Enforcing hidden physics in physics-informed neural networks

A new framework called RB-DeepONet has been introduced to enhance the efficiency of solving parametric partial differential equations (PDEs) with independently varying boundary and source data. This hybrid operator-learning model combines reduced-basis numerical structures with the DeepONet architecture, allowing for improved physical interpretability and stability while ensuring certified error control.

Researchers have introduced Residual Risk-Aware Physics-Informed Neural Networks (RRaPINNs), a novel framework that optimizes tail-focused objectives using Conditional Value-at-Risk (CVaR) and a Mean-Excess (ME) surrogate penalty. This approach aims to enhance the training of physics-informed neural networks (PINNs) by reducing localized errors in the context of various partial differential equations (PDEs) including Burgers and Poisson equations.

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.