5 research outputs found
Controlling Chaotic Maps using Next-Generation Reservoir Computing
In this work, we combine nonlinear system control techniques with
next-generation reservoir computing, a best-in-class machine learning approach
for predicting the behavior of dynamical systems. We demonstrate the
performance of the controller in a series of control tasks for the chaotic
H\'enon map, including controlling the system between unstable fixed-points,
stabilizing the system to higher order periodic orbits, and to an arbitrary
desired state. We show that our controller succeeds in these tasks, requires
only 10 data points for training, can control the system to a desired
trajectory in a single iteration, and is robust to noise and modeling error.Comment: 9 pages, 8 figure
Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing
Forecasting the behavior of high-dimensional dynamical systems using machine
learning requires efficient methods to learn the underlying physical model. We
demonstrate spatiotemporal chaos prediction using a machine learning
architecture that, when combined with a next-generation reservoir computer,
displays state-of-the-art performance with a training time times
faster and training data set times smaller than other machine
learning algorithms. We also take advantage of the translational symmetry of
the model to further reduce the computational cost and training data, each by a
factor of 10.Comment: 8 pages, 9 figure