MLLM-based Discovery of Intrinsic Coordinates and Governing Equations from High-Dimensional Data

TL;DR

This paper introduces a zero-shot approach using multimodal large language models to automatically identify physical coordinates and governing equations from high-dimensional scientific data, enhancing understanding of complex systems.

Contribution

It leverages enhanced visual prompts and domain knowledge in MLLM to navigate high-dimensional equation spaces without prior training, enabling effective discovery of physical laws.

Findings

Improved long-term extrapolation accuracy by approximately 27%.

Effective discovery of physical coordinates and equations from simulated and real data.

Demonstrated capability in high-dimensional and complex systems.

Abstract

Discovering governing equations from scientific data is crucial for understanding the evolution of systems, and is typically framed as a search problem within a candidate equation space. However, the high-dimensional nature of dynamical systems leads to an exponentially expanding equation space, making the search process extremely challenging. The visual perception and pre-trained scientific knowledge of multimodal large language models (MLLM) hold promise for providing effective navigation in high-dimensional equation spaces. In this paper, we propose a zero-shot method based on MLLM for automatically discovering physical coordinates and governing equations from high-dimensional data. Specifically, we design a series of enhanced visual prompts for MLLM to enhance its spatial perception. In addition, MLLM's domain knowledge is employed to navigate the search process within the equation space. Quantitative and qualitative evaluations on two representative types of systems demonstrate that the proposed method effectively discovers the physical coordinates and equations from both simulated and real experimental data, with long-term extrapolation accuracy improved by approximately 26.96% compared to the baseline.