A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge
This work addresses the problem of symbolic regression for scientists and engineers by providing a tool that enhances accuracy and alerts users to missing features, though it appears incremental as it builds on existing methods.
The authors tackled the challenge of discovering physically meaningful symbolic expressions from experimental data by introducing SciMED, a computational framework that integrates domain knowledge with symbolic regression methods, and demonstrated its robustness in correctly identifying expressions for settling sphere configurations, even outperforming state-of-the-art packages in some cases.
Discovering a meaningful symbolic expression that explains experimental data is a fundamental challenge in many scientific fields. We present a novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED), which integrates scientific discipline wisdom in a scientist-in-the-loop approach, with state-of-the-art symbolic regression (SR) methods. SciMED combines a wrapper selection method, that is based on a genetic algorithm, with automatic machine learning and two levels of SR methods. We test SciMED on five configurations of a settling sphere, with and without aerodynamic non-linear drag force, and with excessive noise in the measurements. We show that SciMED is sufficiently robust to discover the correct physically meaningful symbolic expressions from the data, and demonstrate how the integration of domain knowledge enhances its performance. Our results indicate better performance on these tasks than the state-of-the-art SR software packages , even in cases where no knowledge is integrated. Moreover, we demonstrate how SciMED can alert the user about possible missing features, unlike the majority of current SR systems.