35 citations · 50 across the 11 of their papers we have counts for
12 papers
Let There Be Light: Reflection, Refraction and Scattering for Neural Operators
Keke Wu, Yixuan Zhang, Jingrun Chen
Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PD…
Uniformly accurate structure-preserving neural surrogates for radiative transfer
Mengjia Bai, Jingrun Chen, Keke Wu
In this work, we propose a uniformly accurate, structure-preserving neural surrogate for the radiative transfer equation with periodic boundary conditions based on a multiscale par…
A Hybrid Discontinuous Galerkin Neural Network Method for Solving Hyperbolic Conservation Laws with Temporal Progressive Learning
Yan Shen, Jingrun Chen, Keke Wu
For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining t…
Asymptotic-Preserving Neural Networks based on Even-odd Decomposition for Multiscale Gray Radiative Transfer Equations
Keke Wu, Xizhe Xie, Wengu Chen +2
We present a novel Asymptotic-Preserving Neural Network (APNN) approach utilizing even-odd decomposition to tackle the nonlinear gray radiative transfer equations (GRTEs). Our AP l…
A Micro-Macro Decomposition-Based Asymptotic-Preserving Random Feature Method for Multiscale Radiative Transfer Equations
Jingrun Chen, Zheng Ma, Keke Wu
This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively address…
An Unsupervised Deep Learning Approach for the Wave Equation Inverse Problem
Xiong-Bin Yan, Keke Wu, Zhi-Qin John Xu +1
Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. H…
Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONets
Keke Wu, Xiong-bin Yan, Shi Jin +1
In this paper, we introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs) designed to address the multiscale time-dependent linear transpor…
Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations
Shi Jin, Zheng Ma, Keke Wu
In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equatio…
Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations
Shi Jin, Zheng Ma, Keke Wu
In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the networ…
Roughness Index for Loss Landscapes of Neural Network Models of Partial Differential Equations
Keke Wu, Xiangru Jian, Rui Du +2
Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are g…
Enforcing exact boundary and initial conditions in the deep mixed residual method
Liyao Lyu, Keke Wu, Rui Du +1
In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in cl…
A comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions
Jingrun Chen, Rui Du, Keke Wu
Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical…