  Symbolic regression holds great potential for uncovering underlying
mathematical and physical relationships from empirical data. While existing
transformer-based models have recently achieved significant success in this
domain, they face challenges in terms of generalizability and adaptability.
Typically, in cases where the output expressions do not adequately fit
experimental data, the models lack efficient mechanisms to adapt or modify the
expression. This inflexibility hinders their application in real-world
scenarios, particularly in discovering unknown physical or biological
relationships. Inspired by how human experts refine and adapt expressions, we
introduce Symbolic Q-network (Sym-Q), a novel reinforcement learning-based
model that redefines symbolic regression as a sequential decision-making task.
Sym-Q leverages supervised demonstrations and refines expressions based on
reward signals indicating the quality of fitting precision. Its distinctive
ability to manage the complexity of expression trees and perform precise
step-wise updates significantly enhances flexibility and efficiency. Our
results demonstrate that Sym-Q excels not only in recovering underlying
mathematical structures but also uniquely learns to efficiently refine the
output expression based on reward signals, thereby discovering underlying
expressions. Sym-Q paves the way for more intuitive and impactful discoveries
in physical science, marking a substantial advancement in the field of symbolic
regression.
