5 papers
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…
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…
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…
Time-Series Forecasting, Knowledge Distillation, and Refinement within a Multimodal PDE Foundation Model
Derek Jollie, Jingmin Sun, Zecheng Zhang +1
Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-depe…
PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics
Yuxuan Liu, Jingmin Sun, Xinjie He +3
We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics…