7 papers
CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations
Xiaodong Feng, Ziyu Sun, Tao Tang +2
Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss. For evolution equations, howev…
Amortized Filtering and Smoothing with Conditional Normalizing Flows
Tiangang Cui, Xiaodong Feng, Chenlong Pei +2
Bayesian filtering and smoothing are central to data assimilation in nonlinear dynamical systems. Recent advances in deep generative models provide flexible approximations of the a…
Latent representation learning based model correction and uncertainty quantification for PDEs
Wenwen Zhou, Xiaodong Feng, Ling Guo +1
Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning li…
Overcoming Spectral Bias via Cross-Attention
Xiaodong Feng, Tao Tang, Xiaoliang Wan +1
Spectral bias implies an imbalance in training dynamics, whereby high-frequency components may converge substantially more slowly than low-frequency ones. To alleviate this issue,…
LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process
Xiaodong Feng, Ling Guo, Xiaoliang Wan +3
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The…
Integral regularization PINNs for evolution equations
Xiaodong Feng, Haojiong Shangguan, Tao Tang +1
Evolution equations, including both ordinary differential equations (ODEs) and partial differential equations (PDEs), play a pivotal role in modeling dynamic systems. However, achi…
A hybrid FEM-PINN method for time-dependent partial differential equations
Xiaodong Feng, Haojiong Shangguan, Tao Tang +2
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks.…