Asymptotically unbiased estimation of physical observables with neural samplers

Nicoli, Kim A.; Nakajima, Shinichi; Strodthoff, Nils; Samek, Wojciech; Müller, Klaus Robert; Kessel, Pan

doi:10.1103/physreve.101.023304

Cited by 85 publications

(116 citation statements)

References 18 publications

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“…Within these developments machine learning has critically influenced the domain of statistical mechanics, particularly in the study of phase transitions [3,4]. A wide range of machine learning techniques, including neural networks [5][6][7][8][9][10][11][12][13][14][15][16][17], diffusion maps [18], support vector machines [19][20][21][22] and principal component analysis [23][24][25][26][27] have been implemented to study equilibrium and non-equilibrium systems. Transferable features have also been explored in phase transitions, including modified models through a change of lattice topology [3] or form of interaction [28], in Potts models with a varying odd number of states [29], in the Hubbard model [6], in fermions [5], in the neural network-quantum states ansatz [30,31] and in adversarial domain adaptation [32].…”

Section: Introductionmentioning

confidence: 99%

Mapping distinct phase transitions to a neural network

2020

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We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems irrespective of the universality class, order, and the presence of discrete or continuous degrees of freedom. No prior knowledge about the existence of a phase transition is required in the target system and its entire parameter space can be scanned with multiple histogram reweighting to discover one. We establish our approach in q-state Potts models and perform a calculation for the critical coupling and the critical exponents of the φ 4 scalar field theory using quantities derived from the neural network implementation. We view the machine learning algorithm as a mapping that associates each configuration across different systems to its corresponding phase and elaborate on implications for the discovery of unknown phase transitions.

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Section: Introductionmentioning

confidence: 99%

Mapping distinct phase transitions to a neural network

2020

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“…The code for the simulation is written in Python using the NumPy library [38][39][40][41]. We note that using generative neural network, instead of Monte Carlo method, for sampling has also been proposed recently for the 1D quantum spin models [42,43].…”

Section: Methodology a Monte Carlo Samplingmentioning

confidence: 99%

Application of the Variational Autoencoder to Detect the Critical Points of the Anisotropic Ising Model

Baul¹,

Walker²,

Moreno³

et al. 2021

Preprint

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We generalize the previous study on the application of variational autoencoders to the twodimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for the entire range of anisotropic coupling. This presents an excellent test bed for the validity of using a variational autoencoder to characterize an anisotropic classical model. We reproduce the phase diagram for a wide range of anisotropic couplings and temperatures via a variational autoencoder without the explicit construction of an order parameter. Considering that the partition function of (d + 1)-dimensional anisotropic models can be mapped to that of the d-dimensional quantum spin models, the present study provides numerical evidence that a variational autoencoder can be applied to analyze quantum systems via Quantum Monte Carlo.

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“…Likewise, Ref. [193] explores a general framework for the estimation of observables with generative neural samplers focusing on autoregressive networks and normalizing flows that provide an exact sampling probability. These examples anticipate that neural autoregressive models have potential applications in important combinatorial optimization and constraint satisfaction problems, where finding the optimal configurations corresponds to finding ground states of glassy problems, and counting the number of solutions is equivalent to estimating the zero-temperature entropy of the system.…”

Section: Machine Learning Acceleration Of Monte Carlo Simulationsmentioning

confidence: 99%

Machine learning for quantum matter

Carrasquilla

2020

Advances in Physics: X

173

111

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Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested in quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics.

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Asymptotically unbiased estimation of physical observables with neural samplers

Cited by 85 publications

References 18 publications

Mapping distinct phase transitions to a neural network

Mapping distinct phase transitions to a neural network

Application of the Variational Autoencoder to Detect the Critical Points of the Anisotropic Ising Model

Machine learning for quantum matter

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