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Register a new userNeural networks-based variationally enhanced sampling
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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, Physical Review Letters 2014] to determine such potential. This is achieved by expressing the bias as a neural network. The parameters are determined in a reinforcement learning scheme aimed at minimizing the variationally enhanced sampling functional. This required the development of a new and more efficient minimization technique. The expressivity of neural networks allows accelerating sampling in systems with rapidly varying free energy surfaces, removing boundary effects artifacts, and making one more step towards being able to handle several collective variables.
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A popular way to accelerate the sampling of rare events in molecular dynamics simulations is to introduce a potential that increases the fluctuations of selected collective variables. For this strategy to be successful, it is critical to choose appropriate variables. Here we review some recent developments in the data-driven design of collective variables, with a focus on the combination of Fishers discriminant analysis and neural networks. This approach allows to compress the fluctuations of metastable states into a low-dimensional representation. We illustrate through several examples the effectiveness of this method in accelerating the sampling, while also identifying the physical descriptors that undergo the most significant changes in the process.
Conventional artificial neural networks are powerful tools in science and industry, but they can fail when applied to nonlinear systems where order and chaos coexist. We use neural networks that incorporate the structures and symmetries of Hamiltonian dynamics to predict phase space trajectories even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on the canonical Henon-Heiles system, which models diverse dynamics from astrophysics to chemistry. The power of the technique and the ubiquity of chaos suggest widespread utility.
The determination of efficient collective variables is crucial to the success of many enhanced sampling methods. As inspired by previous discrimination approaches, we first collect a set of data from the different metastable basins. The data are then projected with the help of a neural network into a low-dimensional manifold in which data from different basins are well discriminated. This is here guaranteed by imposing that the projected data follows a preassigned distribution. The collective variables thus obtained lead to an efficient sampling and often allow reducing the number of collective variables in a multi-basin scenario. We first check the validity of the method in two-state systems. We then move to multi-step chemical processes. In the latter case, at variance with previous approaches, one single collective variable suffices, leading not only to computational efficiency but to a very clear representation of the reaction free energy profile.
The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested towards its solution. These methods are often grouped into two broad families. On the one hand methods such as umbrella sampling and metadynamics that build a bias potential based on few order parameters or collective variables. On the other hand, tempering methods such as replica exchange that combine different thermodynamic ensembles in one single expanded ensemble. We instead adopt a unifying perspective, focusing on the target probability distribution sampled by the different methods. This allows us to introduce a new class of collective-variables-based bias potentials that can be used to sample any of the expanded ensembles normally sampled via replica exchange. We also provide a practical implementation, by properly adapting the iterative scheme of the recently developed on-the-fly probability enhanced sampling method [Invernizzi and Parrinello, J. Phys. Chem. Lett. 11.7 (2020)], which was originally introduced for metadynamics-like sampling. The resulting method is very general and can be used to achieve different types of enhanced sampling. It is also reliable and simple to use, since it presents only few and robust external parameters and has a straightforward reweighting scheme. Furthermore, it can be used with any number of parallel replicas. We show the versatility of our approach with applications to multicanonical and multithermal-multibaric simulations, thermodynamic integration, umbrella sampling, and combinations thereof.
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that is based on constructing a model probability density from which a bias potential is derived. The model relies on the fact that in a physical system most of the configurations visited can be grouped into isolated metastable islands. To each island we associate a distribution that is fitted to a Gaussian mixture. The different distributions are linearly combined together with coefficients that are computed self consistently. Remarkably, from this biased dynamics, rates of transition between different metastable states can be straightforwardly computed.
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