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Generalizing Hamiltonian Monte Carlo with Neural Networks [article]

Daniel Levy, Matthew D. Hoffman, Jascha Sohl-Dickstein
2018 arXiv   pre-print
We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution.  ...  Our method generalizes Hamiltonian Monte Carlo and is trained to maximize expected squared jumped distance, a proxy for mixing speed.  ...  Monte Carlo').  ... 
arXiv:1711.09268v3 fatcat:e3ls4iags5hshodawirtxkpslq

Bayesian deep neural networks for low-cost neurophysiological markers of Alzheimer's disease severity [article]

Wolfgang Fruehwirt, Adam D. Cobb, Martin Mairhofer, Leonard Weydemann, Heinrich Garn, Reinhold Schmidt, Thomas Benke, Peter Dal-Bianco, Gerhard Ransmayr, Markus Waser, Dieter Grossegger, Pengfei Zhang, Georg Dorffner, Stephen Roberts
2018 arXiv   pre-print
, i.e., Monte Carlo dropout and Hamiltonian Monte Carlo.  ...  Here, we utilize Bayesian neural networks to develop a multivariate predictor for AD severity using a wide range of quantitative EEG (QEEG) markers.  ...  Hamiltonian Monte Carlo [7], which is a Markov Chain Monte Carlo technique that utilises Hamiltonian dynamics to explore the parameter space of networks.  ... 
arXiv:1812.04994v2 fatcat:g4kr766i3jhgjmm2pqqcgohh4u

Self-learning Monte Carlo method with Behler-Parrinello neural networks [article]

Yuki Nagai, Masahiko Okumura, Akinori Tanaka
2018 arXiv   pre-print
We propose a general way to construct an effective Hamiltonian in the Self-learning Monte Carlo method (SLMC) method, which speeds up Monte Carlo simulations by training an effective model to propose uncorrelated  ...  We construct self-learning continuous-time interaction-expansion quantum Monte Carlo method with BPNNs and apply it to quantum impurity models.  ...  Metropolis-Hastings algorithm In the Monte Carlo method, we have to generate the configuration C with the probability distribution w(C).  ... 
arXiv:1807.04955v2 fatcat:sqgqxsofxnez7a24ps24qkv23a

Neural quantum states for supersymmetric quantum gauge theories [article]

Xizhi Han, Enrico Rinaldi
2021 arXiv   pre-print
We employ a neural quantum state ansatz for the wave function of a supersymmetric matrix model and use a variational quantum Monte Carlo approach to discover the ground state of the system.  ...  The wave function of such supersymmetric gauge theories is not known and it is challenging to obtain with traditional techniques.  ...  Methods Variational Quantum Monte Carlo The variational quantum Monte Carlo method consists of three components: a wave function network, a sampler network, and an optimizer.  ... 
arXiv:2112.05333v1 fatcat:khiu7nazqrba7j7mb6ijyyywsq

Machine learning phases of matter

Juan Carrasquilla, Roger G. Melko
2017 Nature Physics  
sampled with Monte Carlo.  ...  We show that this classification occurs within the neural network without knowledge of the Hamiltonian or even the general locality of interactions.  ...  Instead, we construct a fully connected feed-forward neural network, implemented with TensorFlow [6] , to perform supervised learning directly on the raw configurations sampled by a Monte Carlo simulation  ... 
doi:10.1038/nphys4035 fatcat:q7vkd73gwnepldhc4dfpqyhxoi

Accelerating lattice quantum Monte Carlo simulations using artificial neural networks: Application to the Holstein model

Shaozhi Li, Philip M. Dee, Ehsan Khatami, Steven Johnston
2019 Physical review B  
Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science.  ...  We find that both artificial neural networks are capable of learning an unspecified effective model that accurately reproduces the MC configuration weights of the original Hamiltonian and achieve an order  ...  We have extended the use of artificial neural networks in self-learning Monte Carlo methods to lattice Monte Carlo simulations.  ... 
doi:10.1103/physrevb.100.020302 fatcat:tptxfibh3jfjvprtfzzqbqrasy

Sample generation for the spin-fermion model using neural networks [article]

Georgios Stratis, Phillip Weinberg, Tales Imbiriba, Pau Closas, Adrian E. Feiguin
2022 arXiv   pre-print
The simplicity of the architecture we use in conjunction with the model agnostic form of the neural networks can enable fast sample generation without the need of a researcher's intervention.  ...  Quantum Monte-Carlo simulations of hybrid quantum-classical models such as the double exchange Hamiltonian require calculating the density of states of the quantum degrees of freedom at every step.  ...  Moreover, approaches to accelerate Monte-Carlo simulations with machine learning have been explored in the self-learning Monte-Carlo method [26] , using restricted Boltzmann machines [27] , deep [28  ... 
arXiv:2206.07753v1 fatcat:7a5io2dgbvahvbr765hemsrhxu

Network-Initialized Monte Carlo Based on Generative Neural Networks [article]

Hongyu Lu, Chuhao Li, Bin-Bin Chen, Wei Li, Yang Qi, Zi Yang Meng
2022 arXiv   pre-print
We design generative neural networks that generate Monte Carlo configurations with complete absence of autocorrelation from which only short Markov chains are needed before making measurements for physical  ...  We further propose a network-initialized Monte Carlo scheme based on such neural networks, which provides independent samplings and can accelerate the Monte Carlo simulations by significantly reducing  ...  Moreover, we design a network-initialized Monte Carlo (NIMC) scheme with the assistance of such neural networks, MCMC Simulation Observables Ⅰ which "heals" the initial bias due to the unthermalized  ... 
arXiv:2106.00712v6 fatcat:vvruhji4gfewdjmikrtpopg6uq

Stochastic Fractional Hamiltonian Monte Carlo

Nanyang Ye, Zhanxing Zhu
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
The experimental results show that the proposed stochastic fractional Hamiltonian Monte Carlo for training deep neural networks could converge faster than other popular optimization schemes and generalize  ...  In this paper, we propose a novel stochastic fractional Hamiltonian Monte Carlo approach which generalizes the Hamiltonian Monte Carlo method within the framework of fractional calculus and L\'evy diffusion  ...  name the dynamics described by Eq. ( 12 ) and ( 12 ) as Fractional Hamiltonian Monte Carlo (FHMC) due to its similarity with Hamiltonian Monte Carlo.  ... 
doi:10.24963/ijcai.2018/419 dblp:conf/ijcai/YeZ18 fatcat:b2s4slwhsveh7aucgplqe5ckvu

Variational Monte Carlo calculations of 𝐀≤ 4 nuclei with an artificial neural-network correlator ansatz [article]

Corey Adams, Giuseppe Carleo, Alessandro Lovato, Noemi Rocco
2021 arXiv   pre-print
We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually-exact Green's function Monte Carlo results.  ...  Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems.  ...  In a series of recent works [25] [26] [27] deep neural networks have been further developed to tackle ab-initio chemistry problems within variational Monte Carlo, often resulting in accuracy improvements  ... 
arXiv:2007.14282v2 fatcat:dxnayb7oqfd37il6vjmumhl3f4

Machine learning many-electron wave functions via backflow transformations

2020 Journal Club for Condensed Matter Physics  
Combined with Monte Carlo methods to evaluate the highly dimensional integral over all particle coordinates, variational and quantum Monte Carlo calculations have provided most accurate values of the many-body  ...  Can representations based on neural networks reduce this remaining bias similar successful 1  ...  Combined with Monte Carlo methods to evaluate the highly dimensional integral over all particle coordinates, variational and quantum Monte Carlo calculations have provided most accurate values of the many-body  ... 
doi:10.36471/jccm_may_2020_01 fatcat:wrfr6xvihvhrzcdemurzxhcrly

Extending Machine Learning Classification Capabilities with Histogram Reweighting [article]

Dimitrios Bachtis, Gert Aarts, Biagio Lucini
2020 arXiv   pre-print
We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods.  ...  By interpreting the output of the neural network as an order parameter, we explore connections with known observables in the system and investigate its scaling behaviour.  ...  This enables the elimination of any potential bias in the quantity associated with the finiteness of the Monte Carlo generated sample.  ... 
arXiv:2004.14341v1 fatcat:4qpocs6dcfgf3gmykf3gb4bz4i

Neural network gradient Hamiltonian Monte Carlo

Lingge Li, Andrew Holbrook, Babak Shahbaba, Pierre Baldi
2019 Computational statistics (Zeitschrift)  
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models.  ...  We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient.  ...  Background Hamiltonian Monte Carlo Let x ∼ π(x|q) denote a probabilistic model with p a probability density function and q its corresponding parameter.  ... 
doi:10.1007/s00180-018-00861-z pmid:31695242 pmcid:PMC6833949 fatcat:g4t6h7f6rva77hvsyrtjn2xik4

Bayesian Optimization with Robust Bayesian Neural Networks

Jost Tobias Springenberg, Aaron Klein, Stefan Falkner, Frank Hutter
2016 Neural Information Processing Systems  
We obtain scalability through stochastic gradient Hamiltonian Monte Carlo, whose robustness we improve via a scale adaptation.  ...  We present a general approach for using flexible parametric models (neural networks) for Bayesian optimization, staying as close to a truly Bayesian treatment as possible.  ...  [20] and results in an algorithm called generalized stochastic gradient Riemann Hamiltonian Monte Carlo (gSGRHMC).  ... 
dblp:conf/nips/SpringenbergKFH16 fatcat:vmmf3aodjrgc7nqxx7qua6jgfa

Data-Enhanced Variational Monte Carlo for Rydberg Atom Arrays [article]

Stefanie Czischek, M. Schuyler Moss, Matthew Radzihovsky, Ejaaz Merali, Roger G. Melko
2022 arXiv   pre-print
Monte Carlo (VMC).  ...  Today, novel groundstate wavefunction ans\"atze like recurrent neural networks (RNNs) can be efficiently trained not only from projective measurement data, but also through Hamiltonian-guided variational  ...  Hamiltonian-driven training methods common in variational Monte Carlo (VMC) [32] [33] [34] .  ... 
arXiv:2203.04988v1 fatcat:lnu6f5q4mvbmdd7q3zv7cvqin4
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