7 papers
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…
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…
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…
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 …
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…
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…