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 BALAISE

• Name:
  Bilbliothèque d’Assimilation Lagrangienne Adaptée aux Images Séquencées en Environnement
• Keywords:
  Multi-scale analysis, Data assimilation, Optimal control
• Functional Description:
  BALAISE (Bilbliothèque d’Assimilation Lagrangienne Adaptée aux Images Séquencées en Environnement) is a test bed for image data assimilation. It includes a shallow water model, a multi-scale decomposition library and an assimilation suite.
• Contact:
  Patrick Vidard

7.1.3 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

7.1.4 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, Gabriel Derrida, Emilie Duval, Florian Lemarié, Gurvan Madec, Antoine Nasser, Sanal Parameswaran.

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 41 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 57, 13.

In the context of the French initiative CROCO (Coastal and Regional Ocean COmmunity model, www.croco-ocean.org) for the development of a new oceanic modeling system, Emilie Duval worked on the design of methods to couple local nonhydrostatic models to larger scale hydrostatic ones. 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). A thorough analysis of the different families of waves that can be present in these equations was performed. Moreover a decomposition of the solutions into vertical modes, which is quite usual in the hydrostatic case, has been generalized in the nonhydrostatic case, which could be an interesting lead for coupling algorithms. A prototype has been implemented, which allows for analytical solutions in simplified configurations and makes it possible to test different numerical coupling approaches. Emilie Duval defended her PhD on 15 December 2022.

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

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

Participants: Eric Blayo, Florian Lemarié, Sophie Thery, Simon Clément.

1. Continuous and discrete analysis of Schwarz algorithms for OA coupling: we 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. In the framework of S. Thery PhD (defended in February 2021) the well-posedness of the non-linear coupling problem including parameterizations has been addressed and a detailed continuous 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 78, 16. In S. Clement PhD, 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 5. Such framework allows to study more complex coupling problems whose formulation is representative of the discretization used in realistic coupled models 46.

   Within the COCOA project, a Schwarz-like iterative method has been applied in a state-of-the-art Earth-System model to evaluate the consequences of inaccuracies in the usual ad-hoc ocean-atmosphere coupling algorithms used in realistic models 68, 69. 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 significant. The objective now is to reduce the computational cost of Schwarz algorithms using deep learning techniques.

2. Representation of the air-sea interface in coupled models: During the PhD-thesis of Charles Pelletier the scope was on including the formulation of physical parameterizations in the theoretical analysis of the coupling, in particular the parameterization schemes to compute air-sea fluxes. Following this work, a novel and rigorous framework for a consistent two-sided modeling of the surface boundary layer has been proposed 72. This framework allows for a more general representation of the vertical physics at the air-sea interface while improving the mathematical regularity of the numerical solutions. Moreover, it is flexible enough to include additional physical parameters for example to account for the effect of surface waves in the turbulent flux computation. This work is the first step toward more adequate discretization methods for the parameterization of surface and planetary boundary layers in coupled models.

   At a more fundamental level, in collaboration with A. Wirth, we have studied turbulent fluctuations in a coupled Ekman layer problem with randomized drag coefficient 81.

3. A simplified atmospheric boundary layer model for oceanic purposes: Part of our activities within the IMMERSE and SHOM 19CP07 projects 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 65. 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 44. The next step is to find adequate ways to fill some gaps in the 1D approach either using multiple scales asymptotic techniques or by casting the equations in terms of perturbations around an ambient state given by a large-scale dataset.

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). Our work on ocean-atmosphere coupling has steadily matured over the last few years and has reached a point where it triggers interest from the physicists. Through the funding of the projects ANR COCOA (2017-2021, PI: E. Blayo) and SHOM 19CP07 (2020-2024, PI: F. Lemarié), 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: Florian Lemarié, Manolis Perrot, Simon Clement.

In current models, the scale separation between the resolved part of the flow and the unresolved part is carried out via the Reynolds decomposition which corresponds to a filtering of the Navier-Stokes equations. Such a filtering leads to an evolution equation for the large-scale flow containing unknown terms (often called Reynolds stress terms) which represent the average contribution of the small-scale processes. The system is closed by so-called parameterizations that arbitrarily relate the contribution of small-scale processes to large-scale variables. In this context, the AIRSEA team has started work on two aspects:

1. Energetically consistent discretization of boundary layer parameterizations Part of S. Clement's thesis is about the discretization of boundary layer parameterizations. The problem of interest takes the form of an nonstationary nonlinear parabolic equation. The objective is to derive a discretization for which we could prove nonlinear stability criteria and show robustness to large variations in parabolic Courant number while being consistent with our knowledge of the underlying physical principles (e.g. the Monin-Obukhov theory in the surface layer).
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 approach (a.k.a. Boussinesq Hypothesis). In the framework of the PhD of Manolis Perrot a first step is to study the derivation of mass-flux convection schemes, popular in atmospheric models, to extend them specifically to the oceanic context. This extension to the oceanic context will be carried out under certain "consistency" constraints: energetic considerations, scale-awareness and well-posedness of the resulting model. In a second step, reference LES simulations will be developed to guide the formulation of unknown/uncertain terms in the extended mass-flux scheme.

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 Planètre Terre, 2021-2024, PIs: F. Lemarié and G. Madec).

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 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 80. 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 60 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 Direct assimilation of image sequences

At the present time the observation of Earth from space is done by more than thirty satellites. These platforms provide two kinds of observational information:

• Eulerian information as radiance measurements: the radiative properties of the earth and its fluid envelops. These data can be plugged into numerical models by solving some inverse problems.
• Lagrangian information: the movement of fronts and vortices give information on the dynamics of the fluid. Presently this information is scarcely used in meteorology by following small cumulus clouds and using them as Lagrangian tracers, but the selection of these clouds must be done by hand and the altitude of the selected clouds must be known. This is done by using the temperature of the top of the cloud.

Our current developments are targeted at the use of learning methods methods to describe the evolution of the images. This approach has been applied to the tracking of oceanic oil spills in the framework of a Long Li's Phd in co-supervision with Jianwei Ma. It led to the publication of 12.

8.2.2 Observation error representation

Accounting for realistic observations errors is a known bottleneck in data assimilation, because dealing with error correlations is complex. Following a previous study on this subject, we propose to use multiscale modelling, more precisely wavelet transform, to address this question. In 45 we investigate the problem further by addressing two issues arising in real-life data assimilation: how to deal with partially missing data (e.g., concealed by an obstacle between the sensor and the observed system); how to solve convergence issues associated to complex observation error covariance matrices? Two adjustments relying on wavelets modelling are proposed to deal with those, and offer significant improvements. The first one consists in adjusting the variance coefficients in the frequency domain to account for masked information. The second one consists in a gradual assimilation of frequencies. Both of these fully rely on the multiscale properties associated with wavelet covariance modelling.

This kind of work was put to application in STORM, a collaborative project with Université de La Réunion ended this year . Our role vas to prepare for the assimilation of data collected by sea turtles., and in particular work on the description of observation error statistics.

8.3.1 Parameter space dimension reduction and Model order reduction

Participants: Youssef Marzouk, Clémentine Prieur, Arthur Macherey, Ricardo Baptista, Tong Xin, Cui Tiangang, Olivier Zahm.

The high computational cost of complex numerical simulations is a common and major concern when deriving new methodological approaches. This cost increases dramatically with the use of sensitivity analysis or parameter estimation methods, and more generally with any method requiring numerous model integrations. Model reduction, using either stochastic or deterministic methods, is a way to reduce significantly the computing time of a numerical model. Over the past year, our team focused on different reduction aspects, emphasized and described below.

In the paper 29, 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.

In the paper 28, we consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an “informed” subspace of the parameters and an “informative” subspace of the data so that a high-dimensional inference problem can be approximately reformulated in low-to-moderate dimensions, thereby improving the computational efficiency of many inference techniques. To do so, we exploit gradient evaluations of the log-likelihood function. Furthermore, we use an information-theoretic analysis to derive a bound on the posterior error due to parameter and data dimension reduction. This bound relies on logarithmic Sobolev inequalities, and it reveals the appropriate dimensions of the reduced variables. We compare our method with classical dimension reduction techniques, such as principal component analysis and canonical correlation analysis, on applications ranging from mechanics to image processing.

Markov chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods offers a viable route to designing efficient MCMC methods for exploring high-dimensional posterior distributions via exploiting the intrinsic low-dimensional structure of the underlying inverse problem. However, existing LIS methods and the associated performance analysis often assume that the prior distribution is Gaussian. This assumption is limited for inverse problems aiming to promote sparsity in the parameter estimation, as heavy-tailed priors, e.g., Laplace distribution or the elastic net commonly used in Bayesian LASSO, are often needed in this case. To overcome this limitation, we consider in the paper 6 a prior normalization technique that transforms any non-Gaussian (e.g. heavy-tailed) priors into standard Gaussian distributions, which makes it possible to implement LIS methods to accelerate MCMC sampling via such transformations. We also rigorously investigate the integration of such transformations with several MCMC methods for high-dimensional problems. Finally, we demonstrate various aspects of our theoretical claims on two nonlinear inverse problems.

In a joint work 14 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 43. 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. We are now interested in solving parametrized PDE with stochastic algorithms in the framework of potentially high dimensional parameter space. A preliminary step was the development of a PAC algorithm in relative precision for bandit problem with costly sampling 3.

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.

8.5.1 Global sensitivity analysis with dependent inputs

Participants: Elise Arnaud, Eric Blayo, Laurent Gilquin, Maria Belén Heredia, Adrien Hirvoas, Alexandre Janon, Henri Mermoz Kouye, Clémentine Prieur, Arthur Vidard, Emilie Rouzies.

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. 76 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 59. 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. 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 1 (see Section 8.5.2 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.

8.5.2 Green sensitivity for multivariate and functional outputs

Participants: María Belén Heredia, 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 73, 74. 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 42 a non-parametric given data estimator for aggregated Sobol’ indices, introduced in 61 and further developed in 51 for multivariate or functional outputs. We also introduced aggregated Shapley effects and we have extended a nearest neighbor estimation procedure to estimate these indices 1. 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 degenerate U-statistics.

8.5.3 Global sensitivity analysis for parametrized stochastic differential equations

Participants: Henri Mermoz Kouye, 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 50. 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 8.3), 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 submitted, 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 is 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 33. Henri Mermoz Kouye defended in December, 2022.

8.5.4 Sensitivity analysis in pesticide transfer models

Participants: Arthur Vidard, Emilie Rouzies, Katarina Radisic.

Pesticide transfer models are valuable tools to predict and prevent pollution of water bodies. However, using such models in operational contexts requires a strong knowledge of their structure including influential parameters. This project aims at performing global sensitivity analysis (GSA) of the PESHMELBA model (pesticide and hydrology: modelling at the catchment scale). This work is made hard due to the modular, complex structure of the model that couples different physical processes. It results in a large input space dimension and a high computational cost that limits the number of available runs. Using classical GSA tools such as Sobol' indices is thus not feasible. In order to circumvent those limitations, we also explored alternative techniques such as HSIC dependence measure or Random Forest metamodel. The use of such methods in the specific context of spatially distributed output was submitted in a journal paper 36. We extended this work to spatiotemporal output, as presented in 15.

To conclude Section 8.5, let us mention that Clémentine Prieur took part to the writing on a monography on recent trends in sensitivity analysis, which appeared by the end of 2021 79.

8.6.1 Bayesian calibration

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 ow 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 56 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 is 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 in done in collaboration with IFPEN 8, 58.

8.6.2 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 54. 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 8.3, 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 14. 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.

8.8.1 Dynamic compute-resource utilization

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. This also resulted in some prototype implementations with an emulator 20 as well as an implementation based on PMIx 18.

8.8.2 Hardware-aware numerics

We started investigating Domain Specific Languages (DSL) for ocean simulation models targeting to close the increasing gap between the numerics and HPC with a separation of concerns: A DSL allows on the one hand applied mathematicians to express their model equations and on the other hand also HPC experts to develop tools to automatically transform this into highly performing code on the target programming model and corresponding architecture. As part of this, we started working with the PsyIR development (package of PsyClone) and successfully applied it to parsing the entire CROCO ocean model. This forms the basis for currently undergoing work to support different HPC programming models and architectures in a sustainable way for the CROCO model.

8.8.3 New time-integration methods

We investigate new time-integration methods by also taking HPC requirements into account, hence targeting a better wallclocktime vs.  error ratio. These numerical methods include different forms of exponential, semi-Lagrangian as well as parallel-in-time integration methods. Our team and collaborators made significant progress on this 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 preprint available 35. Although this paper's main focus is on seismic wave propagation, these results can be also applied to the linearized fast modes in atmospheric models, e.g., as part of time splitting methods. Theoretical as well as numerical results have been deeply investigated for a variety of wave propagation problems. In 4, we have also studied in detail the application of Runge Kutta exponential integrators and its variants to shallow water equations.

In a 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 55. Motivated by this work, we started to investigate this in collaboration with USP using the MGRIT parallel-in-time method where we expect to have even better results in combination with exponential time integration methods.

On variational data assimilation and parallel-in-time integration methods: Rishabh Bhatt started his PhD in December 2019. Under the supervision of Laurent Debreu and Arthur Vidard, he studies the application of time parallelization algorithms to variational data assimilation methods. Thus, at each step of the optimization algorithm, the direct model is integrated by a time-parallel method (here the Parareal algorithm 67). One of the main difficulties lies in the choice of the stopping criterion of the Parareal algorithm. To do so, we rely on theoretical results on the convergence of conjugate gradient methods in the presence of approximate gradient calculations 52. The first results are encouraging and show the possibility to optimally tune the stopping criterion of the Parareal algorithm (and thus the number of iterations) without affecting the convergence of the conjugate gradient. These results are reported in (30).

8.8.4 Variational data assimilation and parallel in time methods

Rishabh Bhatt started his PhD in December 2019. Under the supervision of Laurent Debreu and Arthur Vidard, he studies the application of time parallelization algorithms to variational data assimilation methods. Thus, at each step of the optimization algorithm, the direct model is integrated by a time-parallel method (here the Parareal algorithm 66). One of the main difficulties lies in the choice of the stopping criterion of the Parareal algorithm. To do so, we rely on theoretical results on the convergence of conjugate gradient methods in the presence of approximate gradient calculations 52. The first results are encouraging and show the possibility to optimally tune the stopping criterion of the Parareal algorithm (and thus the number of iterations) without affecting the convergence of the conjugate gradient. These results are reported in (30). We are now working on taking better advantage of the coupling of these two iterative methods (conjugate gradient and Parareal), in particular by optimally reusing the Krylov bases of the Krylov Enhanced version of the Parareal algorithm.

10.1.1 Inria associate team not involved in an IIL or an international program

10.1.2 STIC/MATH/CLIMAT AmSud projects

10.2.1 Visits of international scientists

10.2.2 Visits to international teams

• Olivier Zahm was invited for 2 weeks at DTU in Copenhagen. This visit is part of a collaboration with the CUQI-group at DTU which support the PhD thesis of Rafael Flock, co-supervised with Yiqiu DONG and Olivier ZAHM.

10.3.1 H2020 projects

10.3.2 Other european programs/initiatives

• Program: C3S2
• Project acronym: ERGO2
• Project title: Advancing ocean data assimilation methodology for climate applications
• Duration: August 2022 - july 2025
• Coordinator: Arthur Vidard
• Other partners: Cerfacs (France), CNR (Italy)
• Abstract: The scope of this contract is to improve ocean data assimilation capabilities at ECMWF, used in both initialization of seasonal forecasts and generation of coupled Earth System reanalyses. In particular it shall focus on i) improving ensemble capabilities in NEMO and NEMOVAR and the use of their information to represent background error statistics; ii) extend NEMOVAR capabilities to allow for multiple resolution in multi-incremental 3D-Var; iii) make better use of ocean surface observations. It shall also involve performing scout experiments and providing relevant diagnostics to evaluate the benefit coming from the proposed developments.

10.3.3 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.

  In 2019, Clémentine Prieur, which is part of this board, as also co-chair of a satellite event on the future of sensitivity analysis. A position paper 75 has been published in 2021, as a synthesis of the discussions hold in Barcelona (autumn 2019).

10.3.4 EuroHPC

• Martin Schreiber is a member of the TIME-X EuroHPC-01-2019 project where he's leading the research on runtime-varying computing resources to optimize the energy and resource efficiency of iterative parallel-in-time methods: time-x.eu.

10.4.1 ANR

• A 4-year contract: ANR MODENA, "Model and data reduction for efficient assimilation", PI: Olivier ZAHM The reliability of numerical predictions strongly rely on our ability to calibrate the unknown model parameters using observable data. Data assimilation is a particularly challenging task in ocean modelling because of the complexity of the computational models and because of the high-dimension of both the parameters and the data. The objective of this project is to explore novel methodologies to improve the probabilistic description of the Bayesian solution to inverse problem while, at the same time, taking into consideration the computational limitations imposed by large scale applications. This project relies on three building blocks and on their interplay:

  1. transport maps as a novel approximation tool of complex probability densities,
  2. reduced order models to alleviate the computational burden of expensive models and
  3. dimension reduction to concentrate the computational efforts onto the most relevant directions.

  In addition, the proposed methodology addresses key challenges present in many real-world applications and therefore we expect that they can find applications in other domains.

• 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

10.4.2 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

10.4.3 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.
• C. Prieur is co-advising the PhD thesis of Henri Mermoz Kouye, in the framework of the Inria-INRA partnership.
• C. Prieur chaired GdR MASCOT NUM 2010-2017, in which are also involved M. Nodet, E. Blayo, C. Helbert, E. Arnaud, L. Viry, S. Nanty, L. Gilquin. She is still strong involved in the group (co-chair). In particular, she will co-chair next GdR annual meeting in Aussois (May 2020, reported to April 2021). .

11.1.1 Scientific events: organisation

• Martin Schreiber organized the “1st EuroHPC Workshop on Malleability in HPC”

11.1.2 Scientific events: selection

11.1.3 Journal

11.1.4 Invited talks

• Eric Blayo was invited as plenary speaker of the workshop "Coastal flow models and boundary conditions" , Toulouse, October 24-27, 2022.
• Elise Arnaud : "Parameter control in the presence of uncertainties", workshop Machine learning and uncertainties in climate simulations, centre Henri Lebesgue, Mon, 06/06/2022 - 06/09/2022 - Logonna-Daoulas, Finistère, France
• Martin Schreiber: Nov. 2022, Enabling I/O and Computation Malleability in High-Performance Computing: Application perspective on dynamic resources, Birds of Feather, Supercomputing 2022, Dallas, Texas, USA
• Martin Schreiber: Oct. 2022, Invasive Computing - Part IX: Return of the Jedi, InvasIC Colloquium, Erlangen, Germany
• Martin Schreiber: Nov. 2022, A Brief Glimpse on Emerging (Parallel-in-)Time Integration Methods for Weather and Climate Simulations, Seminar, University of Colorado Boulder, USA
• Martin Schreiber: Jul. 2022, A Brief Glimpse on Some Emerging (Parallel-in-)Time Integration Methods for Weather and Climate Simulations, International Conference on Scientific Computation and Differential Equations (SciCADE), Reykjavík, Iceland, Minisymposium
• Martin Schreiber: Jun. 2022, A Brief Glimpse on Emerging Time Integration Methods for Weather and Climate Simulations, Seminar series, Université de Pau, France
• Martin Schreiber: May 2022, Using Artificial Neural Network to solve PDEs? International Supercomputing Conference, Panel discussion, Hamburg, Germany, presentation as panel member
• Clémentine Prieur was invited as plenary speaker SAMO 2022 (Florida, US).
• Clémentine Prieur was invited as plenary speaker at SFdS annual conference in Lyon, 2022, France.
• Clémentine Prieur was invited as plenary speaker of the conference in honor of Marc Lavielle and Jose R. León (Montevideo, Uruguay, 2022).

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 https://programmes.insu.cnrs.fr/lefe/cs_actions/manu since April 2018.
• F. Lemarié is the co-leader with Mike Bell (UK Met Office) of the NEMO (www.nemo-ocean.eu) Working Group on numerical kernel development.

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.
• E. Blayo is a member of the ANR selection committee CE40
• F. Lemarié is a member of the CROCO (www.croco-ocean.org) scientific committee in charge of the "numerical methods" topic.
• Martin Schreiber is a member of the MPI Forum (representing the Université Grenoble Alpes) and in particular active in the MPI Session workgroup.
• 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 an external reviewer of the “Neue Methoden und Technologien für das Exascale-Höchstleistungsrechnen” (SCALEXA) funding program from Germany: www.bmbf.de

11.1.7 Research administration

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

11.2.1 Teaching

• Licence (ou équivalent) : E. Arnaud, Mathematics for engineers, 50h, L2, UGA, France
• Licence (ou équivalent) : E. Arnaud, Statistics, 20h, L2, UGA, France
• Licence (ou équivalent) : E. Blayo, analysis and algebra, 145h, L1, University Grenoble Alpes, France
• Licence (ou équivalent) : C. Kazantsev, Mathématiques approfondies pour l'ingénieur, 72h, L2, UGA, France
• Licence (ou équivalent) : C. Kazantsev, Mathématiques pour les sciences de l'ingénieur, 45h, L2, UGA, France
• Licence (ou équivalent) : Martin Schreiber, Advanced Analysis & Algebra, L1, 67.5h, UGA, France
• Licence (ou équivalent) : Martin Schreiber, Analysis, L1, 37h, UGA, France
• Master (ou équivalent) : E. Arnaud, Statistics, 30h, M1, UGA, France
• Master (ou équivalent) : E. Arnaud, Supervision of student in apprenticeship, 30h, M2, UGA, France
• Master (ou équivalent) : E. Blayo, Partial Differential Equations, 18h, M1, University Grenoble Alpes, France
• Master (ou équivalent) : Martin Schreiber, High-Performance Computing, M1, 31.1h, UGA, France
• Master (ou équivalent) : Martin Schreiber, Object oriented programming with C++, M1, 18h, UGA, France
• Master (ou équivalent) : Martin Schreiber, Partial differential equations, M1, 34.5h, UGA, France
• Master (ou équivalent) : Olivier ZAHM, PDE for finance and Geostatistics , 4h, Ensimag, France
• E-learning : E. Arnaud is in charge of the pedagogic platform math@uga : implementation of a collaborative moodle platform math.u-ga.fr 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 2 internship : Exaucé Luweh Adjim Ngarti (supervision : Elise Arnaud and Arthur Vidard)
• Engineer : Aurélien Prat, Multi-resolution techniques for ocean data assimilation, July 2021, December 2022, A. Vidard
• PhD in progress: Manolis Perrot, Consistent subgrid scale modeling for oceanic climate models. October 2021, E. Blayo and F. Lemarié.
• PhD in progress: Pierre Lozano, Coupling hydrostatic and nonhydrostatic ocean circulation models. October 2022, E. Blayo and L. Debreu
• PhD in progress : Qiao CHEN, Low-dimensional structure of ocean data assimilation problems via gradient information, Octobre 2021, Olivier ZAHM and Élise Arnaud.
• 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 : 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 : Rafael Floch, Dimension reduction of large-scale linear Bayesian inverse problems, Octobre 2021, Olivier ZAHM et Yiqiu DONG.
• PhD in progress : Romain Verdière, Nonlinear dimension reduction for uncertainty quantification problems, Septembre 2022, Olivier ZAHM et Clémentine PRIEUR
• PhD in progress : Antoine Nasser, Volume penalization methods for the representation of flows along topography in 3D ocean models, October 2019, L. Debreu and G. Madec.
• PhD in progress : Rishabh Bhatt, Asynchronous parallel in time schemes for data assimilation, December 2019, L. Debreu and A. Vidard.
• PhD in progress: Emilie Rouziès, Assimilation of multi-source data in a pesticide transfer model in a small agricultural watershed, Université Grenoble-Alpes, December 2019, C. Lauvernet (Inrae) and A. Vidard.
• 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 : Emilie Duval, Coupling hydrostatic and nonhydrostatic ocean circulation models. October 2018 - December 2022, L. Debreu and E. Blayo.
• PhD : Henri Mermoz Kouye, Analyse de sensibilité basée sur les indices de Sobol’ pour modèles à sorties stochastiques et fonctionnelles, 26 Octobre 2019, G. Mazo, E. Vergu (INRAE, MIA, Jouy), C. Prieur. Defended in December, 2022.
• PhD: Simon Clément, Numerical analysis for reconciling in space and time the air-sea exchanges and their parameterization, 25 Université Grenoble-Alpes, defended on 23 November 2022, E. Blayo and F. Lemarié.

11.2.3 Juries

• E. Blayo:
  • Oct. 4, 2022: HDR thesis of Pierre Jolivet, Institut National Polytechnique de Toulouse (president)
  • Dec. 9, 2022: PhD thesis of Hugo Frezat, University Grenoble Alpes (president)
• Martin Schreiber:
  • July 1st 2022: PhD thesis of Sebastian FRIEDEMANN, Université Grenoble Alpes (president)
  • Nov. 23rd 2022: PhD thesis of Simon CLEMENT, Université Grenoble Alpes (president)
  • Dec. 15th 2022: PhD thesis of Emilie DUVAL, Université Grenoble Alpes (president)
• E. Arnaud, Dec.14, 2022: PhD thesis of Francois-Remi Mazy, UGA.
• C. Prieur is jury president of Prix de thèse AMIES (2020-2022).

11.3.1 Internal or external Inria responsibilities

• F. Lemarié is a member of the local "comité des emplois scientifiques" (CES) (since Sept 2019)
• F. Lemarié is the local scientific correspondent for national calls for projects (since July 2020)
• E. Arnaud : member of Inria PhD recruitment committee CORDI-S
• E. Arnaud : in charge of the parity commission at Jean Kuntzmann Lab

11.3.2 Articles and contents

• Clémentine Prieur took part to a webcast on The Future of Sensitivity Analysis for Systems Modelling and Policy Support
• Clémentine Prieur gave interviews as a CNRS expert (Figaro, Hoffpost, RCF) on the evolution of COVID19 pandemic.
• C. Prieur was placed on a list of experts who could answer questions on various aspects of the news related to the ongoing Covid-19 epidemic by the CNRS press office. This list is made available to journalists in order to direct them to the appropriate interlocutors according to the angle of their questions.

11.3.3 Education

• 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. These activities were used by more than 12,000 pupils in 2021-2022, despite the sanatory crisis. This is done in collaboration with the Rectorat de Grenoble.
• 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. Three meetings take place in Paris during the year, the first was on October 1.

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/
• C.Kazantsev participated in the creation of a mathematical exposition on Johannes Kepler : "Kepler, les maths pour décrire le monde", in colaboration with Jean-Louis Hodeau, a cristallograph of the Neel Institut and CNRS (Grenoble, France). This exposition was visited on the fête de la science by schoolchildren of secondary schools and by the general public.
• C.Kazantsev had encadred for 3 months a L3 student who participates to the creation of a mathematical activity for secondary schools children.

11.3.5 Interventions

• E. Blayo gave several outreach talks, in particular for middle school and high school students, and for more general audiences.
• E. Arnaud has given a seminar "(se) tromper avec les chiffres", for secondary school students

International journals

• 1 articleM.María Belén Heredia, C.Clémentine Prieur and N.Nicolas Eckert. Global sensitivity analysis with aggregated Shapley effects, application to avalanche hazard assessment.Reliability Engineering and System Safety222108420June 2022, 1-11
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• 2 articleD.Daniele Bigoni, Y.Youssef Marzouk, C.Clémentine Prieur and O.Olivier Zahm. Nonlinear dimension reduction for surrogate modeling using gradient information.Information and InferenceMay 2022
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• 3 articleM.Marie Billaud-Friess, A.Arthur Macherey, A.Anthony Nouy and C.Clémentine Prieur. A PAC algorithm in relative precision for bandit problem with costly sampling.Mathematical Methods of Operations Research962022, 161–185
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• 4 articleM.Matthieu Brachet, L.Laurent Debreu and C.Christopher Eldred. Comparaison of Exponential integrators and traditional time integration schemes for the Shallow Water equations.Applied Numerical Mathematics180October 2022, 55-84
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• 5 articleS.Simon Clement, F.Florian Lemarié and E.Eric Blayo. Discrete analysis of Schwarz waveform relaxation for a diffusion reaction problem with discontinuous coefficients.SMAI Journal of Computational Mathematics8April 2022, 99-124
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• 6 articleT.Tiangang Cui, X.Xin Tong and O.Olivier Zahm. Prior normalization for certified likelihood-informed subspace detection of Bayesian inverse problems.Inverse Problems3812October 2022, 124002
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• 7 articleL.Laurent Debreu, N.Nicholas Kevlahan and P.Patrick Marchesiello. Improved Gulf Stream separation through Brinkman penalization.Ocean Modelling179November 2022, 102121
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• 8 articleA.Adrien Hirvoas, C.Clémentine Prieur, É.Élise Arnaud, F.Fabien Caleyron and M. M.Miguel Munoz Zuniga. Wind Turbine Quantification and Reduction of Uncertainties Based on a Data-Driven Data Assimilation Approach.Journal of Renewable and Sustainable Energy145September 2022, 053303
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• 9 articleN.-R. K.Nicholas K.-R. Kevlahan and F.Florian Lemarié. wavetrisk-2.1: an adaptive dynamical core for ocean modelling.Geoscientific Model Development15172022, 6521-6539
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• 10 articleP. H.Peter H Lauritzen, N.N.K.‐r. Kevlahan, T.T. Toniazzo, C.C. Eldred, T.Thomas Dubos, A.A. Gassmann, V.V.E. Larson, C.C. Jablonowski, O.O. Guba, B.B. Shipway, B.B.E. Harrop, F.Florian Lemarié, R.R. Tailleux, A.A.R. Herrington, W.W. Large, P.P.J. Rasch, A.A.S. Donahue, H.H. Wan, A.A. Conley and J.J.T. Bacmeister. Reconciling and improving formulations for thermodynamics and conservation principles in Earth System Models (ESMs).Journal of Advances in Modeling Earth SystemsAugust 2022, 1-99
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• 11 articleP.Philomène Le Gall, A.-C.Anne-Catherine Favre, P.Philippe Naveau and C.Clémentine Prieur. Improved regional frequency analysis of rainfall data.Weather and Climate Extremes36June 2022, 100456
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• 12 articleL.Long Li, J.Jianwei Ma, F.-X.Francois-Xavier Le Dimet and A.Arthur Vidard. Assimilation of Images via Dictionary Learning-Based Sparsity Regularization Strategy: An Application for Retrieving Fluid Flows.IEEE Transactions on Geoscience and Remote Sensing602022, 5907120:1-20
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• 13 articleP.Patrick Marchesiello, J.Julien Chauchat, H.Hassan Shafiei, R.Rafael Almar, R.Rachid Benshila, F.Franck Dumas and L.Laurent Debreu. 3D wave-resolving simulation of sandbar migration.Ocean Modelling180December 2022, 102127
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• 14 articleM.Matthieu Oliver, D.Didier Georges and C.Clémentine Prieur. Spatialized Epidemiological Forecasting applied to Covid-19 Pandemic at Departmental Scale in France.Systems and Control Letters164June 2022, 105240
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• 15 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 Modelling2022, 1-17
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• 16 articleS.Sophie Thery, C.Charles Pelletier, F.Florian Lemarié and E.Eric Blayo. Analysis of Schwarz Waveform Relaxation for the Coupled Ekman Boundary Layer Problem with Continuously Variable Coefficients.Numerical Algorithms89March 2022, 1145–1181
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• 17 articleO.Olivier Zahm, T.Tiangang Cui, K.Kody Law, A.Alessio Spantini and Y.Youssef Marzouk. Certified dimension reduction in nonlinear Bayesian inverse problems.Mathematics of Computation91April 2022, 1789-1835
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International peer-reviewed conferences

• 18 inproceedingsD.Dominik Huber, M.Maximilian Streubel, I.Isaías Comprés, M.Martin Schulz, M.Martin Schreiber and H.Howard Pritchard. Towards Dynamic Resource Management with MPI Sessions and PMIx.EuroMPI/USA'22: Proceedings of the 29th European MPI Users' Group MeetingEuroMPI/USA'22 - 29th European MPI Users' Group MeetingChattanooga, United StatesACMSeptember 2022, 57-67
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Conferences without proceedings

• 19 inproceedingsA.-L.Anne-Laure Dalibard and F.Florian Lemarié. Potentiels apports de l'analyse mathématique à la modélisation du climat.GDR 2022 - Journées de lancement du GdR "Défis théoriques pour les sciences du climat"Paris, FranceJune 2022, 1-34
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• 20 inproceedingsJ.Jan Fecht, M.Martin Schreiber, M.Martin Schulz, H.Howard Pritchard and D. J.Daniel J Holmes. An Emulation Layer for Dynamic Resources with MPI Sessions.HPCMALL 2022 - Malleability Techniques Applications in High-Performance ComputingHambourg, GermanyJune 2022
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• 21 inproceedingsF.Florian Lemarié, N.Nicolas Ducousso, L.Laurent Debreu and G.Gurvan Madec. Stability and accuracy of Runge-Kutta based split-explicit time-stepping algorithms for free-surface ocean models.EGU 2022 - General Assembly on European Geosciences UnionVienna, AustriaMay 2022, 1-6
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• 22 inproceedingsK.Katarina Radišić, C.Claire Lauvernet and A.Arthur Vidard. Calibrating a Hydrological Model for Pesticide Transfer while Considering Rain Uncertainty.AGU Fall Meeting 2022 - Science Leads the FutureChicago, United States2022, 1-1
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• 23 inproceedingsK.Katarina Radišić, E.Emilie Rouzies, C.Claire Lauvernet and A.Arthur Vidard. Sensitivity analysis of a spatio-temporal hydrological model for water and pesticide transfers.SAMO 2022 - Tenth International Conference on Sensitivity Analysis of Model OutputTallahassee, Florida, United StatesMarch 2022
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• 24 inproceedingsE.Emilie Rouzies, C.Claire Lauvernet and A.Arthur Vidard. Which data assimilation method and data source for a multi-compartment hydrology/water quality model? Application on the PESHMELBA model in a small agricultural catchment.EGU22 - European Geosciences Union General AssemblyVienne, AustriaMay 2022
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Doctoral dissertations and habilitation theses

• 25 thesisS.Simon Clement. Numerical analysis for a combined space-time discretization of air-sea exchanges and their parameterizations.Université Grenoble AlpesNovember 2022
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• 26 thesisH. M.Henri Mermoz Kouye. Sensitivity analysis approaches for stochastic models. Application to compartmental models in epidemiology.Université Paris - SaclayDecember 2022
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Reports & preprints

• 27 miscR.Ricardo Baptista, Y.Youssef Marzouk, R. E.Rebecca E. Morrison and O.Olivier Zahm. Learning non-Gaussian graphical models via Hessian scores and triangular transport.January 2022
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• 28 miscR.Ricardo Baptista, Y.Youssef Marzouk and O.Olivier Zahm. Gradient-based data and parameter dimension reduction for Bayesian models: an information theoretic perspective.November 2022
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• 29 miscR.Ricardo Baptista, Y.Youssef Marzouk and O.Olivier Zahm. On the representation and learning of monotone triangular transport maps.January 2023
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• 30 miscR.Rishabh Bhatt, L.Laurent Debreu and A.Arthur Vidard. Introducing time parallelisation within data assimilation using parareal method.April 2022
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• 31 miscT.Tiangang Cui, S.Sergey Dolgov and O.Olivier Zahm. Conditional Deep Inverse Rosenblatt Transports.January 2022
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• 32 miscC.Clément Duhamel, C.Céline Helbert, M. M.Miguel Munoz Zuniga, C.Clémentine Prieur and D.Delphine Sinoquet. A SUR version of the Bichon criterion for excursion set estimation.September 2022
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• 33 miscH. M.Henri Mermoz Kouye, G.Gildas Mazo, C.Clémentine Prieur and E.Elisabeta Vergu. Exploiting deterministic algorithms to perform global sensitivity analysis for continuous-time Markov chain compartmental models with application to epidemiology.February 2022
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• 34 miscA.-A.Antoine-Alexis Nasser, G.Gurvan Madec, C. D.Casimir De Lavergne, L.Laurent Debreu, F.Florian Lemarie and E.Eric Blayo. Sliding or stumbling on the staircase: numerics of ocean circulation along piecewise-constant coastlines.January 2023
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• 35 miscF. V.Fernando V. Ravelo, P. S.Pedro S. Peixoto and M.Martin Schreiber. An explicit exponential time integrator based on Faber polynomials and its application to seismic wave modelling.December 2022
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• 36 miscE.Emilie Rouzies, C.Claire Lauvernet, B.Bruno Sudret and A.Arthur Vidard. How to perform global sensitivity analysis of a catchment-scale, distributed pesticide transfer model ? Application to the PESHMELBA model.January 2022
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• 37 miscE.Emilie Rouzies, C.Claire Lauvernet, B.Bruno Sudret and A.Arthur Vidard. How to perform global sensitivity analysis of a catchment-scale, distributed pesticide transfer model? Application to the PESHMELBA model.December 2021
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Other scientific publications

• 38 inproceedingsC.Clément Duhamel, C.Clémentine Prieur, C.Céline Helbert, M.Miguel Munoz Zuniga and D.Delphine Sinoquet. A SUR version of the Bichon criterion for excursion set estimation.Mascot Num 2022 -Annual GdR meetingClermont-Ferrand, FranceJune 2022, 1-1
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• 39 inproceedingsK.Katarina Radišić, C.Claire Lauvernet, A.Arthur Vidard and E.Etienne Leblois. 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.OZCAR 2022 - OZCAR Summer school, "la science de la zone critique"Barcelonette, FranceJuly 2022, 1-1
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• 40 inproceedingsV.Victor Trappler, É.Élise Arnaud, L.Laurent Debreu and A.Arthur Vidard. Regret-based calibration using GPs.Journées CIROQUO 2022Grenoble, FranceMay 2022
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