Physics-based linear regression for high-dimensional forward uncertainty quantification

TL;DR

This paper presents a physics-based linear regression method utilizing optimized basis functions for high-dimensional forward uncertainty quantification, demonstrated through a nonlinear vibration example.

Contribution

It introduces a novel physics-informed basis function approach optimized via inner product space geometry for surrogate modeling in high-dimensional settings.

Findings

Effective encoding of problem-specific information

Improved surrogate modeling accuracy

Successful demonstration on a nonlinear vibration problem

Abstract

We introduce linear regression using physics-based basis functions optimized through the geometry of an inner product space. This method addresses the challenge of surrogate modeling with high-dimensional input, as the physics-based basis functions encode problem-specific information. We demonstrate the method using a proof-of-concept nonlinear random vibration example.