Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text

TL;DR

This paper investigates leveraging pretrained Large Language Models to incorporate textual system information into PDE surrogate models, enhancing prediction accuracy with minimal numerical data across various complex benchmarks.

Contribution

It introduces a multimodal fusion approach using LLMs to integrate textual descriptions into PDE learning, demonstrating improved surrogate modeling performance.

Findings

LLMs effectively utilize textual system info for PDE prediction

Multimodal fusion improves accuracy over numerical-only models

Pretrained LLMs generalize well across diverse PDE benchmarks

Abstract

Solving Partial Differential Equations (PDEs) is ubiquitous in science and engineering. Computational complexity and difficulty in writing numerical solvers has motivated the development of data-driven machine learning techniques to generate solutions quickly. The recent rise in popularity of Large Language Models (LLMs) has enabled easy integration of text in multimodal machine learning models, allowing easy integration of additional system information such as boundary conditions and governing equations through text. In this work, we explore using pretrained LLMs to integrate various amounts of known system information into PDE learning. Using FactFormer as our testing backbone, we add a multimodal block to fuse numerical and textual information. We compare sentence-level embeddings, word-level embeddings, and a standard tokenizer across 2D Heat, Burgers, Navier-Stokes, and Shallow-Water data sets. These challenging benchmarks show that pretrained LLMs are able to utilize text descriptions of system information and enable accurate prediction using only initial conditions.