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

2026-02-02

AI Summary

This work proposes a continuous-time Koopman autoencoder framework to address the trade-off between short-term accuracy and long-term stability in traditional data-driven turbulence modeling, as well as the limitations of discrete-time models in temporal resolution and extrapolation capability. By embedding nonlinear fluid dynamics into a latent space where evolution is strictly linear and governed by an analytically solvable matrix exponential, the approach enables inference at arbitrary time steps through numerical integration of ordinary differential equations. Integrating Koopman operator theory, autoencoder architecture, and constrained optimization, the model significantly outperforms existing discrete methods on canonical CFD benchmarks, achieving high accuracy, robust long-term stability, and excellent generalization across time scales.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• fluid dynamics forecasting
• Koopman operator
• continuous-time dynamics
• long-horizon stability
• temporal flexibility

Innovation

• Koopman operator
• continuous-time dynamics
• fluid dynamics forecasting
• latent space modeling
• numerical integration