Physics-Informed MAchine LEArning: From Extraction to Transfer of Knowledge in Surface Engineering

Post-doctoral fellow: Antoine CARADOT

ABSTRACT

The PIMALEA project focuses on two fundamental questions at the intersection of machine learning and self-organization of matter. First, how to discover knowledge (in the form of a Partial Differential Equation, PDE) when only temporally sparse observations are available. Second, how to accelerate neural PDE solution estimation to adapt and compare equations across domains (materials, conditions, etc.)
The project aims at pushing the temporal resolutions limits that are necessary for discovering a PDE governing some observations, and at reducing the number of samples necessary for obtaining a good neural approximation of PDE solutions (with methods like Physics Informed Neural Networks, PINNs).
The project cares particularly about the theoretical guarantees that can be derived for the proposed methods.



 


PUBLICATIONS

  • Eduardo Brandao, Stefan Duffner, Rémi Emonet, Amaury Habrard, François Jacquenet & Marc Sebban, Is My Neural Net Driven by the MDL Principle?, ECML/PKDD 2023 , European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Research Track, https://doi.org/10.1007/978-3-031-43415-0_11
  • Antoine Caradot, Rémi Emonet, Amaury Habrard, Abdel-Rahim Mezidi, Marc Sebban, Provably accurate adaptive sampling for collocation points in physics-informed neural networks, ECML/PKDD 2025 , European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Research Track, https://doi.org/10.1007/978-3-032-06096-9_2
  • Fayad Ali Banna, Antoine Caradot, Eduardo Brandao, Jean-Philippe, Unrolled-SINDy: A Stable Explicit Method for Non Linear PDE Discovery from Sparsely Sampled Data, ECML/PKDD 2026 , European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases: Research Track, https://hal.science/hal-05324777/

CONFERENCES 

  • Eduardo Brandao, Stefan Duffner, Rémi Emonet, Amaury Habrard, François Jacquenet & Marc Sebban, Is My Neural Net Driven by the MDL Principle?, ECML/PKDD 2023, Turin, Italie
  • Fayad Ali Banna, Rémi Emonet, Anton Rudenko, Marc Sebban, Jean-Philippe Colombier, Predicting laser energy absorption on nanostructured surfaces with deep learning, SPIE Photonics Europe, 2024, Strasbourg, France
  • Jean-Philippe Colombier, Eduardo Brandao, Anthony Nakhoul, Rémi Emonet, Amaury Habrard, Florence Garrelie, François Jacquenet, Florent Pigeon, Marc Sebban, Laser-induced surface organization on the nanoscale guided by machine learning, SPIE LASE, 2024, San Francisco, California, United States
  • Antoine Caradot, Rémi Emonet, Amaury Habrard, Abdel-Rahim Mezidi, Marc Sebban, Provably accurate adaptive sampling for collocation points in physics-informed neural networks, ECML/PKDD 2025, Porto, Portugal