175 citations · 317 across the 46 of their papers we have counts for
8 papers · 1 filter
PI-MFM: Physics-informed multimodal foundation model for solving partial differential equations
Min Zhu, Jingmin Sun, Zecheng Zhang +2
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across…
Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space
Xinyue Yu, Hayden Schaeffer
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-…
Finite Element Representation Network (FERN) for Operator Learning with a Localized Trainable Basis
Zecheng Zhang, Hao Liu, Guosheng Fu +2
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from inp…
A Deep Learning Framework for Multi-Operator Learning: Architectures and Approximation Theory
Adrien Weihs, Jingmin Sun, Zecheng Zhang +1
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces…
AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates
Minxin Zhang, Yuxuan Liu, Hayden Schaeffer
The recently proposed Muon optimizer updates weight matrices via orthogonalized momentum and has demonstrated strong empirical success in large language model training. However, it…
Cauchy Random Features for Operator Learning in Sobolev Space
Chunyang Liao, Deanna Needell, Hayden Schaeffer
Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven b…
A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions
Elisa Negrini, Yuxuan Liu, Liu Yang +2
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal c…
BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics
Yuxuan Liu, Jingmin Sun, Hayden Schaeffer
We introduce BCAT, a PDE foundation model designed for autoregressive prediction of solutions to two dimensional fluid dynamics problems. Our approach uses a block causal transform…