Forecasting Sequential Data using Consistent Koopman Autoencoders
This work addresses time series forecasting for applications requiring physics-based modeling, offering an incremental improvement over existing Koopman methods.
The paper tackles the problem of forecasting sequential data by proposing a Consistent Koopman Autoencoder that leverages forward and backward dynamics, achieving accurate predictions for significant horizons and robustness to noise on high-dimensional and short-term dependent problems.
Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.