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Computational fluid dynamics (CFD) simulations of viscous fluids described bythe Navier-Stokes equations are considered. Depending on the Reynolds number ofthe flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior.The system of nonlinear equations resulting from the discretization of theNavier-Stokes equations can be solved using nonlinear iteration methods, suchas Newton's method. However, fast quadratic convergence is typically onlyobtained in a local neighborhood of the solution, and for many configurations,the classical Newton iteration does not converge at all. In such cases,so-called globalization techniques may help to improve convergence.  In this paper, pseudo-transient continuation is employed in order to improvenonlinear convergence. The classical algorithm is enhanced by a neural networkmodel that is trained to predict a local pseudo-time step. Generalization ofthe novel approach is facilitated by predicting the local pseudo-time stepseparately on each element using only local information on a patch of adjacentelements as input. Numerical results for standard benchmark problems, includingflow through a backward facing step geometry and Couette flow, show theperformance of the machine learning-enhanced globalization approach; as thesoftware for the simulations, the CFD module of COMSOL Multiphysics isemployed.

Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks