AI may help predict previously unseen states in dynamical systems

Like the Earth does not stop its orbit around the sun, most physical systems exhibit at least one stable long-term behavior, generically called an attractor. When a system has more than one attractor, it is multistable.

Studying multiple attractors in a system usually requires a mathematical model and careful numerical scheme. Röhm et al. reported a method to map out attractors of a target system without such a mathematical model.

The authors used the machine-learning technique reservoir computing to find the shape, type, and location of all the attractors in a 4D extension of the well-known chaotic Lorenz system. They found they only needed training data about a single attractor to successfully infer the behavior of other unseen attractors in the system.

“Previously, reservoir computing was used to reconstruct attractors from data, i.e., directly learn the shape of the behavior present in some time series. Recently, this has been extended to learning about bifurcations of the system around these attractors,” co-author André Röhm said. “The novelty of our work lies in the fact that we are obtaining information about system states far away from the training data and beyond the corresponding basin of attraction.”

The team trained their reservoir computer to predict the behavior of a system from one time point to the next, first feeding the machine information about known behavior and then using the machine’s own predictions as inputs for subsequent iterations. This approach allowed the team to analyze many possible system states.

With further study, the authors aim to better understand why some reservoir computers fail to learn the right kind of dynamics.

Source: “Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing,” by André Röhm, Daniel J. Gauthier, and Ingo Fischer, Chaos (2021). The article can be accessed at https://doi.org/10.1063/5.0065813 .