Discovering Asymptotic Expansions Using Symbolic Regression

TL;DR

This paper introduces a method combining symbolic regression with asymptotic analysis to discover asymptotic series in physical problems, demonstrating high accuracy and potential for parameter identification using data.

Contribution

The paper adapts symbolic regression to automatically discover asymptotic expansions, including divergent series, from data, aiding in understanding complex physical systems.

Findings

SR accurately reproduces known asymptotic series

Method works for both convergent and divergent series

Potential for material parameter identification

Abstract

Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The main advantage of asymptotic approach involves the robust approximation to the sought for solution bringing a clear idea of the effect of problem parameters. However, the analytic derivation of the asymptotic series is often highly nontrivial especially, when the exact solution is not available. In this paper, we adapt SR methodology to discover asymptotic series. As an illustration we consider three problem in mechanics, including two-mass collision, viscoelastic behavior of a Kelvin-Voigt solid and propagation of Rayleigh-Lamb waves. The training data is generated from the explicit exact solutions of these problems. The obtained SR results are compared to the benchmark asymptotic expansions of the above mentioned exact solutions. Both convergent and divergent asymptotic series are considered. A good agreement between SR expansions and analytical results is observed. It is demonstrated that the proposed approach can be used to identify material parameters, e.g. Poisson's ratio, and has high prospects for utilizing experimental and numerical data.