Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systems
This addresses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems for researchers and practitioners, but it is incremental as it builds on existing KAE methods.
The paper tackles the problem of poor generalizability in Koopman Autoencoders due to limited and noisy training data by introducing a temporally consistent Koopman autoencoder (tcKAE) with a consistency regularization term, achieving superior performance over state-of-the-art models in test cases like pendulum oscillations and fluid flow.
Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the temporally consistent Koopman autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE's superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.