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

Abstract

Learning surrogate models for time-dependent PDEs requires balancing expressivity, stability, and computational efficiency. While highly expressive generative models achieve strong short-term accuracy, they rely on autoregressive sampling procedures that are computationally expensive and prone to error accumulation over long horizons. We propose a continuous-time Koopman autoencoder in which latent dynamics are governed by a parameter-conditioned linear generator. This formulation enables exact latent evolution via matrix exponentiation, allowing predictions at arbitrary temporal resolutions without autoregressive rollouts. We evaluate our method on challenging fluid dynamics benchmarks and compare against autoregressive neural operators and diffusion-based models. We evaluate our method on challenging fluid dynamics benchmarks against autoregressive neural operators and diffusion-based models. Our results demonstrate that imposing a continuous-time linear structure in the latent space yields a highly favorable trade-off: it achieves massive computational efficiency and extreme long-horizon stability while remaining competitive in short-term generative accuracy.

Reproductions