  Mathematical equations have been unreasonably effective in describing complex
natural phenomena across various scientific disciplines. However, discovering
such insightful equations from data presents significant challenges due to the
necessity of navigating extremely high-dimensional combinatorial and nonlinear
hypothesis spaces. Traditional methods of equation discovery, commonly known as
symbolic regression, largely focus on extracting equations from data alone,
often neglecting the rich domain-specific prior knowledge that scientists
typically depend on. To bridge this gap, we introduce LLM-SR, a novel approach
that leverages the extensive scientific knowledge and robust code generation
capabilities of Large Language Models (LLMs) to discover scientific equations
from data in an efficient manner. Specifically, LLM-SR treats equations as
programs with mathematical operators and combines LLMs' scientific priors with
evolutionary search over equation programs. The LLM iteratively proposes new
equation skeleton hypotheses, drawing from its physical understanding, which
are then optimized against data to estimate skeleton parameters. We demonstrate
LLM-SR's effectiveness across three diverse scientific domains, where it
discovers physically accurate equations that provide significantly better fits
to in-domain and out-of-domain data compared to the well-established symbolic
regression baselines. Incorporating scientific prior knowledge also enables
LLM-SR to search the equation space more efficiently than baselines. Code is
available at: https://github.com/deep-symbolic-mathematics/LLM-SR
