LLM4ED: Large Language Models for Automatic Equation Discovery

• URL: http://arxiv.org/abs/2405.07761v2
• Date: Mon, 22 Jul 2024 07:13:18 GMT
• Title: LLM4ED: Large Language Models for Automatic Equation Discovery
• Authors: Mengge Du, Yuntian Chen, Zhongzheng Wang, Longfeng Nie, Dongxiao Zhang,
• Abstract summary: We introduce a new framework that utilizes natural language-based prompts to guide large language models in automatically mining governing equations from data. Specifically, we first utilize the generation capability of LLMs to generate diverse equations in string form, and then evaluate the generated equations based on observations. Experiments are extensively conducted on both partial differential equations and ordinary differential equations.
• Score: 0.8644909837301149
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Equation discovery is aimed at directly extracting physical laws from data and has emerged as a pivotal research domain. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require the design of implementation of complex algorithms. In this paper, we introduce a new framework that utilizes natural language-based prompts to guide large language models (LLMs) in automatically mining governing equations from data. Specifically, we first utilize the generation capability of LLMs to generate diverse equations in string form, and then evaluate the generated equations based on observations. In the optimization phase, we propose two alternately iterated strategies to optimize generated equations collaboratively. The first strategy is to take LLMs as a black-box optimizer and achieve equation self-improvement based on historical samples and their performance. The second strategy is to instruct LLMs to perform evolutionary operators for global search. Experiments are extensively conducted on both partial differential equations and ordinary differential equations. Results demonstrate that our framework can discover effective equations to reveal the underlying physical laws under various nonlinear dynamic systems. Further comparisons are made with state-of-the-art models, demonstrating good stability and usability. Our framework substantially lowers the barriers to learning and applying equation discovery techniques, demonstrating the application potential of LLMs in the field of knowledge discovery.

Related papers

• LLM-based Optimization of Compound AI Systems: A Survey [64.39860384538338]
  In a compound AI system, components such as an LLM call, a retriever, a code interpreter, or tools are interconnected. Recent advancements enable end-to-end optimization of these parameters using an LLM. This paper presents a survey of the principles and emerging trends in LLM-based optimization of compound AI systems.
  arXiv  Detail & Related papers  (2024-10-21T18:06:25Z)
• MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data [22.262191225577244]
  We explore whether a similar approach can be applied to scientific foundation models (SFMs) We collect low-cost physics-informed neural network (PINN)-based approximated prior data in the form of solutions to partial differential equations (PDEs) constructed through an arbitrary linear combination of mathematical dictionaries. We provide experimental evidence on the one-dimensional convection-diffusion-reaction equation, which demonstrate that pre-training remains robust even with approximated prior data.
  arXiv  Detail & Related papers  (2024-10-09T00:52:00Z)
• EVOLvE: Evaluating and Optimizing LLMs For Exploration [76.66831821738927]
  Large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty. We measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications. Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs.
  arXiv  Detail & Related papers  (2024-10-08T17:54:03Z)
• Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text [7.136205674624813]
  We use pretrained Large Language Models (LLMs) to integrate various amounts known system information into PDE learning. Our approach significantly outperforms our baseline model, FactFormer, in both next-step prediction and autore rollout performance. Further analysis shows that pretrained LLMs provide highly structured latent space that is consistent with the amount of system information provided through text.
  arXiv  Detail & Related papers  (2024-10-02T00:19:20Z)
• Large Language Models as Surrogate Models in Evolutionary Algorithms: A Preliminary Study [5.6787965501364335]
  Surrogate-assisted selection is a core step in evolutionary algorithms to solve expensive optimization problems. Traditionally, this has relied on conventional machine learning methods, leveraging historical evaluated evaluations to predict the performance of new solutions. In this work, we propose a novel surrogate model based purely on LLM inference capabilities, eliminating the need for training.
  arXiv  Detail & Related papers  (2024-06-15T15:54:00Z)
• LLM-SR: Scientific Equation Discovery via Programming with Large Language Models [17.64574496035502]
  Traditional methods of equation discovery, known as symbolic regression, largely focus on extracting equations from data alone. We introduce LLM-SR, a novel approach that leverages the scientific knowledge and robust code generation capabilities of Large Language Models. We demonstrate LLM-SR's effectiveness across three diverse scientific domains, where it discovers physically accurate equations.
  arXiv  Detail & Related papers  (2024-04-29T03:30:06Z)
• Machine Learning Insides OptVerse AI Solver: Design Principles and Applications [74.67495900436728]
  We present a comprehensive study on the integration of machine learning (ML) techniques into Huawei Cloud's OptVerse AI solver. We showcase our methods for generating complex SAT and MILP instances utilizing generative models that mirror multifaceted structures of real-world problem. We detail the incorporation of state-of-the-art parameter tuning algorithms which markedly elevate solver performance.
  arXiv  Detail & Related papers  (2024-01-11T15:02:15Z)
• Towards Constituting Mathematical Structures for Learning to Optimize [101.80359461134087]
  A technique that utilizes machine learning to learn an optimization algorithm automatically from data has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. We propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems.
  arXiv  Detail & Related papers  (2023-05-29T19:37:28Z)
• CodeGen2: Lessons for Training LLMs on Programming and Natural Languages [116.74407069443895]
  We unify encoder and decoder-based models into a single prefix-LM. For learning methods, we explore the claim of a "free lunch" hypothesis. For data distributions, the effect of a mixture distribution and multi-epoch training of programming and natural languages on model performance is explored.
  arXiv  Detail & Related papers  (2023-05-03T17:55:25Z)
• Representation Learning with Multi-Step Inverse Kinematics: An Efficient and Optimal Approach to Rich-Observation RL [106.82295532402335]
  Existing reinforcement learning algorithms suffer from computational intractability, strong statistical assumptions, and suboptimal sample complexity. We provide the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics.
  arXiv  Detail & Related papers  (2023-04-12T14:51:47Z)
• Recurrent Localization Networks applied to the Lippmann-Schwinger Equation [0.0]
  We present a novel machine learning approach for solving equations of the generalized Lippmann-Schwinger (L-S) type. As part of a learning-based loop unrolling, we use a recurrent convolutional neural network to iteratively solve the governing equations for a field of interest. We demonstrate our learning approach on the two-phase elastic localization problem, where it achieves excellent accuracy on the predictions of the local (i.e., voxel-level) elastic strains.
  arXiv  Detail & Related papers  (2021-01-29T20:54:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.