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Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl
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abstract
PySR is an open-source library for practical symbolic regression, a type of machine learning which aims to discover human-interpretable symbolic models. PySR was developed to democratize and popularize symbolic regression for the sciences, and is built on a high-performance distributed back-end, a flexible search algorithm, and interfaces with several deep learning packages. PySR's internal search algorithm is a multi-population evolutionary algorithm, which consists of a unique evolve-simplify-optimize loop, designed for optimization of unknown scalar constants in newly-discovered empirical expressions. PySR's backend is the extremely optimized Julia library SymbolicRegression.jl, which can be used directly from Julia. It is capable of fusing user-defined operators into SIMD kernels at runtime, performing automatic differentiation, and distributing populations of expressions to thousands of cores across a cluster. In describing this software, we also introduce a new benchmark, "EmpiricalBench," to quantify the applicability of symbolic regression algorithms in science. This benchmark measures recovery of historical empirical equations from original and synthetic datasets.
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Four parameters suffice to describe dust attenuation curve diversity in TNG simulations, yielding a new symbolic-regression model that recovers curves and fluxes better than existing parameterizations while linking parameters to SFR surface density, metallicity, and geometry.
A convexity-preserving grammar enables symbolic regression to discover thermodynamically admissible dissipation potentials for generalized standard materials from noisy data.
LEE performs iterative amortized inference in a functionally grounded latent space to produce 2-10x simpler symbolic expressions than strong baselines on SRBench.
The Neural Compiler converts symbolic programs into exact differentiable PyTorch modules for hybrid scientific machine learning, enabling precise encoding of known physics with few trainable parameters.
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