Physics-Informed Extreme Learning Machine (PIELM): Opportunities and Challenges

TL;DR

This paper reviews the development of physics-informed extreme learning machines (PIELM), highlighting their advantages, current challenges, and future opportunities for solving complex differential equations efficiently and accurately.

Contribution

It provides a comprehensive overview of PIELM, discussing its recent progress, challenges, and potential for advancing scientific and engineering computations.

Findings

PIELM offers higher efficiency and accuracy than other PIML methods.

Significant efforts have been made to apply PIELM to complex differential equations.

Challenges remain in robustness, interpretability, and generalizability of PIELM.

Abstract

We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a comprehensive summary or review of PIELM is currently unavailable, we would like to take this opportunity to share our perspectives and experiences on this promising research direction. We can see that many efforts have been made to solve ordinary/partial differential equations (ODEs/PDEs) characterized by sharp gradients, nonlinearities, high-frequency behavior, hard constraints, uncertainty, multiphysics coupling, and interpretability. Despite these encouraging successes, many pressing challenges remain to be tackled, which also provides opportunities to develop more robust, interpretable, and generalizable PIELM frameworks for scientific and engineering applications.