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<p>In this paper, we present a symbolic dataset, named FIE-500k, for the second-kind Fredholm integral equations. Our approach systematically generates a dataset for these types of integral equations, enabling various applications in language models, such as modeling and symbolic solving of integral equations. Each record in the dataset includes the key terms of a second-kind Fredholm integral equation. To ensure the generation of valid mathematical expressions, we employ context-free grammars. The basis functions used in these grammars are carefully selected to cover a wide range of function types. The proposed dataset comprises 500,000 records, refined to ensure balance across different function types. A link to download the dataset, along with the code used for its generation, is provided in this paper. Researchers and practitioners can freely download the dataset, generate additional samples, and further enhance the proposed method.</p>

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A symbolic dataset for large language models to solve second kind Fredholm integral equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月8日

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  • Hassan Dana Mazraeh,
  • Sepehr Eslami,
  • Alireza Afzal Aghaei,
  • Kourosh Parand

摘要

In this paper, we present a symbolic dataset, named FIE-500k, for the second-kind Fredholm integral equations. Our approach systematically generates a dataset for these types of integral equations, enabling various applications in language models, such as modeling and symbolic solving of integral equations. Each record in the dataset includes the key terms of a second-kind Fredholm integral equation. To ensure the generation of valid mathematical expressions, we employ context-free grammars. The basis functions used in these grammars are carefully selected to cover a wide range of function types. The proposed dataset comprises 500,000 records, refined to ensure balance across different function types. A link to download the dataset, along with the code used for its generation, is provided in this paper. Researchers and practitioners can freely download the dataset, generate additional samples, and further enhance the proposed method.