Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs
The paper introduces GMM-PIELM, a probabilistic adaptive sampling framework that significantly improves the accuracy and conditioning of Physics-Informed Extreme Learning Machines for stiff PDEs by autonomously concentrating basis function centers in high-error regions like shock fronts, achieving orders-of-magnitude lower errors than baseline methods while retaining rapid closed-form training speeds.