Physical Symbolic Optimization
This addresses the challenge of robust symbolic regression in physics and engineering applications where units are known, offering improved noise resilience.
The authors tackled the problem of recovering analytical functions from physical data by developing a symbolic regression method that enforces dimensional analysis constraints, achieving state-of-the-art results on the SRBench's Feynman benchmark with noise levels up to 10%.
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 $Φ$-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.