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About this paper
Wassim Tenachi, Rodrigo Ibata, Foivos I. Diakogiannis
The Φ-SO framework introduces deep symbolic regression guided by physical units constraints, integrating dimensional consistency directly into the expression generation process. This approach achieved a 58.5% exact symbolic recovery rate on the Feynman benchmark under noiseless conditions and maintained over 53% accuracy at 10% noise, outperforming baseline methods while producing physically interpretable equations.
Key insights
- Directly incorporating dimensional analysis rules 'in situ' during expression generation significantly reduces the combinatorial search space, leading to more efficient and accurate symbolic recovery.
- The neural network actively learns and leverages dimensional consistency, demonstrated by a progressive increase in physically consistent expressions and improved fit quality over training iterations.
- A risk-seeking policy gradient, when combined with strong physical constraints, enables robust recovery of exact symbolic forms even from noisy data.
Summary by alphaXiv.
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