Hutchinson Trace Estimation for High-Dimensional and High-Order
Physics-Informed Neural Networks

Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks

22 December 2023

George Karniadakis

Kenji Kawaguchi

Papers citing "Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks"

12 / 12 papers shown

Title
Integration Matters for Learning PDEs with Backwards SDEs Sungje Park Stephen Tu PINN 50 0 0 02 May 2025
Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators Zekun Shi Zheyuan Hu Min-Bin Lin Kenji Kawaguchi 130 4 0 27 Nov 2024
Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks Zheyuan Hu Kenji Kawaguchi Zhongqiang Zhang George Karniadakis AI4CE 44 1 0 17 Jun 2024
Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations Zheyuan Hu Zhongqiang Zhang George Karniadakis Kenji Kawaguchi 50 0 0 17 Jun 2024
Separable Physics-informed Neural Networks for Solving the BGK Model of the Boltzmann Equation Jaemin Oh Seung-Yeon Cho Seok-Bae Yun Eunbyung Park Youngjoon Hong AI4CE 41 5 0 10 Mar 2024
DOF: Accelerating High-order Differential Operators with Forward Propagation Ruichen Li Chuwei Wang Haotian Ye Di He Liwei Wang AI4CE 24 2 0 15 Feb 2024
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations Zheyuan Hu Zhongqiang Zhang George Karniadakis Kenji Kawaguchi 45 11 0 12 Feb 2024
Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs Zheyuan Hu Zhouhao Yang Yezhen Wang George Karniadakis Kenji Kawaguchi 39 9 0 26 Nov 2023
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks Zheyuan Hu K. Shukla George Karniadakis Kenji Kawaguchi PINN AI4CE 63 85 0 23 Jul 2023
VI-PINNs: Variance-involved Physics-informed Neural Networks for Fast and Accurate Prediction of Partial Differential Equations Bin Shan Ye Li Sheng-Jun Huang PINN 21 2 0 30 Nov 2022
Meta-learning PINN loss functions Apostolos F. Psaros Kenji Kawaguchi George Karniadakis PINN 35 96 0 12 Jul 2021
Physics-informed neural networks with hard constraints for inverse design Lu Lu R. Pestourie Wenjie Yao Zhicheng Wang F. Verdugo Steven G. Johnson PINN 39 493 0 09 Feb 2021