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.
