Konstantinos Gourgoulias

Konstantinos Gourgoulias, Markos A. Katsoulakis, Luc Rey-Bellet

Parallel Kinetic Monte Carlo (KMC) is a potent tool to simulate stochastic particle systems efficiently. However, despite literature on quantifying domain decomposition errors of the particle system for this class of algorithms in the short and in the long time regime, no study yet explores and quantifies the loss of time-reversibility in Parallel KMC. Inspired by concepts from non-equilibrium statistical mechanics, we propose the entropy production per unit time, or entropy production rate, given in terms of an observable and a corresponding estimator, as a metric that quantifies the loss of reversibility. Typically, this is a quantity that cannot be computed explicitly for Parallel KMC, which is why we develop a posteriori estimators that have good scaling properties with respect to the size of the system. Through these estimators, we can connect the different parameters of the scheme, such as the communication time step of the parallelization, the choice of the domain decomposition, and the computational schedule, with its performance in controlling the loss of reversibility. From this point of view, the entropy production rate can be seen both as an information criterion to compare the reversibility of different parallel schemes and as a tool to diagnose reversibility issues with a particular scheme. As a demonstration, we use Sandia Lab's SPPARKS software to compare different parallelization schemes and different domain (lattice) decompositions.

Konstantinos Gourgoulias, Markos A. Katsoulakis, Luc Rey-Bellet

We propose an information-theoretic approach to analyze the long-time behavior of numerical splitting schemes for stochastic dynamics, focusing primarily on Parallel Kinetic Monte Carlo (KMC) algorithms.Established methods for numerical operator splittings provide error estimates in finite-time regimes, in terms of the order of the local error and the associated commutator. Path-space information-theoretic tools such as the relative entropy rate (RER) allow us to control long-time error through commutator calculations. Furthermore, they give rise to an a posteriori representation of the error which can thus be tracked in the course of a simulation. Another outcome of our analysis is the derivation of a path-space information criterion for comparison (and possibly design) of numerical schemes, in analogy to classical information criteria for model selection and discrimination. In the context of Parallel KMC, our analysis allows us to select schemes with improved numerical error and more efficient processor communication. We expect that such a path-space information perspective on numerical methods will be broadly applicable in stochastic dynamics, both for the finite and the long-time regime.

Laura Douglas, Iliyan Zarov, Konstantinos Gourgoulias et al.

We consider the problem of inference in a causal generative model where the set of available observations differs between data instances. We show how combining samples drawn from the graphical model with an appropriate masking function makes it possible to train a single neural network to approximate all the corresponding conditional marginal distributions and thus amortize the cost of inference. We further demonstrate that the efficiency of importance sampling may be improved by basing proposals on the output of the neural network. We also outline how the same network can be used to generate samples from an approximate joint posterior via a chain decomposition of the graph.