7 papers · 1 filter
PDE Identification Using Noise Adaptive Differentiation in Strong Form (S-IDENT)
Roy Y. He, Sung Ha Kang
We explore identifying partial differential equations (PDEs) from noisy observations of single time-space trajectories. Recent developments show the benefits of identifying PDEs in…
From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs
Roy Y. He, Ying Liang, Hongkai Zhao +1
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning…
Phase-IDENT: Identification of Two-phase PDEs with Uncertainty Quantification
Edward L. Yang, Roy Y. He
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phen…
What Can One Expect When Solving PDEs Using Shallow Neural Networks?
Roy Y. He, Ying Liang, Hongkai Zhao +1
We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions.…
Stoch-IDENT: New Method and Mathematical Analysis for Identifying SPDEs from Data
Jianbo Cui, Roy Y. He
In this paper, we propose Stoch-IDENT, a novel framework for identifying stochastic partial differential equations (SPDEs) from observational data. Our method can handle linear and…
IDENT Review: Recent Advances in Identification of Differential Equations from Noisy Data
Roy Y. He, Hao Liu, Wenjing Liao +1
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the und…