Iterative Symbolic Regression for Learning Transport Equations

TL;DR

This paper introduces an iterative method combining active learning and symbolic regression to efficiently derive empirical equations from CFD simulations, reducing computational costs and applicable to complex systems.

Contribution

It presents a scalable approach that integrates active learning with symbolic regression to automatically discover empirical equations from CFD data.

Findings

Successfully derived pressure drop equation in a bent pipe

Developed new predictive equation for heart valve backflow

Method is scalable to multiple CFD parameters

Abstract

Computational fluid dynamics (CFD) analysis is widely used in engineering. Although CFD calculations are accurate, the computational cost associated with complex systems makes it difficult to obtain empirical equations between system variables. Here we combine active learning (AL) and symbolic regression (SR) to get a symbolic equation for system variables from CFD simulations. Gaussian process regression-based AL allows for automated selection of variables by selecting the most instructive points from the available range of possible parameters. The results from these experiments are then passed to SR to find empirical symbolic equations for CFD models. This approach is scalable and applicable for any desired number of CFD design parameters. To demonstrate the effectiveness, we use this method with two model systems. We recover an empirical equation for the pressure drop in a bent pipe and a new equation for predicting backflow in a heart valve under arotic insufficiency.