A model hierarchy for predicting the flow in stirred tanks with physics-informed neural networks

Abstract

This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes equations within a geometrically intricate domain and explore methodologies that allow us to integrate additional physical insights into the model. These approaches include imposing the Dirichlet boundary conditions (BCs) strongly and employing domain decomposition (DD), with both overlapping and non-overlapping subdomains. We adapt the Extended Physics-Informed Neural Network (XPINN) approach to solve different sets of equations in distinct subdomains based on the diverse flow characteristics present in each region. Our exploration results in a hierarchy of models spanning various levels of complexity, where the best models exhibit ℓ 1 prediction errors of less than 1 % for both pressure and velocity. To illustrate the reproducibility of our approach, we track the errors over repeated independent training runs of the best identified model and show its reliability. Subsequently, by incorporating the stirring rate as a parametric input, we develop a fast-toevaluate model of the flow capable of interpolating across a wide range of Reynolds numbers. Although we exclusively restrict ourselves to STRs in this work, we conclude that the steps taken to obtain the presented model hierarchy can be transferred to other applications.1. Introduction. Stirred tank reactors (STRs) play a central role in chemical process industry and biotechnology. A typical STR contains one or more impellers affixed to a shaft as well as baffles mounted to the reactor wall. A diverse set of parameters, including tank and impeller size, stirring rate, as well as the number of baffles, offer flexibility and control over the STR's performance. However, these