New Modules Enhance Physics-Informed AI for PDEs

New research proposes integrating feature interaction modules, inspired by factorization machines, into Physics-Informed Neural Networks (PINNs) and neural operators. This enhancement aims to significantly improve the models' ability to represent and solve solution manifolds for parameterized partial differential equations (PDEs). The core idea is to explicitly model spatio-temporal variable interactions, drawing parallels to the second-order Taylor expansion for characterizing variable couplings. The resulting FM-PINN model demonstrates improved accuracy for smooth high-order PDEs. Furthermore, by grouping features like spatial coordinates, time, and physical parameters, the FM-Operator and FM-DeepONet models prove particularly effective for complex problems such as nonlinear conservation laws and those with sharp gradients or discontinuities, showing substantial accuracy gains on shock-dominated equations.