Analyzing Multimodal Probability Measures with Autoencoders.

Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders.

Autoencoders for dimensionality reduction in molecular dynamics: Collective variable dimension, biasing, and transition states.

The heat shock protein 90 (Hsp90) is a molecular chaperone that controls the folding and activation of client proteins using the free energy of ATP hydrolysis. The Hsp90 active site is in its N-terminal domain (NTD). Our goal is to characterize the dynamics of NTD using an autoencoder-learned collective variable (CV) in conjunction with adaptive biasing force Langevin dynamics.

Computing Surface Reaction Rates by Adaptive Multilevel Splitting Combined with Machine Learning and Molecular Dynamics.

Computing accurate rate constants for catalytic events occurring at the surface of a given material represents a challenging task with multiple potential applications in chemistry. To address this question, we propose an approach based on a combination of the rare event sampling method called adaptive multilevel splitting (AMS) and molecular dynamics. The AMS method requires a one-dimensional reaction coordinate to index the progress of the transition.

Chasing Collective Variables Using Autoencoders and Biased Trajectories.

Free energy biasing methods have proven to be powerful tools to accelerate the simulation of important conformational changes of molecules by modifying the sampling measure. However, most of these methods rely on the prior knowledge of low-dimensional slow degrees of freedom, i.e.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems.

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

On a new class of score functions to estimate tail probabilities of some stochastic processes with adaptive multilevel splitting.

We investigate the application of the adaptive multilevel splitting algorithm for the estimation of tail probabilities of solutions of stochastic differential equations evaluated at a given time and of associated temporal averages. We introduce a new, very general, and effective family of score functions that is designed for these problems. We illustrate its behavior in a series of numerical experiments.

Analysis of the adaptive multilevel splitting method on the isomerization of alanine dipeptide.

We apply the adaptive multilevel splitting (AMS) method to the C → C transition of alanine dipeptide in vacuum. Some properties of the algorithm are numerically illustrated, such as the unbiasedness of the probability estimator and the robustness of the method with respect to the reaction coordinate. We also calculate the transition time obtained via the probability estimator, using an appropriate ensemble of initial conditions.

The Extended Generalized Adaptive Biasing Force Algorithm for Multidimensional Free-Energy Calculations.

Free-energy calculations in multiple dimensions constitute a challenging problem, owing to the significant computational cost incurred to achieve ergodic sampling. The generalized adaptive biasing force (gABF) algorithm calculates n one-dimensional lists of biasing forces to approximate the n-dimensional matrix by ignoring the coupling terms ordinarily taken into account in classical ABF simulations, thereby greatly accelerating sampling in the multidimensional space. This approximation may however occasionally lead to poor, incomplete exploration of the conformational space compared to classical ABF, especially when the selected coarse variables are strongly coupled.

Smoothed Biasing Forces Yield Unbiased Free Energies with the Extended-System Adaptive Biasing Force Method.

We report a theoretical description and numerical tests of the extended-system adaptive biasing force method (eABF), together with an unbiased estimator of the free energy surface from eABF dynamics. Whereas the original ABF approach uses its running estimate of the free energy gradient as the adaptive biasing force, eABF is built on the idea that the exact free energy gradient is not necessary for efficient exploration, and that it is still possible to recover the exact free energy separately with an appropriate estimator. eABF does not directly bias the collective coordinates of interest, but rather fictitious variables that are harmonically coupled to them; therefore is does not require second derivative estimates, making it easily applicable to a wider range of problems than ABF.

Jump Markov models and transition state theory: the quasi-stationary distribution approach.

We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space.

Adaptive Multilevel Splitting Method for Molecular Dynamics Calculation of Benzamidine-Trypsin Dissociation Time.

Adaptive multilevel splitting (AMS) is a rare event sampling method that requires minimal parameter tuning and allows unbiased sampling of transition pathways of a given rare event. Previous simulation studies have verified the efficiency and accuracy of AMS in the calculation of transition times for simple systems in both Monte Carlo and molecular dynamics (MD) simulations. Now, AMS is applied for the first time to an MD simulation of protein-ligand dissociation, representing a leap in complexity from the previous test cases.

ADAPTIVE MULTILEVEL SPLITTING IN MOLECULAR DYNAMICS SIMULATIONS.

Adaptive Multilevel Splitting (AMS) is a replica-based rare event sampling method that has been used successfully in high-dimensional stochastic simulations to identify trajectories across a high potential barrier separating one metastable state from another, and to estimate the probability of observing such a trajectory. An attractive feature of AMS is that, in the limit of a large number of replicas, it remains valid regardless of the choice of reaction coordinate used to characterize the trajectories. Previous studies have shown AMS to be accurate in Monte Carlo simulations.

The adaptive biasing force method: everything you always wanted to know but were afraid to ask.

In the host of numerical schemes devised to calculate free energy differences by way of geometric transformations, the adaptive biasing force algorithm has emerged as a promising route to map complex free-energy landscapes. It relies upon the simple concept that as a simulation progresses, a continuously updated biasing force is added to the equations of motion, such that in the long-time limit it yields a Hamiltonian devoid of an average force acting along the transition coordinate of interest. This means that sampling proceeds uniformly on a flat free-energy surface, thus providing reliable free-energy estimates.

Free energy calculations from adaptive molecular dynamics simulations with adiabatic reweighting.

We propose an adiabatic reweighting algorithm for computing the free energy along an external parameter from adaptive molecular dynamics simulations. The adaptive bias is estimated using Bayes identity and information from all the sampled configurations. We apply the algorithm to a structural transition in a cluster and to the migration of a crystalline defect along a reaction coordinate.

A multiple replica approach to simulate reactive trajectories.

A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many copies of the system, and selecting the replicas which have reached the highest values along a chosen one-dimensional reaction coordinate. This reaction coordinate does not need to precisely describe all the metastabilities of the system for the method to give reliable results.

Free energy calculations: an efficient adaptive biasing potential method.

We develop an efficient sampling and free energy calculation technique within the adaptive biasing potential (ABP) framework. By mollifying the density of states we obtain an approximate free energy and an adaptive bias potential that is computed directly from the population along the coordinates of the free energy. Because of the mollifier, the bias potential is "nonlocal", and its gradient admits a simple analytic expression.

Computation of free energy profiles with parallel adaptive dynamics.

We propose a formulation of an adaptive computation of free energy differences, in the adaptive biasing force or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows us to present a truly unifying framework for these methods, and to prove convergence results for certain classes of algorithms. From a numerical viewpoint, a parallel implementation of these methods is very natural, the replicas interacting through the reconstructed free energy.

An efficient sampling algorithm for variational Monte Carlo.

We propose a new algorithm for sampling the N-body density mid R:Psi(R)mid R:(2)R(3N)mid R:Psimid R:(2) in the variational Monte Carlo framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space (R,P) improved by a Metropolis-Hastings accept/reject step. We show through some representative numerical examples (lithium, fluorine, and copper atoms and phenol molecule) that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).