DecAEvolve: Decompose, Adapt, and Evolve for Effective LLM-based Scientific Equation Discovery

Finding mathematical relations underlying natural phenomena is a fundamental task in scientific discovery. Recent advances in evolutionary search with Large Language Models (LLMs) show great promise by leveraging their embedded scientific knowledge. However, discovering governing equations remains challenging due to vast combinatorial hypothesis spaces with exponentially many possible relations. Existing LLM-based approaches treat LLMs as static hypothesis generators unaware of the observed scientific system, leading to suboptimal and inefficient exploration that over-relies on internal priors. To address this, we introduce Decompose, Adapt, and Evolve (DecAEvolve), a framework that combines granular feedback from symbolic term decomposition with LLM refinement through reinforcement learning fine-tuning. DecAEvolve unifies symbolic decomposition with test-time RL adaptation, enabling adaptive rather than static hypothesis generation. Our experiments across diverse scientific benchmarks demonstrate that DecAEvolve significantly improves both the accuracy of discovered equations and the efficiency of the discovery process, reducing error by up to an order of magnitude compared to state-of-the-art baselines.

Scientists often try to uncover the hidden mathematical rules that explain how nature works — from the motion of planets to patterns in biology and physics. In recent years, researchers have begun using large language models (LLMs), the same kind of AI behind chatbots, to help search for these mathematical models. But this is extremely difficult because there are countless possible mathematical relationships to test. This paper introduces a new AI framework called DecAEvolve that helps language models become better scientific “discoverers.” Instead of having the AI simply guess equations based only on what it learned during training, DecAEvolve allows the model to learn from feedback about how well different parts of an equation match real data. The system breaks equations into smaller pieces, evaluates them step by step, and continuously improves its search strategy through reinforcement learning. By combining these ideas, DecAEvolve explores possible equations more intelligently and efficiently than previous methods. Across several scientific benchmark problems, the approach was able to find more accurate governing equations while requiring fewer attempts, in some cases reducing prediction errors by as much as tenfold compared with existing state-of-the-art techniques. In simple terms, this work moves AI closer to acting like a scientific assistant that can actively adapt and learn from environments, helping researchers to uncover the mathematical laws behind complex natural phenomena.