Koopman Autoencoders with Continuous-Time Latent Dynamics for Fluid Dynamics Forecasting

Abstract: Data-driven surrogate models have emerged as powerful tools for accelerating the simulation of turbulent flows. However, classical approaches which perform autoregressive rollouts often trade off between strong short-term accuracy and long-horizon stability. Koopman autoencoders, inspired by Koopman operator theory, provide a physics-based alternative by mapping nonlinear dynamics into a latent space where linear evolution is conducted. In practice, most existing formulations operate in a discrete-time setting, limiting temporal flexibility. In this work, we introduce a continuous-time Koopman framework that models latent evolution through numerical integration schemes. By allowing variable timesteps at inference, the method demonstrates robustness to temporal resolution and generalizes beyond training regimes. In addition, the learned dynamics closely adhere to the analytical matrix exponential solution, enabling efficient long-horizon forecasting. We evaluate the approach on classical CFD benchmarks and report accuracy, stability, and extrapolation properties.