Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. Using such approaches one can derive interpretable, intelligible, compact and inexpensive analytical models that tend to present excellent generalization capabilities – such models have the potential to complement neural networks in areas where these attributes are important. With new advances in deep learning there has been much renewed interest in such approaches, yet efforts have not been focused on physics, where we have important additional constraints.

I will present Φ-SO, a Physical Symbolic Optimization framework for recovering analytical symbolic expressions from physical data using deep reinforcement learning techniques and its two most innovative features:

(1) Our system is built, from the ground up, to propose solutions where the physical units are consistent by construction. This is useful not only in eliminating physically impossible solutions, but because it restricts enormously the freedom of the equation generator, thus vastly improving performances.

(2) I will present the ‘Class Symbolic Regression’ extension of our system. This is a first framework for automatically finding a single analytical functional form that accurately fits multiple datasets – each governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law.

Papers:

https://arxiv.org/abs/2303.03192 (SR with RL & dimensional analysis)

https://arxiv.org/abs/2312.01816 (Class SR)

Code and demo: