2025​​Activity reportProject-TeamASCII​​​‌

5.1 Footprint of​ research activities

Classic footprint​‌ for researchers: massive computer​​ runs and travel for​​​‌ international conferences and cooperations.​

5.2 Impact of research​‌ results

The research is​​ useful for the risk​​​‌ assessment and managment of​ global interlocked economic instances​‌ and actors in varied​​ industrial, economic, and societal​​​‌ settings.

We have evaluated​ in particular failure probabilities​‌ of complex power production​​ plants as well as​​​‌ of mechanical structures subjected​ to seismic tremors for​‌ seismic surveillance purposes, and​​ the progressive deformation of​​​‌ fuel assemblies in the​ core of nuclear reactors​‌ due to fluid–structure interaction​​ and intense irradiation.

We​​​‌ have obtained advanced results​ on the digital twins​‌ of large urban zones​​ furnished with statistically valid​​​‌ synthetic populations moving according​ to individual hourly activity​‌ agendas. We are developping​​ agent-based models for varied​​​‌ epidemics spreading on these​ twins through contagion between​‌ individuals. We thus aim​​ to provide evaluation tools​​​‌ for health deciders for​ the impact of varied​‌ sanitary measures on the​​ spread of the epidemic​​​‌ as well as on​ the economy and on​‌ social structures. We are​​ part of the numerical​​​‌ twin program of France​ and its territories "Jumeau​‌ numérique de la France​​ et de ses territoires"​​​‌ (IGN, Cerema, Inria), the​ only component retained on​‌ the topic of epidemiology.​​ The twins we develop​​​‌ can be used for​ other purposes such as​‌ urban planning, transportation management,​​ or natural disaster management.​​​‌

7.1​​​‌ New platforms

8.1 Modeling, analysis,​‌ and simulation of cooperative​​ stochastic systems

Participants: Quentin​​​‌ Cormier, Carl Graham​, Denis Talay,​‌ Nicolas Baradel, Samuel​​ Chan-Ashing.

On The​​​‌ Cutoff Phenomenon For Dyson-Laguerre​ Processes

In 21,​‌ Samuel Chan-Ashing studied the​​ convergence to equilibrium in​​​‌ high dimensions, focusing on​ explicit bounds on mixing​‌ times and the emergence​​ of the cutoff phenomenon​​​‌ for Dyson-Laguerre processes. These​ are interacting particle systems​‌ with non-constant diffusion coefficients,​​ arising naturally in the​​​‌ context of sample covariance​ matrices. The infinitesimal generator​‌ of the process admits​​ generalized Laguerre orthogonal polynomials​​​‌ as eigenfunctions. His analysis​ relies on several distances​‌ and divergences, including an​​ intrinsic Wasserstein distance adapted​​​‌ to the non-Euclidean geometry​ of the process. Within​‌ this framework, he employed​​ tools from Riemannian geometry​​​‌ and functional inequalities. In​ particular, he established exponential​‌ decay and derived a​​ regularization inequality for the​​​‌ intrinsic Wasserstein distance via​ comparison with relative entropy.​‌

Kuramoto Mean Field Game​​ with Intrinsic Frequencies

In​​​‌ 19, as part​ of the CIRCUS associated​‌ team between the ASCII​​ team and Princeton University,​​​‌ René Carmona, Quentin Cormier​ and Mete Soner have​‌ been working on the​​ Kuramoto mean-field game problem.​​​‌ This mean-field game model​ captures the diversity within​‌ the population by considering​​ random intrinsic frequencies, which​​​‌ allows to study the​ impact of this heterogeneity​‌ on synchronization patterns and​​ stability. Our findings contribute​​ insights into the interplay​​​‌ between intrinsic frequency diversity‌ and synchronization dynamics, offering‌​‌ a more realistic understanding​​ of complex systems. The​​​‌ proposed framework has broad‌ applications ranging from coupled‌​‌ oscillators in physics to​​ social dynamics, and serves​​​‌ as a valuable tool‌ for studying networks with‌​‌ distributed intrinsic frequencies.

Long​​ time behavior of particle​​​‌ systems and their mean-field‌ limit

Quentin Cormier has‌​‌ studied the long time​​ behavior of a family​​​‌ of McKean-Vlasov stochastic differential‌ equations. He has given‌​‌ conditions ensuring the local​​ stability of an invariant​​​‌ probability measure. The criterion‌ involves the location of‌​‌ the roots of an​​ explicit holomorphic function associated​​​‌ to the dynamics. When‌ all the roots lie‌​‌ on the left-half plane,​​ local stability holds and​​​‌ convergence is proven in‌ Wasserstein norms. The optimal‌​‌ rate of convergence is​​ provided. This method is​​​‌ then applied to study‌ a large class of‌​‌ models of interacting particles​​ on the torus, see​​​‌ 7. This is‌ published in Annales de‌​‌ l'Institut Henri Poincaré.

A​​ stochastic numerical method for​​​‌ the parabolic-parabolic Keller-Segel system‌

The parabolic-parabolic Keller-Segel model‌​‌ is a set of​​ equations that model the​​​‌ process of cell movement.‌ It takes into account‌​‌ the evolution of different​​ chemical components that can​​​‌ aid, hinder or change‌ the direction of movement,‌​‌ a process called chemotaxis.​​

In collaboration with Radu​​​‌ Maftei (who is a‌ past Inria post-doc student),‌​‌ Milica Tomasevic (CNRS, CMAP,​​ Ecole Polytechnique and Inria​​​‌ MERGE) and Denis Talay‌ have continued to analyse‌​‌ the numerical performances of​​ a stochastic particle numerical​​​‌ method for the parabolic-parabolic‌ Keller-Segel model. They also‌​‌ propose and test various​​ algorithmic improvements to the​​​‌ method in order to‌ substantially decrease its execution‌​‌ time without altering its​​ global accuracy.

Communication networks​​​‌ and their algorithms

Carl‌ Graham studies communication networks‌​‌ and the algorithms used​​ to manage efficiently their​​​‌ resources in real-time in‌ a distributed and cooperative‌​‌ fashion. For instance, load​​ balancing algorithms (LBA) strive​​​‌ to avoid server idleness‌ and queue build-up, and‌​‌ are the topic of​​ a lively example-based litterature.​​​‌

Carl Graham has rigorously‌ defined a wide class‌​‌ of LBA on symmetrical​​ Markovian queueing networks for​​​‌ which he has devised‌ perfect simulation methods. The‌​‌ state space is infinite,​​ and the methods use​​​‌ dominated coupling from the‌ past. The dominating process‌​‌ is a network with​​ uniform routing in a​​​‌ coupling preserving a preorder‌ related to the increasing‌​‌ convex order. The use​​ of a preorder is​​​‌ novel in this context.‌ This allows performance evaluation‌​‌ in equilibrium of any​​ LBA in the class​​​‌ using Monte Carlo estimation.‌

Carl Graham is working‌​‌ to extend this study​​ to assymmetrical Markovian queueing​​​‌ networks. In this context‌ it is even unclear‌​‌ how to define LBAs​​ in a tractable and​​​‌ useful way.

8.2 Uncertainty‌ quantification, wave propagation in‌​‌ random media, inverse problems,​​ risk assessment, stochastic numerics​​​‌

Participants: Josselin Garnier,‌ and students and collaborators‌​‌.

Uncertainty quantification using​​ a Bayesian network approach​​​‌ to surrogate modeling

Quantifying‌ the uncertainties associated with‌​‌ the resolution of an​​​‌ inverse problem is crucial​ for decision-making. A conservative​‌ uncertainty quantification procedure is​​ possible by solving a​​​‌ Bayesian inverse problem with​ the help of statistical​‌ surrogate models but generally​​ leads to large uncertainties​​​‌ due to the surrogate​ models’ errors. In 11​‌ P. Lartaud, P. Humbert,​​ and J. Garnier develop​​​‌ two methods for robust​ uncertainty quantification based on​‌ the resolution of Bayesian​​ inverse problems. These methods​​​‌ are applied to neutron​ and gamma noise analysis,​‌ which is a predominant​​ technique for fissile matter​​​‌ identification with passive methods.​ They show that the​‌ uncertainties can be reduced​​ by including information on​​​‌ gamma correlations. The investigation​ of a joint analysis​‌ of the neutron and​​ gamma observations is also​​​‌ conducted with the help​ of active learning strategies​‌ to fine-tune surrogate models.​​

Wave propagation in random​​​‌ media

In 10 J.​ Garnier and B. Lal​‌ Sharma study the propagation​​ of surface waves across​​​‌ structured surfaces with random,​ localized inhomogeneities. A discrete​‌ analogue of the Gurtin–Murdoch​​ model is employed, and​​​‌ surface elasticity, in contrast​ to bulk elasticity, is​‌ captured by distinct point​​ masses and elastic constants​​​‌ for nearest-neighbor interactions parallel​ to the surface. Expressions​‌ for the surface wave​​ reflectance and transmittance, as​​​‌ well as the radiative​ loss, are provided for​‌ every localized patch of​​ point mass perturbation on​​​‌ the surface. As the​ main result in the​‌ article, the statistics of​​ surface wave reflectance and​​​‌ transmittance and the radiative​ loss are obtained for​‌ an ensemble of random​​ mass perturbations, independent and​​​‌ identically distributed with mean​ zero, on the surface.​‌

Waves propagating through weakly​​ disordered smooth linear media​​​‌ undergo a universal phenomenon​ called branched flow. Branched​‌ flow has been observed​​ and studied experimentally in​​​‌ various systems by considering​ coherent waves. Recent experiments​‌ have reported the observation​​ of optical branched flow​​​‌ by using an incoherent​ light source, thus revealing​‌ the key role of​​ coherent phase-sensitive effects in​​​‌ the development of incoherent​ branched flow. By considering​‌ the paraxial wave equation​​ as a generic representative​​​‌ model, J. Garnier, A.​ Picozzi, and T. Torrez​‌ elaborate a stochastic theory​​ of both coherent and​​​‌ incoherent branched flow in​ 9. Closed-form equations​‌ that determine the evolution​​ of the intensity correlation​​​‌ function are derived, as​ well as the value​‌ and the propagation distance​​ of the maximum of​​​‌ the scintillation index, which​ characterize the dynamical formation​‌ of incoherent branched flow.​​ Accurate numerical simulations are​​​‌ found in quantitative agreement​ with the theory without​‌ free parameters. The developed​​ theory highlights the important​​​‌ impact of coherence and​ interference on branched flow,​‌ thereby providing a framework​​ for exploring branched flow​​​‌ in nonlinear media, in​ relation to the formation​‌ of freak waves in​​ oceans. This paper was​​​‌ awarded "Editors' Suggestion" by​ the journal Physical Review​‌ Letters.

In 8 M.​​ Ferraro et al. review​​​‌ recent theoretical and experimental​ advances on complex light​‌ propagation in nonlinear multimode​​ fibers. Using wave turbulence​​​‌ theory, they derive kinetic​ equations describing out-of-equilibrium optical​‌ thermalization toward the Rayleigh–Jeans​​ equilibrium. This framework explains​​ beam self-cleaning (BSC) in​​​‌ graded-index fibers, where increasing‌ input power transforms a‌​‌ speckled beam into a​​ bell-shaped output dominated by​​​‌ the fundamental mode, while‌ higher-order modes persist due‌​‌ to turbulence cascades and​​ conserved quantities. They analyze​​​‌ the impact of random‌ refractive-index fluctuations and show‌​‌ that weak disorder can​​ enhance BSC by accelerating​​​‌ thermalization and condensation, as‌ described by kinetic equations‌​‌ including random mode coupling.​​ Even in regimes where​​​‌ strong disorder dominates over‌ nonlinearity, out-of-equilibrium condensation and‌​‌ thermalization can still occur.​​ The theory is validated​​​‌ by numerical simulations of‌ the generalized nonlinear Schrödinger‌​‌ equation and supported by​​ experiments demonstrating entropy growth,​​​‌ limits to peak-power scaling‌ in multimode fiber lasers,‌​‌ and modal phase-locking accompanying​​ BSC, which explains spatial​​​‌ coherence preservation and motivates‌ further theoretical extensions.

Reduced‌​‌ order modeling for full​​ waveform inversion

Waveform inversion​​​‌ seeks to estimate an‌ inaccessible heterogeneous medium from‌​‌ data gathered by sensors​​ that emit probing signals​​​‌ and measure the generated‌ waves. It is an‌​‌ inverse problem for a​​ second order wave equation​​​‌ or a first order‌ hyperbolic system, with the‌​‌ sensor excitation modeled as​​ a forcing term and​​​‌ the heterogeneous medium described‌ by unknown, spatially variable‌​‌ coefficients. The traditional “full​​ waveform inversion" (FWI) formulation​​​‌ estimates the unknown coefficients‌ via minimization of the‌​‌ nonlinear, least squares data​​ fitting objective function. For​​​‌ typical band-limited and high‌ frequency data, this objective‌​‌ function has spurious local​​ minima near and far​​​‌ from the true coefficients.‌ Thus, FWI implemented with‌​‌ gradient based optimization algorithms​​ may fail, even for​​​‌ good initial guesses. Recently,‌ it was shown that‌​‌ it is possible to​​ obtain a better behaved​​​‌ objective function for wave‌ speed estimation, using data‌​‌ driven reduced order models​​ (ROMs) that capture the​​​‌ propagation of pressure waves,‌ governed by the classic‌​‌ second order wave equation.​​ In 6 L. Borcea,​​​‌ J. Garnier, A. V.‌ Mamonov, and J. Zimmerling‌​‌ introduce ROMs for vectorial​​ waves, satisfying a general​​​‌ first order hyperbolic system.‌ The ROMs are defined‌​‌ via Galerkin projection on​​ the space spanned by​​​‌ the wave snapshots, evaluated‌ on a uniform time‌​‌ grid with appropriately chosen​​ time step. The ROMs​​​‌ are data driven, and‌ computed in an efficient‌​‌ and noniterative manner, from​​ the sensor measurements, without​​​‌ knowledge of the medium‌ and the snapshots. The‌​‌ ROM computation applies to​​ any linear waves in​​​‌ lossless and nondispersive media.‌ For the inverse problem‌​‌ we focus on acoustic​​ waves in a medium​​​‌ with unknown variable wave‌ speed and density. It‌​‌ is shown that these​​ can be determined via​​​‌ minimization of an objective‌ function that uses a‌​‌ ROM based approximation of​​ the vectorial wave field​​​‌ inside the inaccessible medium.‌ The performance of the‌​‌ resulting inversion approach is​​ assessed with numerical simulations​​​‌ and compared to FWI.‌

Risk and failure assesments‌​‌

Seismic fragility curves are​​ key quantities of interest​​​‌ for Seismic Probabilistic Risk‌ Assessment studies. They express‌​‌ the probability of failure​​ of a mechanical structure​​​‌ of interest conditional to‌ a scalar value derived‌​‌ from the ground motion​​​‌ signal coined Intensity Measure.​ In the literature, Bayesian​‌ approaches have emerged to​​ enable their estimation within​​​‌ the difficult context of​ limited data availability. Yet,​‌ the log-normal modeling over​​ which most of them​​​‌ are based requires the​ use of computationally expensive​‌ Markov chain Monte Carlo​​ methods for providing Bayesian​​​‌ estimators. In 14 A.​ Van Biesbroeck, C. Gauchy,​‌ C. Feau, and J.​​ Garnier propose an efficient​​​‌ modeling for the estimation​ of fragility curves in​‌ the Bayesian context, based​​ on a low fidelity​​​‌ model of the structure's​ response to the ground​‌ motion signal and an​​ objective prior. The analytical​​​‌ expression of the modeling​ allows fast generation of​‌ estimates. Also, the representative​​ bias arisen by the​​​‌ modeling choice is handled​ with a judicious design​‌ of experiments methodology. Finally,​​ the proposed method is​​​‌ evaluated on a real​ case study, and the​‌ results highlight its efficiency​​ and its ability to​​​‌ robustly overcome any bias​ when coupled with the​‌ design of experiments we​​ propose.

In the core​​​‌ of nuclear reactors, fluid–structure​ interaction and intense irradiation​‌ lead to progressive deformation​​ of fuel assemblies. When​​​‌ this deformation is significant,​ it can lead to​‌ additional costs and longer​​ fuel unloading and reloading​​​‌ operations. Therefore, it is​ preferable to adopt a​‌ fuel management that avoids​​ excessive deformation and interactions​​​‌ between fuel assemblies. However,​ the prediction of deformation​‌ and interactions between fuel​​ assemblies is uncertain. Uncertainties​​​‌ affect neutronics, thermohydraulics and​ thermomechanics parameters. Indeed, the​‌ initial uncertainties are propagated​​ over several successive power​​​‌ cycles of twelve months​ each through the coupling​‌ of non-linear, nested and​​ multidimensional thermal–hydraulic and thermomechanical​​​‌ simulations. In 5 A.​ Abboud, S. de Lambert,​‌ J. Garnier, B. Leturcq,​​ and N. Lamorte set​​​‌ out to study the​ hydraulic contribution and quantify​‌ the associated uncertainty. To​​ achieve this objective, a​​​‌ multi-stage approach to carry​ out an initial sensitivity​‌ analysis is developed, highlighting​​ the most influential parameters​​​‌ in the hydraulic model.​ By optimally adjusting these​‌ parameters, a more accurate​​ description of the flow​​​‌ redistribution phenomenon in the​ reactor core is obtained.​‌ The aim of the​​ sensitivity analysis is to​​​‌ construct an accurate and​ suitable surrogate model that​‌ represents the in-core lateral​​ hydraulic forces in a​​​‌ given state. This surrogate​ model could then be​‌ coupled with a thermomechanical​​ model to quantify the​​​‌ final uncertainty in the​ simulation of fuel assembly​‌ bow within a pressurized​​ water reactor. This approach​​​‌ provides a better understanding​ of the interactions between​‌ hydraulic and thermomechanical phenomena,​​ thereby improving the reliability​​​‌ and accuracy of the​ simulation results.

Numerical simulation,​‌ computational physics and machine​​ learning

Numerical simulation is​​​‌ widely used to predict​ the behavior of physical​‌ systems, with Bayesian approaches​​ being particularly well suited​​​‌ for this purpose. However,​ experimental observations are necessary​‌ to calibrate certain simulator​​ parameters for the prediction.​​​‌ In 12 C. Sire,​ J. Garnier, B. Kerleguer,​‌ C. Durantin, G. Defaux,​​ and G. Perrin use​​​‌ a multi-output simulator to​ predict all its outputs,​‌ including those that have​​ never been experimentally observed.​​ This situation is referred​​​‌ to as the transposition‌ context. To accurately quantify‌​‌ the discrepancy between model​​ outputs and real data​​​‌ in this context, conventional‌ methods cannot be applied,‌​‌ and the Bayesian calibration​​ must be augmented by​​​‌ incorporating a joint model‌ error across all outputs.‌​‌ To achieve this, the​​ proposed method is to​​​‌ consider additional input parameters‌ within a hierarchical Bayesian‌​‌ model, which includes hyperparameters​​ for the prior distribution​​​‌ of the calibration variables.‌ This approach is applied‌​‌ to a computer code​​ with three outputs that​​​‌ models the Taylor cylinder‌ impact test with a‌​‌ small number of observations.​​ The outputs are considered​​​‌ as the observed variables‌ one at a time,‌​‌ to work with three​​ different transposition situations. The​​​‌ proposed method is compared‌ with other approaches that‌​‌ embed model errors to​​ demonstrate the significance of​​​‌ the hierarchical formulation.

In‌ computational physics, machine learning‌​‌ has now emerged as​​ a powerful complementary tool​​​‌ to explore efficiently candidate‌ designs in engineering studies.‌​‌ Outputs in such supervised​​ problems are signals defined​​​‌ on meshes, and a‌ natural question is the‌​‌ extension of general scalar​​ output regression models to​​​‌ such complex outputs. Changes‌ between input geometries in‌​‌ terms of both size​​ and adjacency structure in​​​‌ particular make this transition‌ non-trivial. In 20 R.‌​‌ Carpintero Perez, S. Da​​ Veiga, J. Garnier, and​​​‌ B. Staber propose an‌ innovative strategy for Gaussian‌​‌ process regression where inputs​​ are large and sparse​​​‌ graphs with continuous node‌ attributes and outputs are‌​‌ signals defined on the​​ nodes of the associated​​​‌ inputs. The methodology relies‌ on the combination of‌​‌ regularized optimal transport, dimension​​ reduction techniques, and the​​​‌ use of Gaussian processes‌ indexed by graphs. In‌​‌ addition to enabling signal​​ prediction, the main point​​​‌ of the proposal is‌ to come with confidence‌​‌ intervals on node values,​​ which is crucial for​​​‌ uncertainty quantification and active‌ learning. Numerical experiments highlight‌​‌ the efficiency of the​​ method to solve real​​​‌ problems in fluid dynamics‌ and solid mechanics.

Designing‌​‌ algorithms for solving high-dimensional​​ Bayesian inverse problems directly​​​‌ in infinite-dimensional function spaces‌ — in which such‌​‌ problems are naturally formulated​​ — is crucial to​​​‌ ensure stability and convergence‌ as the discretization of‌​‌ the underlying problem is​​ refined. In 16 L.​​​‌ Baldassari, J. Garnier, K.‌ Sølna, and M. V.‌​‌ de Hoop contribute to​​ this line of work​​​‌ by analyzing a widely‌ used sampler for linear‌​‌ inverse problems: Langevin dynamics​​ driven by score-based generative​​​‌ models (SGMs) acting as‌ priors, formulated directly in‌​‌ function space. Building on​​ the theoretical framework for​​​‌ SGMs in Hilbert spaces,‌ they give a rigorous‌​‌ definition of this sampler​​ in the infinite-dimensional setting​​​‌ and derive, for the‌ first time, error estimates‌​‌ that explicitly depend on​​ the approximation error of​​​‌ the score. As a‌ consequence, they obtain sufficient‌​‌ conditions for global convergence​​ in Kullback–Leibler divergence on​​​‌ the underlying function space.‌ Preventing numerical instabilities requires‌​‌ preconditioning of the Langevin​​ algorithm and they prove​​​‌ the existence and the‌ form of an optimal‌​‌ preconditioner. The preconditioner depends​​​‌ on both the score​ error and the forward​‌ operator and guarantees a​​ uniform convergence rate across​​​‌ all posterior modes. The​ analysis applies to both​‌ Gaussian and a general​​ class of non-Gaussian priors.​​​‌ This paper was selected​ as a “Spotlight" at​‌ NEURIPS 2025 conference.

8.3​​ Artificial intelligence (AI) for​​​‌ finance

Participants: Nicolas Baradel​.

In incomplete financial​‌ markets, there is not​​ a unique no-arbitrage price​​​‌ or hedge for European​ options. This fact is​‌ due to the presence​​ of unhedgeable risks.

We​​​‌ propose in 18 a​ constrained deep learning method​‌ striving to find option​​ prices and hedging strategies​​​‌ that keep the Profit​ and Loss (P&L) distribution​‌ as close to zero​​ as possible. A single​​​‌ neural network represents the​ option price, with its​‌ gradient providing the hedging​​ strategy. The network is​​​‌ trained with a loss​ that enforces the self-financing​‌ condition. In order to​​ handle non-smooth or even​​​‌ discontinuous payoffs (vanilla calls,​ digital options, exotics,etc.), we​‌ compare standard (unconstrained) networks​​ with constrained architectures that​​​‌ explicitly incorporate the terminal​ payoff condition.

The numerical​‌ application uses two tradable​​ assets: the underlying and​​​‌ a liquid call option​ that captures volatility. Numerical​‌ tests on simple non-smooth​​ options, the exotic Equinox​​​‌ option, and jump scenarios​ show that constrained networks​‌ produce better (tighter) P&L​​ distributions than unconstrained networks.​​​‌

9.1​‌ CIROQUO Research & Industry​​ Consortium

Participants: Josselin Garnier​​​‌.

Several Inria teams,​ including ASCII, are involved​‌ in the CIROQUO Research​​ & Industry Consortium –​​​‌ Consortium Industrie Recherche pour​ l'Optimisation et la QUantification​‌ d'incertitude pour les données​​ Onéreuses – (Industry Research​​​‌ Consortium for the Optimization​ and QUantification of Uncertainty​‌ for Onerous Data). Josselin​​ Garnier is the Inria​​​‌ Saclay representative on the​ steering committee.

The principle​‌ of this Consortium is​​ to bring together academic​​​‌ and technological research partners​ to solve problems related​‌ to the exploitation of​​ numerical simulators, such as​​​‌ code transposition (how to​ go from small to​‌ large scale when only​​ small-scale simulations are possible),​​​‌ taking into account the​ uncertainties that affect the​‌ result of the simulation,​​ validation and calibration (how​​​‌ to validate and calibrate​ a computer code from​‌ collected experimental data).

This​​ project is the result​​​‌ of a simple observation:​ industries using computer codes​‌ are often confronted with​​ similar problems during the​​​‌ exploitation of these codes,​ even if their fields​‌ of application are very​​ diverse. Indeed, the increase​​​‌ in the availability of​ computing cores is counterbalanced​‌ by the growing complexity​​ of the simulations, whose​​​‌ computational times are usually​ of the order of​‌ an hour or a​​ day. In practice, this​​​‌ limits the number of​ simulations. This is why​‌ the development of mathematical​​ methods to make the​​​‌ best use of simulators​ and the data they​‌ produce is a source​​ of progress. The experience​​​‌ acquired over the last​ thirteen years in the​‌ DICE and ReDICE projects​​ and the OQUAIDO Chair​​​‌ shows that the formalization​ of real industrial problems​‌ often gives rise to​​ first-rate theoretical problems that​​ can feed scientific and​​​‌ technical advances.

The creation‌ of the CIROQUO Research‌​‌ & Industry Consortium, led​​ by the Ecole Centrale​​​‌ de Lyon and co-animated‌ with the IFPEN, follows‌​‌ these observations and responds​​ to a desire for​​​‌ collaboration between technological research‌ partners and academics in‌​‌ order to meet the​​ challenges of exploiting large​​​‌ computing codes.

Scientific approach.‌ The limitation of the‌​‌ number of calls to​​ simulators implies that some​​​‌ information – even the‌ most basic information such‌​‌ as the mean value,​​ the influence of a​​​‌ variable or the minimum‌ value of a criterion‌​‌ – cannot be obtained​​ directly by the usual​​​‌ methods. The international scientific‌ community, structured around computer‌​‌ experiments and uncertainty quantification,​​ took up this problem​​​‌ more than twenty years‌ ago, but a large‌​‌ number of problems remain​​ open. On the academic​​​‌ level, this is a‌ dynamic field which is‌​‌ notably the subject of​​ the French CNRS Research​​​‌ Group MascotNum since 2006‌ and renewed in 2020.‌​‌

Composition. The CIROQUO Research​​ & Industry Consortium aims​​​‌ to bring together a‌ limited number of participants‌​‌ in order to make​​ joint progress on test​​​‌ cases from the industrial‌ world and on the‌​‌ upstream research that their​​ treatment requires. The overall​​​‌ approach that it will‌ focus on is metamodeling‌​‌ and related areas such​​ as experiment planning, optimization,​​​‌ inversion and calibration. IRSN,‌ STORENGY, CEA, IFPEN, and‌​‌ BRGM are the Technological​​ Research Partners and Mines​​​‌ Saint-Etienne, Centrale Lyon, CNRS,‌ UCA, UPS, UT3 and‌​‌ Inria the Academic Partners​​ of the consortium.

Scientific​​​‌ objectives. On the practical‌ level, the expected impacts‌​‌ of the project are​​ a concretization of the​​​‌ progress of numerical simulation‌ by a better use‌​‌ of computational time, which​​ allows the determination of​​​‌ better solutions and associated‌ uncertainties. On the theoretical‌​‌ level, this project will​​ allow to create an​​​‌ emulation around the major‌ scientific locks of the‌​‌ discipline such as code​​ transposition/calibration/validation, modeling for complex​​​‌ environments, or stochastic codes.‌ In each of these‌​‌ scientific axes, a particular​​ attention will be paid​​​‌ to large dimensions. Real‌ problems sometimes involve several‌​‌ tens or hundreds of​​ inputs. Methodological advances will​​​‌ be proposed to take‌ into account this additional‌​‌ difficulty. The work expected​​ from the consortium differs​​​‌ from the dominant research‌ in machine learning by‌​‌ specificities linked to the​​ exploration of expensive numerical​​​‌ simulations. However, it seems‌ important to build bridges‌​‌ between the many recent​​ developments in machine learning​​​‌ and the field of‌ numerical simulation.

Philosophy. The‌​‌ CIROQUO Research & Industry​​ Consortium is a scientific​​​‌ collaboration project aiming to‌ mobilize means to achieve‌​‌ methodological advances. The project​​ promotes cross-fertilization between partners​​​‌ coming from different backgrounds‌ but confronted with problems‌​‌ related to a common​​ methodology. Its main goals​​​‌ are:

• The development of‌ exchanges between technological research‌​‌ partners and academic partners​​ on issues, practices and​​​‌ solutions through periodic scientific‌ meetings and collaborative work,‌​‌ particularly through the co-supervision​​ of students,
• The contribution​​​‌ of common scientific skills‌ thanks to regular training‌​‌ in mathematics and computer​​​‌ science,
• The recognition of​ the Consortium at the​‌ highest level thanks to​​ publications in international journals​​​‌ and the diffusion of​ free reference software.

Extension.​‌ CIROQUO was supposed to​​ end in December 2024,​​​‌ but has been extended​ for four years under​‌ the same terms. New​​ partners are included, in​​​‌ particular, EDF (Électricité de​ France) and Michelin. Within​‌ the consortium, a new​​ CIFRE thesis started in​​​‌ November 2025, co-advised by​ Josselin Garnier (ASCII) and​‌ Mickael Binois (Inria Sophia​​ Antipolis in the Acumes​​​‌ project-team).

9.2 Collaboration with​ EdF on industrial risks​‌

This collaboration has been​​ going on for several​​​‌ years, with Josselin Garnier​ as the leader for​‌ ASCII. It concerns the​​ assessment of the reliability​​​‌ of hydraulic and nuclear​ power plants built and​‌ operated by EDF (Électricité​​ de France). The failure​​​‌ of a power plant​ may have major consequences,​‌ such as floods, dam​​ failures, or core meltdowns.​​​‌ For regulatory and safety​ reasons EDF must ensure​‌ that the probability of​​ failure of a power​​​‌ plant is suitably small.​

The failure of such​‌ systems occurs when the​​ values of certain physical​​​‌ variables (temperature, pressure, water​ level) exceed some critical​‌ thresholds. Typically, these variables​​ enter this critical region​​​‌ when several components of​ the system are deteriorated.​‌ Therefore, in order to​​ estimate the probability of​​​‌ system failure, it is​ necessary to model jointly​‌ the behavior of the​​ components and of the​​​‌ physical variables.

For this​ purpose, a model based​‌ on Piecewise Deterministic Markovian​​ Piecewise Processes (PDMP) is​​​‌ devised and used. The​ platform called PYCATSHOO has​‌ been developed by EDF​​ in order to simulate​​​‌ this type of process.​ This platform allows to​‌ estimate the probability of​​ failure of the system​​​‌ by Monte Carlo simulation​ as long as the​‌ probability of failure is​​ not too low. When​​​‌ the probability becomes too​ low, the classical Monte​‌ Carlo estimation method requires​​ a very large number​​​‌ of simulations in order​ to estimate the probabilities​‌ of such rare events,​​ and is much too​​​‌ slow to be used​ in our context. It​‌ is then necessary to​​ use methods using fewer​​​‌ simulations to estimate the​ probability of system failure,​‌ such as variance reduction​​ methods. Among the variance​​​‌ reduction methods are “importance​ sampling” and “splitting” methods,​‌ but these methods present​​ difficulties when used with​​​‌ PDMPs.

This had first​ lead to the defense​‌ of a CIFRE thesis​​ by Thomas Galtier in​​​‌ 2019. It was followed​ by a CIFRE thesis​‌ by Guillaume Chennetier, defended​​ on September 24, 2024,​​​‌ after which he moved​ to a postdoc position​‌ at Ecole des Ponts.​​ In his thesis Guillaume​​​‌ has proposed new methods​ for estimating rare event​‌ probabilities for PDMPs, which​​ offer the flexibility needed​​​‌ to represent complex dynamic​ industrial systems. The industrial​‌ challenge was to enable​​ the tool PyCATSHOO, used​​​‌ by EDF for its​ probabilistic safety assessment studies,​‌ to efficiently estimate the​​ failure probability of such​​​‌ systems with guaranteed accuracy.​ Guillaume has proposed a​‌ theoretical framework for implementing​​ importance sampling of PDMPs,​​ and has highlighted the​​​‌ connection between the optimal‌ biased distribution and the‌​‌ so-called “committor function" of​​ the process. Using tools​​​‌ from reliability analysis and‌ the theory of random‌​‌ walks on graphs, new​​ families of approximations of​​​‌ the committor function were‌ introduced in the thesis.‌​‌ The proposed methodology is​​ adaptive: an approximation of​​​‌ the committor function is‌ constructed a priori and‌​‌ then refined during the​​ simulations of a cross-entropy​​​‌ procedure. The simulations are‌ then recycled to produce‌​‌ an importance sampling estimator​​ of the target probability.​​​‌ Convergence results have been‌ obtained, making it possible‌​‌ to overcome the dependence​​ between simulations and to​​​‌ construct asymptotic confidence intervals.‌ The method produced excellent‌​‌ results on the tested​​ industrial systems. Theoretical articles​​​‌ have been written and‌ submitted to journals.

9.3‌​‌ Fondation NATIXIS

Participants: Nicolas​​ Baradel.

The Fondation​​​‌ Natixis is funding a‌ two year contract of‌​‌ Nicolas Baradel as a​​ research engineer for ASCII,​​​‌ running from May 1,‌ 2023 to April 30,‌​‌ 2025. Nicolas is performing​​ theoretical and numerical studies​​​‌ on the general theme‌ of artificial inteligence (AI)‌​‌ for finance. See 8.3​​ for some details.

10.1 International​​ research visitors

10.2 National initiatives

Participants:​​​‌ Quentin Cormier, Josselin‌ Garnier, Carl Graham‌​‌, Denis Talay,​​ Maxime Colomb.

Quentin​​​‌ Cormier visited Julien Tugaut‌ at Université Jean Monnet‌​‌ (UJM, Saint-Étienne). They work​​ together on the long​​​‌ time behavior of some‌ McKean-Vlasov equations.

11.1 Promoting scientific activities​​

11.2 Teaching​​ - Supervision - Juries​​​‌ - Educational and pedagogical​ outreach

Together with Romain​‌ Veltz, Quentin Cormier gave​​ the course “Mathematical tools​​​‌ for neurosciences” at the​ Master 2 Mathématiques, Vision,​‌ Apprentissage (MVA) of University​​ Paris-Saclay. He also taught​​​‌ the course Markov Chains​ for the Bachelor students​‌ of Ecole Polytechnique.

Maxime​​ Colomb is in charge​​​‌ of the module "données​ massives spatialisées" at the​‌ master MEDAS of Convervatoire​​ National des Arts et​​​‌ Métiers CNAM. He also​ is part of the​‌ ExModelo doctoral school on​​ model exploration.

12.1​​​‌ Major publications

• 1 proceedings‌Preconditioned Langevin Dynamics with‌​‌ Score-based Generative Models for​​ Infinite-Dimensional Linear Bayesian Inverse​​​‌ Problems.NEURIPS 2025‌San Diego (CA), United‌​‌ StatesDecember 2025HAL​​
• 2 miscR.Rene​​​‌ Carmona, Q.Quentin‌ Cormier and M.Mete‌​‌ Soner. Kuramoto Mean​​ Field Game with Intrinsic​​​‌ Frequencies.September 2025‌HAL
• 3 articleJ.‌​‌Josselin Garnier, A.​​Antonio Picozzi and T.​​​‌Theo Torres. Stochastic‌ Dynamics of Incoherent Branched‌​‌ Flows.Physical Review​​ Letters13422June​​​‌ 2025, 223803HAL‌DOI

12.2 Publications of‌​‌ the year