(747f) Learning Free Energy Landscapes Using Artificial Neural Networks

The use of adaptive biasing potential methods to estimate free energies of relevant chemical processes from molecular simulation have gained popularity in recent years. Although metadynamics and its well-tempered variant remain the most widely used, new methods such as basis function sampling, variationally enhanced sampling and Green’s function sampling have been developed which improve upon some of the shortcomings of metadynamics. In particular, the use of a basis expansion to represent the biasing potential overcomes the limitations of a Gaussian-shaped kernel and offer more flexibility in representing the often nuanced and highly nonlinear free energy landscapes. Though said approaches can outperform traditional metadynamics under many circumstances, they remain limited by the functional form or basis set chosen to represent the underlying free energy surface (FES) of interest. Without a priori knowledge of the FES, the choice of parameters, such as the number of terms in a basis expansion, can significantly affect the accuracy and convergence behavior of the algorithm. FESs that have sharp curvature can also introduce characteristic oscillations due to the Runge or Gibbs phenomenon. This limitation can lead to oscillations which lead to dramatic under-sampling and a non-convergent bias.

Here we develop a powerful method wherein artificial neural networks (ANNs) are used to obtain the adaptive biasing potential, and thus learn free energy landscapes. As ANNs typically represent a form of supervised learning, we develop an iterative scheme which refines an unbiased estimator of a system's partition function. We demonstrate that this method is capable of rapidly adapting to complex free energy landscapes and is not prone to boundary or oscillation problems. The method offers a substantial degree of flexibility to the end-user in specifying the network architecture when the topological features of the FES of interest are not known. Importantly, because the bias learned by the ANN obtains the best continuous approximation of the free energy, we see a dramatic improvement in convergence, especially for poorly sampled states over currently available and broadly used techniques.