Symbolic Regression Algorithms For Discovering Mathematical Laws In Noisy Experimental

Abstract

Symbolic regression is a highly effective paradigm for discovering interpretable mathematical expressions from experimental observations without having any a priori knowledge about the physical laws behind the data. In this paper, a comprehensive paradigm for symbolic regression is developed combining the strength of genetic algorithms along with multi-objective optimization and robust evaluation metrics to discover compact mathematical expressions from noisy experimental data. The developed methodology utilizes adaptive operator selection, lexicographic fitness function, and constraint-based mathematical expression generation for searching the solution space of mathematical models. An innovative denoising pre-processing approach using the iterative application of median filtering and wavelet decomposition helps to increase the signal-to-noise ratio of experimental data, while retaining its essential properties. The robustness and effectiveness of the proposed methodology have been demonstrated using synthetic experimental data corrupted by different noise levels (5%-50% Gaussian noise) as well as actual experimental data for various mechanical systems. The results reveal that the proposed algorithm discovers the ground truth mathematical expressions with 96.3% accuracy from 25% noisy data. Moreover, it outperforms traditional symbolic regression techniques in terms of mean absolute percentage error by 34%.