Hybrid machine learning--finite element solvers for solid and fluid mechanics

Author(s) Information

Victor Alcantara-Arias, California Polytechnic State University, San Luis ObispoFollow
Spandan Suthar, California Polytechnic State University, San Luis ObispoFollow

College - Author 1

College of Engineering

Department - Author 1

Aerospace Engineering Department

College - Author 2

College of Engineering

Department - Author 2

Computer Science Department

Advisor

Amuthan Ramabathiran, College of Engineering, Aerospace Engineering Department

Funding Source

Metrea

Date

10-2025

Abstract/Summary

The goal of this project is to develop a new class of hybrid solvers for partial differential equations (PDEs) encountered in solid and fluid mechanics that blend traditional finite element methods (FEM) with modern machine learning algorithms. While FEM solvers are well developed, they can be computationally expensive for realistic problems. Machine learning algorithms have emerged as possible new solutions to cut down the computational cost associated with expensive FEM simulations, but these are typically not interpretable. Previous work on this topic resulted in a class of fully interpretable machine learning solvers for PDEs that had two primary drawbacks: (i) they were not competitive with FEM solvers, and (ii) the enforcement of boundary conditions is both inaccurate and inefficient. The present project aims to overcome both these limitations by developing hybrid solvers that extend a coarse FEM solver with an adaptive machine learning model building on previous research by the PI. These hybrid solvers will be applied to solve a variety of problems in solid and fluid mechanics, and specifically for fluid-structure interaction problems. The latter are of significant importance to aerospace applications.

October 1, 2025.