GPU accelerated population annealing algorithm

Abstract

Population annealing is a promising recent approach for Monte Carlo simulations in statistical physics, in particular for the simulation of systems with complex free-energy landscapes. It is a hybrid method, combining importance sampling through Markov chains with elements of sequential Monte Carlo in the form of population control. While it appears to provide algorithmic capabilities for the simulation of such systems that are roughly comparable to those of more established approaches such as parallel tempering, it is intrinsically much more suitable for massively parallel computing. Here, we tap into this structural advantage and present a highly optimized implementation of the population annealing algorithm on GPUs that promises speed-ups of several orders of magnitude as compared to a serial implementation on CPUs. While the sample code is for simulations of the 2D ferromagnetic Ising model, it should be easily adapted for simulations of other spin models, including disordered systems. Our code includes implementations of some advanced algorithmic features that have only recently been suggested, namely the automatic adaptation of temperature steps and a multi-histogram analysis of the data at different temperatures.

12 pages, 3 figures and 5 tables, code at https://github.com/LevBarash/PAising

References in corpus (10)

• Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering
• Simulating spin models on GPU
• Random number generators for massively parallel simulations on GPU
• The critical behavior of 3D Ising glass models: universality and scaling corrections
• Universal critical behavior of the 2d Ising spin glass
• Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions
• Massively parallel multicanonical simulations
• Optimized GPU simulation of continuous-spin glass models
• Population Annealing Simulations of a Binary Hard Sphere Mixture
• Exploring first-order phase transitions with population annealing

Cited by in corpus (34)

• Understanding population annealing Monte Carlo simulations
• Model-Free Data-Driven Inference in Computational Mechanics
• Optimization of population annealing Monte Carlo for large-scale spin-glass simulations
• Analysis and Optimization of Population Annealing
• Computational hardness of spin-glass problems with tile-planted solutions
• Accelerating molecular dynamics simulations with population annealing
• Estimating the Density of States of Frustrated Spin Systems
• Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions
• Weighted averages in population annealing: analysis and general framework
• Three-dimensional universality class of Ising model with power-law-correlated critical disorder
• Equilibrium Microcanonical Annealing for First-Order Phase Transitions
• GPU Based Parallel Ising Computing for Combinatorial Optimization Problems in VLSI Physical Design
• Melting of a two-dimensional monodisperse cluster crystal to a cluster liquid
• Approximate ground states of the random-field Potts model from graph cuts
• Blume-Capel model analysis with microcanonical population annealing method
• Optimal schedules for annealing algorithms
• An effective introduction to the Markov Chain Monte Carlo method
• Superdiffusion-like behavior in zero-temperature coarsening of the $d=3$ Ising model
• A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Annealed Flow Transport Monte Carlo
• Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
• Comparison of the microcanonical population annealing algorithm with the Wang-Landau algorithm
• Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions
• Nonflat Histogram Techniques for Spin Glasses
• Algorithm for the replica redistribution in the implementation of parallel annealing method on the hybrid supercomputer architecture
• Flat histogram method comparison on 2D Ising Model
• Massively parallel simulations for disordered systems
• Massive-Scale Simulations of 2D Ising and Blume-Capel Models on Rack-Scale Multi-GPU Systems
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass
• Frustrated Ising model on the honeycomb lattice: Metastability and universality
• Resampling schemes in population annealing -- numerical results
• Quasi-exact ground-state algorithm for the random-field Potts model
• GPU-based Ising Computing for Solving Balanced Min-Cut Graph Partitioning Problem