[Paper Review] Expressions found by PySR software from dataset of equations of state for neutron star matter based on relativistic mean field model with a non-linear mesonic interaction

Demigio, Felipe|arXiv (Cornell University)|May 2, 2023

Machine Learning in Materials Science176 citations

TL;DR

The paper reports symbolic expressions discovered by PySR from an EOS dataset for neutron star matter modeled with a relativistic mean field approach including nonlinear mesonic interactions.

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.

Motivation & Objective

• Motivate the use of symbolic regression to extract interpretable EOS relations for neutron star matter.
• Describe the dataset of equations of state generated from a relativistic mean field model with nonlinear mesonic interactions.
• Present the symbolic expressions discovered by PySR that relate EOS quantities.
• Assess the interpretability and potential utility of the discovered expressions for neutron star physics.

Proposed method

• Apply PySR symbolic regression to a dataset of EOS data produced by a relativistic mean field model with nonlinear mesonic interaction.
• Obtain and catalog the symbolic expressions that fit or describe the EOS data.
• Evaluate the expressions in terms of simplicity, interpretability, and potential physical relevance.

Experimental results

Research questions

• RQ1 What forms of symbolic expressions best capture the relationships in the neutron star EOS dataset?
• RQ2 How do the PySR-discovered expressions balance accuracy with interpretability for EOS variables?
• RQ3 Do the resulting expressions generalize beyond the training EOS dataset within the RMF with nonlinear mesonic interaction framework?

Key findings

• PySR yields explicit symbolic expressions that describe relationships in the neutron star EOS dataset.
• The discovered expressions provide interpretable mappings within the RMF-based EOS context.
• The study demonstrates the feasibility of using symbolic regression to obtain physically meaningful EOS relations.