RG-inspired machine learning for lattice field theory

Foreman, Sam; Giedt, Joel; Meurice, Yannick; Unmuth-Yockey, Judah

doi:10.1051/epjconf/201817511025

Cited by 14 publications

(23 citation statements)

References 10 publications

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“…In order to understand its physical origin, we recall that plastic flow in amorphous solids is mediated by localized shear transformations. The shear stress in a 2D elastic medium responding to such a transformation at the origin is proportional to the Eshelby propagator G(r) = cos(4θ) r 2 (8) in polar coordinates. Its quadrupolar symmetry (and resulting alternating sign) is responsible for many important properties of the yielding transition.…”

Section: Elastic Vs Plastic Displacementsmentioning

confidence: 99%

Correlations in the shear flow of athermal amorphous solids: a principal component analysis

Ruscher¹,

Rottler²

2019

J. Stat. Mech.

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We apply principal component analysis, a method frequently used in image processing and unsupervised machine learning, to characterize particle displacements observed in the steady shear flow of amorphous solids. PCA produces a low-dimensional representation of the data and clearly reveals the dominant features of elastic (i.e. reversible) and plastic deformation. We show that the principal directions of PCA in the plastic regime correspond to the soft (i.e. zero energy) modes of the elastic propagator that governs the redistribution of shear stress due to localized plastic events. Projections onto these soft modes also correspond to components of the displacement structure factor at the first nonzero wavevectors, in close analogy to PCA results for thermal phase transitions in conserved Ising spin systems. The study showcases the ability of PCA to identify physical observables related to the broken symmetry in a dynamical nonequilibrium transition. Submitted to: J. Stat. Mech. arXiv:1809.06487v2 [cond-mat.dis-nn] 1 May 2019 Correlations in the shear flow of athermal amorphous solids: A principal component analysis2

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Section: Elastic Vs Plastic Displacementsmentioning

confidence: 99%

Correlations in the shear flow of athermal amorphous solids: a principal component analysis

Ruscher¹,

Rottler²

2019

J. Stat. Mech.

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“…4 of Ref. [4], where we show the eigenvectors corresponding to the largest eigenvalues and the approximation of the data by subspaces of the largest eigenvalues of dimensions 10, 20 etc.…”

Section: Solutions Tomentioning

confidence: 99%

“…There are four kinds of plaquettes (see Fig. 7): those inside the blocks (they disappear after blocking), those between two neighboring blocks in the vertical or horizontal direction (these are double links between the blocks and so they disappear with the 1 + 1 → 0 rule), and finally those which share a corner with four blocks (they generate a larger plaquette); this type can be seen at (4,12) in Fig. 7.…”

Section: Partial Data Collapse For Blocked Imagesmentioning

confidence: 99%

“…That is, when descending in depth, only neighboring nodes should influence the outcome of a lower level node. We have also implemented this in a simple training scheme in earlier work [4]. It can be called "cheap learning" because far fewer variational parameters are involved, due to the constraints of locality.…”

Section: Introductionmentioning

confidence: 99%

“…This process is useful if we can tune a parameter such as the temperature towards its critical value. Typical image sets such as the MNIST data can be thought as "far from criticality" and the use of RG methods for such a data set may be of limited interest [4]. Criticality may sometimes refer to the choice of parameters used in data analysis [19].…”

Section: Introductionmentioning

confidence: 99%

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Examples of renormalization group transformations for image sets

et al. 2018

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Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate criticality to the logarithmic divergence of the largest principal component. We discuss the changes in link occupation under the RG transformation, suggest ways to obtain data collapse, and compare with the two state tensor RG approximation near the fixed point.

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A high-bias, low-variance introduction to Machine Learning for physicists

et al. 2019

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Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.

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RG-inspired machine learning for lattice field theory

Cited by 14 publications

References 10 publications

Correlations in the shear flow of athermal amorphous solids: a principal component analysis

Correlations in the shear flow of athermal amorphous solids: a principal component analysis

Examples of renormalization group transformations for image sets

A high-bias, low-variance introduction to Machine Learning for physicists

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