Physical Symbolic Optimization

TL;DR

This paper introduces $\Phi$-SO, a physical symbolic optimization framework that integrates dimensional analysis constraints with reinforcement learning to improve symbolic regression of physical equations, especially under noisy conditions.

Contribution

The paper presents a novel method combining dimensional analysis with reinforcement learning for symbolic regression, achieving state-of-the-art results on physical data benchmarks.

Findings

Outperforms existing methods on SRBench's Feynman benchmark.

Maintains high accuracy with noise levels up to 10%.

Effectively recovers physical equations from data with known units.

Abstract

We present a framework for constraining the automatic sequential generation of equations to obey the rules of dimensional analysis by construction. Combining this approach with reinforcement learning, we built $\Phi$-SO, a Physical Symbolic Optimization method for recovering analytical functions from physical data leveraging units constraints. Our symbolic regression algorithm achieves state-of-the-art results in contexts in which variables and constants have known physical units, outperforming all other methods on SRBench's Feynman benchmark in the presence of noise (exceeding 0.1%) and showing resilience even in the presence of significant (10%) levels of noise.