Accelerated and data-efficient flow prediction in stirred tanks via physics-informed learning

TL;DR

This paper explores physics-informed neural networks to predict steady flow fields in stirred tanks efficiently, reducing data needs and improving accuracy with physics constraints, while analyzing the trade-offs involved.

Contribution

It demonstrates the effectiveness of physics-informed learning for flow prediction, showing improved accuracy and stability with limited data in industrial stirred tanks.

Findings

Physics-based constraints improve accuracy in low-data regimes.

Prediction error decreases with more data but with diminishing returns.

Physics-informed models enhance tracer transport stability.

Abstract

The simulation of fluid flows is computationally expensive due to the complexity of its governing partial differential equations. Machine learning models offer a potential surrogate, enabling learning from simulations and significantly faster predictions of flow fields. However, these models require large training datasets, which introduces a trade-off between dataset generation cost and predictive accuracy. In this work, we investigate the relationship between the size of the training-set and accuracy of the prediction when learning steady flow fields in an industrial-scale stirred vessel. A data set of steady flows is generated using Reynolds Averaged Navier Stokes (RANS) simulations in a range of realistic operating conditions, including impeller speeds and liquid heights. We train implicit neural representations of flow fields and compare purely data-driven and constrained variants. Model performance is evaluated using global mean squared error (MSE), qualitative spatial comparisons of predicted and reference flow fields, and tracer transport simulations. We find that the prediction error decreases monotonically with increasing training data, but also that it exhibits clear diminishing returns beyond moderate dataset sizes. Physics-based constraints significantly improve accuracy and reduce variability across training runs in low-data regimes, and they lead to more stable tracer-transport behavior. Furthermore, reasonable interpolation can be achieved over different impeller speeds and liquid heights. However, these benefits come with an increase in the complexity of training, and their relative advantage diminishes as the training set grows.