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

arXiv: https://arxiv.org/abs/2510.24577 · HTML: https://mlsanity.com/paper/2510.24577/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 1 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Built on by (most cited first, 1 of 1)

- [Frequency Shift Physics-Informed Extreme Learning Machine for Solving High-Frequency Partial Differential Equations](https://mlsanity.com/paper/2607.01694/) (2026)

## Abstract (arXiv)

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.