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math.NA2026
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Zhen Zhang, Alessandro Alla, George Em Karniadakis
Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-infor…
math.NA2026
Neural Evolutionary Kernel Method: A Knowledge-Guided Framework for Solving Evolutionary PDEs
Shuo Ling, Wenjun Ying, Zhen Zhang
Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerg…