2025‌Activity reportProject-TeamPLATON‌​‌

3.1.1 Surrogate modeling‌ for UQ

Challenges. Surrogate‌​‌ models are crucial to​​ enable the solution of​​​‌ both forward and backward‌ UQ problems. Several alternative‌​‌ approaches, such as Polynomial​​ Chaos, Gaussian Processes, and​​​‌ tensor format approximation, have‌ been proposed and developed‌​‌ over the last decades.​​ These approaches have been​​​‌ successfully applied to many‌ different domains. Still, surrogates‌​‌ models for UQ management​​ are facing many remaining​​​‌ limitations that require significant‌ research works to handle‌​‌ large scale simulation-based studies​​ and account for complex​​​‌ dependencies. These limitations concern‌ multiple aspects, including the‌​‌ complexity related to the​​ dimensionality of the input​​​‌ parameter, the definition of‌ suitable basis representations, the‌​‌ complexity of the surrogate​​ construction, and the control​​​‌ of the surrogate error.‌

Proposed actions. Platon will‌​‌ pursue long time efforts​​ in the continuity of​​​‌ previous developments, such as‌ the improvement of advanced‌​‌ sparse grid methods, sparsity​​ promoting strategies and low-rank​​​‌ methods. Besides these generic‌ developments, a first research‌​‌ axis will focus on​​ the construction of surrogates​​​‌ for multi-physics problems (fluids,‌ structures, chemistry,...) simulated by‌​‌ a system of coupled​​ solvers. Classical surrogate methods​​​‌ consider the system of‌ solvers as a single‌​‌ entity, and their construction​​ requires the complete simulation​​​‌ with a high cost‌ as a result. In‌​‌ contrast, we are proposing​​ a divide to simplify​​​‌ strategy, using a surrogate‌ of each constitutive solver,‌​‌ which reduces the input​​ dimensionality of the local​​​‌ models, enables parallel construction‌ and more flexible control‌​‌ of the computational effort.​​ We will have to​​​‌ derive suitable error estimates‌ of the contributions of‌​‌ the individual solver and​​ procedures to decide the​​​‌ new computer experiments to‌ reduce the error optimally.‌​‌ A second research axis​​ on surrogate models will​​​‌ concern complexity reduction using‌ transformation methods. Transformations can‌​‌ act on the input​​ or output spaces of​​​‌ the model. In the‌ first case, dimensionality reduction‌​‌ is achieved by finding​​ low dimensional subspaces of​​​‌ the input space that‌ convey most of the‌​‌ output variability. Platon will​​ extend these methodologies to​​​‌ incorporate non-linear subspaces and‌ alternative importance measures, in‌​‌ particular, to account for​​ the surrogate's final usage​​​‌ (goal-oriented reduction). For the‌ reduction of the output,‌​‌ we will consider generalizations​​ of the preconditioning approach,​​​‌ which transforms the model‌ output to a form‌​‌ admitting a much simpler​​ surrogate and implicit enforcement​​​‌ of physical constraints. Here,‌ the main challenges will‌​‌ be the automatic selection​​ of the transformation among​​​‌ a dictionary and the‌ design of computer experiments‌​‌ in this context (see​​ below).

3.1.2 Uncertainty model,​​​‌ information theory and inference‌

Challenges. Uncertainty management in‌​‌ simulation can be considered​​ in its infancy, and​​​‌ the control of the‌ whole process, from the‌​‌ definition of the uncertainty​​​‌ model to the design​ of new simulations or​‌ experiments for uncertainty reduction,​​ is still facing multiple​​​‌ challenges. Most past works​ on UQ have focused​‌ on forward-propagation and inverse​​ problems when, in contrast,​​​‌ input uncertainty models and​ uncertainty reduction strategies, in​‌ general, have received much​​ less attention.

Proposed actions.​​​‌ The uncertainty model directly​ affects the conclusion of​‌ UQ analyses (e.g.​​, sensitivity analyses, estimation​​​‌ of failure probabilities, rare​ events). Therefore, it is​‌ crucial to propose uncertainty​​ models that consistently and​​​‌ objectively integrate all available​ information and expert knowledge(s).​‌ Platon will explore the​​ application of maximum entropy​​​‌ principle, likelihood maximization and​ moment matching methods, for​‌ the construction of uncertainty​​ models in engineering problems.​​​‌

For the inverse problem,​ the Team will continue​‌ its efforts in Bayesian​​ inference toward better treatment​​​‌ of the model error​ in the calibration procedure.​‌

Concerning uncertainty reduction, a​​ central question is the​​​‌ prediction of the improvement​ toward the specific objective​‌ brought by a new​​ simulation (computer experiment). Platon​​​‌ will investigate different strategies​ of design of experiment​‌ (DoE) based on measures​​ of the improvement, such​​​‌ as entropy reduction, besides​ the classical reduction of​‌ variance.

The DoE in​​ inference consists in proposing​​​‌ new physical experiments to​ reduce the posterior uncertainty​‌ optimally. Optimizing information gain​​ leads to expensive numerical​​​‌ procedures, and suitable model​ error and noise models​‌ are critical to ensure​​ the robustness of these​​​‌ optimal DoE procedures when​ applied to real-life data.​‌ Platon will work on​​ approximation and reduction methods​​​‌ for optimal DoE to​ enable applications in large-scale​‌ engineering problems; the extension​​ of the optimization to​​​‌ uncertainty reduction in general​ model-prediction, not just the​‌ model parameter uncertainty.

3.1.3​​ Multi-fidelity, Multi-level and optimization​​​‌ under uncertainty

Challenges. Multi-fidelity​ and Multi-level (MF&​‌L) methods have been​​ proposed to reduce the​​​‌ cost of surrogate model​ construction or statistics estimations,​‌ by relying on simulators​​ of different complexity (in​​​‌ the modeled physics, discretization,​ or both). Although these​‌ methods have proved to​​ be effective, particularly in​​​‌ the context of expensive​ simulations, existing algorithms must​‌ be adapted to other​​ tasks. MF&L​​​‌ strategies are also missing​ in Robust Optimization (RO)​‌ and Reliability-Based Optimization (RBO),​​ where one has to​​​‌ evaluate the objective accurately,​ typically some statistics of​‌ the model output (moments,​​ quantiles, ...).

Proposed action.​​​‌ The Team Platon will​ explore MF&L​‌ approaches and the design​​ of computer experiments to​​​‌ obtain the best estimation​ at the lowest cost​‌ (or for a prescribed​​ computational budget) for nontrivial​​​‌ goal, specifically optimization and​ reliability problems where the​‌ accuracy needed is not​​ uniform, possibly unknown a​​​‌ priori and to be​ estimated as the construction​‌ proceeds.

In RO and​​ RBO, our research will​​​‌ focus on the estimation​ of robustness and reliability​‌ measures with tunable fidelity​​ to adapt the convergence​​​‌ of the statistics to​ the advancement of the​‌ optimization procedure. Platon will​​ include MF&L​​​‌ in the so-called bounding-box​ approach to track the​‌ level of error in​​ the statistical estimates. Another​​ research axis will focus​​​‌ on alternative estimation methods,‌ e.g. the Quantile Bayesian‌​‌ regression, to include​​ MF&L features.​​​‌

3.1.4 HPC and UQ‌ problems

Challenges. Both intrusive‌​‌ and non-intrusive UQ methods​​ are associated to large​​​‌ computational costs, ranging from‌ several to millions of‌​‌ times the cost of​​ a deterministic solution depending​​​‌ on the problem and‌ task considered. This situation‌​‌ is a significant obstacle​​ to the deployment of​​​‌ UQ analysis in large‌ scale simulations, and computational‌​‌ aspects have been central​​ for a long time.​​​‌ However, works concerning the‌ exploitation of High-Performance Computing‌​‌ platforms with massive parallelism​​ are still scarce, besides​​​‌ the trivial parallelism of‌ some sampling methods (‌​‌e.g., Monte Carlo).​​ Further, past efforts have​​​‌ concerned the formulation of‌ the stochastic problem and‌​‌ relied on existing advanced​​ solution methods (e.g.​​​‌ Domain Decomposition, linear algebra‌ libraries, parallelism). However, few‌​‌ works have fully considered​​ exploiting stochastic structures and​​​‌ HPC aspects to design‌ novel computational strategies fully‌​‌ dedicated to UQ problems.​​

Proposed actions. Platon will​​​‌ continue to develop solvers‌ for the resolution of‌​‌ multiple large systems resulting​​ from the discretization of​​​‌ sampled stochastic problems. In‌ particular, we shall focus‌​‌ on linear and non-linear​​ (Newton-like) solvers, exchanging information​​​‌ (Krylov spaces) between successive‌ solves to improve convergence‌​‌ rates of iterative methods.​​ Besides the extension to​​​‌ non-linear problems, the work‌ will focus on the‌​‌ implementation aspect and consider​​ communication strategies when several​​​‌ instances of the random‌ system are solved in‌​‌ parallel.

Platon will continue​​ to develop specific domain​​​‌ decomposition methods for stochastic‌ problems, and to propose‌​‌ effective stochastic preconditioners exploiting​​ the independence of the​​​‌ local (uncertain) sub-problems. An‌ additional but critical point‌​‌ concerns the association of​​ adaptive mesh refinement (AMR,​​​‌ in space) with multiple‌ resolution analysis (MRA, in‌​‌ the parameters) methods. Few​​ works have solved UQ​​​‌ problems with deterministic AMR,‌ and combining the two‌​‌ adaptive approaches within a​​ parallel framework remains challenging;​​​‌ progress in this direction‌ would enable efficient intrusive‌​‌ solvers for conservation laws.​​

Pollution reduction​​​‌ in commercial aircrafts

In‌ EASA's 2019 annual report,‌​‌ in-flight icing was identified​​​‌ as a priority 1​ issue for large aeroplanes.​‌ Therefore, to comply with​​ certification rules, airframes and​​​‌ engine manufacturers must demonstrate​ safe operation under icing​‌ conditions which leads to​​ significant costs before the​​​‌ new product is put​ into service. Wind tunnel​‌ tests and flight tests​​ in icing conditions are​​​‌ usually required due to​ the low confidence of​‌ certification authorities place in​​ simulations, due to the​​​‌ complexity of the icing​ process.

A breakthrough, leading​‌ to a reduction of​​ time-to-market and certification costs,​​​‌ would be obtained by​ creating a consensus among​‌ certification authorities about the​​ reliability of simulation tools​​​‌ for predicting in-flight ice​ accretion and the operation​‌ of IPS.

TRACES is​​ a European Joint Doctorate​​​‌ network whose main goal​ is to provide high-level​‌ training in the field​​ of in-flight icing to​​​‌ deliver a new generation​ of high achieving Doctoral​‌ Researchers (DR) in the​​ diverse disciplines necessary for​​​‌ mastering the complexity of​ ice accretion and its​‌ mitigation in aircraft and​​ aeroengines. In TRACES, Platon​​​‌ is developing novel methods​ to assess the calibration​‌ procedure by detecting potential​​ inaccuracies of icing model​​​‌ and to perform an​ uncertainty quantification study propagating​‌ systematically the posterior distribution​​ of each model's parameter.​​​‌

Renewable energy sources

Platon​ is involved in the​‌ development of advanced numerical​​ tools to simulate Organic​​​‌ Rankine Cycles (ORCs), which​ are of key-importance in​‌ renewable energy systems. Specifically,​​ we are working on​​​‌ the inference of thermodynamic​ models parameters for complex​‌ molecular compounds, using experimental​​ data of the worldwide​​​‌ first facility at Politecnico​ di Milano. Secondly, we​‌ are developing a robust​​ optimization framework for the​​​‌ shape design of ORC​ turbines.

Project-team positioning

Many​​ research groups are presently​​​‌ working on Uncertainty Quantification​ (UQ) and inference problems​‌ over the world and​​ in France. For instance,​​​‌ the US has created​ and continues to expand​‌ large multi-disciplinary groups to​​ address UQ challenges in​​​‌ energy and military domains​ through their national laboratories​‌ (SANDIA, Oak-Ridge, LLNL,...). These​​ groups aim at providing​​​‌ generic methods and tools​ (mostly software) for the​‌ resolution of UQ problems​​ (for example, the Dakota​​ code from Sandia-Albuquerque) faced​​​‌ by other research groups‌ from diverse application domains.‌​‌ Other countries are supporting​​ smaller initiatives, including the​​​‌ CEA (civil and military)‌ in France. Several large‌​‌ industrial groups, such as​​ Bosch, EADS, or EdF,​​​‌ are also deploying UQ‌ methodologies and tools (for‌​‌ example, the OpenTurns code​​ from EADS/EDF) through dedicated​​​‌ RD units or services,‌ responding to the demands‌​‌ of other services. These​​ UQ activities have often​​​‌ emerged in well-established groups‌ working in specific application‌​‌ domains (e.g., fluid dynamics,​​ solid mechanics, electromagnetics, chemistry,​​​‌ material sciences, earth sciences,‌ life sciences, ...), in‌​‌ response to some UQ​​ aspects related to these​​​‌ particular domains. We cite‌ G. Iaccarino (Uncertainty Quantification‌​‌ Lab within the Center​​ for Turbulence Research, Stanford​​​‌ University), Y. Marzouk (Aerospace‌ Computational Design Laboratory, MIT)‌​‌ and K. Wilcox (Institute​​ for Computational Engineering and​​​‌ Sciences, University of Texas).‌ The situation is globally‌​‌ similar in applied mathematics,​​ where several groups develop​​​‌ advanced UQ methods within‌ a broader research area‌​‌ (e.g., stochastic numerics, statistics,​​ numerical analysis,...), sometimes with​​​‌ only a distant connection‌ to engineering domains. For‌​‌ example, we can mention​​ the research groups of​​​‌ M. Giles (Oxford), I.‌ Bilionis (Purdue University), J.‌​‌ Garnier (Ecole Polytechnique), R.​​ Abgrall (University of Zurich).​​​‌

The objective of Platon‌ is to team-up participants‌​‌ with the main interest​​ in the development of​​​‌ UQ methodologies. While primarily‌ targeting our current applications,‌​‌ our objective is to​​ propose new applications through​​​‌ collaborations and progressive team‌ development while maintaining the‌​‌ UQ as the project's​​ identity. This strategy gives​​​‌ a somehow unique position‌ of the Team within‌​‌ the national and international​​ research landscapes. As far​​​‌ as computational mechanics and‌ engineering are concerned, no‌​‌ group has been created​​ with UQ management as​​​‌ the principal working area.‌

Then, the identity of‌​‌ Platon is to be​​ contrasted with initiatives, including​​​‌ within Inria, which may‌ have a UQ component,‌​‌ but within different methodological​​ contexts and not as​​​‌ a central activity. For‌ instance, some teams (‌​‌e.g. SIERRA, TAO, SELECT,​​ MODAL) develop statistical methods​​​‌ for data analysis, machine‌ learning, and the treatment‌​‌ of large databases. Overall,​​ the problems targeted in​​​‌ Platon are usually too‌ costly, with high parametric‌​‌ dimension, and with few​​ experimental data, so existing​​​‌ statistical methods can not‌ be reused "as is",‌​‌ and require dedicated approaches.​​

On the application side,​​​‌ there are already Inria‌ teams working on CFD‌​‌ applications, some even incorporating​​ uncertainty quantification and sensitivity​​​‌ analysis activities. We mention‌ here AIRSEA, which focuses‌​‌ on oceanic and atmospheric​​ flows, CARDAMOM on free-surface​​​‌ hydraulics, and ACUMES on‌ unsteady models in traffic‌​‌ flow and biology. In​​ contrast to our project,​​​‌ all these efforts primarily‌ address challenges in their‌​‌ respective application areas.

Scientific​​ achievements

Our research activity​​​‌ features two main axes.‌ The first is related‌​‌ to methodological developments, while​​ the second is oriented​​​‌ to UQ problems with‌ industrial interests.

The first‌​‌ contribution concerns parameter calibration​​ of computer models, which​​​‌ are widely used for‌ the prediction of complex‌​‌ physical phenomena. Based on​​​‌ observations of these physical​ phenomena, it is possible​‌ to calibrate the model​​ parameters. In most cases,​​​‌ such computer models are​ mis-specified, and the calibration​‌ process must be improved​​ by including a model​​​‌ error term. The model​ error hyperparameters are, however,​‌ rarely learned jointly with​​ the model parameters to​​​‌ reduce the dimensionality of​ the problem. Sequential and​‌ non-sequential approaches have been​​ introduced to estimate the​​​‌ hyperparameters. The former, such​ as the Kennedy and​‌ O'Hagan (KOH) framework, estimates​​ the model error hyperparameters​​​‌ before calibrating the model​ parameters. The latter, such​‌ as the Full Maximum​​ a Posteriori (FMP), introduces​​​‌ a functional dependence between​ the model parameters and​‌ the model error hyperparameters.​​ Despite being more reliable​​​‌ in some cases (bimodality​ e.g.), the FMP method​‌ still fails to estimate​​ correctly the posterior distribution​​​‌ shape. We proposed in​ 9 a new methodology​‌ for treating the model​​ error term in computer​​​‌ code calibration. It builds​ upon the KOH and​‌ FMP framework. Called the​​ Complete Maximum a Posteriori​​​‌ (CMP) method, it provides​ a closed-form expression for​‌ the marginalization integral over​​ the model error hyperparameters,​​​‌ significantly reducing the dimensionality​ of the calibration problem.​‌ Such expression re- lies​​ on a set of​​​‌ assumptions that are more​ general and less stringent​‌ than the ones usually​​ employed. The CMP method​​​‌ is applied to four​ examples of increasing complexity,​‌ from elementary to real​​ fluid dynamics problems, including​​​‌ or not bimodality. Compared​ to the true reference​‌ solution and unlike the​​ KOH and FMP, the​​​‌ CMP method correctly captures​ the shape of the​‌ posterior distribution, including all​​ modes and their weights.​​​‌ Moreover, it provides an​ accurate estimate of the​‌ distribution tails.

We worked​​ on four physical problems​​​‌ under an Uncertainty Quantification​ perspective.

The first problem​‌ is related to the​​ modeling of gas–surface interaction​​​‌ phenomena, which is crucial​ for accurately predicting the​‌ heat flux and the​​ mass loss experienced by​​​‌ hypersonic vehicles. Gas–surface interactions​ refer to the phenomena​‌ occurring between the reacting​​ gas and the thermal​​​‌ protection material. An important​ part of the modeling​‌ concerns the description of​​ the surface chemical reactions.​​​‌ In this regard, we​ proposed a novel methodology​‌ 6 to infer the​​ parameters underlying such surface​​​‌ chemistry models. It combines​ uncertainty quantification techniques with​‌ state-of-the-art modeling and different​​ types of experiments. The​​​‌ methodology is used to​ calibrate, in a Bayesian​‌ sense, the rates of​​ the elementary reactions between​​​‌ a nitrogen gas and​ a carbon surface. We​‌ rely on both molecular​​ beam and plasma wind​​​‌ tunnel observations. The former​ provides detailed data on​‌ the chemical mechanisms but​​ is characterized by pressures​​​‌ nonrepresentative of atmospheric entries.​ By contrast, plasma wind​‌ tunnel experiments are conducted​​ at representative pressures but​​​‌ contain only macroscopic information.​ The parameters’ posterior distributions​‌ are then propagated through​​ the models representing the​​​‌ two experiments. The calibrated​ model is able to​‌ satisfactorily explain both experiments,​​ highlighting the robustness of​​​‌ the proposed methodology.

A​ second contribution concerns nonlinear​‌ systems, which exhibit a​​ plethora of complex dynamic​​ behaviours that are difficult​​​‌ to model and predict‌ accurately. This difficulty often‌​‌ arises from a lack​​ of knowledge of the​​​‌ physics that induces the‌ nonlinear behaviours and the‌​‌ strong sensitivity of the​​ nonlinear dynamics to parameter​​​‌ variation. We introduce in‌ 11 a methodology to‌​‌ carry out nonlinear model​​ updating based on bifurcations.​​​‌ The proposed approach involves‌ minimising the distance between‌​‌ experimental and numerical bifurcation​​ curves, which are key​​​‌ dynamic features that define‌ stability boundaries and regions‌​‌ of multi-stability. For the​​ model, bifurcation curves are​​​‌ computed via standard numerical‌ bifurcation tracking analyses. In‌​‌ the experiment, we use​​ control-based continuation to obtain​​​‌ the data. The approach‌ is first demonstrated on‌​‌ a Duffing and a​​ beam system using synthetic​​​‌ data, before being applied‌ to experimental data collected‌​‌ on a base-excited energy​​ harvester with magnetic nonlinearity.​​​‌

The third contribution concerns‌ the application to wind‌​‌ turbines. The multi-physics nature​​ of the problem combined​​​‌ with its structural complexity‌ has limited prediction accuracy.‌​‌ Numerous unknown or uncertain​​ properties within the system​​​‌ contribute to discrepancies between‌ model simulations and actual‌​‌ turbine responses, making behavior​​ prediction challenging. An effective​​​‌ approach to address these‌ discrepancies is by tuning‌​‌ key model parameters using​​ data from real-structure measurements.​​​‌ This approach, known as‌ model updating, has been‌​‌ extensively studied in the​​ field of structural dynamics.​​​‌ Wind turbines present unique‌ challenges due to their‌​‌ time-periodic nature. In fact,​​ the rotational motion of​​​‌ the blades induces time-periodic‌ behavior, rendering it incompatible‌​‌ with classical vibration-based model​​ updating techniques. In this​​​‌ work 14, we‌ propose a numerical framework‌​‌ to perform model updating​​ on operating wind turbines.​​​‌ More precisely, a Bayesian‌ framework is employed on‌​‌ the Floquet-Fourier approximation of​​ the operating wind turbines.​​​‌

Finally, we worked on‌ a Bayesian inference approach‌​‌ 10 for inferring the​​ source of marine pollution​​​‌ released from a moving‌ source in an uncertain‌​‌ flow field. A Markov​​ Chain Monte Carlo (MCMC)​​​‌ algorithm is developed and‌ applied for inferring single‌​‌ and multiple release events​​ from vessels moving at​​​‌ known velocity along a‌ predefined path in the‌​‌ Mediterranean Sea. The likelihood​​ is based on a​​​‌ logistic regression cost function‌ that measures the discrepancy‌​‌ between the modeled spill​​ distribution and a binary​​​‌ representation of the observed‌ images. We assess the‌​‌ performance of the proposed​​ methodology using a synthetic​​​‌ release scenario employing realistic‌ ocean currents to drive‌​‌ a stochastic Lagrangian Particle​​ Tracking (LPT) algorithm to​​​‌ generate a probabilistic representation‌ of the spill distribution.‌​‌ The MCMC algorithm employs​​ an adaptive scheme to​​​‌ robustly ensure convergence and‌ well-mixed chains. The proposed‌​‌ Bayesian framework is tested​​ by inferring the location,​​​‌ or injection time, and‌ relative contributions of single‌​‌ and multiple moving sources,​​ contributing to separate and​​​‌ common observation patches, with‌ a focus on various‌​‌ scenarios that demonstrate the​​ efficiency of our sampling​​​‌ algorithm. The performance of‌ the proposed framework was‌​‌ further assessed by comparing​​ the model predictions with​​​‌ the most probable release‌ parameters predicted by a‌​‌ global optimization algorithm.

Collaborations​​​‌

Since many years, we​ have several long-term partnerships​‌ with KAUST, von Karman​​ Institute for Fluid-Dynamics (VKI),​​​‌ Politecnico di Milano and​ CEA.

With KAUST, we​‌ are working on new​​ stochastic particle tracking methods​​​‌ to identify and track​ oil spills in open​‌ waters, combining satellite images​​ and uncertainties in predicted​​​‌ currents. We also develop​ new assimilation schemes, inference​‌ methods for fractional diffusion​​ models, and the selection​​​‌ and reduction of observations.​ There are several joint​‌ publications and exchanges of​​ students.

With VKI, we​​​‌ work on UQ methods​ and inverse problems for​‌ atmospheric re-entry and ablation​​ problems. In terms of​​​‌ production, there are several​ joint publications and one​‌ joint PhDs (M. Capriati).​​

With Politecnico di Milano,​​​‌ we have several activities​ in the Aeronautical and​‌ Energy fields. We work​​ on the characterization of​​​‌ the thermodynamic model with​ Bayesian approaches, uncertainty on​‌ the turbulence model for​​ RANS aerodynamic simulation, multi-fidelity​​​‌ approaches. We are currently​ involved in the EU​‌ TRACES project. We have​​ also a strong collaboration​​​‌ with Giulio Gori, former​ member of Platon, and​‌ now Assistant Professor at​​ Politecnico di Milano.

With​​​‌ CEA Saclay, we have​ a long-term collaboration since​‌ four years. Nicolas Leoni​​ defended his thesis last​​​‌ year, and another student​ is doing her PhD​‌ (Sanae Idrissi).

External support​​

• MSCA Doctoral Network TRACES​​​‌ Project (2022-2026)
• Industrials contracts​ with CEA
• Industrial contract​‌ with 3DS

Self assessment​​

In addition to developing​​​‌ methods-oriented research, we proposed​ UQ methods tailored to​‌ specific applications in collaboration​​ with other academic and​​​‌ industrial partners. This action​ has allowed us to​‌ position ourselves with high-impact​​ papers in many application​​​‌ areas.

A weakness may​ be finding a balance​‌ between two different axes.​​ The first axis concerns​​​‌ the development of high-level​ research from a methodological​‌ point of view, while​​ the second one involves​​​‌ collaborations with industrial partners​ within research contracts and​‌ European projects. We think​​ that the team's current​​​‌ size does not fit​ very well in the​‌ long term with this​​ double effort. For this​​​‌ reason, the recruitment of​ new forces seems mandatory​‌ to keep sustaining a​​ good balance between these​​​‌ two main axes of​ research.

Personnel

Participants:​​​‌ P.M. Congedo, O.​ Le Maître, E.​‌ Denimal Goy, M.​​ Duvillard, H. Dornier​​​‌, H. Masson,​ C. Papagiannis.

Project-team​‌ positioning

Research on solvers,​​ numerical schemes, and HPC​​​‌ algorithms specifically dedicated to​ UQ problems is scarce.​‌ Indeed, advanced sampling and​​ stochastic estimation procedures, the​​​‌ subject of intensive outgoing​ research, rely on state-of-the-art​‌ deterministic solvers to generate​​ the solution samples. To​​​‌ our knowledge, there is​ no research group (within​‌ or outside Inria) focusing​​ entirely on the computational​​​‌ aspects of UQ problems.​ Groups producing computational utilities​‌ for UQ (e.g., Sandia's​​ Dakota, OpenTurns) focus on​​​‌ the sampling part (statistical​ treatment), and the efficient​‌ generation of the samples​​ is left to the​​​‌ user. In recent years,​ few works have concerned​‌ Galerkin solvers, their preconditioning,​​ and the adaptation of​​ domain decomposition methods (DDM)​​​‌ for (usually elliptic) stochastic‌ PDEs. We can mention‌​‌ some activities in Manchester​​ (preconditioning), Munich and Lausanne​​​‌ (DDM), and Bath (solvers‌ for multi-level methods). In‌​‌ Platon, we are trying​​ to exploit the structure​​​‌ of the stochastic problems‌ to propose new strategies‌​‌ for their resolution (Galerkin​​ method) or the generation​​​‌ of solution samples. These‌ strategies can consist of‌​‌ adapting deterministic solvers to​​ factorize the computational effort​​​‌ over multiple samples or,‌ on the contrary, the‌​‌ definition of entirely new​​ solution procedures to exploit​​​‌ parallel methods in stochastic‌ problems better, beyond the‌​‌ independent resolution of independent​​ samples. Our objective is​​​‌ to produce parallel and‌ scalable methods for large-scale‌​‌ stochastic problems.

It becomes​​ more and more critical​​​‌ to devise solution methods‌ tailored to the stochastic‌​‌ problem when the numerical​​ complexity of the underlying​​​‌ deterministic problem increases. For‌ elliptic problems, highly efficient‌​‌ deterministic solvers' availability has​​ somehow limited the research​​​‌ on stochastic solvers. The‌ situation is different for‌​‌ models based on fractional​​ diffusion operators (in space​​​‌ or time), where the‌ numerical difficulties to solve‌​‌ these operators have virtually​​ prevented any work on​​​‌ problems with stochastic fractional‌ and diffusion coefficients. A‌​‌ few years ago, KAUST​​ (Omar Knio) and KFUPM​​​‌ (Kassem Mustapha) initiated a‌ research program on fractional‌​‌ diffusion models. Platon is​​ involved in this program​​​‌ to deal with the‌ stochastic extensions. Several new‌​‌ numerical schemes and algorithms​​ to solve deterministic fractional​​​‌ diffusion equations have been‌ designed. These schemes are‌​‌ suitable for an extension​​ to stochastic problems (e.g.,​​​‌ allowing for spatially variable‌ coefficients and achieving efficient‌​‌ -scalability- enabling sampling methods​​ and inverse problems).

Scientific​​​‌ achievements

In computational fluid‌ dynamics, evaluating accurately quantities‌​‌ of interest (global or​​ local) requires capturing complex​​​‌ local phenomena and interactions,‌ such as shocks and‌​‌ flow separations, while controlling​​ the global error. The​​​‌ latter depends highly on‌ the discretization of the‌​‌ computational domain, hence the​​ mesh. In general, the​​​‌ location of the flow‌ structures within the domain‌​‌ is sensitive to boundary​​ and flow conditions. Proposing​​​‌ an a priori mesh‌ with a discretization effort‌​‌ that concentrates on the​​ demanding parts of the​​​‌ domain is thus usually‌ impossible. Adaptive Mesh Refinement‌​‌ (AMR is a method​​ developed to iteratively adjust​​​‌ the local mesh resolution‌ to the computed flow‌​‌ structures and construct meshes​​ that achieve a prescribed​​​‌ accuracy for limited discretization‌ and computational cost. This‌​‌ work concerns the problem​​ of mesh adaptation when​​​‌ the operating conditions are‌ variable and follow a‌​‌ prescribed continuous distribution. For​​ instance, variability of the​​​‌ flow conditions appears in‌ uncertainty quantification, operating domain‌​‌ analysis, and robust optimization.​​ These analyses typically require​​​‌ many simulations for different‌ conditions, making the cost-accuracy‌​‌ trade-off even more crucial​​ for these problems. Several​​​‌ mesh adaption methods have‌ been proposed for variable‌​‌ conditions, but they typically​​ focus primarily on error​​​‌ control without simultaneously optimizing‌ for cost. In this‌​‌ context, we propose two​​ original methodologies. The first​​​‌ one, called Mean Mesh‌ adaptation 7, builds‌​‌ a unique adapted mesh​​​‌ to minimize the average​ error over the continuous​‌ operating conditions for a​​ given discretization effort. A​​​‌ key ingredient of MMA​ is using a small​‌ sample set of conditions​​ to estimate the local​​​‌ average error at each​ iteration of the AMR​‌ process. The second method,​​ Error-based Mesh Selection (EMS)​​​‌ 18, tackles the​ optimal element selection within​‌ a library of adapted​​ meshes to achieve the​​​‌ smallest possible error for​ any given flow conditions.​‌ The library consists of​​ meshes independently adapted for​​​‌ different conditions in an​ offline stage, for cost​‌ efficiency, the selection uses​​ a priori error estimations​​​‌ requiring no additional simulation.​ We used analytical and​‌ full CFD supersonic simulations​​ to analyze the proposed​​​‌ methods. We show that​ MMA is robust and​‌ accurately approximates the optimal​​ mesh minimizing the average​​​‌ error for a limited​ construction cost. Similarly, EMS​‌ provides a robust approximation​​ of the optimal selection​​​‌ with limited cost overheads.​ The EMS method is​‌ suitable to be extended​​ for progressive library enrichment​​​‌ and a-posteriori correction of​ the error estimates.

Collaborations​‌

With KAUST, we worked​​ with Omar Knio on​​​‌ numerical schemes for fractional​ diffusion equation and their​‌ extension to the stochastic​​ case.

With CEA-CESTA, we​​​‌ worked on scientific machine​ learning techniques within the​‌ thesis of Paul Novello.​​

External support

• Industrial contracts​​​‌ with CEA
• Industrial contract​ with 3DS
• Industrial contract​‌ with Framatome

Self assessment​​

Concerning the fractional diffusion​​​‌ models, we are already​ engaged in the extension​‌ of the hierarchical matrix​​ method to solve the​​​‌ spatial stochastic fractional diffusion​ equation with a Galerkin​‌ method and to develop​​ sparse storage strategies to​​​‌ reduce the complexity of​ the stochastic time-fractional problem.​‌ These are promising and​​ very original researches. We​​​‌ (Platon) are dependent on​ the collaboration to access​‌ some of the numerical​​ utilities (H-matrices).

Personnel

Participants: P.M.​‌ Congedo, O. Le​​ Maître, E. Denimal​​​‌ Goy, Z. Jones​, H. Nicolas.​‌

Project-team positioning

Optimization Under​​ Uncertainty is an important​​​‌ axis of research, due​ to both the evergrowing​‌ computational power available and​​ the need for efficiency,​​​‌ reliability and cost optimality.​ The presence of uncertainty​‌ could make the solution​​ of a deterministic optimization​​​‌ problem suboptimal or even​ infeasible. Since this behavior​‌ could impact strongly the​​ design performances, both academia​​​‌ and industry focused their​ effort to developing optimization​‌ under uncertanty methodologies. Optimization​​ under uncertainty is a​​​‌ broad domain including several​ modeling paradigms, such as​‌ for example stochastic programming,​​ Reliability-Based Design Optimization (RBDO,​​​‌ that deals with probabilistic​ and worst-case feasibility constraints),​‌ and Robust Design Optimization​​ (RDO, where the deterministic​​​‌ objectives are replaced with​ averaged or worst-case ones,​‌ possibly in a multi-objective​​ context such as the​​​‌ classical Taguchi optimization).

Note​ that most of the​‌ groups active in optimization​​ under uncertainty also have​​​‌ strong activities in uncertainty​ quantification. Thus there is​‌ an overlap with the​​ state of the art​​​‌ presented in Section 7.1​. The Optimization &​‌ Uncertainty Quantification Group of​​ Sandia-Albuquerque aim at providing​​ advanced methods for the​​​‌ resolution of optimization under‌ uncertainty problems. We mention‌​‌ as well optimization under​​ uncertainties activities emerged in​​​‌ well-established groups working in‌ specific application domains. We‌​‌ cite the Aerospace Computational​​ Design Laboratory from MIT​​​‌ and the Institute for‌ Computational Engineering and Sciences‌​‌ from University of Texas.​​ In France, we can​​​‌ mention the OQUAIDO Chair‌ ( Optimization and QUAntification‌​‌ of Uncertainties), hosted by​​ the École des Mines​​​‌ de Saint-Étienne from 2016‌ to 2021, aiming to‌​‌ bring together academic and​​ industrial partners to solve​​​‌ problems related to uncertainty‌ quantification, inversion and optimization.‌​‌

In the context of​​ the Optimization under Uncertainty,​​​‌ Platon is devoted to‌ developing novel methods to‌​‌ tackle constrained multi-objective optimization,​​ with specific attention on​​​‌ cost-efficient and mainly derivative-free‌ strategies. Specifically, we look‌​‌ for an optimal trade-off​​ between computational cost and​​​‌ accuracy in the case‌ of problems involving complex‌​‌ and expensive numerical solvers.​​ Platon is exploring also​​​‌ dedicated representation and the‌ design of computer experiments‌​‌ to obtain the best​​ estimation at the lowest​​​‌ cost (or for a‌ prescribed computational budget) for‌​‌ nontrivial goal, specifically optimization​​ and reliability problems where​​​‌ the accuracy needed is‌ not uniform, possibly unknown‌​‌ a priori and to​​ be estimated as the​​​‌ construction proceeds. More recently,‌ we have worked also‌​‌ on sample average approximation​​ methods using a risk-averse​​​‌ stochastic programming formulations.

Several‌ Inria Teams have the‌​‌ optimization problem as core​​ activity, such as for​​​‌ example BONUS, EDGE, INOCS,‌ POLARIS, RANDOPT. Main difference‌​‌ is that we are​​ not interested in working​​​‌ on generic optimization algorithms,‌ as mentioned before. In‌​‌ our past and current​​ works, we use standard​​​‌ optimization algorithms, mainly for‌ continuous optimization. We focus‌​‌ our attention on dedicated​​ representations to efficiently estimate​​​‌ uncertainty-based metrics within an‌ optimization problem. The Inria‌​‌ teams POLARIS and INOCS​​ work on innovative methods​​​‌ for stochastic optimization that‌ are quite different from‌​‌ those proposed by Platon.​​

Scientific achievements

We propose​​​‌ a multifidelity formulation for‌ generating cokriging surrogates of‌​‌ complex physics models 8​​. First, we show​​​‌ that the standard autoregressive‌ recursive approach may be‌​‌ subject to substantial limitations​​ due to possible modeler’s​​​‌ biases/errors. These are inherent‌ to the process of‌​‌ establishing a nested hierarchy​​ concerning the alleged fidelity​​​‌ of the available models.‌ The formulation we propose‌​‌ mitigates this issue. At​​ each hierarchy level, the​​​‌ predictor consists of a‌ linear combination of all‌​‌ previous levels instead of​​ just the underlying one.​​​‌ The methodology implies a‌ slightly higher training cost‌​‌ for the surrogate. However,​​ the higher training cost​​​‌ is acceptable, considering the‌ effort typically required to‌​‌ generate data in aerospace​​ applications. A few artificial​​​‌ tests, including the optimization‌ of a two-dimensional airfoil,‌​‌ illustrate strengths and weaknesses​​ of the approach.

A​​​‌ second contribution concerns quantile‌ regression. In the frequentist‌​‌ approach, the quantile regression​​ problem is cast as​​​‌ the minimization of a‌ loss function, possibly complemented‌​‌ with regularization terms. The​​ Bayesian counterpart formulates the​​​‌ problem as posterior inference‌ over a function space.‌​‌ Of particular interest is​​​‌ Gaussian process quantile regression,​ which formulates the regression​‌ problem as posterior inference​​ over the latent conditional​​​‌ quantiles, where prior knowledge​ is encoded in the​‌ form of a Gaussian​​ process. Existing approaches to​​​‌ Gaussian process quantile regression​ either perform the regression​‌ directly on observed data​​ or resort to sparse​​​‌ approximations to mitigate computational​ costs. However, in the​‌ latter case, the approximation​​ is typically defined over​​​‌ a small set of​ latent auxiliary variables that​‌ act as compact representations​​ of the quantile, but​​​‌ whose locations are fixed​ in advance, ultimately resulting​‌ in suboptimal predictive performance.​​ In this work, we​​​‌ introduce an adaptive strategy​ that exploits the Gaussian​‌ process predictive variance to​​ infill the set of​​​‌ auxiliary variable locations. Inference​ of the posterior distribution​‌ over these auxiliary variables​​ is recast as its​​​‌ Laplace approximation. The impact​ of finite training data​‌ on the auxiliary variables​​ is estimated through bootstrap​​​‌ resampling. Building on this,​ we introduce an active​‌ learning strategy 20 that​​ acquires new observations of​​​‌ the response variable via​ rejection sampling, with the​‌ sampling density guided by​​ the uncertainties in the​​​‌ auxiliary estimates. Our algorithm​ combines adaptive auxiliary variable​‌ allocation and active learning,​​ leading to a sequential​​​‌ approach that ensures a​ rich and well-balanced representation​‌ of the quantile function.​​ Finally, we extend our​​​‌ quantile regression method and​ its enrichment criteria to​‌ the quantile minimization problem​​ within a Bayesian optimization​​​‌ framework.

The third contribution​ concerns topology optimization applied​‌ to 3D printing. Mechanical​​ properties of additively manufactured​​​‌ metals differ significantly from​ usual methods (casting, milling,​‌ etc), and parts show​​ unique defects and variability​​​‌ in shape or performances.​ Cooling conditions during manufacturing​‌ can vary based on​​ several parameters, including the​​​‌ object's geometry, the material's​ thermal properties, and the​‌ number of parts on​​ the build plate, among​​​‌ others. Some of those​ parameters are subjected to​‌ great variability which are​​ reflected in the mechanical​​​‌ properties of the as-printed​ object. Thus, design of​‌ structural parts with topology​​ optimization should account for​​​‌ such variability to reach​ robust designs. This work​‌ 19 focuses on a​​ change of isotropic and​​​‌ anisotropic properties of the​ printed component. To do​‌ so, a simple and​​ low dimension material model​​​‌ featuring a transition from​ anisotropic to isotropic material​‌ in the build direction​​ is developed. This model​​​‌ serves as an input​ to a robust topology​‌ optimization code, with the​​ weighted sum of the​​​‌ average and variance of​ the compliance, considering the​‌ material variabilities, as objective​​ function. The robust solver​​​‌ is constructed based on​ a SIMP topology optimization​‌ algorithm with Optimality Criterion.​​ At each optimization iteration,​​​‌ the objective function is​ evaluated efficiently using a​‌ Gauss quadrature to ensure​​ reasonable computational cost. Impacts​​​‌ of the material model​ are studied with compliance​‌ minimization problems with volume​​ constraints of varying complexity,​​​‌ ranging from a 2D​ cantilever beam to 3D​‌ turbine blade infill demonstrating​​ the applicability of the​​​‌ approach. Fine tuning of​ the weights in the​‌ objective function shows that​​ the method is able​​ to decrease the standard​​​‌ deviation in compliance between‌ 5% and 20% compared‌​‌ to standard isotropic topology​​ optimization.

Collaborations

We worked​​​‌ with DLR (German Aerospace‌ Center) within the EU‌​‌ NEXTAIR project for robust​​ optimization, and the thesis​​​‌ of Zachary Jones.

Several‌ collaborations are with Politecnico‌​‌ di Milano within the​​ TRACES project.

The collaboration​​​‌ with KAUST has brought‌ specific stochastic optimization problems‌​‌ with structures that considerably​​ differ from our other​​​‌ researches (e.g. two-stages optimization,‌ introduction of recourse, discrete‌​‌ optimization, ...). These problems​​ also involve different risk​​​‌ mitigation approaches. Working on‌ these problems we have‌​‌ learn alternative formulations and​​ uncertainty treatments that we​​​‌ plan to apply to‌ engineering applications. Similarly, we‌​‌ have contributed with sampling​​ and uncertainty modelling strategies​​​‌ that are original for‌ this types of problems.‌​‌

External support

• MSCA Doctoral​​ Network TRACES Project (2022-2026)​​​‌
• EU NEXTAIR Project (2022-2026)‌
• Industrial contract with Bañulsdesign‌​‌

Self assessment

Concerning the​​ strong point, we proposed​​​‌ advanced state-of-the-art methods in‌ different aspects of optimization‌​‌ under uncertainty, which are​​ topics of great interest​​​‌ in academia. At the‌ same time, we consolidated‌​‌ industrial collaborations that have​​ allowed us to develop​​​‌ high-impact projects with a‌ relevant societal impact.

Concerning‌​‌ a potential weakness, we​​ think it is particularly​​​‌ challenging, given the size‌ of the team, to‌​‌ keep proposing innovative methods​​ and, at the same​​​‌ time, to contribute to‌ projects at the industrial‌​‌ and European scale. New​​ recruitments seem necessary to​​​‌ ensure this twofold effort.‌

8.1.1 3DS

Since 2022,‌​‌ the team benefits from​​ a "contrat d'accompagnement" for​​​‌ the thesis of Meryem‌ Benmahdi.

8.1.2 CEA

Since‌​‌ 2022, the team benefits​​ from a "contrat d'accompagnement"​​​‌ for the thesis of‌ Sanae Idrissi.

8.1.3 Framatome‌​‌

Since 2023, the team​​ benefits from a "research​​​‌ contrat" in the context‌ of the Pré-Defi project‌​‌ with Framatome.

9.1.1 Inria​​​‌ associate team not involved‌ in an IIL or‌​‌ an international program

9.2.1 Visits​ of international scientists

9.2.2 Visits to international​​​‌ teams

9.3.1 Horizon Europe​​

9.4.1 ANR‌ LabCom

9.4.2 ANR​​ JCJC

9.4.3 France 2030​​

10.1.1​​ Scientific events: organisation

• Enora​​​‌ Denimal Goy was in​ the organisation and scientific​‌ committee of the GDR​​ EX-MODELI 2025 workshop.
• Enora​​​‌ Denimal Goy was in​ the organisation and scientific​‌ committee of the CSMA​​ Junior workshop 2025.
• Olivier​​​‌ Le Maître has served​ in the scientific committee​‌ of the UNCECOMP Conference​​ 2025 (Rhodes, June 2025).​​​‌
• Pietro Marco Congedo has​ been one of the​‌ main organizers of the​​ Interactive Mathematics Day of​​​‌ the FMJH, November 5,​ 2025.

10.1.2 Scientific events:​‌ selection

10.1.3 Journal

10.1.4 Invited talks​​​‌

• Pietro Marco Congedo has‌ given an invited talk‌​‌ at the Workshop Mathematical​​ Foundations of AI, SCAI/DATAIA,​​​‌ Paris, March 25 2025.‌
• Pietro Marco Congedo has‌​‌ given an invited talk​​ at the 37th seminar​​​‌ CEA/GAMNI of numerical fluid‌ mechanics.
• Enora Denimal Goy‌​‌ gave a seminar at​​ the LJLL in November​​​‌ 2025.
• Enora Denimal Goy‌ gave a seminar at‌​‌ the GDR EX-MODELI 2025​​ workshop.
• Olivier Le Maìtre​​​‌ gave a seminar at‌ Dassault Systèmes in December‌​‌ 2025.
• Olivier Le Maìtre​​ gave an invited talk​​​‌ at the Forum Mer‌ et Océans in Feb‌​‌ 2025.

10.1.5 Leadership within​​ the scientific community

• Enora​​​‌ Denimal Goy is a‌ board member of the‌​‌ French GDR EX-MODELI.
• Enora​​ Denimal Goy is an​​​‌ elected board member of‌ the CSMA Junior (French‌​‌ Computational Structural Mechanics Association)​​

10.1.6 Research administration

• Pietro​​​‌ Marco Congedo is the‌ Scientific Director of the‌​‌ Inria International Lab CWI-Inria.​​
• Olivier Le Maître is​​​‌ the Scientific Director of‌ the MATritime Labcom.
• Enora‌​‌ Denimal Goy is the​​ head of the Associate​​​‌ Team HYPATIE in collaboration‌ with Imperial College London.‌​‌
• Enora Denimal Goy is​​ the PI of the​​​‌ ANR JCJC MeMoRa.
• Enora‌ Denimal Goy is the‌​‌ Inria Scientific leader and​​ PI of the WP3​​​‌ of the ANR FlexHALE.‌

10.2.1​​​‌ Teaching

• E. Denimal Goy,‌ 2025: INSA Rennes, Graduate‌​‌ Level (10h/y), academic advisor​​ of an apprentice.
• Enora​​​‌ Denimal Goy: Ecole Polytechnique,‌ 2025: 36h Dynamics of‌​‌ Solids and Structures –​​ CM and PC. 3A​​​‌ and M1 student from‌ the international master of‌​‌ IPP.
• O. Le Maitre,​​ 2025: Doctoral School SMEMAG,​​​‌ Graduate Level (22h/y), Course‌ on Uncertainty Quantification Methods.‌​‌
• O. Le Maître, 2025:​​ Ecole Polytechnique, Dept. Applied​​​‌ Math, last year Engineering‌ Degree, PC on Uncertainty‌​‌ and Risk Management (22h/y).​​
• PM Congedo, 2025: ENSTA​​​‌ ParisTech, Palaiseau, Graduate level‌ (20h/y), Numerical methods in‌​‌ Fluid Mechanics.

10.2.2 Supervision​​

• Olivier Le Maître has​​​‌ been the co-advisor of‌ the thesis of Marius‌​‌ Duvillard in collaboration with​​ CEA Cadarache.
• Olivier Le​​​‌ Maître has been the‌ co-advisor of the thesis‌​‌ of Nadège Polette in​​ collaboration with CEA DAM.​​​‌
• Pietro Marco Congedo and‌ Olivier Le Maître are‌​‌ advisors of the thesis​​ of Meryem Benmahdi, in​​​‌ collaboration with 3DS.
• Pietro‌ Marco Congedo and Olivier‌​‌ Le Maître are advisors​​ of the thesis of​​​‌ Sanae Idrissi Janati, in‌ collaboration with CEA Saclay.‌​‌
• Pietro Marco Congedo and​​ Olivier Le Maître are​​​‌ advisors of the thesis‌ of Zachary Jones.
• Pietro‌​‌ Marco Congedo and Olivier​​ Le Maître are advisors​​​‌ of the thesis of‌ Christos Papagiannis, in collaboration‌​‌ with LEGI Lab.
• Pietro​​ Marco Congedo and Olivier​​​‌ Le Maître have been‌ the advisors of the‌​‌ thesis of Hugo Dornier,​​ in collaboration with ONERA.​​​‌
• Pietro Marco Congedo and‌ Olivier Le Maître are‌​‌ advisors of the thesis​​​‌ of Hugo Nicolas, in​ collaboration with Bañulsesign (Projet​‌ Matritime).
• Pietro Marco Congedo,​​ Olivier Le Maître and​​​‌ Enora Denimal Goy are​ advisors of the thesis​‌ of Omar Kahol.
• Enora​​ Denimal Goy is the​​​‌ co-advisor of the thesis​ of Hugo Masson, in​‌ collaboration with Ecole des​​ Ponts.
• Enora Denimal Goy​​​‌ is the co-advisor of​ the thesis of Nina​‌ Delette, in collaboration with​​ IFPEN.
• Enora Denimal Goy​​​‌ is the co-advisor of​ the thesis of Erwan​‌ Dehillerin, in collaboration with​​ Ecole Centrale de Lyon.​​​‌
• Pietro Marco Congedo, Olivier​ Le Maître and Enora​‌ Denimal Goy have been​​ the supervisors of Hanane​​​‌ Khatouri, research engineer in​ the context of the​‌ Pré-DEFI project with Framatome.​​
• Olivier Le Maître is​​​‌ advisor of the thesis​ of Lucien Gonthier (in​‌ collaboration with Nicole Spillane​​ from CMAP).
• Pietro Marco​​​‌ Congedo and Enora Denimal​ Goy are the avdisors​‌ of the thesis of​​ Carlos Neves (in collaboration​​​‌ with Alberto Guardone from​ Politecnico di Milano).
• Enora​‌ Denimal Goy has been​​ the co-supervisor of the​​​‌ MSc Victor Moulinier in​ collaboration with Imperial College​‌ London.
• Olivier Le Maître​​ has been the co-supervisor​​​‌ of the MSc Lucien​ Gontier at Inria and​‌ CMAP.
• Pietro Marco Congedo​​ has been the supervisor​​​‌ of the MSc Vittorio​ Piro at Inria.

10.2.3​‌ Juries

• Pietro Marco Congedo​​ served as an examiner​​​‌ for the PhD defense​ of Maxime Lalande at​‌ the University of Toulouse,​​ 1 December 2025.
• Pietro​​​‌ Marco Congedo served as​ an examiner for the​‌ PhD defense of Axelle​​ Drouard at the University​​​‌ Paris-Saclay, 3 November 2025.​
• Enora Denimal Goy served​‌ as an examiner for​​ the PhD defense of​​​‌ Pau Becerra Zunig at​ CEA Saclay/INSA Lyon in​‌ Feb 2025.
• Enora Denimal​​ Goy served as an​​​‌ examiner for the PhD​ defense of Oceane Tapenot​‌ at Safran/FEMTO-ST in June​​ 2025.
• Olivier Le Maìtre​​​‌ served as a Director​ for the PhD defense​‌ of Hugo Dornier at​​ the Institut Polytechnique de​​​‌ Paris, in Dec 2025.​
• Olivier Le Maìtre served​‌ as a co-Director for​​ the PhD defense of​​​‌ Nadège Polette at the​ École des Mines de​‌ Paris, in Nov 2025.​​
• Olivier Le Maìtre served​​​‌ as an examiner for​ the PhD defense of​‌ Antoine Van Biesbroeck at​​ the Institut Polytechnique de​​​‌ Paris, in Oct 2025.​
• Olivier Le Maìtre served​‌ as a reviewer for​​ the PhD defense of​​​‌ Pierre Robin at École​ Centrale de Nantes in​‌ Sep 2025.
• Olivier Le​​ Maìtre served as a​​​‌ reviewer for the PhD​ defense of Adama Barry​‌ at Université de Toulouse​​ in Jun 2025.
• Olivier​​​‌ Le Maìtre served as​ a Director for the​‌ PhD defense of Marius​​ Duvillar at the Institut​​​‌ Polytechnique de Paris, in​ Jan 2025.
• Olivier Le​‌ Maìtre served as an​​ examiner for the PhD​​​‌ defense of Adrien Béguinet​ at Centrale-Supélec, in Jan​‌ 2025.

10.2.4 Internal or​​ external Inria responsabilities

• Enora​​​‌ Denimal Goy is an​ elected member of the​‌ "Comité de Centre" of​​ the Inria Saclay research​​​‌ center.
• Enora Denimal Goy​ is a member of​‌ the Inria national committee​​ on gender equality.
• Enora​​ Denimal Goy in the​​​‌ INSMI international referent for‌ the CMAP since 2025.‌​‌
• Enora Denimal Goy was​​ a member of the​​​‌ admission committee of CRCN‌ Inria concours in 2025.‌​‌
• Enora Denimal Goy was​​ a member of a​​​‌ CoS at INSA Haut‌ de France.
• Enora Denimal‌​‌ Goy was a member​​ of a CoS at​​​‌ Centrale Lyon-ENISE.
• Pietro Marco‌ Congedo is a member‌​‌ of the BCEP (Bureau​​ du comité des équipes-projets)​​​‌ of the Inria Center‌ of Saclay.
• Pietro Marco‌​‌ Congedo is the coordinator​​ of the Committee for​​​‌ the sustainable development of‌ the Center Inria Saclay‌​‌ Île-de-France.
• Pietro Marco Congedo​​ is the Deputy Head​​​‌ of Science of the‌ Center of Saclay since‌​‌ October 1 2025.
• Pietro​​ Marco Congedo is member​​​‌ of the CE (Commission‌ d'évaluation) of Inria since‌​‌ October 1 2025.
• Olivier​​ Le Maìtre was a​​​‌ member of the Jury‌ for the EDMH PhD‌​‌ Grants.
• Olivier Le Maìtre​​ was a member of​​​‌ the IPP PhD Track‌ selection committee.
• Olivier Le‌​‌ Maìtre was a member​​ of the AMX selection​​​‌ committee (PhD funding for‌ Polytechnique’s students).

10.3.1 Specific official responsibilities​​ in science outreach structures​​​‌

• Pietro Marco Congedo has‌ been a Committee member‌​‌ of the ANR AI​​ PEPR (Priority Research Programs​​​‌ and Equipment for AI)‌ program, 2025.
• Pietro Marco‌​‌ Congedo is the Coordinator​​ of "Maths/Engineering" Program of​​​‌ the Labex Mathématiques Hadamard‌ (IPP and Paris-Saclay University),‌​‌ since 2022.
• Olivier Le​​ Maître is a member​​​‌ of the Conseil du‌ Laboratoire du CMAP (Ecole‌​‌ Polytechnique, IPP).
• Olivier Le​​ Maître is the Adjunct​​​‌ Director of the Ecole‌ Doctorale de Mathématiques Hadamard‌​‌ (EDMH).
• Olivier Le Maître​​ is member of math​​​‌ committee of the PhD‌ Track Program of IP-Paris.‌​‌
• Pietro Marco Congedo is​​ the coordinator of the​​​‌ "Pôle Analyse" of CMAP‌ Lab (Ecole Polytechnique, IPP).‌​‌
• Olivier Le Maître is​​ the corresponding member of​​​‌ the Inria SIF center‌ with the French Agency‌​‌ for Math and Industry​​ (AMIES).

10.3.2 Productions (articles,​​​‌ videos, podcasts, serious games,‌ ...)

• Pietro Marco Congedo:‌​‌ Contribution à l’article "L’IA​​ prend son envol", Science​​​‌ & Vie, Juillet 2025‌ pp. 34-37.
• Enora Denimal‌​‌ Goy made interventions in​​ front of teenage girls​​​‌ for two events organised‌ by the Séphora Berrebi‌​‌ Association ("rencontre maths -​​ jeunes filles et chercheuses"​​​‌ et programme "Lionnes" events):‌ plenary presentation of research‌​‌ activities, small group discussions,​​ group activity.

International journals

• 6​​​‌ articleM.Michele Capriati​, A.Anabel del​‌ Val, T.Thomas​​ Schwartzentruber, T.Timothy​​​‌ Minton, P. M.​Pietro Marco Congedo and​‌ T.Thierry Magin.​​ Combining Molecular Beam and​​​‌ Plasmatron Data for Robust​ Calibration of Nitridation Mechanism​‌.AIAA JournalSeptember​​ 2025, 1-15HAL​​​‌DOIback to text​
• 7 articleH.Hugo​‌ Dornier, O.Olivier​​ Le Maitre, P.​​​‌ M.Pietro Marco Congedo​, I.Itham Salah​‌ El Din, J.​​Julien Marty and S.​​​‌Sébastien Bourasseau. Mean​ Mesh Adaptation for Efficient​‌ CFD Simulations with Operating​​ Conditions Variability.Computers​​​‌ and Fluids298May​ 2025, 106666HAL​‌DOIback to text​​
• 8 articleG.Giulio​​​‌ Gori, O. P.​Olivier P Le Maître​‌ and P. M.Pietro​​ Marco Congedo. Debiased​​​‌ Multifidelity Approach to Surrogate​ Modeling in Aerospace Applications​‌.Journal of Aircraft​​July 2025, 1-14​​​‌HALDOIback to​ text
• 9 articleO.​‌Omar Kahol, P.​​ M.Pietro Marco Congedo​​​‌, O.Olivier Le​ Maitre and E.Enora​‌ Denimal Goy. Efficient​​ treatment of the model​​​‌ error in the calibration​ of computer codes: the​‌ Complete Maximum a Posteriori​​ method.International Journal​​​‌ for Uncertainty Quantification2025​HALDOIback to​‌ text
• 10 articleI.​​Issam Lakkis, A.​​​‌Alexios Rustom, M.​ A.Mohamad Abed El​‌ Rahman Hammoud, L.​​Leila Issa, O.​​​‌Omar Knio, O.​Olivier Le Maitre and​‌ I.Ibrahim Hoteit.​​ Identification of moving sources​​​‌ in stochastic flow fields:​ A bayesian inferential approach​‌ with application to marine​​ traffic in the mediterranean​​​‌ sea.Computational Geosciences​292April 2025​‌, 18HALDOI​​back to text
• 11​​​‌ articleA.Adrien Mélot​, E.Enora Denimal​‌ Goy and L.Ludovic​​ Renson. Nonlinear model​​​‌ calibration through bifurcation curves​.Mechanical Systems and​‌ Signal Processing242January​​ 2026, 113589HAL​​​‌back to text
• 12​ articleC.Christos Papagiannis​‌, G.Guillaume Balarac​​, P. M.Pietro​​​‌ Marco Congedo and O.​ P.Olivier P Le​‌ Maître. Autoregressive Multiplier​​ Bootstrap for In-situ Error​​​‌ Estimation and Quality Monitoring​ of Finite Time Averages​‌ in Turbulent Flow Simulations​​.Computer Methods in​​​‌ Applied Mechanics and Engineering​452April 2026,​‌ 118664HALDOI

International​​ peer-reviewed conferences

• 13 inproceedings​​N.Nina Delette,​​​‌ E.Enora Denimal Goy‌, J.-L.Jean-Lou Pfister‌​‌, R.Reda El​​ Amri and L.Laurent​​​‌ Mevel. Model Updating‌ of Rotating Wind Turbines‌​‌ Using Operational Modal Analysis​​ and Floquet Mode Decomposition​​​‌.IOMAC 2025 -‌ 11th International Operational Modal‌​‌ Analysis ConferenceRennes, France​​May 2025, 1-7​​​‌HAL
• 14 inproceedingsN.‌Nina Delette, J.-L.‌​‌Jean-Lou Pfister, E.​​Enora Denimal Goy,​​​‌ M. R.Mohamed Reda‌ El Amri and L.‌​‌Laurent Mevel. Bayesian​​ model updating of rotating​​​‌ wind turbines.WESC‌ 2025 - Wind Energy‌​‌ Science ConferenceNantes, France​​June 2025, 1-3​​​‌HALback to text‌
• 15 inproceedingsE.Enora‌​‌ Denimal Goy. A​​ Surrogate Modelling Approach Based​​​‌ on Anti-Resonance Properties for‌ FRF Prediction of Uncertain‌​‌ Dynamical Systems.Model​​ Validation and Uncertainty Quantification,​​​‌ Vol. 3 - Proceedings‌ of the 43rd IMAC,‌​‌ A Conference and Exposition​​ on Structural Dynamics 2025​​​‌IMAC 2025 - 43rd‌ Conference and Exposition on‌​‌ Structural DynamicsOrlando, United​​ StatesRiver PublishersAugust​​​‌ 2025, 81 -‌ 92HALDOI
• 16‌​‌ inproceedingsE.Enora Denimal​​ Goy, Y.Yichang​​​‌ Shen, S.Samuel‌ Fruchard, A.Adrien‌​‌ Mélot and L.Ludovic​​ Renson. Topology Optimization​​​‌ of Isolated Response Curves‌ in 3D Geometrically-nonlinear Beam‌​‌.Nonlinear Structures &​​ Systems, Vol. 1 -​​​‌ Proceedings of the 43rd‌ IMAC, A Conference and‌​‌ Exposition on Structural Dynamics​​ 2025IMAC 2025 -​​​‌ 43rd Conference and Exposition‌ on Structural DynamicsOrlando,‌​‌ United StatesRiver Publishers​​August 2025, 81​​​‌ - 92HALDOI‌
• 17 inproceedingsH.Hugo‌​‌ Nicolas, O.Olivier​​ Le Maître and P.​​​‌ M.Pietro Marco Congedo‌. A sequential variational‌​‌ Bayesian approach to Gaussian​​ process quantile regression for​​​‌ optimization.UNCECOMP 2025‌ ProceedingsUNCECOMP 2025 -‌​‌ 6th International Conference on​​ Uncertainty Quantification in Computational​​​‌ Sciences and EngineeringRhodes‌ Island, GreeceJune 2025‌​‌HAL

Conferences without proceedings​​

• 18 inproceedingsH.Hugo​​​‌ Dornier, O. P.‌Olivier P Le Maître‌​‌, P. M.Pietro​​ Marco Congedo, I.​​​‌Itham Salah El Din‌, S.Sébastien Bourasseau‌​‌ and J.Julien Marty​​. Mesh Adaptation Strategies​​​‌ for CFD Simulations Over‌ a Set of Operating‌​‌ Conditions.ADMOS 2025​​ - 12th International Conference​​​‌ on Adaptive Modeling and‌ SimulationBarcelona, SpainJune‌​‌ 2025HALback to​​ text
• 19 inproceedingsH.​​​‌Hugo Masson, M.‌Michaël Peigney and E.‌​‌Enora Denimal Goy.​​ Robust topology optimization accounting​​​‌ for uncertain microstructural changes‌.WCSMO 2025 -‌​‌ 16th World Congress of​​ Structural and Multidisciplinary Optimization​​​‌Kobe, JapanMay 2025‌HALback to text‌​‌
• 20 inproceedingsH.Hugo​​ Nicolas and O.Olivier​​​‌ Le Maître. A‌ sequential Bayesian approach to‌​‌ Gaussian process quantile regression​​ for optimization.PGMO​​​‌ DAYS 2025 - Programme‌ Gaspard Monge pour l'Optimisation‌​‌Palaiseau, FranceNovember 2025​​, 115HALback​​​‌ to text

Reports &‌ preprints

• 21 miscH.‌​‌Hugo Dornier, O.​​ P.Olivier P Le​​​‌ Maître, P. M.‌Pietro Marco Congedo,‌​‌ I.Itham Salah El​​​‌ Din, J.Julien​ Marty and S.Sébastien​‌ Bourasseau. Error-Based mesh​​ selection for efficient numerical​​​‌ simulations with variable parameters​.November 2025HAL​‌
• 22 miscZ.Zachary​​ Jones, P. M.​​​‌Pietro Marco Congedo and​ O.Olivier Le Maitre​‌. Stochastic Tangential Pareto​​ Dynamics Provably Samples the​​​‌ Whole Pareto Set.​February 2025HAL
• 23​‌ reportV.Vittorio Piro​​, M.Michele Capriati​​​‌, F.Federico Bariselli​, P. M.Pietro​‌ Marco Congedo and T.​​ E.Thierry E. Magin​​​‌. Robust calibration of​ an air-carbon ablation model​‌ employing Plasmatron and molecular​​ beam data.von​​​‌ Karman Institute for Fluid​ DynamicsJune 2025HAL​‌