A Physics Informed Machine Learning Framework for Optimal Sensor Placement and Parameter Estimation

The introduction of the Kernel-Adaptive Physics-Informed Extreme Learning Machine (KAPI-ELM) addresses challenges in solving partial differential equations (PDEs) with sharp gradients, enhancing the capabilities of existing physics-informed machine learning frameworks like PINNs and PI-ELMs. This new approach utilizes Bayesian optimization to refine Radial Basis Function (RBF) parameters, improving performance in both sharp gradient and smooth-flow scenarios.

A recent study has demonstrated the application of Physics-Informed Neural Networks (PINNs) to detect bifurcation phenomena in ecological migration models, specifically focusing on Hopf bifurcations. By integrating diffusion-advection-reaction equations with deep learning, this research offers a more efficient alternative to traditional numerical methods for solving partial differential equations (PDEs), which often require extensive computational resources.

Researchers have introduced a novel sampling strategy called WbAR, which utilizes white-box adversarial attacks to enhance the localization and refinement of failure regions in physics-informed neural networks (PINNs). This approach aims to address the challenges faced by vanilla PINNs when solving complex partial differential equations (PDEs) with multi-scale behaviors and sharp characteristics.