Information-distilled physics informed deep learning for high order differential inverse problems with extreme discontinuities

Standard physics informed deep learning and their enhanced variants encounter challenges in addressing inverse problems characterized by extreme discontinuities and high-order parameterized differential equations due to the use of globally smooth activation functions, especially when the unknown parameters exhibit spatially distributed characteristics. Phenomena such as discontinuous loads, boundary truncations, and abrupt changes in material properties introduce singularities in the derivatives, which in turn lead to ill-conditioned information in the gradient flow. To address these limitations, here we propose an information-distilled physics-informed deep-learning framework that combines reduced-order modeling, multi-level domain decomposition, and an ill-conditioning-suppression mechanism. The framework captures rapid variations in variables within highly localized regions induced by discontinuities. Through an information propagation mechanism and information distillation, the ill-conditioned information in the gradient flow of the system is suppressed. Even in scenarios where specific subnetworks fail, the framework preserves the accuracy of the majority of subnetworks.