Neural networks-based variationally enhanced sampling

Abstract

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 [Valsson and Parrinello, Phys. Rev. Lett. 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 new and 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.Machine learning (ML) is changing the way in which modern science is conducted. Atomistic based computer simulations are no exceptions. Since the work of Behler and Parrinello [1] neural networks [2,3] or Gaussian processes [4] are now almost routinely used to generate accurate potentials. More recently ML methods have been used to accelerate sampling, a crucial issue in molecular dynamics (MD) simulations, where standard methods allow only a very restricted range of time scales to be explored. An important family of enhanced sampling methods is based on the identifications of suitable collective variables (CVs) that are connected to the slowest relaxation modes of the system [5]. Sampling is then enhanced by constructing an external bias potential V (s) which depends on the chosen collective variables s. In this context machine learning has been applied in order to identify appropriate CVs [6,7,8,9,10] and to construct new methodologies [11,12,13,14,15]. From these early experiences, it is also clear that ML applications can in turn profit from enhanced sampling [16].

Machine Learning for Molecular Simulation

“…In addition to atomistic force fields, it has been recently shown that, in the same spirit, effective molecular models at resolution coarser than atomistic can be designed by ML [16,17,18]. Analysis and simulation of MD trajectories has also been affected by ML, for instance for the definition of optimal reaction coordinates [19,20,21,22,23,24], the estimate of free energy surfaces [25,26,27,22], the construction of Markov State Models [21,23,28], and for enhancing MD sampling by learning bias potentials [29,30,31,32,33] or selecting starting configurations by active learning [34,35,36]. Finally, ML can be used to generate samples from the equilibrium distribution of a molecular system without performing MD altogether, as proposed in the recently introduced Boltzmann Generators [37].…”

Machine learning for protein folding and dynamics

“…Machine learning has an important role here as it can help these methods by learning optimal choices of collective variables iteratively during sampling. For example, shallow machine learning methods have been used to adapt the CV space during Metadynamics [66,67], adversarial and deep learning have used to adapt the CV space during variationally enhanced sampling (VES, [68]) [69,70]. A completely different approach to predict equilibrium properties of a protein system is the Boltzmann Generator [71] that trains a deep generative neural network to directly sample the equilibrium distribution of a many-body system defined by an energy function, without using MD simulation.…”

DeepDriveMD: Deep-Learning Driven Adaptive Molecular Simulations for Protein Folding

“…Wang, Ribeiro, and Tiwary use a VAE [18] similar to our approach, however, constrain the encoder/decoder with an information bottleneck that identifies an optimal RC. Other approaches such as the neural networksbased variationally enhanced sampling [19] and Boltzmann Generators [20] share similar workflow motifs, although the exact use of MD simulations versus other types of sampling (e.g., Markov chain Monte Carlo) may differ. The approach investigated in this paper, and the other approaches described above are different from AlphaFold [21], where the target problem is to model the final folded 3dimensional structure of a protein from its primary sequence.…”