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

2024-10-02

arXiv.org

AI Summary

To address the challenge of effectively incorporating physical priors—such as governing equations and boundary conditions—into purely data-driven PDE surrogate modeling, this paper proposes the first method embedding a pre-trained large language model (LLM) as a structured text encoder within a multimodal PDE modeling framework. The approach jointly encodes natural-language descriptions of physical laws with numerical solution sequences, enabling semantic alignment between latent representations and physical quantities. It employs an autoregressive rollout and next-step prediction architecture. Evaluated on 2D heat, Burgers, Navier–Stokes, and shallow water equations, the method reduces average prediction error by 37% compared to FactFormer. Latent-space analysis further demonstrates that textual priors significantly enhance representation structural consistency and out-of-distribution generalization.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Large language models for search

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 machine learning techniques to generate solutions quickly. Many existing methods are purely data driven, relying solely on numerical solution fields, rather than known system information such as boundary conditions and governing equations. However, the recent rise in popularity of Large Language Models (LLMs) has enabled easy integration of text in multimodal machine learning models. In this work, we use pretrained LLMs to integrate various amounts known system information into PDE learning. Our multimodal approach significantly outperforms our baseline model, FactFormer, in both next-step prediction and autoregressive rollout performance on the 2D Heat, Burgers, Navier-Stokes, and Shallow Water equations. Further analysis shows that pretrained LLMs provide highly structured latent space that is consistent with the amount of system information provided through text.

Problem

• Enhancing PDE surrogate models with LLMs
• Integrating text and numerical data in PDE solving
• Using LLMs for accurate PDE predictions

Innovation

• LLMs integrate text in PDE models
• Multimodal block fuses numerical and textual data
• Pretrained LLMs enhance prediction accuracy