37 citations · 75 across the 11 of their papers we have counts for
12 papers
PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations
Jin Song, Kenji Kawaguchi, Zhenya Yan
Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. How…
HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals
Xianquan Yan, Hakan Akgün, Kenji Kawaguchi +2
AI is transforming scientific research by revealing new ways to understand complex physical systems, but its impact remains constrained by the lack of large, high-quality domain-sp…
Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators
Zekun Shi, Zheyuan Hu, Min Lin +1
Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to …
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…
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks
Zheyuan Hu, Zekun Shi, George Em Karniadakis +1
Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data…
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs
Zheyuan Hu, Zhouhao Yang, Yezhen Wang +2
While physics-informed neural networks (PINNs) have been proven effective for low-dimensional partial differential equations (PDEs), the computational cost remains a hurdle in high…