Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts
This addresses the challenge of physics-informed domain decomposition for researchers in computational physics and engineering, though it appears incremental as it builds on existing PINN methods.
The study tackled the problem of identifying spatial subdomains with specific governing physics in ill-posed inverse problems by introducing an unsupervised framework using partition of unity networks, which improved accuracy in applications like porous media thermal ablation and ice-sheet modeling.
Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing physics. It uses the partition of unity networks (POUs) to divide the space into subdomains, assigning unique nonlinear model parameters to each, which are integrated into the physics model. A vital feature of this method is a physics residual-based loss function that detects variations in physical properties without requiring labeled data. This approach enables the discovery of spatial decompositions and nonlinear parameters in partial differential equations (PDEs), optimizing the solution space by dividing it into subdomains and improving accuracy. Its effectiveness is demonstrated through applications in porous media thermal ablation and ice-sheet modeling, showcasing its potential for tackling real-world physics challenges.