Enhancing Symbolic Regression with Quality-Diversity and Physics-Inspired Constraints
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910892127420416 |
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| author | Bruneton, J. -P. |
| author_facet | Bruneton, J. -P. |
| contents | This paper presents QDSR, an advanced symbolic Regression (SR) system that integrates genetic programming (GP), a quality-diversity (QD) algorithm, and a dimensional analysis (DA) engine. Our method focuses on exact symbolic recovery of known expressions from datasets, with a particular emphasis on the Feynman-AI benchmark. On this widely used collection of 117 physics equations, QDSR achieves an exact recovery rate of 91.6~$\%$, surpassing all previous SR methods by over 20 percentage points. Our method also exhibits strong robustness to noise. Beyond QD and DA, this high success rate results from a profitable trade-off between vocabulary expressiveness and search space size: we show that significantly expanding the vocabulary with precomputed meaningful variables (e.g., dimensionless combinations and well-chosen scalar products) often reduces equation complexity, ultimately leading to better performance. Ablation studies will also show that QD alone already outperforms the state-of-the-art. This suggests that a simple integration of QD, by projecting individuals onto a QD grid, can significantly boost performance in existing algorithms, without requiring major system overhauls. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_19043 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enhancing Symbolic Regression with Quality-Diversity and Physics-Inspired Constraints Bruneton, J. -P. Neural and Evolutionary Computing Symbolic Computation Data Analysis, Statistics and Probability 68T05, 68T20 I.2.6; J.2 This paper presents QDSR, an advanced symbolic Regression (SR) system that integrates genetic programming (GP), a quality-diversity (QD) algorithm, and a dimensional analysis (DA) engine. Our method focuses on exact symbolic recovery of known expressions from datasets, with a particular emphasis on the Feynman-AI benchmark. On this widely used collection of 117 physics equations, QDSR achieves an exact recovery rate of 91.6~$\%$, surpassing all previous SR methods by over 20 percentage points. Our method also exhibits strong robustness to noise. Beyond QD and DA, this high success rate results from a profitable trade-off between vocabulary expressiveness and search space size: we show that significantly expanding the vocabulary with precomputed meaningful variables (e.g., dimensionless combinations and well-chosen scalar products) often reduces equation complexity, ultimately leading to better performance. Ablation studies will also show that QD alone already outperforms the state-of-the-art. This suggests that a simple integration of QD, by projecting individuals onto a QD grid, can significantly boost performance in existing algorithms, without requiring major system overhauls. |
| title | Enhancing Symbolic Regression with Quality-Diversity and Physics-Inspired Constraints |
| topic | Neural and Evolutionary Computing Symbolic Computation Data Analysis, Statistics and Probability 68T05, 68T20 I.2.6; J.2 |
| url | https://arxiv.org/abs/2503.19043 |