  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.
