34 citations · 35 across the 9 of their papers we have counts for
7 papers · 1 filter
Structure-preserving upwind Lagrange multiplier schemes for solid-state dewetting with a logarithmic Flory--Huggins potential
Qiong-Ao Huang, Ying-wei Wang, Cheng Yuan
Phase-field simulations of solid-state dewetting based on polynomial potentials may exhibit spurious bulk-diffusion coarsening, inconsistent with the surface-diffusion-dominated ph…
An alternating learning-based collocation method for solving inverse elliptic problems
Zhizhong Kong, Jerry Zhijian Yang, Cheng Yuan
We propose the Alternating Learning-Based Collocation (ALBC) method for solving inverse elliptic problems. Our approach employs sinusoidal shallow networks as adaptive basis genera…
A weighted scalar auxiliary variable method for solving gradient flows: bridging the nonlinear energy-based and Lagrange multiplier approaches
Qiong-Ao Huang, Wei Jiang, Jerry Zhijian Yang +1
Two primary scalar auxiliary variable (SAV) approaches are widely applied for simulating gradient flow systems, i.e., the nonlinear energy-based approach and the Lagrange multiplie…
Nonlinear Assimilation via Score-based Sequential Langevin Sampling
Zhao Ding, Chenguang Duan, Yuling Jiao +3
This paper introduces score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed…
Solving the inverse source problem of the fractional Poisson equation by MC-fPINNs
Rui Sheng, Peiying Wu, Jerry Zhijian Yang +1
In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks and …
A Stabilized Physics Informed Neural Networks Method for Wave Equations
Yuling Jiao, Yuhui Liu, Jerry Zhijian Yang +1
In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretica…
Deep Neural Network Approximation of Composition Functions: with application to PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +2
In this paper, we focus on approximating a natural class of functions that are compositions of smooth functions. Unlike the low-dimensional support assumption on the covariate, we…