Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times, Physics-Informed Extreme Learning Machines (PIELMs) offer a rapid, closed-form linear solution but are fundamentally limited by physics-agnostic, random initialization. We introduce the Gaussian Mixture Model Adaptive PIELM (GMM-PIELM), a probabilistic framework that learns a probability density function representing the ``location of physics'' for adaptively sampling kernels of PIELMs. By employing a weighted Expectation-Maximization (EM) algorithm, GMM...
| Authors | Akshay Govind Srinivasan, Balaji Srinivasan |
|---|---|
| Primary category | cs.CE |
| Published | 6 March 2026 |
| Last updated at source | 6 March 2026 |
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