Bias-Variance Trade-off in Physics-Informed Neural Networks with
Randomized Smoothing for High-Dimensional PDEs

Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

26 November 2023

George Karniadakis

Kenji Kawaguchi

Papers citing "Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs"

9 / 9 papers shown

Title
Memory-Efficient LLM Training by Various-Grained Low-Rank Projection of Gradients Yezhen Wang Zhouhao Yang Brian K Chen Fanyi Pu Bo-wen Li Tianyu Gao Kenji Kawaguchi 41 0 0 03 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
Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions Mohan Ren Zhihao Fang Keren Li Anirbit Mukherjee PINN AI4CE 39 0 0 30 Jul 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
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations Zheyuan Hu Zhongqiang Zhang George Karniadakis Kenji Kawaguchi 48 11 0 12 Feb 2024
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks Zheyuan Hu Zekun Shi George Karniadakis Kenji Kawaguchi AI4CE PINN 41 21 0 22 Dec 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
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