Finite-element Gaussian processes for the machine learning of steady-state linear partial differential equations (original) (raw)

Dalton, David, Gao, Hao ORCID: https://orcid.org/0000-0001-6852-9435 and Husmeier, Dirk ORCID: https://orcid.org/0000-0003-1673-7413(2026) Finite-element Gaussian processes for the machine learning of steady-state linear partial differential equations.Computer Methods in Applied Mechanics and Engineering, 451, 118580. (doi: 10.1016/j.cma.2025.118580)

Abstract

We introduce finite-element Gaussian processes (FEGPs), a novel physics-informed machine learning approach for solving inverse problems involving steady-state, linear partial differential equations (PDEs). Our framework combines a Gaussian process prior for the unknown solution function with a likelihood that incorporates the PDE in its weak form, using a finite-element approximation. This approach offers significantly better scalability than physics-informed Gaussian processes (PIGPs), which rely on the strong form of the PDE. Through numerical experiments on a range of synthetic benchmark problems, we show that FEGPs offer results which outperform PIGPs, and are competitive with physics-informed neural networks (PINNs) with improved uncertainty quantification.

University Staff: Request a correction | Enlighten Editors: Update this record

Funder and Project Information

The SofTMech Statistical Emulation and Translation Hub

Dirk Husmeier

EP/T017899/1

M&S - Statistics

A whole-heart model of multiscale soft tissue mechanics and fluid structureinteraction for clinical applications (Whole-Heart-FSI)

Nicholas Hill

EP/S020950/1

M&S - Mathematics

Deposit and Record Details