Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learning
The discovery of first integrals is of fundamental scientific importance for understanding conservation laws in dynamical systems. However, existing symbolic computation tools and Large Language Models (LLMs) remain limited on this task because high-quality training data are scarce and successful solutions often depend on mathematical intuition. This paper presents FISolver, an LLM-based solver developed to address this challenge. First, we introduce a "Backward Generation" algorithm that systematically builds large-scale datasets of (differential equation, first integral) pairs by deriving differential equations from sampled integrals, thereby alleviating the data scarcity bottleneck. Se...
| Authors | Jingfeng Zhong, Zhengxiang Liu, Zhijie Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 20 May 2026 |
| Last updated at source | 20 May 2026 |
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