CHATGPT FOR COMPUTATIONAL TOPOLOGY.

IF 1.7 Q2 MATHEMATICS, APPLIED Foundations of data science (Springfield, Mo.) Pub Date : 2024-06-01 DOI:10.3934/fods.2024009
Jian Liu, Li Shen, Guo-Wei Wei
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Abstract

ChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathematical contexts has been somewhat constrained by its susceptibility to conceptual errors. Concurrently, topological data analysis (TDA), a relatively new discipline, has garnered substantial interest in recent years. Nonetheless, the advancement of TDA is impeded by the limited understanding of computational algorithms and coding proficiency among theoreticians. This work endeavors to bridge the gap between theoretical topological concepts and their practical implementation in computational topology through the utilization of ChatGPT. We showcase how a pure theoretician, devoid of computational experience and coding skills, can effectively transform mathematical formulations and concepts into functional codes for computational topology with the assistance of ChatGPT. Our strategy outlines a productive process wherein a mathematician trains ChatGPT on pure mathematical concepts, steers ChatGPT towards generating computational topology codes, and subsequently validates the generated codes using established examples. Our specific case studies encompass the computation of Betti numbers, Laplacian matrices, and Dirac matrices for simplicial complexes, as well as the persistence of various homologies and Laplacians. Furthermore, we explore the application of ChatGPT in computing recently developed topological theories for hypergraphs and digraphs, as well as the persistent harmonic space, which has not been computed in the literature, to the best of our knowledge. This work serves as an initial step towards effectively transforming pure mathematical theories into practical computational tools, with the ultimate goal of enabling real applications across diverse fields.

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用于计算拓扑学的 chatgpt
ChatGPT 是人工智能(AI)领域的一个重要里程碑,被广泛应用于各个领域。然而,由于易受概念错误的影响,它在数学背景下的有效性受到了一定的限制。与此同时,拓扑数据分析(TDA)作为一门相对较新的学科,近年来受到了广泛关注。然而,理论家们对计算算法和编码能力的理解有限,阻碍了拓扑数据分析的发展。本研究利用 ChatGPT,努力弥合理论拓扑概念与计算拓扑实际应用之间的差距。我们展示了缺乏计算经验和编码技能的纯理论者如何在 ChatGPT 的帮助下有效地将数学公式和概念转化为计算拓扑学的功能代码。我们的策略概述了这样一个富有成效的过程:数学家对 ChatGPT 进行纯数学概念的培训,引导 ChatGPT 生成计算拓扑代码,然后用已有的实例验证生成的代码。我们的具体案例研究包括简单复数的贝蒂数、拉普拉斯矩阵和狄拉克矩阵的计算,以及各种同调和拉普拉斯的持久性。此外,我们还探索了 ChatGPT 在计算最近开发的超图和数图拓扑理论以及持久谐波空间中的应用,据我们所知,持久谐波空间还没有在文献中计算过。这项工作是将纯数学理论有效转化为实用计算工具的第一步,其最终目标是在不同领域实现实际应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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CiteScore
3.30
自引率
0.00%
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0
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