Many psychological phenomena may be understood as nonlinear dynamical systems, which may have sensitive dependence on initial conditions. These systems increase in uncertainty as predictions are forecast further into the future. Few methods exist for predicting nonlinear time series. HAVOK (Hankel Alternative View of Koopman; Brunton et al., 2017) analysis is an exception. HAVOK was designed to globally linearize and model nonlinear and chaotic systems by decomposing nonlinear systems into intermittently forced linear systems. A forcing parameter allows HAVOK to demarcate regions where a time series is approximately linear from those that are nonlinear. Obtaining linear representations for strongly nonlinear and chaotic systems could revolutionize the prediction and control of these systems. HAVOK is a robust modeling method that can model noisy Likert-type data with missingness, making it a powerful tool for the prediction and control of psychological processes.
HAVOK is exceptionally good at modeling dynamic phenomena across different fields when the right hyperparameters are found. Two years ago, we introduced the havok R package (Moulder, Martynova & Boker, 2020), which allows estimation of HAVOK models for any time series given user selected hyperparameters. However, determining a set of hyperparameters that will produce a well-fitting model might be challenging as the relationship between hyperparameters does not follow a consistently predictable pattern. Unlike havok(), parallel HAVOK (phavok) is a parallelized optimization routine for HAVOK that optimizes hyperparameter/model selection and consistently yields well-fitting models (given at least one exists). phavok() runs multiple models simultaneously across many sets of hyperparameters and generates model fit surfaces in a reasonable amount of time. In this presentation, I will demonstrate some results from both theoretical and applied examples, discuss phavok()’s implementation, discuss differences between havok() and phavok(), and our plans on the havok package’s further development and upcoming CRAN release.