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

Pouya Behzadifar, Parshin Shojaee, Sanchit Kabra, Kazem Meidani, Chandan K. Reddy
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:7391-7411, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-behzadifar26a, title = {{D}ec{AE}volve: Decompose, Adapt, and Evolve for Effective {LLM}-based Scientific Equation Discovery}, author = {Behzadifar, Pouya and Shojaee, Parshin and Kabra, Sanchit and Meidani, Kazem and Reddy, Chandan K.}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {7391--7411}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/behzadifar26a/behzadifar26a.pdf}, url = {https://proceedings.mlr.press/v306/behzadifar26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T DecAEvolve: Decompose, Adapt, and Evolve for Effective LLM-based Scientific Equation Discovery %A Pouya Behzadifar %A Parshin Shojaee %A Sanchit Kabra %A Kazem Meidani %A Chandan K. Reddy %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-behzadifar26a %I PMLR %P 7391--7411 %U https://proceedings.mlr.press/v306/behzadifar26a.html %V 306 %X 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.
APA
Behzadifar, P., Shojaee, P., Kabra, S., Meidani, K. & Reddy, C.K.. (2026). DecAEvolve: Decompose, Adapt, and Evolve for Effective LLM-based Scientific Equation Discovery. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:7391-7411 Available from https://proceedings.mlr.press/v306/behzadifar26a.html.

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