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Machine Learning for Symbolic Mathematics and Physics Discovery /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Machine Learning for Symbolic Mathematics and Physics Discovery /Kazem Meidani.
Author:	Meidani, Kazem,
Description:	1 electronic resource (203 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-07, Section: B.
Notes:	Advisors: Barati Farimani, Amir Committee members: McComb, Christopher; Welleck, Sean; Reddy, Chandan; Cranmer, Miles.
Contained By:	Dissertations Abstracts International86-07B.
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31563371
ISBN:	9798346890584

Machine Learning for Symbolic Mathematics and Physics Discovery /
Meidani, Kazem,

Machine Learning for Symbolic Mathematics and Physics Discovery /Kazem Meidani. - 1 electronic resource (203 pages)

Source: Dissertations Abstracts International, Volume: 86-07, Section: B.

Mathematics has proven to be an unreasonably effective language for modeling complex scientific phenomena. Discovering symbolic governing equations from empirical data is crucial for comprehension and prediction of physical systems. While traditional theory-driven scientific discovery can be arduous, the growth in scientific data availability and advancements in artificial intelligence offer new avenues for automating this process. Symbolic regression, which aims to uncover interpretable mathematical models from observations, has emerged as a powerful tool in this domain. However, challenges persist in data availability, robustness, model generalization, and incorporation of domain-specific knowledge.This dissertation presents a series of innovations in symbolic regression to address these limitations. The research begins with the Identification of Parametric dynamical systems using Integer Programming (IP2), which integrates dimension analysis and integer programming in linear models with nonlinear basis functions to recover dynamical system equations from noisy video data. Moving from linear models to neural symbolic regression, Transformer-based Planning for Symbolic Regression (TPSR) combines Monte Carlo tree search with pre-trained transformers to optimize symbolic equation generation, enhancing performance over traditional models. To bridge the gap between symbolic equations and numeric data, the Symbolic-Numeric Integrated Pre-training (SNIP) model is introduced. SNIP employs contrastive learning to develop a unified understanding between these domains, enabling cross-modal property prediction and symbolic regression via optimization in a rich continuous representation space. The research culminates in LLM-SR, a novel approach leveraging Large Language Models (LLMs) for scientific equation discovery. By treating equations as programs and combining LLMs' scientific priors with evolutionary search, LLM-SR demonstrates superior performance across diverse scientific domains, discovering physically accurate equations with improved fit and generalization.These works collectively contribute to the field of symbolic regression and scientific discovery, exploring connections between symbolic methods, neural networks, and large language models. The approaches presented aim to enhance the interpretability, accuracy, and reliability of data-driven scientific discovery. By exploring diverse approaches, from linear models to LLMs, this research contributes to the development of AI systems capable of understanding and uncovering mathematical models of physical phenomena. These advancements represent steps toward the vision of an "AI Scientist," aiming to support the scientific community in efficiently exploring complex systems and potentially accelerating the process of scientific discovery.

English

ISBN: 9798346890584Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Deep learning

Machine Learning for Symbolic Mathematics and Physics Discovery /
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520 $a Mathematics has proven to be an unreasonably effective language for modeling complex scientific phenomena. Discovering symbolic governing equations from empirical data is crucial for comprehension and prediction of physical systems. While traditional theory-driven scientific discovery can be arduous, the growth in scientific data availability and advancements in artificial intelligence offer new avenues for automating this process. Symbolic regression, which aims to uncover interpretable mathematical models from observations, has emerged as a powerful tool in this domain. However, challenges persist in data availability, robustness, model generalization, and incorporation of domain-specific knowledge.This dissertation presents a series of innovations in symbolic regression to address these limitations. The research begins with the Identification of Parametric dynamical systems using Integer Programming (IP2), which integrates dimension analysis and integer programming in linear models with nonlinear basis functions to recover dynamical system equations from noisy video data. Moving from linear models to neural symbolic regression, Transformer-based Planning for Symbolic Regression (TPSR) combines Monte Carlo tree search with pre-trained transformers to optimize symbolic equation generation, enhancing performance over traditional models. To bridge the gap between symbolic equations and numeric data, the Symbolic-Numeric Integrated Pre-training (SNIP) model is introduced. SNIP employs contrastive learning to develop a unified understanding between these domains, enabling cross-modal property prediction and symbolic regression via optimization in a rich continuous representation space. The research culminates in LLM-SR, a novel approach leveraging Large Language Models (LLMs) for scientific equation discovery. By treating equations as programs and combining LLMs' scientific priors with evolutionary search, LLM-SR demonstrates superior performance across diverse scientific domains, discovering physically accurate equations with improved fit and generalization.These works collectively contribute to the field of symbolic regression and scientific discovery, exploring connections between symbolic methods, neural networks, and large language models. The approaches presented aim to enhance the interpretability, accuracy, and reliability of data-driven scientific discovery. By exploring diverse approaches, from linear models to LLMs, this research contributes to the development of AI systems capable of understanding and uncovering mathematical models of physical phenomena. These advancements represent steps toward the vision of an "AI Scientist," aiming to support the scientific community in efficiently exploring complex systems and potentially accelerating the process of scientific discovery.
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