6 papers
A Schauder Basis for Multiparameter Persistence
Peter Bubenik, Zachariah Ross
Certain classes of multiparameter persistence modules may be encoded as signed barcodes, represented as points in a polyhedral subset of Euclidean space, we refer to as signed pers…
Mesh-Informed Neural Operator : A Transformer Generative Approach
Yaozhong Shi, Zachary E. Ross, Domniki Asimaki +1
Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential…
Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multi-Stage Training
Qingkai Kong, Caifeng Zou, Youngsoo Choi +5
The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulatio…
Ambient Noise Full Waveform Inversion with Neural Operators
Caifeng Zou, Zachary E. Ross, Robert W. Clayton +2
Numerical simulations of seismic wave propagation are crucial for investigating velocity structures and improving seismic hazard assessment. However, standard methods such as finit…
InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences
Hongkai Zheng, Wenda Chu, Bingliang Zhang +9
Plug-and-play diffusion priors (PnPDP) have emerged as a promising research direction for solving inverse problems. However, current studies primarily focus on natural image restor…
Stochastic Process Learning via Operator Flow Matching
Yaozhong Shi, Zachary E. Ross, Domniki Asimaki +1
Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for lea…