One way to bridge the scale between full atomistic models and more coarse-grained descriptions is to use Markov State models parameterized by the Eyring Kramers formulas. These formulas give the hopping rates between local minima of the potential energy function. They require to identify the local minima and saddle points of the potential energy function. This approach is for example used in...
I will discuss two methods to coarse-grain and predict atomic kinetics generated by molecular dynamics, with application to diffusion and plasticity in metals. When the energy landscape is metastable, atomic kinetics can be mapped to a discrete Markov chain with robust Bayesian bounds on unseen transitions. These bounds are used to allocate resources in massively parallel computation and...
As a meta-algorithm, population annealing can be combined with a wide range of simulation methods, including Monte Carlo and molecular dynamics. In the past, we have analyzed the approach regarding the scaling of statistical and systematic errors, proposed improvements and implemented the method on highly-efficient graphics processing units. In the present talk I will discuss recent...
In this talk, I will introduce sampling issues in glassy disordered systems, particularly glass-forming liquids, which consist of a long-standing problem in condensed matter physics. I will explain why this is important and difficult, and I will review various previous attempts.
In probability theory, the notion of "weak convergence" is often used to describe two equivalent probability distributions. This metric requires equivalence of the average value of well-behaved functions under the two probability distributions being compared. In coarse-grained modeling, Noid and Voth developed a thermodynamic equivalence principle that has a similar requirement. Nevertheless,...
Energy-based models (EBMs) are powerful generative machine learning models that are able to encode the complex distribution of a dataset in the Gibbs-Boltzmann distribution of a model energy function. This means that, if properly trained, they can be used to synthesize new patterns that resemble those of the data set as closely as possible, but also that this energy function can be used to...
Deep generative models parametrize very flexible families of distributions able to fit complicated datasets of images or text. These models provide independent samples from complex high-distributions at negligible costs. On the other hand, sampling exactly a target distribution, such a Bayesian posterior, is typically challenging: either because of dimensionality, multi-modality,...
The Koopman Operator presents a powerful framework for dimensionality reduction of (stochastic) dynamical systems. In addition, metastable sets and their rates of transition can be obtained by analysing its spectrum. In this talk, we first recap the basics of Koopman methods, and then move on to discuss recent advances and current challenges.
(joint work with Luca Nenna)
In this talk, we will present recent mathematical results about the Lieb functional in Density Functional Theory. More precisely, the Lieb functional, for a given electronic density, can be viewed as a generalized form of optimal transport problem for which the electronic density plays the role of a marginal. A numerical discretization of this problem can be...
This talk introduces Barrier Hamiltonian Monte Carlo (BHMC), a version of HMC which aims at sampling from a Gibbs distribution π on a manifold M, endowed with a Hessian metric g derived from a self-concordant barrier. Like Riemannian Manifold HMC, our method relies on Hamiltonian dynamics which comprise g. It incorporates the constraints defining M and is therefore able to exploit its...
Overdamped Langevin dynamics are stochastic differential equations, where gradient dynamics are perturbed by noise in order to sample high dimensional probability measures such as the ones appearing in computational statistical physics and Bayesian inference. By varying the diffusion coefficient, there are in fact infinitely many overdamped Langevin dynamics which preserve the target...
Modifying or biasing the dynamics of atomistic systems can result in faster mixing and convergence of thermodynamic observables, but it generally yields non-physical kinetics. I will introduce a family of so called "Accelerated Molecular Dynamics" methods that are specifically designed to produce statistically accurate "state-to-state" dynamics for metastable systems at a much reduced...
Coupling from the past is a method for obtaining perfect samples from Markov chain Monte Carlo algorithms. The price paid is that the running time becomes random. We will present some recent results concerning the limit behaviour of this random time, and discuss a number of open conjectures.
How to parallelize computation and how to diagnose convergence remain largely open questions regarding MCMC. Since Glynn & Rhee (Journal of Applied Probability, Vol. 51A, 2014), various advances based on couplings of MCMC algorithms have been proposed. The key is the design of coupled chains that, if properly constructed, can be employed to construct estimators that do not suffer from the...
