1 citations · 2 across the 7 of their papers we have counts for
7 papers
GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems
Meenakshi Krishnan, Pranav Pulijala, Ke Chen +2
Operator learning for partial differential equations (PDEs) on arbitrary geometries builds fast neural surrogates for large-scale simulation. Although recent geometry-adaptive neur…
Data Completion for Electrical Impedance Tomography by Conditional Diffusion Models
Ke Chen, Haizhao Yang, Chugang Yi
Data scarcity is a fundamental barrier in Electrical Impedance Tomography (EIT), as undersampled Dirichlet-to-Neumann (DtN) measurements can substantially degrade conductivity reco…
Error analysis for learning the time-stepping operator of evolutionary PDEs
Ke Chen, Meenakshi Krishnan, Haizhao Yang
Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems.…
Neural Correction Operator: A Reliable and Fast Approach for Electrical Impedance Tomography
Amit Bhat, Ke Chen, Chunmei Wang
Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its…
Towards Better Generalization: Weight Decay Induces Low-rank Bias for Neural Networks
Ke Chen, Chugang Yi, Haizhao Yang
We study the implicit bias towards low-rank weight matrices when training neural networks (NN) with Weight Decay (WD). We prove that when a ReLU NN is sufficiently trained with Sto…
Pseudo-differential integral autoencoder network for inverse PDE operators
Ke Chen, Jasen Lai, Chunmei Wang
Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within…
Let data talk: data-regularized operator learning theory for inverse problems
Ke Chen, Chunmei Wang, Haizhao Yang
Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determini…