8 papers
Boundary-Adapted PINNs for Elliptic Dirichlet Problems: A Priori Error Bounds with Application to Mean Escape Time Computation
Nathanael Tepakbong, Jun Fan, Xiang Zhou +1
Motivated by the numerical computation of the Mean Escape Time (MET) of a stochastic process from a bounded domain , we study elliptic…
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…
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…
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…
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…
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…