A hybrid Reduced Basis and Machine-Learning algorithm for building Surrogate Models: a first application to electromagnetism

Alejandro Ribés (1) , Ruben Persicot (2) , Lucas Meyer (3, 4, 1) , Jean-Pierre Ducreux (1)

1 SINCLAIR AI Lab - Saclay Industrial Lab for Artificial Intelligence Research
2 ENPC - École des Ponts ParisTech
3 UGA - Université Grenoble Alpes
4 DATAMOVE - Data Aware Large Scale Computing

A surrogate model approximates the outputs of a Partial Differential Equations (PDEs) solver with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs, which are PDEs that depend on a set of parameters but are also temporal and spatial processes. Our contribution is a method hybridizing the Proper Orthogonal Decomposition and several Support Vector Regression machines. We present promising results on a first electromagnetic use case (a primitive single-phase transformer).

Domaines: Apprentissage [cs.LG]; Analyse numérique [cs.NA]; Modélisation et simulation

Alejandro Ribés, Ruben Persicot, Lucas Meyer, Jean-Pierre Ducreux. A hybrid Reduced Basis and Machine-Learning algorithm for building Surrogate Models: a first application to electromagnetism. Workshop on Machine Learning and the Physical Sciences workshop at NeurIPS 2022, Dec 2022, New Orleans, United States. pp.1-6. ⟨hal-03850571⟩