The workshop will start on Tuesday, February 2nd at 9:00, and end on Friday, February 5th at 14:00.

**Tuesday, February 2nd**

09h00-09h45 Registration and coffee

09h45-10h30 **M. Freidlin**, Longtime influence of small perturbations

10h30-11h15 **N. Berglund**, Sharp estimates on metastable lifetimes for one- and two-dimensional Allen-Cahn SPDEs (pdf)

11h15-12h00 **P. Dupuis**, Qualitative properties of parallel tempering and its infinite swapping limit (pdf)

12h30-14h00 Lunch break

14h00-14h45 **A. Beskos**, Hybrid Monte Carlo: Analytical Results and Improved Mixing in High Dimensions

14h45-15h30 **N. Kantas**, Calculating principal eigenfunctions of non-negative integral kernels: particle approximations and applications (pdf)

15h30-16h00 Coffee break

16h00-16h45 **G. Csanyi**, Exploration, sampling and free energy surface reconstruction: using Gaussan processes to improve adaptive potential of mean force methods (pdf)

16h45-17h30 **S. Schmidler**, cancelled

19h00-22h00 Reception

**Wednesday, February 3rd**

09h00-09h45 **A. Stuart**, Understanding Transition Paths using Gamma Convergence (pdf)

09h45-10h30 **A. Eberle, **Quantitative contraction rates for Markov chains on continuous state spaces (pdf)

10h30-11h00 Coffee break

11h00-11h45 **N. Chopin, **Sequential Quasi-Monte Carlo (pdf)

11h45-12h30 **S. Olla**, Diffusive macroscopic transport in non-acoustic chains (pdf)

12h30-13h30 Lunch break

13h30-14h45 Poster session (1)

14h45-15h30 **J. Garnier**, Uncertainty quantification and systemic risk (pdf)

15h30-16h00 Coffee break

16h00-16h45 **C. Andrieu**, Towards scalable Monte Carlo algorithms for some models involving latent variables

16h45-17h30 **G. Hummer**, Bayesian formulation of ensemble refinement and hybrid structural modeling with molecular simulations

**Thursday, February 4th**

09h00-09h45 **F. Malrieu**, Long time behavior of some Piecewise Deterministic Markov Processes (pdf)

09h45-10h30 **W. Krauth**, Fast Irreversible Monte Carlo simulations beyond the Metropolis paradigm (pdf)

10h30-11h00 Coffee break

11h00-11h45 **G. Lebeau**, Spectral analysis of random walks of Metropolis type (pdf)

11h45-12h30 **A. Voter**, Local Hyperdynamics (pdf)

12h30-13h30 Lunch break

13h30-14h45 Poster session (2)

14h45-15h30 **E. Moulines**, Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

15h30-16h00 Coffee break

16h00-16h45 **L. Bornn**, Moment conditions and Bayesian nonparametrics

16h45-17h30 **P. Espanol**, Energy-conserving Coarse-Graining of Complex Molecules (pdf)

19h30-22h30 Conference dinner

**Friday, February 5th**

09h00-09h45 **T. Bodineau**, Derivation of the linearized Boltzmann equation from a deterministic dynamics of diluted hard spheres (pdf)

09h45-10h30 ** L. Rey-Bellet**, Information theoretic tools for sensitivity analysis and numerical analysis of stochastic systems

10h30-11h00 Coffee break

11h00-11h45 **F. Bouchet**, Rare event algorithms and large deviations of turbulent atmosphere dynamics (pdf)

11h45-12h30 ** E. Vanden-Eijnden**, Infinite-Swap Replica Exchange Molecular Dynamics via Stochastic Simulation Algorithm Replica Exchange

12h30-14h00 Lunch break

** **

**Manon Baudel** (Université d'Orléans), Spectral theory for random Poincare maps

**Charles-Edouard Brehier** (CNRS and Universite de Lyon), Generalized Adaptive Multilevel Splitting for the simulation of rare events

**Kyrylo Chimisov** (University of Warwick), Adaptive Gibbs Sampler

**Gabriela Ciolek** (Université Paris Ouest ), Bootstrapping Harris recurrent Markov chains

**Matthew Dobson** (University of Massachussetts), Algorithms for the Long-time Simulation of Steady Nonequilibrium Flow

**Clement Erignoux** (Ecole polytechnique), Hydrodynamic limit for an active lattice gas: Swarming and phase transitions

**Gerome Faure** (CEA/DAM and Ecole des Ponts), Multiscale simulation with SDPD

**Gregoire Ferre** (CEA/DAM and Ecole des Ponts), Permutation invariant distance between atomic configurations

**Ahmed-Amine Homman** (CEA/DAM and Ecole des Ponts), New parallelizable schemes for the integration of the Dissipative Particle Dynamics with Energy conservation

**Jere Koskela** (University of Warwick), Importance Sampling Rare Trajectories in Reverse Time

**Jakub Krajniak** (KU Leuven), Generic reverse mapping method of polymers

**Antoine Levitt** (Inria Paris), numerical analysis of walker methods for saddle search

**Han Cheng Lie** (Freie Universitaet Berlin), Strongly convex approximation of a stochastic optimal control problem for importance sampling of diffusions

**Samuel Livingstone** (University of Bristol), On the geometric ergodicity of Hamiltonian Monte Carlo

**Yvon Maday** (Paris VI), Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics

**Bert Mortier** (KU Leuven), Conservative Monte Carlo estimators for neutrals in nuclear fusion simulations

**Antonietta Mira** (Università della Svizzera italiana), Variance reduction techniques for Monte Carlo simulation

**Keith Myerscough** (KU Leuven), Parareal computation of SDEs with time-scale separation

**Boris Nectoux** (Ecole des Ponts), Metastability and Transition State Theory

**Lara Neureither** (Freie Universitaet Berlin), On different notions of timescales in molecular dynamics

**Nikolas Nüksen **(Imperial College London), Nonreversible Langevin Samplers

**Zielinski Przemyslaw** (KU Leuven), A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations

** Jannes Quer **(Zuse Institue Berlin), Estimating exit rates in rare event dynamical systems via extrapolation

**Titles and abstracts**

**C. Andrieu** (University of Bristol)

Towards scalable Monte Carlo algorithms for some models involving latent variables

The probabilistic modelling of observed phenomena sometimes require the introduction of (unobserved) latent variables, which may or may not be of direct interest. This is for example the case when a realisation of a Markov chain is observed in noise and one is interested in inferring its transition matrix from the data. In such models inferring the parameters of interest (e.g. the transition matrix above) requires one to incorporate the latent variables in the inference procedure, resulting in practical difficulties. The standard approach to carry out inference in such models consists of integrating the latent variables numerically, most often using Monte Carlo methods. In the toy example above there are as many latent variables as there are observations, making the problem high-dimensional and potentially difficult.

We will show how recent advances in Markov chain Monte Carlo methods, in particular the development of “exact approximations” of the Metropolis-Hastings algorithm (which will be reviewed), can lead to algorithms which scale better than existing solutions.

This is joint work with Arnaud Doucet and Sinan Yildirim.

**Nils Berglund** (Université d'Orléans)

Sharp estimates on metastable lifetimes for one- and two-dimensional Allen-Cahn SPDEs

Consider an Allen-Cahn SPDE on the d-dimensional torus, for d=1 or 2, driven by weak space-time white noise. We provide Eyring-Kramers-type asymptotics for the mean transition time between stable stationary solutions, going beyond large-deviation (Arrhenius) estimates. In the case d=1, which is joint work with Barbara Gentz (Bielefeld), the mean transition time is known for all finite domain sizes. It contains a prefactor expressible in terms of ratios of spectral determinants. In the case d=2, the SPDE is only well-defined after a suitable renormalization is carried out. I will report on work in progress with Hendrik Weber (Warwick) and Giacomo di Gesu (CERMICS), yielding an expression for the prefactor when the domain is sufficiently small.

**Alexandros Beskos** (University College London)

Hybrid Monte Carlo: Analytical Results and Improved Mixing in High Dimensions

We investigate the performance of the nowadays popular Hybrid Monte Carlo (HMC) in high dimensions. For a class of target distributions, we characterise the optimal average acceptance probability for increasing dimension. In addition, we show that for the class of target distributions determined as a change of measure from Gaussian laws on Hilbert spaces, a modification of the standard HMC method can give an advanced algorithm whose mixing does not deteriorate upon mesh-refinement (in contract to the standard HMC). We show examples from diffusion models and SDEs driven by fractional Brownian motion.

**Thierry Bodineau **(Ecole polytechnique)

Derivation of the linearized Boltzmann equation from a deterministic dynamics of diluted hard spheres

We derive the time correlations of the fluctuation field associated to a Newtonian dynamics of hard-spheres starting from equilibrium. We will show that, in the Boltzmann-Grad limit, the covariance of the fluctuation field relaxes according to the linearized Boltzmann equation.

**Freddy Bouchet **(ENS Lyon)

Rare event algorithms and large deviations of turbulent atmosphere dynamics

Many natural and experimental turbulent flows display a bistable behavior: rare and abrupt dynamical transitions between two very different subregions of the phase space. The most prominent natural examples are probably the Earth magnetic field reversals (over geological timescales), the Kuroshio current bistability, or the Dansgaard-Oeschger events that have affected the Earth climate during the last glacial period. I will present recent results that show similar bistability for the turbulent dynamics of atmosphere jets. Those abrupt transitions are extremely rare events that change drastically the nature of the flow and the associated climate and are thus of paramount importance. Large deviation theory and rare event algorithms are the key tools for the future science of those phenomena.

I will present recent study of turbulent atmosphere dynamics rare events. The theoretical results are based on averaging and large deviation theory applied to stochastic partial differential equations. Those results are complemented by numerical results using rare event algorithms (the adaptive multilevel splitting algorithm, and the Giardina-Kurchan-Leconte-Tailleur algorithm) applied to turbulent dynamics. Applications to Jupiter's atmosphere bistability and Earth’s atmosphere will be discussed.

** Luke Bornn** (Harvard University)

Moment conditions and Bayesian nonparametrics

Models phrased though moment conditions are central to much of modern statistics and econometrics. Here these moment conditions are embedded within a nonparametric Bayesian setup. Handling such a model is not probabilistically straightforward as the posterior has support on a manifold. We solve the relevant issues, building new probability and computational tools using Hausdorff measures to analyze them on real and simulated data. These new methods can be applied widely, including providing Bayesian analysis of quasi-likelihoods, linear and nonlinear regression and quantile regression, missing data, set identified models, and hierarchical models.

**Nicolas Chopin** (ENSAE)

Sequential Quasi-Monte Carlo

(joint work with Mathieu Gerber, Harvard University)

We derive and study SQMC (Sequential Quasi-Monte Carlo), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array-RQMC algorithm of L'Ecuyer et al. (2006). The complexity of SQMC is O(N logN), where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate O(N^{−1/2}). The only requirement to implement SQMC is the ability to write the simulation of X_t given X_{t-1} as a deterministic function of X_{t-1} and a fixed number of uniform variates. We show that SQMC is amenable to the same extensions as standard SMC, such as forward smoothing, backward smoothing, unbiased likelihood evaluation, and so on. In particular, SQMC may replace SMC within a PMCMC (particle Markov chain Monte Carlo) algorithm. We establish several convergence results. We provide numerical evidence that SQMC may significantly outperform SMC in practical scenarios.

**Gabor Csanyi** (University of Cambridge)

Exploration, sampling and free energy surface reconstruction: using Gaussan processes to improve adaptive potential of mean force methods

The task of determining the free energy surface in a low dimensional collective variable space can be separated into the three subtasks of exploration, sampling and reconstruction. A wide range of existing methods can be usefully grouped according to the approach they take to solving each of these. I will show what overall performance gains can be obtained by picking the best-of-breed technique for each subtask.

**Paul Dupuis** (Brown University)

Qualitative properties of parallel tempering and its infinite swapping limit

We review the construction of the infinite swapping limit of parallel tempering, as well as sense in which a large deviations analysis shows it to be optimal. We then describe an easy-to-compute diagnostic, and present a theoretical result showing that the convergence of the diagnostic to its (a priori known) limit is a necessary condition for the convergence of the empirical measure for infinite swapping to its limit. If time permits we will also describe some new applications of the infinite swapping algorithm.

**Andreas Eberle** (University of Bonn)

Quantitative contraction rates for Markov chains on continuous state spaces

We introduce a new approach for quantifying contraction properties of Markov chains. The contraction rates are based on a Wasserstein distance that is adjusted to the chain. Upper bounds for the rates are obtained by variants of reflection couplings. The approach is applied to Euler schemes and to different types of Metropolis-Hastings methods on high dimensional Euclidean spaces.

**Pep Espanol** (UNED, Madrid)

Energy-conserving Coarse-Graining of Complex Molecules

Coarse-graining (CG) of complex molecules is a way to reach time scales that would be impossible to access through brute force molecular simulations. In this paper, we formulate a coarse-grained model for complex molecules from first principles that ensures energy conservation. Each molecule is described in a coarse way by a thermal blob characterized by the position and momentum of the center of mass of the molecule, together with its internal energy as an additional degree of freedom. This level of description gives rise to an entropy-based framework instead of the usual one based on the configurational free energy (i.e. potential of mean force). The resulting dynamic equations, which account for a proper description of heat transfer at the coarse grained level, have the structure of the energy conserving Dissipative Particle Dynamics model but with a clear microscopic underpinning. Under suitable approximations, we provide explicit microscopic expressions for each component (entropy, mean force, friction and conductivity coefficients) appearing in the coarse-grained model. These quantities can be computed directly with MD simulations. The proposed non-isothermal coarse-grained model is thermodynamically consistent and opens up a first principles CG strategy to the study of energy transport issues that are not accessible with current isothermal models.

**Mark Freidlin** (University of Maryland)

Long time influence of small perturbations

I will consider small deterministic and stochastic perturbations of dynamical systems and stochastic processes. If the non-perturbed system has a unique normalized invariant measure the perturbed system (or process) can have many invariant measures, but these measures, under mild assumptions, will be close in the weak topology to the invariant measure of the original system. The long time behavior of the perturbed system in this case will be, in a sense, close to the behavior of the non-perturbed system. But if the original system has many stationary measures (such normalized measures form a simplex), the perturbations, in an appropriate time scale, will induce a motion on the simplex of invariant probability measures. This motion determines the long time behavior of the perturbed system. Each simplex is a convex envelope of its extreme points which in our case are the ergodic probability measures. A parameterization of the set of extreme points allows to describe the motion on the simplex using the large deviation theory, modified averaging principle, or a diffusion approximation. I will demonstrate how such an approach works in the case of deterministic thermostat-like perturbations of oscillators. In particular, we will see that deterministic perturbations can lead to a stochastic long time behavior.

**Josselin Garnier **(University Paris VII)

Uncertainty quantification and systemic risk

(Joint work with G. Papanicolaou and T.-W. Yang (Stanford University))

The quantification of uncertainty in large-scale scientific and engineering computations is emerging as a research area that poses very challenging problems which go beyond sensitivity analysis and small fluctuation theories. We want to understand complex systems that operate in regimes where small changes in parameters can lead to very different solutions. We would like to analyze these regimes and calculate the small probabilities of large (possibly catastrophic) changes. These questions lead us into systemic risk analysis, that is, the calculation of probabilities that a large number of components in a complex interconnected system will fail simultaneously. We will discuss in some detail two model problems. One is a mean field model of interacting diffusive particles and the other one is a large deviation problem for a scalar conservation law.

**Gerhard Hummer** (Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Frankfurt am Main)

Bayesian formulation of ensemble refinement and hybrid structural modeling with molecular simulations

As the focus of structural biology moves toward dynamic and partially disordered biomolecular structures, ensemble refinement becomes increasingly important. We employ a Bayesian framework to formulate the problem of ensemble refinement and hybrid modeling of diverse experimental data. With this formulation, we can show that seemingly different approaches give identical results in the appropriate limits. We also introduce novel sampling methods that allow us to integrate data from a broad range of experiments with proper relative weights.

**Nikolas Kantas** (Imperial College London)

Calculating principal eigenfunctions of non-negative integral kernels: particle approximations and applications

Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigen-function and eigen-value of a non-negative integral kernel. Except in the finite-dimensional case, usually neither the principal eigen-function nor the eigen-value can be computed exactly. In this paper, we develop numerical approximations for these quantities. We show how a generic interacting particle algorithm can be used to deliver numerical approximations of the eigen-quantities and the associated so-called "twisted" Markov kernel as well as how these approximations are relevant to the aforementioned applications. In addition, we study a collection of random integral operators underlying the algorithm, address some of their mean and path-wise properties, and obtain Lr error estimates. Finally, numerical examples are provided in the context of importance sampling for computing tail probabilities of Markov chains and computing value functions for a class of stochastic optimal control problems. This is joint work with Nick Whiteley.

**Werner Krauth** (Statistical Physics Laboratory, Ecole normale supérieure)

Fast Irreversible Monte Carlo simulations beyond the Metropolis paradigm

I show how the lifting principle and a new pairwise decomposition of the Metropolis filter allows one to design a class of powerful rejection-free Markov-chain Monte Carlo algorithms that break detailed balance yet satisfy detailed balance. These algorithms generalize our recent hard-sphere event-chain Monte Carlo method. The new approach breaks with all the three paradigms of common Markov-chain methods: 1/ Moves are infinitesimal rather than finite; 2/ Detailed balance is broken yet global balance is satisfied; 3/ Rejections are replaced by liftings, and moves are persistent.

As an application, I demonstrate considerable speed-up of the event-chain algorithm for particle systems and spin models. I then sketch extensions to the simulation of long-range models without cutoffs or Ewald summations.

E. P. Bernard, W. Krauth, D. B. Wilson Phys.Rev. E 80 056704 (2009)

E. P. Bernard, W. Krauth Phys. Rev. Lett. 107, 155704 (2011)

M. Michel, S. C. Kapfer, W. Krauth J. Chem. Phys. 140 54116 (2014)

S. C. Kapfer, W. Krauth Phys. Rev. Lett. 114, 035702 (2015)

**Gilles Lebeau** (Université de Nice)

Spectral analysis of random walks of Metropolis type

We will present some results on the spectral analysis of reversible Markov chains of Metropolis type. These random walks depends on a small parameter h \in ]0,h_0] which is roughly the size of each step of the walk and the results are uniform with respect to h. This includes uniform bounds with respect to $h$ on the rate of convergence to equilibrium, and the convergence when h \to 0 to the associated continuous diffusion. We will focus on: hard spheres (the original Metropolis algorithm), hypoelliptic walks, and the relationships with classical PDE's estimates and pseudodifferential calculus.

(works in collaboration with L. Michel and P. Diaconis)

**Florent Malrieu** (Université de Tours)

Long time behavior of some Piecewise Deterministic Markov Processes

The dynamics of a PDMP is very simple: a deterministic motion punctuated by random jumps. These processes naturally arise in many modelization areas (biology, communication networks) but also as the limiting dynamics of some Metropolis-Hastings algorithms for example. In this talk, I will review some tools to get precise estimates for the long time behavior of these processes.

**Eric Moulines** (Ecole polytechnique)

Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

(joint work with Alain Durmus)

Sampling distribution over high-dimensional state-space is a problem which has recently attracted a lot of research efforts; applications include Bayesian non-parametrics, Bayesian inverse problems and aggregation of estimators. All these problems boil down to sample a target distribution (known up to a normalization factor) which is log-concave (but not necessarily smooth). In this paper, we study a sampling technique based on the Euler discretization of the Langevin stochastic differential equation. Contrarily to the Metropolis Adjusted Langevin Algorithm (MALA), we do not apply a Metropolis-Hastings correction. We obtain for both constant and decreasing step sizes in the Euler discretization, non-asymptotic bounds for the convergence to stationarity in both total variation and Wasserstein distances. A particular attention is paid on the dependence on the dimension of the state space, to demonstrate the applicability of this method in the high dimensional setting. These bounds extend the results obtained earlier by Dalalyan (2014) and in several recent works of Eberle (2015,2016). We also investigate the convergence of an appropriately weighted empirical measure and we report sharp bounds for the mean sq uare error and exponential deviation inequality for Lipschitz functions. Some Monte Carlo experiments will be presented to support our findings.

**Stefano Olla** (University Paris Dauphine)

Diffusive macroscopic transport in non-acoustic chains

We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the curvature (or bending) of the chain satisfy, in a diffusive space-time scaling, an autonomous system of equations. The curvature and momentum evolve following a linear system that corresponds to a damped Euler-Bernoulli beam equation. The macroscopic energy density evolves following a non linear diffusive equation. In particular the energy transfer is diffusive in this dynamics. This provides a first rigorous example of a normal diffusion of energy in a one dimensional dynamics that conserves the momentum (work in collaboration with T. Komorowski). We expect a similar behavior for non-linear non-acoustic chains. Simulations are currently running (work in collaboration with J. Roussel and G. Stoltz).

**Luc Rey-Bellet** (University of Massachussetts)

Information theoretic tools for sensitivity analysis and numerical analysis of stochastic systems

We are interested stochastic dynamics in the long-time (steady state) regime for systems with possible a large number of degrees of freedom. Of particular interest are non-equilibrium systems for which the steady state is not known explicitly. We show that both the sensitivity analysis and the numerical analysis of such systems can be performed using tools from statistical mechanics, that is relative entropies rate, Fisher information rate, and relative free energies if we concentrate on the path-space measures of such processes. The results rely in part on a new information inequality originating in the work from Chowdhary and Dupuis.

**Andrew Stuart** (Warwick University)

Understanding Transition Paths using Gamma Convergence

(Joint work with Yulong Lu and Hendrik Weber)

Determining the structure of transition paths at small temperature is a challenging computational and mathematical problem. This problem is studied here in the overdampled limit and in the regime where the transition time scales as the inverse temperature. Rescaling to a unit interval gives a diffusion with large potential and order one noise. Use of the idea of paths of maximal probability leads to transitions which exhibit physically unrealistic charcteristics, and this is demonstrated numerically, and through the use of gamma convergence, in [1] and [2]. The difficulty is associated with ignorning entropic contributions to the pathspace probabilities. In [3] a method for finding the best Gaussian approximation to a pathspace measure was introduced, and this allows the possibility of including entropic effects; the method is based on minimizing the Kullback-Liebler divergence between the Gaussian approximation and the desired measure. Development of numerical methods based on this approach is described in [4].

In this work the methodology from [3] is applied and gamma limits of the resulting minimization problem, over a subclass of Gaussian measures, is studied. It is shown that this approach removes the unphysical effects described in [1,2] and links with the large deviation approach to the problem are established. Furthermore the methodology provides Gaussian approximations, based on inhomogeous Ornstein-Uhlenbeck processes, which characterize fluctuations about the mean transition path.

[1] F.J. Pinski and A.M. Stuart, Transition paths in molecules: gradient descent in pathspace. Journal of Chemical Physics 132 (2010), 184104.

[2] F.Pinski, A.M.Stuart and F. Theil, Gamma limit for transition paths of maximal probability. Journal of Statistical Physics 146/5 (2012) 955-974.

[3] F.J. Pinski, G. Simpson, A.M. Stuart and H. Weber, Kullback-Leibler approximation for probability measures on infinite dimensional spaces. arxiv.org/abs/1310.7845 (SIAM J. Math. Analysis, to appear)

[4] F.J. Pinski, G. Simpson, A.M. Stuart and H. Weber, Algorithms for Kullback-Leibler approximation for probability measures in infinite dimensions. arxiv.org/abs/1408.1920 (SIAM J. Sci. Comp. to appear)

**Eric Vanden-Eijnden** (Courant Institute)

Infinite-Swap Replica Exchange Molecular Dynamics via Stochastic Simulation Algorithm Replica Exchange

Molecular Dynamics (REMD) is a popular method to accelerate conformational sampling of complex molecular sys- tems. The idea is to run several replica of the system at different temperatures that are inter-swapped periodically. These swaps are typically enforced using a discrete-time Markov scheduling based on Metropolis-Hasting acceptance/rejection criterion so as to guarantee that the joint distribution of the replica is the normalized sum of the symmetrized product of the canonical distribu- tions of these replicas at the different temperatures. I will discuss a different implementation of REMD in which the temperature swaps obey a continuous-time Markov jump process implemented via Gillespie’s stochastic simulation algorithm (SSA). This REMD-SSA also samples exactly the aforementioned joint distribution and has the advantage to be rejection free. As a result it permits to accelerate the rate of swapping of the temperature and reach the infinite-swap limit that is known to optimize sampling efficiency. In practice, this infinite-swap limit is implemented by combining REMD-SSA with the heterogeneous multi-scale method (HMM). The method is easy to implement and can be trivially parallelized. I will illustrate its accuracy and efficiency by making the free energy landscape of alanine dipeptide in vacuum and C-terminal β-hairpin of protein G in explicit solvent.

**Arthur Voter** (Theoretical Division, Los Alamos National Laboratory)

Local Hyperdynamics

I will present a new, local formulation of hyperdynamics that makes it suitable for very large systems. In standard hyperdynamics, the requirement that the bias potential be zero everywhere on the dividing surface bounding the state has the consequence that for large systems the boost factor decays to unity, regardless of the form of the bias potential. In the new method, the bias force on each atom (or bond) is obtained by differentiating a local bias energy that depends only on the coordinates of atoms within a finite range of this atom or bond. I will discuss why this is expected to give accurately boosted dynamics in spite of the fact that the dynamics are no longer conservative, and I will show that for realistic atomistic systems the method gives escape rates in excellent agreement with direct molecular dynamics simulations.

This work has been supported by United States Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.