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A symbolic dataset for large language models to solve second kind Fredholm integral equations
Hassan Dana Mazraeh1, Sepehr Eslami2, Alireza Afzal Aghaei3
1School of Mathematics and Computer Sciences, Damghan University, Damghan, P.O. Box 36715-364, Iran.
We introduce FIE-500k, a large symbolic dataset for second-kind Fredholm integral equations. This dataset aids language models in modeling and symbolically solving these complex mathematical equations.
Area of Science:
- Mathematics
- Computer Science
- Artificial Intelligence
Background:
- Second-kind Fredholm integral equations are crucial in various scientific and engineering fields.
- Existing datasets for these equations are limited, hindering advancements in computational methods.
- Symbolic approaches offer potential for precise modeling and solving.
Purpose of the Study:
- To introduce FIE-500k, a comprehensive symbolic dataset for second-kind Fredholm integral equations.
- To facilitate the development and application of language models in integral equation analysis.
- To provide a valuable resource for researchers and practitioners in computational mathematics.
Main Methods:
- Systematic generation of symbolic data for second-kind Fredholm integral equations.
- Utilization of context-free grammars to ensure mathematical validity of expressions.
- Careful selection of basis functions to encompass diverse function types.
- Refinement of 500,000 records for balanced representation across function categories.
Main Results:
- Creation of the FIE-500k dataset with 500,000 records.
- Demonstration of a robust method for generating symbolic integral equation datasets.
- Provision of dataset download link and generation code for public access.
Conclusions:
- The FIE-500k dataset is a significant contribution to the field of integral equation research.
- The dataset enables novel applications in natural language processing and symbolic computation.
- Open access to the dataset and code encourages further research and development.
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