Enhanced retrospective forecasting in dissipative dynamical systems using transformer and multi-scale ESRGAN models

Abstract

Accurate characterization of complex dynamical systems is crucial for understanding their intrinsic behavior, and retrospective prediction provides a promising solution. However, traditional methods often fail to effectively predict dissipative terms, which are key in dissipative dynamical systems. This study introduces a deep learning method (DLM) that combines a Transformer model with a multiscale enhanced super-resolution generative adversarial network (MS-ESRGAN) to improve retrospective predictions by extracting implicit information from temporal evolution data. The Transformer excels at capturing past dynamics, while MS-ESRGAN refines the predicted fields, achieving resolutions on par with ground truth data. The effectiveness of the DLM is demonstrated using two canonical flow cases: forced isotropic turbulence and a transitional boundary layer. The model closely matches the velocity fields of the ground truth, with only minor deviations attributed to the nonlinearity of the governing equations and the inherent difficulty in resolving small-scale structures. In addition, the DLM has been applied to National Oceanic and Atmospheric Administration (NOAA) sea surface temperature (SST) data, demonstrating its practical utility for climate science. Despite the challenges associated with capturing small-scale structures, the data-driven DLM outperforms traditional numerical methods that either neglect the dissipative term or utilize negative dissipative coefficients, representing a significant advancement in retrospective predictions.

Keywords

• Retrospective prediction
• Deep learning
• Transformer
• Generative adversarial network
• Dissipative dynamical systems