Reconstructing a dynamical system and forecasting time series by self-consistent deep learning
This work addresses the challenge of analyzing noisy time series for researchers in fields like physics or finance, but it appears incremental as it builds on existing deep-learning approaches for dynamical systems.
The authors tackled the problem of reconstructing and forecasting noisy deterministic time series by introducing a self-consistent deep-learning framework that performs unsupervised filtering, state-space reconstruction, identification of underlying differential equations, and forecasting, demonstrating its filtering ability and predictive power on a chaotic time series with additive Gaussian noise.
We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting. Without a priori information on the signal, we embed the time series in a state space, where deterministic structures, i.e. attractors, are revealed. Under the assumption that the evolution of solution trajectories is described by an unknown dynamical system, we filter out stochastic outliers. The embedding function, the solution trajectories and the dynamical systems are constructed using deep neural networks, respectively. By exploiting the differentiability of the neural solution trajectory, the neural dynamical system is defined locally at each time, mitigating the need for propagating gradients through numerical solvers. On a chaotic time series masked by additive Gaussian noise, we demonstrate the filtering ability and the predictive power of the proposed framework.