Predicting catastrophes: the role of criticality
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Is prediction feasible in systems at criticality? While conventional scale-invariant arguments suggest a negative answer, evidence from simulation of driven-dissipative systems and real systems such as ruptures in material and crashes in the financial market have suggested otherwise. In this dissertation, I address the question of predictability at criticality by investigating two non-equilibrium systems: a driven-dissipative system called the OFC model which is used to describe earthquakes and damage spreading in the Ising model. Both systems display a phase transition at the critical point. By using machine learning, I show that in the OFC model, scaling events are indistinguishable from one another and only the large, non-scaling events are distinguishable from the small, scaling events. I also show that as the critical point is approached, predictability falls. For damage spreading in the Ising model, the opposite behavior is seen: the accuracy of predicting whether damage will spread or heal increases as the critical point is approached. I will also use machine learning to understand what are the useful precursors to the prediction problem.