PhD Position F/M EDF Lab Paris Saclay PhD Cifre Deep PDE Surrogates and Inverse Problems for Industrial Applications

Le descriptif de l’offre ci-dessous est en Anglais

Type de contrat : CDD

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Doctorant

Niveau d'expérience souhaité : Jeune diplômé

Contexte et atouts du poste

Hired by EDF under a CIFRE PhD Contract.

General Positioning

Artificial intelligence (AI) began revolutionizing digital services in 2013 with its application to image processing and computer vision. A second revolution arrived around 2020 with language models (e.g., ChatGPT). More recently, AI has begun to be applied to scientific and engineering problems. Its goal is to create an "augmented engineer" who can carry out studies and make decisions with greater efficiency. In this context, digital twins appear as fundamental tools for the engineering of the future. A digital twin is a virtual model of an industrial piece of equipment. It covers the object's entire life cycle and uses real-time data sent by sensors on the object to simulate its behavior, monitor operations, and anticipate its functioning. Partial differential equation (PDE) solvers are a key element in simulating dynamics, but their execution times, even on supercomputers, make them difficult to deploy for digital twins subject to strong reactivity constraints.

Meta-models (or surrogate models) are approximations of classical numerical solvers with a very low computational cost. They form the core of a digital twin. Using machine learning techniques to build these meta-models presents multiple theoretical and practical challenges.

Supercomputers currently have the capacity to support the large-scale executions of numerous numerical simulations. This makes it possible to carry out parametric studies following a design of experiments and to generate databases of physical fields that can be used to train generic meta-models [McCabe et al., 2025]. Furthermore, since industrial equipment is fitted with sensors, we can also access precise physical measurements. Recent work in AI-for-Science has shown that neural-network-based meta-models can also assimilate measurements. Machine learning techniques for meta-models of numerical simulations of industrial equipment, with the integration of sensor measurements from that equipment, will be at the center of the research questions of this thesis.

Mission confiée

Thesis Problem Statement

Modern artificial intelligence techniques will be at the heart of this thesis's research. On one hand, supervised learning will be used to build surrogate models for physical phenomena. New meta-model architectures based on learning may be proposed and tested on complex EDF use cases. However, this is not sufficient: can such a surrogate, learned from simulation data, predict the real-world behavior of an industrial piece of equipment? One challenge is to calibrate this new type of surrogate against sensor observations. Calibration involves solving an inverse problem. A promising approach is based on neural techniques known as SBI (Simulation-Based Inference) [Cranmer et al., 2020]. SBI enables the resolution of inverse problems using generative AI methods and Bayesian statistics with uncertainty quantification. However, this type of approach has not yet been used on problems as complex as an industrial piece of equipment. This thesis will be devoted to the use and development of SBI in this context. The thesis will focus on the co-development of neural surrogate architectures (often derived from ViT) and neural posterior estimators (of the score-matching type), with the aim of optimizing both accuracy and computational cost. The question of methodologies for validating results and quantifying uncertainty - critical in an industrial environment - will also be addressed. Two industrial applications will be tackled. The first concerns electrical machines like power plant alternators for which EDF has developped numerical simulators and has large sets of sensor data (measuring leaking flux for instance). The second will be in the domain of sismology.

The results developped during this PhD will be published at international venues (AI and application domain conferences and/or journals)

Collaborative Context and Expertise

Since 2018, EDF has been studying the construction of meta-models based on deep neural networks (i.e., deep learning). Initially, based on fluid simulations using Code_Saturne (www.code-saturne.org), EDF developed recognized expertise in neural-network-based learning for handling simple fluid flows with high accuracy [Meyer et al., 2021].

In 2022, an algorithm hybridizing POD (Proper Orthogonal Decomposition) with SVR (Support Vector Regression) was designed, with promising results [Ribes et al., 2022]. In 2024, an industrial use case - a power plant alternator - was successfully modeled using an evolution of this algorithm, which replaces the SVRs with a multilayer neural network [Ribes et al., 2024]. In 2025, it was used in an inverse-computation context using Bayesian inversion (MCMC methods hybridized with learning).

Inria Grenoble's Statify team is among the leading players in simulation-based inference (SBI), with an ambitious and structured research program since 2021. Its contributions span the entire methodological chain: from automatic dimension reduction via learned summary features [Rodrigues & Gramfort, 2020], to the rigorous statistical calibration of conditional probability approximators for solving inverse problems [Linhart et al., 2021], up to the most recent developments in flow matching to address physical model misspecification in SBI [Ruhlmann et al., 2026]. This progression illustrates a growing mastery of the theoretical and applied challenges of modern probabilistic inference.

Inria Grenoble's Datamove team has a long-standing collaboration with EDF. We co-developed the Melissa environment for managing large ensembles of numerical simulations, applied to sensitivity analysis [Terraz et al., 2017] and meta-model learning [Meyer et al., 2023]. The Datamove team has also contributed methodologies for online learning and active learning of advanced meta-models on supercomputers [Cesar et al., 2026].

The Inria Grenoble teams Datamove and Statify are partnered with EDF in a research chair centered on SBI (https://sbi4c.inria.fr), funded by the Grenoble MIAI AI institute. This thesis is part of this collaborative context, to which two complementary theses are also attached: the first focused on the methodological foundations of SBI for complex problems, and the second on large-scale online SBI.

References

J. Linhart, A. Gramfort, P.L.C. Rodrigues. L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference. Accepted at NeurIPS 2023. arXiv:2306.03580

L. Meyer, L. Poittier, A. Ribes, B. Raffin. Deep Surrogate for Direct Time Fluid Dynamics. Machine Learning and the Physical Sciences workshop at NeurIPS. December 2021.

A. Ribes, R. Persicot, L. Meyer, J-P. Ducreux. A hybrid Reduced Basis and Machine-Learning algorithm for building Surrogate Models: a first application to electromagnetism. Machine Learning and the Physical Sciences workshop at NeurIPS. December 2022.

A. Ribes, N. Benchekroun, T. Delagnes. A Fast Learning-Based Surrogate of Electrical Machines using a Reduced Basis. AI for Science workshop at ICML. July 2024, Vienna, Austria.

5. P.L.C. Rodrigues and A. Gramfort. Learning summary features of time series likelihood free inference. Accepted at the Workshop on Machine Learning and the Physical Sciences at NeurIPS 2020. arXiv:2012.02807

6. P-L. Ruhlmann, M. Arbel, F. Forbes, P.L.C. Rodrigues. Flow Matching for Robust Simulation-Based Inference under Model Misspecification. Accepted at ICML 2026. arXiv:2509.23385

R.C. Smith. Uncertainty Quantification. SIAM, 2014.

McCabe, Michael, Payel Mukhopadhyay, Tanya Marwah, et al. Walrus: A Cross-Domain Foundation Model for Continuum Dynamics. November 19, 2025. https://doi.org/10.48550/arXiv.2511.15684

Cranmer, Kyle, Johann Brehmer, and Gilles Louppe. The Frontier of Simulation-Based Inference. Colloquium Paper. Proceedings of the National Academy of Sciences 117, no. 48 (2020): 30055–62. https://doi.org/10.1073/pnas.1912789117

Lucas Meyer, Marc Schouler, Robert Alexander Caulk, Alejandro Ribés, and Bruno Raffin. High Throughput Training of Deep Surrogates from Large Ensemble Runs. In SC 2023 - The International Conference for High Performance Computing, Networking, Storage. Nov. 2023. https://hal.science/hal-04213978

Pierre Cesar, Sofya Dymchenko, Abhishek Purandare, Bruno Raffin. Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training. 2026. https://inria.hal.science/hal-05646322

Théophile Terraz, Alejandro Ribés, Yvan Fournier, Bertrand Iooss, Bruno Raffin. Melissa: Large Scale In Transit Sensitivity Analysis Avoiding Intermediate Files. The International Conference for High Performance Computing, Networking, Storage and Analysis (Supercomputing), Nov 2017, Denver, United States.

Principales activités

Expected Profile and Application

We seek candidates with an Engineering school title or Master's degree (M2) and a background in artificial intelligence and/or statistics and/or numerical simulation. Good Python programming skills and expertise with the AI classical software stack (Pytorch, Jax) are expected.

Send your curiculum, your academic mark record, availables reports (master thesis for instance),

and any other element that may help assess your adequacy to the profile (open code repos for instance).

Apply exclusively through this web side. We will not answer to direct emails.

Terms

Contract: The candidate will be hired by EDF under a CIFRE PhD Contract

Duration: 3 years

Location: EDF Lab Paris-Saclay, with visiting periods at Inria Grenoble

Computing environment:** EDF's hybrid HPC/AI supercomputers, French and European supercomputers (Jean-Zay and Leonardo).

Thesis Supervision

EDF Lab Paris-Saclay:

A. Ribes

N. Benchekroun

INRIA Grenoble:

B. Raffin

P. Rodrigues

Avantages

EDF Lab working conditions.

Rémunération

EDF Lab working conditions.

Informations générales

Thème/Domaine : Calcul distribué et à haute performance

Ville : Saclay

Centre Inria : Centre Inria de l'Université Grenoble Alpes

Date de prise de fonction souhaitée : 2026-10-01

Durée de contrat : 3 ans

Date limite pour postuler : 2026-09-07

Attention: Les candidatures doivent être déposées en ligne sur le site Inria. Le traitement des candidatures adressées par d'autres canaux n'est pas garanti.

Consignes pour postuler

Sécurité défense :

Ce poste est susceptible d’être affecté dans une zone à régime restrictif (ZRR), telle que définie dans le décret n°2011-1425 relatif à la protection du potentiel scientifique et technique de la nation (PPST). L’autorisation d’accès à une zone est délivrée par le chef d’établissement, après avis ministériel favorable, tel que défini dans l’arrêté du 03 juillet 2012, relatif à la PPST. Un avis ministériel défavorable pour un poste affecté dans une ZRR aurait pour conséquence l’annulation du recrutement.

Politique de recrutement :

Dans le cadre de sa politique diversité, tous les postes Inria sont accessibles aux personnes en situation de handicap.

Contacts

Équipe Inria : DATAMOVE

Directeur de thèse :

Raffin Bruno / bruno.raffin@inria.fr

A propos d'Inria