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

@article{Pathak2018HybridFO, title={Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model}, author={Jaideep Pathak and Alexander Wikner and Rebeckah Fussell and Sarthak Chandra and Brian R. Hunt and Michelle Girvan and Edward Ott}, journal={Chaos}, year={2018}, volume={28 4}, pages={ 041101 } }

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the mechanistic 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…

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## References

SHOWING 1-10 OF 18 REFERENCES

### Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data.

- Computer Science, GeologyChaos
- 2017

This work uses recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process to form a modified autonomous reservoir.

### Reservoir observers: Model-free inference of unmeasured variables in chaotic systems.

- MathematicsChaos
- 2017

It is shown that the reservoir observer can be a very effective and versatile tool for robustly reconstructing unmeasured dynamical system variables.

### Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach.

- Computer SciencePhysical review letters
- 2018

We demonstrate the effectiveness of using machine learning for model-free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from…

### A hybrid neural network‐first principles approach to process modeling

- Engineering
- 1992

A hybrid neural network-first principles modeling scheme is developed and used to model a fedbatch bioreactor. The hybrid model combines a partial first principles model, which incorporates the…

### Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations

- Computer ScienceNeural Computation
- 2002

A new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks, based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry.

### Reservoir computing approaches to recurrent neural network training

- Computer ScienceComput. Sci. Rev.
- 2009

### Reservoir computing with a single time-delay autonomous Boolean node

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

We demonstrate reservoir computing with a physical system using a single autonomous Boolean logic element with time-delay feedback. The system generates a chaotic transient with a window of…

### Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication

- Computer ScienceScience
- 2004

We present a method for learning nonlinear systems, echo state networks (ESNs). ESNs employ artificial recurrent neural networks in a way that has recently been proposed independently as a learning…

### Brain-Inspired Photonic Signal Processor for Generating Periodic Patterns and Emulating Chaotic Systems

- Computer Science
- 2017

This work presents a photonic reservoir computer with output feedback, and demonstrates its capacity to generate periodic time series and to emulate chaotic systems, and introduces several metrics, based on standard signal processing techniques, to evaluate the quality of the emulation.

### Long Short-Term Memory

- Computer ScienceNeural Computation
- 1997

A novel, efficient, gradient based method called long short-term memory (LSTM) is introduced, which can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units.