Learning Dynamical Systems from Partial Observations

TL;DR

This paper introduces a neural network-based framework for forecasting complex nonlinear dynamical systems from partial observations, effectively learning system dynamics and hidden states without direct supervision, validated on water and ocean simulations.

Contribution

The paper presents a novel data-driven approach that models unknown time-varying differential equations using neural networks, enabling accurate long-term forecasting from partial data.

Findings

High-quality long-term forecasts achieved

Hidden states closely match true system states

Outperforms classical baselines on ocean simulations

Abstract

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.