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Finding the stationary states of a free energy functional is an important problem in phase field crystal (PFC) models. Many efforts have been devoted for designing numerical schemes with energy dissipation and mass conservation properties.…
Predicting the binding affinity between small molecules and target macromolecules while combining both speed and accuracy, is a cornerstone of modern computational drug discovery which is critical for accelerating therapeutic development.…
We propose a formulation of adaptive computation of free energy differences, in the ABF or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows to present a truly…
We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting…
Free energy calculations are widely used tools in computational chemistry, but their dependence on the assignment of partial charges during force field parametrization reduces their accuracy and reproducibility. In this work, we highlight…
We present an efficient classical algorithm for training deep Boltzmann machines (DBMs) that uses rejection sampling in concert with variational approximations to estimate the gradients of the training objective function. Our algorithm is…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
We develop a method to fit high-temperature Gibbs free energy data for the development of interatomic potentials for atomic systems. The approach is based on Hamiltonian thermodynamic integration, enabling the identification of suitable…
We introduce a simple enhanced sampling approach for the calculation of free energy differences and barriers along a one-dimensional reaction coordinate. First, a small number of short nonequilibrium simulations are carried out along the…
We present an Adaptively Biased Molecular Dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using non-equilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling…
A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A…
Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…
The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free energy based on work measurements of nonequilibrium, finite-time processes and their reversed counterparts by applying Bennett's acceptance…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for…
We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…
This paper develops and analyzes a stochastic derivative-free optimization strategy. A key feature is the state-dependent adaptive variance. We prove global convergence in probability with algebraic rate and give the quantitative results in…
Restricted Boltzmann machines (RBMs) constitute one of the main models for machine statistical inference and they are widely employed in Artificial Intelligence as powerful tools for (deep) learning. However, in contrast with countless…
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field…
Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation…