Real-time prediction of turbulent flow using physics-informed neural networks with coarse spatiotemporal data

The Encoder-based DeepONet (E-DeepONet) framework developed in this study demonstrates robust predictive capabilities even with coarse spatiotemporal data. Building upon the success of the Latent DeepONet framework (Kontolati et al., Nat. Commun., 2024) in predicting complex physical systems in real-time, our research aims to enhance this approach by incorporating physical equations into the learning process. We achieve this by learning the latent space of coarse spatiotemporal data using an autoencoder, which then serves as input to the E-DeepONet for integrating physical equation learning. Instantaneous high-fidelity flow datasets are obtained from direct numerical simulation (DNS) of turbulent channel flow, providing both coarse training data and validation benchmarks. Once trained, E-DeepONet can infer continuous high-fidelity spatiotemporal flow fields in real-time from arbitrary coarse spatiotemporal flow fields. Our results indicate that the physics-informed E-DeepONet significantly outperforms models without physics information, particularly when dealing with increasingly coarse data, thus demonstrating its potential for robust and physically consistent predictions in various complex systems.