Related papers: Scaling properties of multiscale equilibration
We investigate the increase in efficiency of simulated and parallel tempering MCMC algorithms when using non-reversible updates to give them "momentum". By making a connection to a certain simple discrete Markov chain, we show that, under…
Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…
Calculations of topological observables in lattice gauge theories with traditional Monte Carlo algorithms have long been known to be a difficult task, owing to the effects of long autocorrelations times. Several mitigation strategies have…
Using the Metropolis algorithm, we simulate the relaxation process of the three-dimensional kinetic Ising model. Starting from a random initial configuration, we first present the average equilibration time across the entire phase boundary.…
Metastability is a formidable challenge to Markov chain Monte Carlo methods. In this paper we present methods for algorithm design to meet this challenge. The design problem we consider is temperature selection for the infinite swapping…
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based…
A Markov chain update scheme using a machine-learned flow-based generative model is proposed for Monte Carlo sampling in lattice field theories. The generative model may be optimized (trained) to produce samples from a distribution…
We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolutions given by a generic master equation. Its two…
Whether and how a system reaches thermalization is a fundamental issue of statistical physics. While for one-dimensional lattices this issue has been intensively studied in terms of energy equipartition for more than half a century, few…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
We propose a new mathematical tool for the study of transport properties of models for lattice vibrations in crystalline solids. By replication of dynamical degrees of freedom, we aim at a new dynamical system where the "local" dynamics can…
A new approach to the dynamics of relaxation and kinetics of thermalization in a scalar field theory is presented that incorporates the relevant time scales through the resummation of hard thermal loops. An alternative derivation of the…
We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called…
Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…
The Markov length was recently proposed as an information-theoretic diagnostic for quantum mixed-state phase transitions [Sang & Hsieh, Phys. Rev. Lett. 134, 070403 (2025)]. Here, we show that the Markov length diverges even under classical…
It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case…
The finite-size scaling method in the equilibrium Monte Carlo(MC) simulations and the finite-time scaling method in the nonequilibrium-relaxation simulations are compromised. MC time data of various physical quantities are scaled by the MC…
We investigate the thermalization of a stochastic system with discrete phase space, initially at equilibrium at temperature $T_i$ and then termalizing in an environment at temperature $T_f$ , considering both cases $T_i > T_f$ and $T_i <…
We consider the equilibrium dynamics of Ising spin models with multi-spin interactions on sparse random graphs (Bethe lattices). Such models undergo a mean field glass transition upon increasing the graph connectivity or lowering the…