Learning Invertible Observables for Structurally Consistent Koopman Modeling

Dongming Xie, Ye Yuan

Keywords: Koopman operator, Normalizing flows, Data-driven modeling, Invertible

TL;DR: Using invertible normalizing flows to learn invertible, input-conditioned observables, we build a probabilistic Koopman model that is structurally consistent, scalable and robust to missing data and noise. Ablations confirm the need for each part.

Abstract: Understanding the intricate dynamics of systems, from molecular interactions to climate patterns, remains a central challenge in science and engineering. The Koopman operator provides a powerful mathematical framework by translating nonlinear dynamics into a tractable linear form. However, current methods face significant limitations, including lack of invertibility, inadequate handling of system input, and inability to represent measurement distributions. We introduce an invertible, Koopman-consistent framework, built on principles of invertible normalizing flows, that addresses these issues. Our approach provides a structurally sound architecture that supports invertible observable functions, is explicitly conditioned on exogenous inputs, and captures the probabilistic nature of dynamic systems. This modular and scalable framework enables efficient learning of Koopman representations across diverse systems. Ablation studies confirm the necessity of each component. Experiments on simulated and real-world data demonstrate resilience to missing information, infrequent measurements, and noise, highlighting its potential for constructing structurally consistent, accurate models of real-world phenomena.

Primary Area: learning on time series and dynamical systems

Submission Number: 2491