迁移方程学习的迭代符号回归
Iterative Symbolic Regression for Learning Transport Equations
摘要：
计算流体动力学（CFD）分析在工程中有着广泛的应用。虽然CFD计算是准确的，但与复杂系统相关的计算成本使得难以获得系统变量之间的经验方程。在这里，我们结合主动学习（AL）和符号回归（SR），从CFD模拟中获得系统变量的符号方程。基于高斯过程回归的AL允许通过从可用的可能参数范围中选择最有指导意义的点来自动选择变量。然后将这些实验的结果传递给SR，以找到CFD模型的经验符号方程。这种方法是可扩展的，适用于任何所需数量的CFD设计参数。为了证明这种方法的有效性，我们用两个模型系统。我们恢复的经验方程的压力下降，在弯曲的管道和一个新的方程预测回流下的心脏瓣膜动脉功能不全。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
