Echo-State-Networks-Nonlinear-Vector-Autoregression-and-Data-Assimilation-for-Chaotic-Systems

- THESE ARE ONLY PRELIMINARY RESULTS

1. To Include
   • Data Assimilation Methods
   • Narration of results
   • Mathematical Methods/Detail

Stochastic Processes Comparison of Accuracy: Data Assimilation, Echo State Machines and Nonlinear Vector Autoregressive Learning Methods.

Comparing discrete and variational data assimilation methods to reservoir computing - machine learning for synthetic chaotic nonlinear dynamical systems

1. The Attractors Used

   • Lorenz 1963 Model for Atmospheric Convection (Rayleigh Benard Convection)
   • Mackey Glass Dataset

2. Reservoir Computing Methods

   • Echo State Machine - Hierarchial Structure
   • Echo State Machine - Deep ESN with nonlinear activation function, externally applied

3. Other Neural Network Models

   • Nonlinear Vector AutoRegression (NVAR) - Next Generation Reservoir Computer

4. Data Assimilation Methods

   • Kalman Filter (Discrete - Ensemble)
   • 3D Variational Data Assimilation
   • Particle Filter