The standard Echo State Network (ESN) model has gained wide recognition for its success in modeling nonlinear auto-regressive (NAR) dynamical systems. For example, it is suitable for modeling the Mackey-Glass system, which is used for analyzing bifurcations in physiological applications. It is also employed to analyze the Lorenz system, which models several physical phenomena such as the...
Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations that govern many problems ranging from weather and climate prediction to turbulence simulations. Recent advances have seen machine learning (ML) increasingly...