1 citations · 1 across the 7 of their papers we have counts for
8 papers
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…
Generating Samples of Stationary Distributions of Weakly Interacting Diffusion Models Without Finite Particle Truncation: A Weak Generative Approach
Zhiqiang Cai, Chengyu Liu, Xiang Zhou
Computing the stationary probability density and generating corresponding samples for the mean-field model of an infinite number of weakly interacting diffusion particles pose sign…
ChemBOMAS: Accelerated BO in Chemistry with LLM-Enhanced Multi-Agent System
Dong Han, Zhehong Ai, Pengxiang Cai +16
Bayesian optimization (BO) is a powerful tool for scientific discovery in chemistry, yet its efficiency is often hampered by the sparse experimental data and vast search space. Her…
Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition
Nathanael Tepakbong, Xiang Zhou, Ding-Xuan Zhou
We study the classical binary classification problem for hypothesis spaces of Deep Neural Networks (DNNs) under Tsybakov's low-noise condition with exponent , as well as its l…
Iterative Proximal-Minimization for Computing Saddle Points with Fixed Index
Shuting Gu, Hao Zhang, Xiaoqun Zhang +1
Computing saddle points with a prescribed Morse index on potential energy surfaces is crucial for characterizing transition states for nosie-induced rare transition events in physi…
StringNET: Neural Network based Variational Method for Transition Pathways
Jiayue Han, Shuting Gu, Xiang Zhou
Rare transition events in meta-stable systems under noisy fluctuations are crucial for many non-equilibrium physical and chemical processes. In these processes, the primary contrib…