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A Priori Error Bounds for Boundary-Adapted PINNs Solving Elliptic Dirichlet Problems
Nathanael Tepakbong, Jun Fan, Xiang Zhou +1
We study the numerical resolution of uniformly elliptic Dirichlet boundary value problems (BVPs) by minimization of the PDE residual over a hypothesis space of Neural Networks made…
Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds
Nathanael Tepakbong, Hanyu Hu, Chengyu Liu +1
Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-con…
Early warning prediction: Onsager-Machlup vs Schrödinger
Xiaoai Xu, Yixuan Zhou, Xiang Zhou +2
Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristi…