1 citations · 2 across the 9 of their papers we have counts for
9 papers
ROMNet: a hybrid reduced order modeling and machine learning approach to waveform inversion
Liliana Borcea, Alexander Mamonov, Kui Ren +2
Waveform inversion seeks to estimate the wave speed of a heterogeneous, inaccessible medium, from time-resolved measurements of the waves at user controlled sensors. We consider th…
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.…
Efficient Kilometer-Scale Precipitation Downscaling with Conditional Wavelet Diffusion
Chugang Yi, Minghan Yu, Weikang Qian +2
Effective hydrological modeling and extreme weather analysis demand precipitation data at a kilometer-scale resolution, which is significantly finer than the 10 km scale offered by…
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…
FMint: Bridging Human Designed and Data Pretrained Models for Differential Equation Foundation Model
Zezheng Song, Jiaxin Yuan, Haizhao Yang
The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With…
A Fast Algorithm for the Finite Expression Method in Learning Dynamics on Complex Networks
Zezheng Song, Chunmei Wang, Haizhao Yang
Complex network data is prevalent in various real-world domains, including physical, technological, and biological systems. Despite this prevalence, predicting trends and understan…
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…