Learning transition states: approximation, sampling, and optimization with rare data
Grant Rostkoff, CIMS


The surprising flexibility and undeniable empirical success of machine learning algorithms has inspired many theoretical explanations for the efficacy of neural networks. Here, I will briefly introduce one perspective that provides not only asymptotic guarantees of trainability and accuracy in high-dimensional learning problems, but also provides some prescriptions and design principles for learning. Bolstered by the favorable scaling of these algorithms in high dimensional problems, I will turn to a central problem in computational condensed matter physics---that of computing reaction pathways. From the perspective of an applied mathematician, these problems typically appear hopeless; they are not only high-dimensional, but also dominated by rare events. However, with neural networks in the toolkit, at least the dimensionality is somewhat less intimidating. I will describe an algorithm that combines stochastic gradient descent with importance sampling to optimize a function representation of a reaction pathway for an arbitrary system. Finally, I will provide numerical evidence of the power and limitations of this approach.