Learning physics simulations for improving design processes in the industry

Abstract

This article is the written version of the Felix Klein prize lecture, given on 16 July 2024, at the $9$th European Congress of Mathematics in Seville. In the same fashion as the lecture, general ideas and results are given, and references are provided for the reader interested in details and rigorous developments.

In an industrial group like Safran, numerical simulation of physics phenomena is used in the majority of the design processes of its manufactured products. At Safran’s corporate research center, we develop technologies to improve these processes by deriving fast and reliable surrogate models for various domains of physics.

We address two technologies developed in recent years. First, a physical reduced-order modeling method for non-linear structural mechanics and thermal analysis. This method is applied to the lifetime computation of high-pressure turbine blades and the fast heat analysis of high-pressure compressors. Second, the learning of physics simulations under non-parameterized geometrical variability using classical machine learning tools, thanks to non-linear deterministic dimensionality reduction (involving morphing and principal component analysis) and Gaussian process regression, with predictive uncertainties. We also present some of our contributions to the open-source and open-data community.