Sparse Autoregressive Neural Networks for Classical Spin Systems
arxiv(2024)
摘要
Efficient sampling and approximation of Boltzmann distributions involving
large sets of binary variables, or spins, are pivotal in diverse scientific
fields even beyond physics. Recent advancements in generative neural networks
have significantly impacted this domain. However, those neural networks are
often treated as black boxes, with architectures primarily influenced by
data-driven problems in computational science. Addressing this gap, we
introduce a novel autoregressive neural network architecture named TwoBo,
specifically designed for sparse two-body interacting spin systems. We directly
incorporate the Boltzmann distribution into its architecture and parameters,
resulting in enhanced convergence speed, superior free energy accuracy, and
reduced trainable parameters. We perform numerical experiments on disordered,
frustrated systems with more than 1000 spins on grids and random graphs, and
demonstrated its advantages compared to previous autoregressive and recurrent
architectures. Our findings validate a physically informed approach and suggest
potential extensions to multi-valued variables and many-body interaction
systems, paving the way for broader applications in scientific research.
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