Information metrics for long-time errors in splitting schemes for stochastic dynamics and parallel KMC
For researchers in stochastic dynamics and parallel KMC, this provides a new framework to control long-time numerical errors and design better schemes, though the results are theoretical and not yet demonstrated on specific benchmarks.
The paper proposes an information-theoretic approach using relative entropy rate to analyze long-time errors in numerical splitting schemes for stochastic dynamics, particularly Parallel KMC. It enables a posteriori error tracking and scheme selection, leading to improved numerical error and processor communication efficiency.
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.