37 citations · 75 across the 11 of their papers we have counts for
7 papers · 1 filter
State-space models are accurate and efficient neural operators for dynamical systems
Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen +2
Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable soluti…
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang +1
Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional nu…
Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations
Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis +1
We introduce an innovative approach for solving high-dimensional Fokker-Planck-Lévy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance,…
Tensor neural networks for high-dimensional Fokker-Planck equations
Taorui Wang, Zheyuan Hu, Kenji Kawaguchi +2
We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor product…
Towards Robust Out-of-Distribution Generalization Bounds via Sharpness
Yingtian Zou, Kenji Kawaguchi, Yingnan Liu +3
Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different…
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis +1
The Fokker-Planck (FP) equation is a foundational PDE in stochastic processes. However, curse of dimensionality (CoD) poses challenge when dealing with high-dimensional FP PDEs. Al…
Towards Continual Learning Desiderata via HSIC-Bottleneck Orthogonalization and Equiangular Embedding
Depeng Li, Tianqi Wang, Junwei Chen +3
Deep neural networks are susceptible to catastrophic forgetting when trained on sequential tasks. Various continual learning (CL) methods often rely on exemplar buffers or/and netw…