We are very delighted to see the fast development of physics-informed extreme learning machine (PIELM) in recent years for higher computation efficiency and accuracy in physics-informed machine learning. As a summary or review on PIELM is currently not available, we would like to take this opportunity to show our perspective and experience for this promising research direction. We can see many efforts are made to solve PDEs with sharp gradients, nonlinearities, high-frequency behavior, hard constraints, uncertainty, multiphysics coupling. Despite the success, many urgent challenges remain to be tackled, which also provides us opportunities to develop more robust, interpretable, and generalizable PIELM frameworks with applications in science and engineering.

翻译：近年来，物理信息极限学习机（PIELM）在物理信息机器学习领域迅速发展，以实现更高的计算效率和精度，我们对此深感欣喜。鉴于目前尚缺乏关于PIELM的总结或综述，我们愿借此机会分享对这一前景广阔的研究方向的见解与经验。我们观察到大量研究致力于求解具有陡峭梯度、非线性、高频特性、硬约束、不确定性及多物理场耦合的偏微分方程。尽管已取得显著成功，仍有许多紧迫挑战亟待解决，这也为我们提供了机遇，以开发更稳健、可解释且泛化能力更强的PIELM框架，推动其在科学与工程领域的应用。