Réunion

Johannes Bransdetter (Johannes Kepler University Linz)

"Embracing the next wave of scientific breakthroughs"

Abstract: In the era of scaling and LLMs, one gets notoriously confronted with the question of where we stand with applicability of such powerful techniques within scientific or engineering domains. The discussion starts by reiterating on recent triumphs in weather and climate modeling, making connections to computer vision, physics-informed learning and neural operators. Secondly, we discuss challenges and conceptual barriers which need to be overcome for the next wave of disruption in science and engineering. We showcase recent breakthroughs in multi-physics modeling, molecular dynamics, computational fluid dynamics, nuclear fusion and related fields.

Guillaume Couairon (Inria Paris)

"Skillful and compute-efficient probabilistic weather forecasting with ArchesWeatherGen"

Abstract: Deep learning weather forecasting models trained with the next state prediction objective on ERA5 have shown great success compared to numerical global circulation models. However, for a wide range of applications, being able to provide representative samples from the distribution of possible future weather states is critical. In this talk, we will present ArchesWeatherGen, a methodology to leverage deterministic weather models in the design of probabilistic weather models, leading to improved performance and reduced computing costs. ArchesWeatherGen is based on flow matching, a modern variant of diffusion models, that is trained to project ArchesWeather's predictions to the distribution of ERA5 weather states. It is a true stochastic emulator of ERA5 and surpasses IFS ENS and NeuralGCM on all WeatherBench headline variables (except for NeuralGCM's geopotential). Our work also aims to democratize the use of deterministic and generative machine learning models in weather forecasting research, with academic computing resources.

Laure Raynaud (CNRM Toulouse, Météo France)

"Large-scale deep-learning for weather and climate prediction" 

Abstract: A new paradigm for weather and climate prediction has emerged recently : data-driven prediction models have become competitive with standard physics-based models on many aspects, thanks to an accurate encoding of the data distribution. Most models have been developed for task-specific purposes and are trained on a single type of data (such as the ERA5 reanalysis). The next challenge to expand the capabilities of data-driven modeling is to fully exploit the vast range of atmospheric observations, characterized by spatio-temporal variations and heterogeneous outputs (point or spatial time series, vertical profiles, vertically integrated data, … ). This naturally leads to the development of foundation models that learn a task-agnostic representation of the atmosphere. An overview of the most advanced models will be presented, as well as early results for integrating heterogeneous data sources. How physically-consistent and explainable these new models are is still an open question, that will be discussed in the presentation.

Frédéric Barbaresco (Thales)

"Réseaux de neurones informés par la thermodynamique et la géométrie symplectique : TINN et simulation des phénomènes dissipatifs"

Résumé : La thermodynamique est une expression de la physique à un niveau épistémique élevé. À ce titre, son potentiel en tant que biais inductif pour aider les procédures d'apprentissage automatique à obtenir des prédictions précises et crédibles a été récemment reconnu dans de nombreux domaines. La thermodynamique fournit des informations utiles dans le processus es phénomènes dissipatifs. Nous allons expliquer le lien entre les TINN (Réseaux de Neurones Informés par la Thermodynamique), le flot métriplectique et la thermodynamique des groupes de Lie et comment ces concepts cherchent collectivement à intégrer les principes de la thermodynamique et des symétries dans la modélisation mathématique, l'apprentissage automatique et les systèmes physiques.

Joel Soffo (Airbus, Nantes Université, LMJL)

"Nonlinear manifold approximation using compositional polynomial networks"

Abstract: We present a new method for nonlinear reduced order modeling (dimensionality reduction). More precisely, we consider the problem of approximating a subset  M of a Hilbert space X by a low-dimensional manifold M_n , using samples from M. M_n := { D(a) : a in Rⁿ} is defined as the range of a smooth nonlinear decoder  D defined on  Rⁿ with values in a possibly high-dimensional linear space X_N, and a linear encoder  E which associates to an element from  M its coefficients  a = E(u) on a basis of a n-dimensional subspace X_n from X_N , where  X_n and  X_N are optimal or near to optimal linear spaces. The linearity of the encoder allows to easily obtain the parameters  E(u) associated with a given element  u in M. The proposed decoder is a polynomial map from Rⁿ  to  X_N which is obtained by a tree-structured composition of polynomial maps, estimated sequentially from samples in M. Rigorous error and stability analyses are provided, as well as an adaptive strategy for constructing a decoder that guarantees an approximation of the set M with controlled mean-squared or wort-case errors, and a controlled stability (Lipschitz continuity) of the encoder and decoder pair. The performance of the method is demonstrated on different partial differential equations, such as Korteweg-de Vries equation and Burgers equation.

Ben Gao (LaHC, Université Saint-Etienne)

"Conformal Online Learning of nonlinear dynamical systems"

Abstract: We introduce Conformal Online Learning of Koopman embeddings (COLoKe), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep feature learning with multi-step prediction consistency in the lifted space, where the dynamics evolve linearly. To prevent overfitting, COLoKe employs a conformal-style mechanism that shifts the focus from evaluating the conformity of new states to assessing the consistency of the current Koopman model. Updates are triggered only when the current model’s prediction error exceeds a calibrated threshold, allowing selective refinement of the Koopman operator and embedding. Empirical results on benchmark dynamical systems demonstrate the effectiveness of COLoKe in maintaining long-term predictive accuracy while significantly reducing unnecessary updates.

Clément Veyer (LARIS, Université Angers)

"Morphometry-aware Graph Neural Network for applied semantic segmentation"

Abstract: Our work extends the use of graph neural networks (GNN) to improve semantic segmentation in specific segmentation tasks with limited input data, such as brain structures segmentation. Previous work presented a method to refine a suboptimal segmentation map predicted by a Convolutional Neural Network (CNN), by performing a node classification of the segmented structures, using an edge-filtered convolution operator to enhance the GNN’s ability to represent high semantic relations between structures to segment. In domains like brain structures segmentation, morphometric properties can help to discriminate correct segmented structures from artifacts and mismatches and are often used by medical experts to make causal links between the shape of brain structures and visible outcomes. Therefore, we propose to increase segmentation metrics by using a morphometry-aware GNN architecture.

Etienne Lehembre (LIFO, Université Orléans)

"Prédiction sur les nappes phréatiques : utilisation d'équations physiques et variables non observables"

Résumé : La gestion des réserves d'eau devient un enjeu crucial dans le contexte du changement climatique. Afin de prédire la disponibilité future de l’eau dans les nappes phréatiques, le BRGM utilise le logiciel Gardénia qui repose sur un modèle physique simplifié basé sur des réservoirs et des siphons exponentiels, intégrant à la fois des variables observables (comme les précipitations ou le niveau d’eau) et non observables (comme les facteurs de demi-vie ou le facteur d’équilibre entre écoulement et percolation). Notre travail vise à prédire le niveau d’eau d’une nappe phréatique en conservant la cohérence avec le modèle Gardénia. Pour cela, nous développons un modèle de deep learning inspiré par la physique (physics-informed), intégrant les équations de Gardénia comme contraintes pendant l'apprentissage.

Valentin Mercier (CERFACS, IRIT Toulouse)

"Fast Flood Prediction Using Graph Neural Networks: Application to the Têt River Basin"

Abstract: Fast and reliable flood forecasting is needed for operational situations where decisions must be made quickly to reduce damages. Physically-based hydrodynamic models, such as those solving the shallow water equations on unstructured meshes, are well known for their accuracy and ability to describe complex river systems. However, for real-time forecasting, these models face a trade-off: achieving high precision requires a lot of computation, which can be too slow when many forecasts are needed under strict time constraints. In this work, we study if Graph Neural Networks (GNNs) can provide real-time flood predictions that are accurate enough for operational use. Our method uses the same unstructured mesh representations found in hydraulic simulations, which makes it easy to connect with existing workflows and data. We conduct our study on the Têt River basin (Pyrénées-Orientales, France), using a synthetic dataset produced by high-resolution numerical simulations. Our approach adapts the MeshGraphNet architecture to process unstructured meshes as graphs.

Eiji Kawasaki (Université Paris Saclay, CEA LIST)

"Physics-Aware Machine Learning for Complex Materials"

Abstract: The accurate prediction of material properties in chemically disordered systems presents a formidable challenge for materials science. These systems, where atoms are arranged in a non-repeating, irregular fashion, have an enormous number of possible atomic configurations. Traditional computational methods struggle to explore this vast configurational space efficiently. This leads to high computational costs and limits our ability to predict material behavior across the full range of possible atomic arrangements. We present here the recent work by Maciej J. Karcz, Luca Messina, Eiji Kawasaki, and Emeric Bourasseau (arXiv:2408.14928), that leverages generative modeling to efficiently target a crucial quantity: the partition function

Merveille Cyndie Talla Makougne (INRAE, INRIA Rennes)

"Multiplicative Score-based generative models inspired by physics"

Abstract: Score-based generative models (SGM) are a class of generative models that aim to sample the probability distribution of a given set of observations from an easy-to-sample distribution. They rely on gradients of log probability density functions, known as score functions. Modeling complex physical systems using generative models remains a significant challenge. They need to accurately incorporate the underlying physical laws governing the system's dynamics. In this work, we propose a new approach to SGM, named multiplicative score-based generative models (MSGM) inspired by the transport noises. We expect MSGM to efficiently model turbulent dynamics by preserving structure of the flow and ensuring energy conservation. Like the usual SGM, our method relies on a forward and a backward diffusion. However, the forward diffusion is driven by a stochastic differential equation (SDE) with a skew-symmetric multiplicative noise. It transforms the data distribution into a rotation-invariant distribution. This distribution conserves a portion of the original dataset information. It depends on the one-dimensional distribution of the norm of the original data, making it easy to sample. The backward diffusion samples the data distribution through a multiplicative reverse-time SDE. It involves a neural network that models the score function and is trained using score matching. We proved that it is equivalent to maximizing the ELBO in our new noise setting. Through numerical experiments, MSGM efficiently estimates complex and fat-tailed distributions, predicting extreme events. Compared to classical SGM, our method requires fewer backward steps to sample the data distribution of interest.

Robin Matha (Université Côte d’Azur, LEAT)

"Réseaux de neurones pour la mesure physique : évaluation de la fiabilité de mesure par des cartes auto-organisées"

Résumé : L’interféromètre par réinjection optique est un instrument de mesure compact et simple idéal pour être embarqué. Dans le cadre d’une cible en déplacement longitudinal à distance les signaux générés par l’interféromètre contiennent l’information de la vitesse de cette cible. Depuis quelques années, une nouvelle approche de traitement de ces signaux via des réseaux de neurones convolutifs est proposée. Cependant, cette solution seule ne donne aucune indication quant à la qualité de reconstruction. Dans ce cadre, nous proposons une association entre un réseau de neurones convolutifs (CNN) pré-entraîné et tronqué, utilisé comme extracteur de caractéristiques, associé à une carte auto-organisée de Kohonen (SOM) placée en sortie. Cette architecture est également facilement chargeable sur des supports facilement embarquables et donc compatible avec les caractéristiques de l’instrument. Cette SOM est munie de fonctions et de cartes adjacentes particulières nous permettant d’effectuer l’inférence à partir de celle-ci. Sa topologie nous permet aussi d’évaluer la confiance en la prédiction obtenue.

Abdel-Rahim Mezidi (LaHC, Université Saint-Etienne)

"Les opérateurs neuronaux vus par le prisme de l'optimisation proximale"

Résumé: Nous présentons plusieurs avancées sur les opérateurs neuronaux en considérant l'action des couches d'opérateurs comme les minimiseurs de problèmes d'optimisation régularisés par divergence de Bregman sur les espaces de fonctions de Banach. Le cadre proposé permet d'interpréter les opérateurs d'activation comme des opérateurs de proximité de Bregman de l'espace dual à l'espace primaire. Ce nouveau point de vue est suffisamment général pour inclure les opérateurs neuronaux classiques ainsi qu'une nouvelle variante, appelée opérateurs neuronaux de Bregman, qui inclut l'opérateur d'activation inverse et présente la même expressivité que les opérateurs neuronaux standard. Des expériences numériques confirment les avantages supplémentaires de la variante de Bregman des opérateurs neuronaux de Fourier pour la formation de modèles plus profonds et plus précis.

Dimitrios Tzivrailis (CEA, LPTMS)

"Uncertainty in AI driven physical simulation"

Abstract: In this work, we present a framework for quantifying and mitigating the epistemic error introduced by neural network surrogate models during MCMC sampling. Our approach leverages model ensembles—a well-established method in machine learning for estimating predictive uncertainty—to approximate the mean and variance of the model's output for a given input. Rather than relying on a single deterministic prediction, we use the ensemble to characterize both the expected value and the confidence in each force component prediction. We integrate this uncertainty quantification into the Monte Carlo sampling process via a novel penalty-based correction to the Metropolis acceptance criterion. Specifically, we propose a modification of the acceptance probability that penalizes proposed configurations according to the variance of the model predictions. In regions where the ensemble disagreement (i.e., epistemic uncertainty) is high, the acceptance probability is reduced, effectively rejecting unreliable proposals. This correction acts as a conservative bias, prioritizing configurations where the model is more trustworthy and thereby preserving the fidelity of the sampling process. Importantly, this penalty does not require ground truth knowledge at inference time—it relies solely on internal model statistics, making it scalable and efficient. Our methodology is evaluated in the context of the 2D  lattice field theory, a prototypical model in statistical physics. We demonstrate that the penalty method consistently improves the quality of samples compared to using a raw neural network model alone, particularly in both the ferromagnetic and paramagnetic phases. The ensemble-based correction aligns the sampled distributions with those generated by the ground truth Metropolis-Hastings algorithm. We also show that the method generalizes across system sizes, indicating that the learned correction is not limited to a specific domain of the configuration space.

Fayad Ali Banna (LaHC, Université Saint-Etienne)

"Multi-step SINDy pour la découverte d'EDP à partir d'observations très espacées dans le temps"

Résumé : L'algorithme SINDy a permis une avancée importante dans l'identification des équations différentielles à partir des données d'observation. Cependant, comme toutes ses variantes depuis lors, SINDy repose principalement sur des estimations numériques précises de la dérivée temporelle, imposant ainsi de fortes contraintes sur la taille des pas de temps sous peine de perdre les garanties de stabilité. Bien que ces méthodes soient beaucoup plus simples à mettre en œuvre que les schémas implicites (en termes de mémoire et de programmation), cette limitation du pas de temps peut s'avérer trop restrictive pour les applications réelles où les données peuvent être collectées de manière éparse. Nous présentons Multi-step-SINDy, un nouvel algorithme de découverte explicite d'EDP qui déroule chaque étape numérique en s'appuyant sur des estimations successives de la solution, bénéficiant ainsi d'un pas de temps intrinsèquement plus petit sans nécessiter de données supplémentaires. Multi-step-SINDy est polyvalent et peut être utilisé avec n'importe quel algorithme de découverte d'EDP reposant sur des techniques de différences finies explicites, telles que les méthodes d'Euler ou de Runge-Kutta. Nous étudions en outre ses erreurs de troncature et le lien entre la stabilité de l'approximation numérique et le succès de la récupération des équations sous-jacentes. Ces résultats sont étayés par une étude expérimentale complète montrant l'efficacité de notre méthode dans des scénarios complexes où les données peuvent être rares et échantillonnées à des pas de temps croissants.