# Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems

arXiv: https://arxiv.org/abs/2002.05514 · HTML: https://mlsanity.com/paper/2002.05514/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 23 of 23)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations](https://mlsanity.com/paper/2108.03561/) (2021)
- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [Online Dynamics Learning for Predictive Control with an Application to Aerial Robots](https://mlsanity.com/paper/2207.09344/) (2022)
- [Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution](https://mlsanity.com/paper/2103.14629/) (2021)
- [Online model error correction with neural networks in the incremental 4D-Var framework](https://mlsanity.com/paper/2210.13817/) (2022)
- [Reduced-Order Autodifferentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2301.11961/) (2023)
- [A comparison of combined data assimilation and machine learning methods for offline and online model error correction](https://mlsanity.com/paper/2107.11114/) (2021)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [State, global and local parameter estimation using local ensemble Kalman filters: applications to online machine learning of chaotic dynamics](https://mlsanity.com/paper/2107.11253/) (2021)
- [Stabilizing Machine Learning Prediction of Dynamics: Noise and Noise-inspired Regularization](https://mlsanity.com/paper/2211.05262/) (2022)
- [Gradient-free online learning of subgrid-scale dynamics with neural emulators](https://mlsanity.com/paper/2310.19385/) (2023)
- [Master memory function for delay-based reservoir computers with single-variable dynamics](https://mlsanity.com/paper/2108.12643/) (2021)
- [Model-free prediction of emergence of extreme events in a parametrically driven nonlinear dynamical system by Deep Learning](https://mlsanity.com/paper/2107.08819/) (2021)
- [Stochastic dynamics learning with state-space systems](https://mlsanity.com/paper/2508.07876/) (2025)
- [Development of an offline and online hybrid model for the Integrated Forecasting System](https://mlsanity.com/paper/2403.03702/) (2024)
- [Tailored Forecasting from Short Time Series via Meta-learning](https://mlsanity.com/paper/2501.16325/) (2025)
- [Knowledge-based Neural Ordinary Differential Equations for Cosserat Rod-based Soft Robots](https://mlsanity.com/paper/2408.07776/) (2024)
- [Leveraging Predictive Models for Adaptive Sampling of Spatiotemporal Fluid Processes](https://mlsanity.com/paper/2304.00732/) (2023)
- [Prediction Beyond the Medium Range with an Atmosphere-Ocean Model that Combines Physics-based Modeling and Machine Learning](https://mlsanity.com/paper/2405.19518/) (2024)

## Abstract (arXiv)

We consider the commonly encountered situation (e.g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches:(i) a parallel machine learning prediction scheme; and (ii) a hybrid technique, for a composite prediction system composed of a knowledge-based component and a machine-learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems, but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics ("subgrid-scale closure").