Machine Learning for Physics

Credits

3 ECTS, 18h

Instructors

Vincent Acary

Objectives

  1. Physics-Informed Neural Networks (PINNs): leveraging neural networks for the resolution of physical problems by directly embedding the governing partial differential equations (PDEs) into the loss function, enabling learning constrained by the underlying physics ;
  2. Data-driven models grounded in operator theory: investigation of DeepONet and Neural Operators (FNO, CNO…) as universal approximators of operators between functional spaces, offering discretization-independent generalization capabilities ;
  3. Convexity-preserving networks, convex optimization layers, and equilibrium networks: examination of advanced techniques such as Input Convex Neural Networks (ICNNs), OptNet layers, and implicit fixed-point networks, with applications to structured modeling and differentiable optimization ;
  4. Critical comparison between physics-informed methods and classical solvers: systematic benchmarking of machine learning approaches against established numerical methods — finite elements (FEM), finite differences (FDM), finite volumes (FVM) — across dimensions of accuracy, computational complexity, scalability, and physical interpretability.

Prerequisites

Statistics (Master 1 level), Probability (Master 1 level)

MSCI