  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.
