# Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model

arXiv: https://arxiv.org/abs/1803.04779 · HTML: https://mlsanity.com/paper/1803.04779/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2018.

## Built on by (most cited first, 30 of 57)

- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Will Artificial Intelligence supersede Earth System and Climate Models?](https://mlsanity.com/paper/2101.09126/) (2021)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Adaptable Hamiltonian neural networks](https://mlsanity.com/paper/2102.13235/) (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)
- [When are dynamical systems learned from time series data statistically accurate?](https://mlsanity.com/paper/2411.06311/) (2024)
- [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)
- [Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics](https://mlsanity.com/paper/2108.09446/) (2021)
- [Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response](https://mlsanity.com/paper/2402.17233/) (2024)
- [Catch-22s of reservoir computing](https://mlsanity.com/paper/2210.10211/) (2022)
- [ReservoirComputing.jl: An Efficient and Modular Library for Reservoir Computing Models](https://mlsanity.com/paper/2204.05117/) (2022)
- [Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint](https://mlsanity.com/paper/2109.11446/) (2021)
- [Chaotic attractor reconstruction using small reservoirs -- the influence of topology](https://mlsanity.com/paper/2402.16888/) (2024)
- [Data-driven prediction and control of extreme events in a chaotic flow](https://mlsanity.com/paper/2204.11682/) (2022)
- [Comparison of neural closure models for discretised PDEs](https://mlsanity.com/paper/2210.14675/) (2022)
- [Hybridizing Traditional and Next-Generation Reservoir Computing to Accurately and Efficiently Forecast Dynamical Systems](https://mlsanity.com/paper/2403.18953/) (2024)
- [Neural ODEs with Irregular and Noisy Data](https://mlsanity.com/paper/2205.09479/) (2022)
- [How more data can hurt: Instability and regularization in next-generation reservoir computing](https://mlsanity.com/paper/2407.08641/) (2024)
- [Gradient-free optimization of chaotic acoustics with reservoir computing](https://mlsanity.com/paper/2106.09780/) (2021)
- [Master memory function for delay-based reservoir computers with single-variable dynamics](https://mlsanity.com/paper/2108.12643/) (2021)
- [Predicting Ship Responses in Different Seaways using a Generalizable Force Correcting Machine Learning Method](https://mlsanity.com/paper/2405.08033/) (2024)
- [Machine Learning for Predicting Chaotic Systems](https://mlsanity.com/paper/2407.20158/) (2024)
- [Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems](https://mlsanity.com/paper/2407.18057/) (2024)
- [Reconstruction of Three-dimensional Scroll Waves in Excitable Media from Two-Dimensional Observations using Deep Neural Networks](https://mlsanity.com/paper/2209.06860/) (2022)
- [Digital twins of nonlinear dynamical systems](https://mlsanity.com/paper/2210.06144/) (2022)

## Abstract (arXiv)

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone.