Inversion of equations of state by combining multi-task neural networks and Newton's method

Abstract

In this work, we address the problem of numerical multidimensional inversion of equations of state for fluid dynamic problems. Particularly, we study the cases where the thermodynamic region of interest contains phase transitions with possible discontinuities of derivatives. In these cases, straight applications of common iterative solvers such as Newton's method with fixed initial guess may lead to divergences. To address this issue, we present a novel method for inverting non-linear equations. The method combines deep multi-task learning techniques with an iterative solver such as Newton's method and allows to handle non-linear equations of complex structure. In order to test the efficiency of the new approach, we apply the method to the problem of inverting equations of state for the pure fluids water, heptane and ethanol. We observe that the proposed method allows to significantly speed-up inversion and avoid divergences, especially in the vicinity of phase boundaries.