用于自动发现非线性动力学方程的大型语言模型

IF 4.1 2区 工程技术 Q1 MECHANICS Physics of Fluids Pub Date : 2024-09-10 DOI:10.1063/5.0224297
Mengge Du, Yuntian Chen, Zhongzheng Wang, Longfeng Nie, Dongxiao Zhang
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引用次数: 0

摘要

方程发现的目的是从数据中直接提取物理规律,它已成为非线性系统的一个关键研究领域。以往基于符号数学的方法取得了长足的进步,但通常需要手工制定表示规则和复杂的优化算法。在本文中,我们介绍了一种新颖的框架,它利用基于自然语言的提示来引导大型语言模型(LLM)自动从数据中提取支配方程。具体来说,我们首先利用 LLM 的生成能力以字符串形式生成各种候选方程,然后根据观测结果对生成的方程进行评估。保留最佳方程,并利用 LLM 的推理能力进一步迭代完善。我们提出了两种交替迭代的策略来协同优化生成的方程。第一种策略将 LLMs 作为黑盒优化器,根据历史样本及其性能实现方程的自我改进。第二种策略指示 LLMs 执行全局搜索的进化操作。我们对偏微分方程描述的各种非线性系统进行了实验,包括伯格斯方程、查菲-因方特方程和纳维-斯托克斯方程。结果表明,我们的框架可以发现正确的方程,揭示基本的物理规律。与最先进的广泛常微分方程模型的进一步比较表明,我们的框架发现的方程具有物理意义,并能更好地概括未见数据。
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Large language models for automatic equation discovery of nonlinear dynamics
Equation discovery aims to directly extract physical laws from data and has emerged as a pivotal research domain in nonlinear systems. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require handcrafted representation rules and complex optimization algorithms. In this paper, we introduce a novel framework that utilizes natural language-based prompts to guide large language models (LLMs) in automatically extracting governing equations from data. Specifically, we first utilize the generation capability of LLMs to generate diverse candidate equations in string form and then evaluate the generated equations based on observations. The best equations are preserved and further refined iteratively using the reasoning capacity of LLMs. We propose two alternately iterated strategies to collaboratively optimize the generated equations. The first strategy uses LLMs as a black-box optimizer to achieve equation self-improvement based on historical samples and their performance. The second strategy instructs LLMs to perform evolutionary operations for a global search. Experiments are conducted on various nonlinear systems described by partial differential equations, including the Burgers equation, the Chafee–Infante equation, and the Navier–Stokes equation. The results demonstrate that our framework can discover correct equations that reveal the underlying physical laws. Further comparisons with state-of-the-art models on extensive ordinary differential equations showcase that the equations discovered by our framework possess physical meaning and better generalization capability on unseen data.
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来源期刊
Physics of Fluids
Physics of Fluids 物理-力学
CiteScore
6.50
自引率
41.30%
发文量
2063
审稿时长
2.6 months
期刊介绍: Physics of Fluids (PoF) is a preeminent journal devoted to publishing original theoretical, computational, and experimental contributions to the understanding of the dynamics of gases, liquids, and complex or multiphase fluids. Topics published in PoF are diverse and reflect the most important subjects in fluid dynamics, including, but not limited to: -Acoustics -Aerospace and aeronautical flow -Astrophysical flow -Biofluid mechanics -Cavitation and cavitating flows -Combustion flows -Complex fluids -Compressible flow -Computational fluid dynamics -Contact lines -Continuum mechanics -Convection -Cryogenic flow -Droplets -Electrical and magnetic effects in fluid flow -Foam, bubble, and film mechanics -Flow control -Flow instability and transition -Flow orientation and anisotropy -Flows with other transport phenomena -Flows with complex boundary conditions -Flow visualization -Fluid mechanics -Fluid physical properties -Fluid–structure interactions -Free surface flows -Geophysical flow -Interfacial flow -Knudsen flow -Laminar flow -Liquid crystals -Mathematics of fluids -Micro- and nanofluid mechanics -Mixing -Molecular theory -Nanofluidics -Particulate, multiphase, and granular flow -Processing flows -Relativistic fluid mechanics -Rotating flows -Shock wave phenomena -Soft matter -Stratified flows -Supercritical fluids -Superfluidity -Thermodynamics of flow systems -Transonic flow -Turbulent flow -Viscous and non-Newtonian flow -Viscoelasticity -Vortex dynamics -Waves
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