3,945 research outputs found
q-State Potts model metastability study using optimized GPU-based Monte Carlo algorithms
We implemented a GPU based parallel code to perform Monte Carlo simulations
of the two dimensional q-state Potts model. The algorithm is based on a
checkerboard update scheme and assigns independent random numbers generators to
each thread. The implementation allows to simulate systems up to ~10^9 spins
with an average time per spin flip of 0.147ns on the fastest GPU card tested,
representing a speedup up to 155x, compared with an optimized serial code
running on a high-end CPU. The possibility of performing high speed simulations
at large enough system sizes allowed us to provide a positive numerical
evidence about the existence of metastability on very large systems based on
Binder's criterion, namely, on the existence or not of specific heat
singularities at spinodal temperatures different of the transition one.Comment: 30 pages, 7 figures. Accepted in Computer Physics Communications.
code available at:
http://www.famaf.unc.edu.ar/grupos/GPGPU/Potts/CUDAPotts.htm
Exact Combinatorial Optimization with Graph Convolutional Neural Networks
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose to learn a variable selection policy for branch-and-bound in mixed-integer linear programming, by imitation learning on a diversified variant of the strong branching expert rule. We encode states as bipartite graphs and parameterize the policy as a graph convolutional neural network. Experiments on a series of synthetic problems demonstrate that our approach produces policies that can improve upon expert-designed branching rules on large problems, and generalize to instances significantly larger than seen during training
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