物理引导的极限学习机提升计算效率与精度，解决复杂微分方程难题。
Physics-Informed Extreme Learning Machine (PIELM): Opportunities and Challenges
- 融合物理规律的极限学习机框架，加速求解微分方程。
- 在陡峭梯度、非线性等复杂场景下表现优于传统方法。
- 适合需要高效、可解释建模的科学与工程领域研究者。
我们欣喜地看到，物理引导的极限学习机（PIELM）相比其他物理引导机器学习（PIML）范式，在计算效率和精度方面表现出显著优势。由于目前尚无对PIELM的全面综述，本文借此机会分享我们在这一有前景方向上的见解与经验。当前已有大量工作致力于求解具有陡峭梯度、非线性、高频特性、硬约束、不确定性、多物理场耦合及可解释性要求的常微分/偏微分方程（ODEs/PDEs）。尽管取得诸多成功，仍存在诸多亟待解决的挑战，这也为构建更鲁棒、可解释、通用的PIELM框架提供了发展机遇，适用于科学与工程应用。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。