# Learning Dynamical Systems from Partial Observations

arXiv: https://arxiv.org/abs/1902.11136 · HTML: https://mlsanity.com/paper/1902.11136/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2019.

## Built on by (most cited first, 30 of 36)

- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks](https://mlsanity.com/paper/2203.08852/) (2022)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems](https://mlsanity.com/paper/2402.04467/) (2024)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [Hybrid FEM-NN models: Combining artificial neural networks with the finite element method](https://mlsanity.com/paper/2101.00962/) (2021)
- [Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series](https://mlsanity.com/paper/2111.02922/) (2021)
- [Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems](https://mlsanity.com/paper/2301.10391/) (2023)
- [On latent dynamics learning in nonlinear reduced order modeling](https://mlsanity.com/paper/2408.15183/) (2024)
- [Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2108.02318/) (2021)
- [Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response](https://mlsanity.com/paper/2402.17233/) (2024)
- [NeuralPDE: Modelling Dynamical Systems from Data](https://mlsanity.com/paper/2111.07671/) (2021)
- [DynaBench: A benchmark dataset for learning dynamical systems from low-resolution data](https://mlsanity.com/paper/2306.05805/) (2023)
- [Continuous-time identification of dynamic state-space models by deep subspace encoding](https://mlsanity.com/paper/2204.09405/) (2022)
- [Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data](https://mlsanity.com/paper/2303.06972/) (2023)
- [Advancing Generalization in PINNs through Latent-Space Representations](https://mlsanity.com/paper/2411.19125/) (2024)
- [SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemics](https://mlsanity.com/paper/2211.08277/) (2022)
- [A memory-efficient neural ODE framework based on high-level adjoint differentiation](https://mlsanity.com/paper/2206.01298/) (2022)
- [Learning Absorption Rates in Glucose-Insulin Dynamics from Meal Covariates](https://mlsanity.com/paper/2304.14300/) (2023)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)
- [Reconstructing a dynamical system and forecasting time series by self-consistent deep learning](https://mlsanity.com/paper/2108.01862/) (2021)
- [DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data](https://mlsanity.com/paper/2405.02661/) (2024)
- [Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data](https://mlsanity.com/paper/2509.07280/) (2025)
- [A Deep Learning Approach To Estimation Using Measurements Received Over a Network](https://mlsanity.com/paper/2201.08020/) (2022)
- [Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamics](https://mlsanity.com/paper/2203.08655/) (2022)
- [Stability of implicit neural networks for long-term forecasting in dynamical systems](https://mlsanity.com/paper/2305.17155/) (2023)

## Abstract (arXiv)

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.