Exploring neural network training strategies to determine phase transitions in frustrated magnetic models

Corte, I.; Acevedo, Santiago Daniel; Arlego, Marcelo José Fabián; Lamas, Carlos Alberto

doi:10.1016/j.commatsci.2021.110702

Cited by 19 publications

(10 citation statements)

References 42 publications

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“…One possible next step is to investigate transfer learning for the models that are trained here. Indeed, the case investigated here is the J 1 = 1, J 2 = 0 special case of the J 1 -J 2 Ising model that has recently been investigated from the machinelearning perspective [17,18], and it would be interesting to see how our neural networks trained on the case J 2 /J 1 = 0 perform for other values of J 2 /J 1 .…”

Section: Discussionmentioning

confidence: 99%

“…The square-lattice Ising model is an exactly solved model [12]. Notwithstanding its exact solution, it is commonly employed in the ML context [3][4][5][13][14][15][16][17][18]. Motivations for such ML studies of the Ising model in 2D include the readily available comparison to the exact solution and that training data can be easily generated using standard Monte-Carlo simulations.…”

Section: Introductionmentioning

confidence: 99%

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Machine Learning the Square-Lattice Ising Model

Çivitcioğlu

Römer

Honecker

2022

J. Phys.: Conf. Ser.

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Recently, machine-learning methods have been shown to be successful in identifying and classifying different phases of the square-lattice Ising model. We study the performance and limits of classification and regression models. In particular, we investigate how accurately the correlation length, energy and magnetisation can be recovered from a given configuration. We find that a supervised learning study of a regression model yields good predictions for magnetisation and energy, and acceptable predictions for the correlation length.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Machine Learning the Square-Lattice Ising Model

Çivitcioğlu

Römer

Honecker

2022

J. Phys.: Conf. Ser.

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“…In the present study we focus on the highly frustrated region of R < −1/4, for which both the EFT and CMF analytical approximations predicted no phase transition but the numerical approaches indicated some kind of phase transition to a highly degenerate low-temperature phase with no long-range ordering Corte et al 2021;Acevedo et al 2021). In our previous study, focused on the less frustrated case of −1/4 < R < 0, we demonstrated that with the increasing frustration (R → −1/4 and T → 0) the system tends to freeze in metastable domain states separated by large energy barriers with extremely sluggish dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…This frustrated model is also interesting from the experimental point of view, since it can be applied to some real materials (Matsuda et al 2010;Tsirlin et al 2010). The ground state of the J 1 − J 2 Ising model was investigated in some earlier papers (Houtappel 1950;Kudō and Katsura 1976;Katsura et al 1986) but its critical behavior was studied only recently by the effective field theory (EFT) (Bobák et al 2016), the MC simulation ( Žukovič et al 2020; Žukovič 2021), cluster mean-field (CMF) (Schmidt and Godoy 2021) and machine learning (ML) (Corte et al 2021;Acevedo et al 2021) approaches. For smaller degree of frustration, namely within the interval −1/4 < R < 0, the critical behavior resembles that for the square lattice.…”

Section: Introductionmentioning

confidence: 99%

Digital Twins for Lighting Analysis: Literature Review, Challenges, and Research Opportunities

Hassan¹,

Angelaki²,

Alfaro³

et al. 2022

ECMS 2022 Proceedings Edited by Ibrahim A. Hameed, Agus Hasan, Saleh Abdel-Afou Alaliyat

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Light modelling, simulation, and photometric calculations are by now common tasks in the lighting design process. These practices contribute to the definition and comparison of suitable layout arrangements and help predict the impact of lighting devices. Those tasks demand the use of tools to support the simulation of different scenarios, the analyses of their pros and cons according to different criteria (e.g., health and safety, perception, aesthetics, energy consumption, and costs), and decision-making. Digital twins have emerged as relevant technologies to simulate and visualize different ``what-if'' scenarios associated with physical entities and processes. In this paper, we investigate the state-of-the-art research concerning the use of digital twins for supporting lighting analysis in the urban/outdoor context. We also present and discuss challenges and research opportunities related to the design, implementation, and validation of digital twins in this domain.

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“… 20 – 30 . In the field of nanomagnetism and micromagnetics, deep neural networks are used to extract microstructural features in magnetic thin film elements 31 – 34 , and to explore materials with ease 35 . Refrences 36 – 38 use a sophisticated combination of machine learning techniques to predict the magnetization dynamics of magnetic thin film elements over one nanosecond.…”

Section: Introductionmentioning

confidence: 99%

Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations

et al. 2022

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Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation of an experimental physical system. Here we show that a dynamical neural network, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to the micromagnetic simulations that are usually employed to model them. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters. We demonstrate with Neural Ordinary Differential Equations an acceleration factor over 200 compared to micromagnetic simulations for a complex problem – the simulation of a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). In a second realization, we show that we can predict the noisy response of experimental spintronic nano-oscillators to varying inputs after training Neural Ordinary Differential Equations on five milliseconds of their measured response to a different set of inputs. Neural Ordinary Differential Equations can therefore constitute a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present. Our approach can also be generalized to other electronic devices involving dynamics.

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Exploring neural network training strategies to determine phase transitions in frustrated magnetic models

Cited by 19 publications

References 42 publications

Machine Learning the Square-Lattice Ising Model

Machine Learning the Square-Lattice Ising Model

Digital Twins for Lighting Analysis: Literature Review, Challenges, and Research Opportunities

Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations

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