3 citations · 3 across the 8 of their papers we have counts for
9 papers
Kernel Methods for Learning Operators with Multiple Inputs and Outputs
Adrien Weihs, Chunyang Liao, Jingmin Sun +1
Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning. We introduce a general kernel-based encoder-decoder framework for oper…
Geometric Prototype Learning in Quantum Hilbert Space with Matrix Product States
Kun Zhang, Lei Ding, Sheng-Chen Bai +4
Quantum probability provides a novel framework for formulating machine-learning (ML) problems in Hilbert space. We introduce a prototype-based learning scheme where class represent…
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…
LeMON: Learning to Learn Multi-Operator Networks
Jingmin Sun, Zecheng Zhang, Hayden Schaeffer
Single-operator learning involves training a deep neural network to learn a specific operator, whereas recent work in multi-operator learning uses an operator embedding structure t…
Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation
Jingmin Sun, Yuxuan Liu, Zecheng Zhang +1
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foun…