# Learning Dynamical Systems from Partial Observations

Source: [Learning Dynamical Systems from Partial Observations](<https://www.sota2.com/research/paper/68fa39531e209131ce8c19f2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-05T05:01:50.956Z

Authors: Ibrahim Ayed, Emmanuel de B\\'ezenac, Arthur Pajot, Julien Brajard, Patrick Gallinari

Published: 2019-02-26T12:50:49.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Dynamical system modeling on Lotka-Volterra (LV) m=10, n=1 (train)](<https://www.sota2.com/research/sota/dynamical-system-modeling-on-lotka-volterra-lv-m-10-n-1-train.md>): Dynamical system modeling; Lotka-Volterra (LV) m=10, n=1 (train); MSE: 0.457.

- [Dynamical system modeling on Gray-Scott (GS) m=3, n=1 (train)](<https://www.sota2.com/research/sota/dynamical-system-modeling-on-gray-scott-gs-m-3-n-1-train.md>): Dynamical system modeling; Gray-Scott (GS) m=3, n=1 (train); MSE: 0.0155.

- [Dynamical system modeling on Navier-Stokes (NS) m=4, n=8 (train)](<https://www.sota2.com/research/sota/dynamical-system-modeling-on-navier-stokes-ns-m-4-n-8-train.md>): Dynamical system modeling; Navier-Stokes (NS) m=4, n=8 (train); MSE: 0.0517.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1902.11136>)

[PDF](<https://arxiv.org/pdf/1902.11136.pdf>)