Stabilizing machine learning prediction of dynamics: Novel noise-inspired regularization tested with reservoir computing.

Recent work has shown that machine learning (ML) models can skillfully forecast the dynamics of unknown chaotic systems. Short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics ("climate") can be produced by employing a feedback loop, whereby the model is trained to predict forward only one time step, then the model output is used as input for multiple time steps. In the absence of mitigating techniques, however, this feedback can result in artificially rapid error growth ("instability").

Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity.

We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the "climate" associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time.

Combining machine learning with knowledge-based modeling for scalable forecasting and subgrid-scale closure of large, complex, spatiotemporal systems.

We consider the commonly encountered situation (e.g., in weather forecast) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics.

Forecasting chaotic systems with very low connectivity reservoir computers.

We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate of the forecasted system rather than short-term prediction. We find that optimizing over this measure more quickly excludes reservoirs that fail to reproduce the climate.

Stability of Boolean networks: the joint effects of topology and update rules.

We study the stability of orbits in large Boolean networks. We treat the case in which the network has a given complex topology, and we do not assume a specific form for the update rules, which may be correlated with local topological properties of the network. While recent past work has addressed the separate effects of complex network topology and certain classes of update rules on stability, only crude results exist about how these effects interact.