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Iterative Symbolic Regression for Learning Transport Equations

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.