Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

TL;DR

This paper introduces a convolutional transformer model for autoregressive, long-term prediction of turbulent flow fields, demonstrating improved accuracy and stability in modeling complex chaotic fluid dynamics.

Contribution

It presents a novel combination of convolutional neural networks and transformers for spatio-temporal turbulence modeling, enabling long-term stable predictions.

Findings

Model achieves significant agreement with ground truth data.

Predictions remain stable over long time horizons.

The approach handles highly nonlinear turbulent flows effectively.

Abstract

A convolutional encoder-decoder-based transformer model is proposed for autoregressively training on spatio-temporal data of turbulent flows. The prediction of future fluid flow fields is based on the previously predicted fluid flow field to ensure long-term predictions without diverging. A combination of convolutional neural networks and transformer architecture is utilized to handle both the spatial and temporal dimensions of the data. To assess the performance of the model, a priori assessments are conducted, and significant agreements are found with the ground truth data. The a posteriori predictions, which are generated after a considerable number of simulation steps, exhibit predicted variances. The autoregressive training and prediction of a posteriori states are deemed crucial steps towards the development of more complex data-driven turbulence models and simulations. The highly nonlinear and chaotic dynamics of turbulent flows can be handled by the proposed model, and accurate predictions over long time horizons can be generated. Overall, the potential of using deep learning techniques to improve the accuracy and efficiency of turbulence modeling and simulation is demonstrated by this approach. The proposed model can be further optimized and extended to incorporate additional physics and boundary conditions, paving the way for more realistic simulations of complex fluid dynamics.