Neural networks-based variationally enhanced sampling

Significance Atomistic-based simulations are one of the most widely used tools in contemporary science. However, in the presence of kinetic bottlenecks, their power is severely curtailed. In order to mitigate this problem, many enhanced sampling techniques have been proposed. Here, we show that by combining a variational approach with deep learning, much progress can be made in extending the scope of such simulations. Our development bridges the fields of enhanced sampling and machine learning and allows us to benefit from the rapidly growing advances in this area. Sampling complex free-energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a small number of key collective variables and to introduce a bias potential that is able to favor their fluctuations in order to accelerate sampling. Here, we propose to use machine-learning techniques in conjunction with the recent variationally enhanced sampling method [O. Valsson, M. Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] in order to determine such potential. This is achieved by expressing the bias as a neural network. The parameters are determined in a variational learning scheme aimed at minimizing an appropriate functional. This required the development of a more efficient minimization technique. The expressivity of neural networks allows representing rapidly varying free-energy surfaces, removes boundary effects artifacts, and allows several collective variables to be handled.