Learning Dynamical Systems from Partial Observations
This addresses the problem of predicting complex systems like ocean simulations for researchers, offering improvements over classical baselines but is incremental as it builds on existing neural ODE frameworks.
The paper tackles forecasting nonlinear space-time processes from partial observations by modeling dynamics with a neural network and solving via an ODE solver, achieving high-quality long-term forecasts and learning hidden states resembling true states without direct supervision.
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled by an unknown time-varying differential equation, and the evolution term is estimated from the data, using a neural network. Any future state can then be computed by placing the associated differential equation in an ODE solver. We first evaluate our approach on shallow water and Euler simulations. We find that our method not only demonstrates high quality long-term forecasts, but also learns to produce hidden states closely resembling the true states of the system, without direct supervision on the latter. Additional experiments conducted on challenging, state of the art ocean simulations further validate our findings, while exhibiting notable improvements over classical baselines.