Learning High-Dimensional Functions for Rare Events Sampling In and Out of Equilibrium
The surprising flexibility and undeniable empirical success of machine learning algorithms have 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 the problem of variational rare events calculations that arise in chemical physics. With neural networks in the toolkit, I will show it is possible to generate high-dimensional representations of free energies and a nonequilibrium analog of the free energy for dynamical observables. I will describe a class of algorithms that combines stochastic gradient descent with importance sampling to accurately determine these solutions.