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<p>This study investigates the capability of small reasoning-oriented language models to construct analytical solutions to differential equations. Computational experiments are conducted on such models as DeepSeek-R1-Distill-Qwen-1.5B, Qwen2.5-1.5B, and Open-Reasoner-Zero-1.5B. To extract the final answers from the models reasoning processes, postprocessing is applied using two additional language models, Qwen2.5:latest and Llama3.2: latest. The extracted solutions are then compared with reference solutions using the BLEU metric. Our results demonstrate that, on average, Open-Reasoner-Zero-1.5B achieves superior performance, reaching the highest BLEU score (0.978) for second-order homogeneous equations.</p>

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Solving Differential Equations with Pretrained Out-of-the-Box Models: The Potential of Small-Scale LLMs

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • S. N. Koltcov,
  • V. V. Ignatenko,
  • A. Yu. Surkov,
  • V. O. Zakharov

摘要

This study investigates the capability of small reasoning-oriented language models to construct analytical solutions to differential equations. Computational experiments are conducted on such models as DeepSeek-R1-Distill-Qwen-1.5B, Qwen2.5-1.5B, and Open-Reasoner-Zero-1.5B. To extract the final answers from the models reasoning processes, postprocessing is applied using two additional language models, Qwen2.5:latest and Llama3.2: latest. The extracted solutions are then compared with reference solutions using the BLEU metric. Our results demonstrate that, on average, Open-Reasoner-Zero-1.5B achieves superior performance, reaching the highest BLEU score (0.978) for second-order homogeneous equations.