Prediction of Events in Metastable Systems Near Criticality

Predicting nucleation of metastable systems is an important but challenging problem. It can help society forecast, prevent, or prepare for upcoming catastrophes. Unfortunately, many metastable systems in nature operate near a critical point, and are empirically unpredictable. We developed machine learning predictors, applied them to the prediction of nucleation events in a metastable Ising model, near and far from the spinodal critical point. We observed decreasing predictability as the system approaches critical point, and found that this unpredictability is due to the vanishing difference between the fluctuations of local densities and the precursor of events. We also successfully predicted nucleation in a Lennard-Jones liquid. We developed a visual representation of Lennard-Jones configuration using the particles' symmetry order parameters. We determined the distinguishing order parameters that give major precursors before nucleation. Finally, we investigated the noise-induced critical point in two variations of the OFC model -- a coupled OFC model and an OFC model with multiplicative noise. In both variations, we found a critical phase boundary that separates the ergodic and non-ergodic phase of the OFC model, and the termination point of the phase boundary, which may imply a higher-order phase transition.