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

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. • This study presents a deep learning method (DLM) that integrates a Transformer model with a multiscale enhanced super-resolution generative adversarial network (MS-ESRGAN) to improve retrospective predictions in dissipative dynamical systems. • The Transformer excels at capturing historical dynamics, while MS-ESRGAN refines the predicted fields to achieve resolutions comparable to ground truth data, resulting in greater accuracy for modeling dissipative systems. • The DLM leverages temporal evolution data to extract implicit information, enabling more accurate retrospective predictions and overcoming the limitations of traditional methods that often neglect dissipative terms or use negative dissipative coefficients, marking a significant advancement in the field.