3 papers
math.NA2025
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.…
math.NA2025
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…
cs.LG2024
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…