-MANU on mathematical and numerical methods for ocean and atmosphere programmes.insu.cnrs.fr/lefe/cs_actions/manu/ since April 2018.
• F. Lemarié is the co-leader with Mike Bell (UK Met Office) and Sybille Téchené (CNRS) of the NEMO (www.nemo-ocean.eu) Working Group on numerical kernel development.
• M. Schreiber is a co-organizer of Birds of feather “Enabling I/O and Computation Malleability in High-Performance Computing” at Supercomputing 2023, Denver, USA

11.1.6 Scientific expertise

• L. Debreu is a member of the steering committee of the CROCO ocean model www.croco-ocean.org
• L. Debreu is a member of the evaluation committee of the axis Interfaces: mathematics, numerical sciences - earth and and environmental sciences of the French National Research Agency.
• Martin Schreiber is a member of the MPI Forum (representing the Université Grenoble Alpes) and in particular active in the MPI Session workgroup.
• Martin Schreiber is a member of the OpenMP ARB (representing Inria).
• As part of the TIME-X project, Martin Schreiber is responsible for organizing and determining possible collaboration topics with other EuroHPC-19 projects.
• Martin Schreiber was a reviewer in “SIGAP CNRS”
• E. Blayo is a member of the scientific committee of IMPT (Institut Mathématique pour la Planète Terre)
• Clémentine Prieur is advisor to the scientific council of IFPEN.

11.1.7 Research administration

• E. Blayo is a deputy director of the Jean Kuntzmann Lab.
• Clémentine Prieur is local correspondant in Grenoble for the Mathematical Society of France (SMF).  
• Clémentine Prieur is a member of the MSTIC pole council of UGA.  
• Clémentine Prieur is responsible for the applied math speciality for doctoral school MSTII edmstii.univ-grenoble-alpes.fr

11.2.1 Teaching

• Licence: E. Blayo, analysis and algebra, 145h, L1, University Grenoble Alpes, France
• Licence: E. Arnaud, Mathematics for engineers, 50h, L2, UGA, France
• Licence: E. Arnaud, Statistics, 20h, L2, UGA, France
• Licence: Martin Schreiber, Advanced Analysis & Algebra, L1, 69h, UGA, France
• Licence: C. Kazantsev, Mathématiques approfondies pour l'ingénieur, 36h, L2, UGA, France
• Licence: C. Kazantsev, Mathématiques pour les sciences de l'ingénieur, 36h, L2, UGA, France
• Master: E. Blayo, Partial Differential Equations, 24h, M1, University Grenoble Alpes, France
• Master: E. Blayo, Optimal control of PDEs, 15h, M2, University Grenoble Alpes, France
• Master: E. Arnaud, Statistics, 30h, M1, UGA, France
• Master: E. Arnaud, Supervision of student in apprenticeship, 30h, M2, UGA, France
• Master: Martin Schreiber, High-Performance Computing, M1, 31.1h, UGA, France
• Master: Martin Schreiber, Parallel Algorithms and Programming, M1, 11.25h, UGA, France
• Master: Martin Schreiber, Object oriented programming with C++, M1, 18h, UGA, France
• Master: Martin Schreiber, Partial differential equations, M1, 34.5h, UGA, France
• E-learning: E. Arnaud is in charge of the pedagogic platform math@uga : implementation of a collaborative moodle platform to share pedagogical resources within teachers and towards students.
• E. Blayo is in charge of the Ecole des Mathématiques Appliquées: organization and coordination of pedagogical and administrative aspects related to teaching for the applied maths department.

11.2.2 Supervision

• Master 1 internship, Julien Remy (“Automatic differentiation with PSyclone”, supervision by M. Schreiber, A. Vidard and M. Brémond)
• PhD in progress: Pierre Lozano, Coupling hydrostatic and nonhydrostatic ocean circulation models. October 2022, E. Blayo and L. Debreu
• PhD in progress: Benjamin Zanger, Compositional surrogates for reduced order modeling, Septembre 2022, M. Schreiber, O. Zahm
• PhD in progress: Dominik Huber, “Dynamic Resource Management with MPI Sessions and PMIx” (preliminary title), PhD candidate at the Technical University of Munich (TUM), M. Schulz (TUM), M. Schreiber
• PhD in progress: Fernando V. Ravelo, PhD candidate at the University of Sao Paulo (USP), P. Peixoto (USP), M. Schreiber
• PhD in progress: Gabriel Derrida, Design of flexible and numerically-sound generalised vertical coordinates with vertical ALE (V-ALE) algorithm for operational ocean forecasting. October 2023, L. Debreu and F. Lemarié.
• PhD in progress: Manolis Perrot, Consistent subgrid scale modeling for oceanic climate models. October 2021, E. Blayo and F. Lemarié.
• PhD in progress: Katarina Radisic, Prise en compte d'incertitudes externes dans l'estimation de paramètres d'un modèle de transfert d'eau et de pesticides à l'échelle du bassin versant, Université Grenoble-Alpes December 2021, C. Lauvernet (Inrae) and A. Vidard.
• PhD in progress: Exaucé Luweh Adjim Ngarti, deep learning for inverse problem in geophysics, Université Grenoble-Alpes Avril 2023, E. Arnaud, L. Nicoletti (Atos) and A. Vidard.
• PhD in progress: Hélène Hénon, Assimilation de données variationnelles multi-fidélité pour les prévisions océaniques , Université Grenoble-Alpes Octobre 2023, A. Vidard.
• PhD in progress : Adama Barry, Plans d'expériences pour la calibration et la validation d'un simulateur numérique, January 2022, F. Bachoc (Institut de Mathématiques de Toulouse), C. Prieur, promoted by M. Munoz Zuniga and S. Bouquet.
• PhD in progress : Ri Wang, Apprentissage statistique pour l'analyse de sensibilité globale avec entrées dépendantes, October 2021, V. Maume-Deschamps (Université Lyon 1), C. Prieur.
• PhD in progress: Robin Vaudry, Analyse de Sensibilité, quantification d'incerTitudes et calibRAtion pour des modèles épidémioloGiques structurés, October 2021, D. Georges (Grenoble INP), C. Prieur.
• PhD in progress: Clément Duhamel, Inversion robuste d'un code de calcul prenant en entrées des données de nature fonctionnelle. Application à la conception d'éoliennes, October 2020, C. Helbert (Ecole Centrale Lyon), C. Prieur, promoted by M. Munoz Zuniga, D. Sinoquet (IFPEN)
• PhD in progress: Romain Verdière, Nonlinear dimension reduction for uncertainty quantification problems, Septembre 2022, O. Zahm
• PhD in progress: Angélique Saillet, Design of experiments, climate scenarios and ocean simulation, Octobre 2023, Eric Blayo and Élise Arnaud.d C. Prieur
• PhD in progress: Qiao Chen, Low-dimensional structure of ocean data assimilation problems via gradient information, October 2021, É. Arnaud and O. Zahm
• PhD in progress: Rafael Flock, Certified coordinate selection for high-dimensional imaging problems, October 2021, and Y. Dong O. Zahm
• PhD in progress: Keerthi Gaddameedi, “Dynamic Resource Management for Parallel-In-Time Simulations” (preliminary title), PhD candidate at the Technical University of Munich (TUM), H.-J. Bungartz (TUM), T. Neckel (TUM), M. Schreiber
• Postdoctoral student: Alexis Anagnostakis, Kernel-based Sensitivity Analysis for Hypoelliptic Systems, P. Etoré (LJK, DATA) and C. Prieur.
• Postdoctoral student: Valentin Breaz, Semi-Supervised dimension reduction, M. Munoz-Zuniga (IFPEN) and O. Zahm.
• PhD: Emilie Rouziès, Quantification et réduction de l'incertitude dans un modèle de transfert de pesticides à l'échelle du bassin versant, Université Grenoble-Alpes, 23 février 2023, C. Lauvernet (Inrae) and A. Vidard.
• PhD: Rishabh Bhatt, Algorithmes parallèles en temps pour l'assimilation de données, Université Grenoble-Alpes, 23 Novembre 2023, L. Debreu and A. Vidard

11.2.3 Juries

• F. Lemarié: May 17, 2023 Jury member for the recruitment of a lecturer (MCF, CNU26) at the Ecole Centrale de Lyon on the topic Modeling for adaptation and/or transitions and/or the environment, Numerical Analysis, PDEs
• Arthur Vidard: Dec. 11, 2023, PhD thesis of Jules Guillot, Univ. Bretagne Sud de, "Quantification des incertitudes en assimilation de données", (reviewer).
• E. Blayo:
  • Sept. 29, 2023: PhD thesis of Benjamin Dufée, Univ. Rennes 1 (reviewer)
  • Dec. 7, 2023: PhD thesis of Eliot Jager, Univ. Grenoble Alpes (president)
  • Dec. 8, 2023: PhD thesis of Youness El-Ouartassy, Univ. Toulouse III (reviewer)
  • Dec. 21, 2023: PhD thesis of Juliette Dubois, Sorbonne University (reviewer)
• Martin Schreiber:
  • Jun. 12, 2023: PhD thesis of Nicolas Monnier “ExaSKA: Parallelization on a High Performance Computing server for the exascale radiotelescope SKA”, Université Paris-Saclay (reviewer)
  • Nov. 23, 2023: PhD thesis of Rishabh Bhatt “Parallel In Time Algorithms for Data Assimilation”, University Grenoble Alpes (president)

11.3.1 Internal or external Inria responsibilities

• E. Arnaud: member of Inria PhD recruitment committee CORDI-S
• E. Arnaud: in charge of the parity commission at Jean Kuntzmann Lab
• Martin Schreiber represents Inria in the OpenMP ARB.

11.3.2 Articles and contents

• Article “Zeitintegration: Hochskalierbare rationale Approximation von exponentiellen Integratoren” of M. Schreiber Quartl_106.pdf is published in the “Quartl” which is a journal for scientific outreach.

11.3.3 Education

• Martin Schreiber participated in an activity for students of the Colorado University of Boulder by providing answers to 35 questions related to novel time integration methods for weather and climate simulations.
• Ch. Kazantsev and E. Blayo are strongly involved in the creation and dissemination of pedagogic suitcases with mathematical activities designed for primary and secondary schools, as well as an escape game.
• C. Kazantsev is a member of an IREM group for creation of scientific activities for professional development of secondary schools teachers.
• C. Kazantsev is a member of an International Inter-IREM commission, which work on the multi-languages problem for children in the mathematical learning.

11.3.4 Creation of media or tools for science outreach

• C.Kazantsev participated in the edition of the Teachers notebooks which explain and advise how to use the "La Grange Suitcases" (sets of mathematical games, problems and animations) destined for primary and secondary schools teachers as well as for the general public.
• C.Kazantsev participated in the creation of mathematical activities that can be autonomously used by schoolchildren of primary and secondary schools and by the general public.
• C.Kazantsev participated in the creation of a mathematical serious game that can be played by schoolchildren of secondary schools and by the general public. See www.la-grange-des-maths.fr/mission-exoplanetes/

11.3.5 Interventions

• E. Blayo gave several outreach talks, in particular for high school students, and for more general audiences.

International journals

• 1 articleR.Ricardo Baptista, Y.Youssef Marzouk and O.Olivier Zahm. On the representation and learning of monotone triangular transport maps.Foundations of Computational MathematicsNovember 2023HALDOIback to text
• 2 articleE.Emanuele Borgonovo, E.Elmar Plischke and C.Clémentine Prieur. Total Effects with Constrained Features.Statistics and Computing2024, 1-29HALback to text
• 3 articleT.Tiangang Cui, S.Sergey Dolgov and O.Olivier Zahm. Scalable conditional deep inverse Rosenblatt transports using tensor trains and gradient-based dimension reduction.Journal of Computational PhysicsJuly 2023, 112103HALDOIback to text
• 4 articleC.Clément Duhamel, C.Céline Helbert, M.Miguel Munoz Zuniga, C.Clémentine Prieur and D.Delphine Sinoquet. A SUR version of the Bichon criterion for excursion set estimation.Statistics and Computing332April 2023, 41HALDOIback to text
• 5 articleM. R.Mohamed Reda El Amri, C.Céline Helbert, M.Miguel Munoz Zuniga, C.Clémentine Prieur and D.Delphine Sinoquet. Feasible Set Estimation under Functional Uncertainty by Gaussian Process Modelling.Physica D: Nonlinear Phenomena455December 2023, 133893HALDOI
• 6 articleP.Pierre Etoré, J. R.Jose R León and C.Clémentine Prieur. A probabilistic point of view for the Kolmogorov hypoelliptic equations.ESAIM: Probability and Statistics27July 2023, 668-693HALDOIback to text
• 7 articleA.-A.Antoine-Alexis Nasser, G.Gurvan Madec, C.Casimir de Lavergne, L.Laurent Debreu, F.Florian Lemarié and E.Eric Blayo. Sliding or stumbling on the staircase: numerics of ocean circulation along piecewise-constant coastlines.Journal of Advances in Modeling Earth Systems155May 2023, e2022MS003594HALDOIback to text
• 8 articleK.Katarina Radišić, E.Emilie Rouzies, C.Claire Lauvernet and A.Arthur Vidard. Global sensitivity analysis of the dynamics of a distributed hydrological model at the catchment scale.Socio-Environmental Systems Modelling2023, 1-17HALDOIback to text
• 9 articleE.Emilie Rouzies, C.Claire Lauvernet, B.Bruno Sudret and A.Arthur Vidard. How is a global sensitivity analysis of a catchment-scale, distributed pesticide transfer model performed? Application to the PESHMELBA model.Geoscientific Model Development1611June 2023, 3137-3163HALDOIback to text

International peer-reviewed conferences

• 10 inproceedingsS.Simon Clement, F.Florian Lemarié and E.Eric Blayo. Discrete analysis of Schwarz Waveform Relaxation for a simplified air-sea coupling problem with nonlinear transmission conditions.Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering,26th International Domain Decomposition Conference145Hong Kong, ChinaSpringer ChamApril 2023, 189-196HALDOI
• 11 inproceedingsS.Simon Clement, F.Florian Lemarié and E.Eric Blayo. Semi-discrete analysis of a simplified air-sea coupling problem with nonlinear coupling conditions.27th International Domain Decomposition ConferencePrague, Czech Republic2023HALback to text
• 12 inproceedingsS.Simon Clément, F.Florian Lemarié and E.Eric Blayo. Towards a finite volume discretization of the atmospheric surface layer consistent with physical theory.PROMS - Springer Proceedings in Mathematics & StatisticsFVCA 2023 - Finite Volumes for Complex Applications 10432Strasbourg, France2023, 1-8HALDOIback to text
• 13 inproceedingsD.Dominik Huber, M.Martin Schreiber and M.Martin Schulz. A Case Study on PMIx-Usage for Dynamic Resource Management.High Performance 2023 - 38th International Conference, ISC High Performance13999Lecture Notes in Computer ScienceHambourg, GermanySpringer Nature SwitzerlandAugust 2023, 42-55HALDOIback to text
• 14 inproceedingsA.Amir Raoofy, R.Roman Karlstetter, M.Martin Schreiber, C.Carsten Trinitis and M.Martin Schulz. Overcoming Weak Scaling Challenges in Tree-Based Nearest Neighbor Time Series Mining.38th International Conference, ISC High Performance 202313948Lecture Notes in Computer ScienceHambourg, GermanySpringer Nature SwitzerlandMay 2023, 317-338HALDOI

Conferences without proceedings

• 15 inproceedingsK.Kevin Elie-Dit-Cosaque, B.-A.Bérénice-Alexia Jocteur, V.Véronique Maume-Deschamps, C.Clémentine Prieur, P.Pierre Ribereau and R.Ri Wang. Goal oriented random forest (GORF).Séminaire Phimeca 2023Paris, France2023HAL
• 16 inproceedingsC.Claire Lauvernet, E.Emilie Rouzies, A.Arthur Vidard, A.Alexandre Devers, J.-P.Jean-Philippe Vidal, L.Laura Gatel, K.Katarina Radišić and C.Claudio Paniconi. Data assimilation to quantify and reduce uncertainty in ecohydrology modelling.Séminaire ITES 2023Strasbourg, France2023HAL
• 17 inproceedingsK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Calibrating a hydrological model robustly to rain perturbations with stochastic surrogates.LEFE/MANU 2023 - Colloque sur les Méthodes mathématiques et numériquesToulouse, France2023HALback to text
• 18 inproceedingsK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Robust calibration of a hydrological model with stochastic surrogates.MASCOT-NUM 2023 - Workshop Méthodes d'Analyse Stochastique pour les Codes et Traitement NUMériquesLe Croisic, France2023, 1-2HAL
• 19 inproceedingsK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Sensitivity analysis with external stochastic forcings : application to a water and pesticide transfer model.MEXICO 2023 - Rencontres annuelles du réseau MexicoPalaiseau, France2023, 1-36HAL

Doctoral dissertations and habilitation theses

• 20 thesisR.Rishabh Bhatt. Parallel In Time Algorithms for Data Assimilation.Universite Grenoble AlpesNovember 2023HALback to text
• 21 thesisA.-A.Antoine-Alexis Nasser. Advancing the representation of flows along topography in z-coordinate ocean models.Sorbonne UniversitéSeptember 2023HALback to text

Reports & preprints

• 22 miscV.Vincent Bansaye, P.-Y.Pierre-Yves Boëlle, S.Simon Cauchemez, B.Bernard Cazelles, P.Pascal Crepey, L.Lina Cristancho-Fajardo, J.-S.Jean-Stéphane Dhersin, S.Sorin Dumitrescu, P.Pauline Ezanno, A.Antoine Flahault, J.-L.Jean-Louis Golmard, P.Patrick Hoscheit, H.Henri Mermoz Kouye, M.Madeleine Kubasch, C.Catherine Laredo, A.Alain Mallet, L.Lulla Opatowski, C.Clémentine Prieur and A.Amandine Véber. Hommage à Elisabeta Vergu.November 2023HAL
• 23 miscM.Marie Billaud-Friess, A.Arthur Macherey, A.Anthony Nouy and C.Clémentine Prieur. A probabilistic reduced basis method for parameter-dependent problems.April 2023HALback to text
• 24 miscT.Tiangang Cui, S.Sergey Dolgov and O.Olivier Zahm. Self-reinforced polynomial approximation methods for concentrated probability densities.March 2023HALback to text
• 25 miscS.Sébastien Da Veiga, F.Fabrice Gamboa, A.Agnès Lagnoux, T.Thierry Klein and C.Clémentine Prieur. New estimation of Sobol' indices using kernels.March 2023HALback to text
• 26 miscR.Rafael Flock, Y.Yiqiu Dong, F.Felipe Uribe and O.Olivier Zahm. Certified coordinate selection for high-dimensional Bayesian inversion with Laplace prior.October 2023HALDOIback to text
• 27 miscH. M.Henri Mermoz Kouye, G.Gildas Mazo, C.Clémentine Prieur and E.Elisabeta Vergu. Exploiting deterministic algorithms to perform global sensitivity analysis of continuous-time Markov chain compartmental models with application to epidemiology.January 2024HALback to text
• 28 miscM. T.Matthew T. C. Li, Y.Youssef Marzouk and O.Olivier Zahm. Principal Feature Detection via $$-Sobolev Inequalities.May 2023HALback to text
• 29 miscM.Manolis Perrot and F.Florian Lemarié. Energetically consistent Eddy-Diffusivity Mass-Flux schemes for Atmospheric and Oceanic Convection.February 2024HAL
• 30 miscM.Martin Schreiber and J.Jed Brown. A generalized rational approximation of exponential integration (rexi) for massively parallel time integration.2023HAL
• 31 miscJ. G.João Guilherme Caldas Steinstraesser, P. d.Pedro da Silva Peixoto and M.Martin Schreiber. Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT.June 2023HALDOIback to text
• 32 miscR.Romain Verdière, C.Clémentine Prieur and O.Olivier Zahm. Diffeomorphism-based feature learning using Poincaré inequalities on augmented input space.December 2023HALback to text

Other scientific publications

• 33 miscK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Consideration of external uncertainties in the estimation of parameters of a water and pesticide transfer model at the watershed scale.February 2023HAL
• 34 inproceedingsV.Victor Trappler and A.Arthur Vidard. State-dependent Preconditioning for Data Assimilation.2023 - 54th International Liège Colloquium on Ocean Dynamics : Machine Learning and Data Analysis in OceanographyLiège, BelgiumMay 2023, 1-1HALback to text
• 35 inproceedingsV.Victor Trappler and A.Arthur Vidard. State-dependent Preconditioning for Data Assimilation: Application to a Shallow Water Assimilation system.ISDA 2023 - 9th International Symposium on Data AssimilationBologne, Italy2023, 1-1HALback to text
• 36 inproceedingsF.Fernando Valdés, P.Pedro Peixoto and M.Martin Schreiber. The application of a time exponential integrator to the wave equations, oriented to seismic imaging.LACIAM 2023 - First Latin American Congress of Industrial and Applied MathematicsValparaíso, ChileJanuary 2023, 1-1HALback to text