Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations

Abstract

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis is made possible by explicit forms for the gradients of a cost function in terms of the susceptibility of driven trajectories to changes in variational parameters. We consider probabilities of time-integrated dynamical observables as characterized by their large deviation functions, and find that in many cases the variational estimate is quantitatively accurate. Additionally, we provide expressions to exactly correct the variational estimate that can be evaluated directly. We benchmark this algorithm against the numerically exact solution of a model of a driven particle in a periodic potential, where the control force can be represented with a complete basis. We then demonstrate the utility of the algorithm in a model of repulsive particles on a line, which undergo a dynamical phase transition, resulting in singular changes to the form of the optimal control force. In both systems, we find fast convergence and are able to evaluate large deviation functions with significant increases in statistical efficiency over alternative Monte Carlo approaches.

arXiv comment14 pages, 10 figures

References in corpus (57)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• Motility-Induced Phase Separation
• Fluctuation theorem for stochastic dynamics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Topological mechanics of gyroscopic metamaterials
• Dynamics on the Way to Forming Glass: Bubbles in Space-time
• Growth and Division of Active Droplets: A Model for Protocells
• Forward Flux Sampling for rare event simulations
• A Variational Approach to Enhanced Sampling and Free Energy Calculations
• Direct evaluation of large-deviation functions
• Nonequilibrium Markov processes conditioned on large deviations
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Space-time Thermodynamics of the Glass Transition
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Simulating rare events in dynamical processes
• Numerically exact path integral simulation of nonequilibrium quantum transport and dissipation
• Neural networks-based variationally enhanced sampling
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Variational and optimal control representations of conditioned and driven processes
• Computing stationary distributions in equilibrium and non-equilibrium systems with Forward Flux Sampling
• Population dynamics method with a multi-canonical feedback control
• Effective interactions and large deviations in stochastic processes
• Current large deviations for driven periodic diffusions
• Design principles for non-equilibrium self-assembly
• Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
• Turning Statistical Physics Models Into Materials Design Engines
• The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics
• Robust nonequilibrium pathways to microcompartment assembly
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Dynamic transition in an atomic glass former: a molecular dynamics evidence
• Importance sampling large deviations in nonequilibrium steady states. I
• Large Deviation Function for a Driven Underdamped Particle in a Periodic Potential
• Adaptive sampling of large deviations
• Efficient Rare Event Simulation by Optimal Nonequilibrium Forcing
• Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
• Large deviations of Lyapunov exponents
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Current fluctuations of interacting active Brownian particles
• Rayleigh-Ritz Calculation of Effective Potential Far From Equilibrium
• Sampling rare events across dynamical phase transitions
• Dominant Reaction Pathways in High Dimensional Systems
• Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems
• Brownian asymmetric simple exclusion process
• Nonlinear transport coefficients from large deviation functions
• Dynamical phase transitions in supercooled liquids: interpreting measurements of dynamical activity
• A large-deviation approach to space-time chaos
• Preserving Correlations Between Trajectories for Efficient Path Sampling
• Direct evaluation of dynamical large-deviation rate functions using a variational ansatz
• Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions: Numerical Approach in Continuous Time
• Transport Coefficients from Large Deviation Functions
• Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories
• Three-body correlations and conditional forces in suspensions of active hard disks
• Malliavin weight sampling: a practical guide
• Enhanced diffusion of molecular motors in the presence of adenosine triphosphate and external force

Cited by in corpus (25)

• Ergodicity and large deviations in physical systems with stochastic dynamics
• Entropy production fluctuations encode collective behavior in active matter
• A reinforcement learning approach to rare trajectory sampling
• Collective motion in large deviations of active particles
• Learning nonequilibrium control forces to characterize dynamical phase transitions
• Dissipation bounds the amplification of transition rates far from equilibrium
• Reinforcement learning of rare diffusive dynamics
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Dynamical large deviations of linear diffusions
• Finite time large deviations via matrix product states
• Direct evaluation of rare events in active matter from variational path sampling
• Variational design principles for nonequilibrium colloidal assembly
• Phase Coexistence Implications of Violating Newton's Third Law
• A large deviation theory perspective on nanoscale transport phenomena
• Variational deep learning of equilibrium transition path ensembles
• Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization
• Modeling of biomolecular machines in non-equilibrium steady states
• Stochastic thermodynamic bounds on logical circuit operation
• Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control
• Variational time reversal for free energy estimation in nonequilibrium steady states
• Long-ranged correlations in large deviations of local clustering
• Time-Asymmetric Fluctuation Theorem and Efficient Free Energy Estimation
• Non-equilibrium pathways between cluster morphologies in active phase separation: necking, rupture and cavitation
• Steering Active-Colloid Assembly by Biasing Dissipation
• Making rare events typical in $d$-dimensional chaotic maps