Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systems

Predictive simulations are essential for applications ranging from weather forecasting to material design. The veracity of these simulations hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the systems dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation. On the other hand, reduced order models are fast but often limited by the linearization of the system dynamics and the adopted heuristic closures. We propose a novel systematic framework that bridges large scale simulations and reduced order models to extract and forecast adaptively the effective dynamics (AdaLED) of multiscale systems. AdaLED employs an autoencoder to identify reduced-order representations of the system dynamics and an ensemble of probabilistic recurrent neural networks (RNNs) as the latent time-stepper. The framework alternates between the computational solver and the surrogate, accelerating learned dynamics while leaving yet-to-be-learned dynamics regimes to the original solver. AdaLED continuously adapts the surrogate to the new dynamics through online training. The transitions between the surrogate and the computational solver are determined by monitoring the prediction accuracy and uncertainty of the surrogate. The effectiveness of AdaLED is demonstrated on three different systems - a Van der Pol oscillator, a 2D reaction-diffusion equation, and a 2D Navier-Stokes flow past a cylinder for varying Reynolds numbers (400 up to 1200), showcasing its ability to learn effective dynamics online, detect unseen dynamics regimes, and provide net speed-ups. To the best of our knowledge, AdaLED is the first framework that couples a surrogate model with a computational solver to achieve online adaptive learning of effective dynamics. It constitutes a potent tool for applications requiring many expensive simulations.