Unsupervised machine learning for detection of phase transitions in off-lattice systems. I. Foundations

Jadrich, Ryan B.; Lindquist, Beth A.; Truskett, Thomas M.

doi:10.1063/1.5049849

Cited by 44 publications

(24 citation statements)

References 48 publications

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“…For the output layers, the number of neurons is set to be equal to the number of lattice points in the configuration under investigation. The activation function used is ReLu, as given in equation (6), for all hidden layers, and for the output layer, tanh is used, as per equation (7).…”

Section: Proposed Autoencoder Modelmentioning

confidence: 99%

“…Recent advances in the implementation of Artificial Intelligence (AI) for physical systems, especially, on those which can be formulated on a lattice, appear to be suitable for observing the corresponding underlying phase structure [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. So far methods such as the Principal Component Analysis (PCA) [6,10,12,18,19], Supervised Machine Learning (ML) [2,15,20], Restricted Boltzmann Machines (RBMs) [21,22], as well as autoencoders [6,13] appear to successfully identify different phase regions of classical statistical systems, such as the 2-dimensional (2D) Ising model that describes the (anti)ferromagneticparamagnetic transition.…”

Section: Introductionmentioning

confidence: 99%

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The critical temperature of the 2D-Ising model through deep learning autoencoders

et al. 2020

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We investigate deep learning autoencoders for the unsupervised recognition of phase transitions in physical systems formulated on a lattice. We focus our investigation on the 2-dimensional ferromagnetic Ising model and then test the application of the autoencoder on the anti-ferromagnetic Ising model. We use spin configurations produced for the 2-dimensional ferromagnetic and anti-ferromagnetic Ising model in zero external magnetic field. For the ferromagnetic Ising model, we study numerically the relation between one latent variable extracted from the autoencoder to the critical temperature Tc. The proposed autoencoder reveals the two phases, one for which the spins are ordered and the other for which spins are disordered, reflecting the restoration of the ℤ2 symmetry as the temperature increases. We provide a finite volume analysis for a sequence of increasing lattice sizes. For the largest volume studied, the transition between the two phases occurs very close to the theoretically extracted critical temperature. We define as a quasi-order parameter the absolute average latent variable z̃, which enables us to predict the critical temperature. One can define a latent susceptibility and use it to quantify the value of the critical temperature Tc(L) at different lattice sizes and that these values suffer from only small finite scaling effects. We demonstrate that Tc(L) extrapolates to the known theoretical value as L →∞ suggesting that the autoencoder can also be used to extract the critical temperature of the phase transition to an adequate precision. Subsequently, we test the application of the autoencoder on the anti-ferromagnetic Ising model, demonstrating that the proposed network can detect the phase transition successfully in a similar way. Graphical abstract

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Section: Proposed Autoencoder Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The critical temperature of the 2D-Ising model through deep learning autoencoders

et al. 2020

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“…Machine learning methods have emerged as powerful tools for analyzing a wide range of fluid mechanics problems 43 , 44 such as turbulence 45 – 49 , phase transition 50 , ignition 51 , vortex vibrations 52 , 53 , and aerodynamics disturbances 54 . Image processing and pattern recognition techniques have been employed to analyze the remaining stains after evaporation of sessile droplets.…”

Section: Introductionmentioning

confidence: 99%

Data-driven time-dependent state estimation for interfacial fluid mechanics in evaporating droplets

Andalib

Taira

Kavehpour

2021

Sci Rep

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Droplet evaporation plays crucial roles in biodiagnostics, microfabrication, and inkjet printing. Experimentally studying the evolution of a sessile droplet consisting of two or more components needs sophisticated equipment to control the vast parameter space affecting the physical process. On the other hand, the non-axisymmetric nature of the problem, attributed to compositional perturbations, introduces challenges to numerical methods. In this work, droplet evaporation problem is studied from a new perspective. We analyze a sessile methanol droplet evolution through data-driven classification and regression techniques. The models are trained using experimental data of methanol droplet evolution under various environmental humidity levels and substrate temperatures. At higher humidity levels, the interfacial tension and subsequently contact angle increase due to higher water uptake into droplet. Therefore, different regimes of evolution are observed due to adsorption–absorption and possible condensation of water which turns the droplet from a single component into a binary system. In this work, machine learning and data-driven techniques are utilized to estimate the regime of droplet evaporation, the time evolution of droplet base diameter and contact angle, and level of surrounding humidity. Droplet regime is estimated by classification algorithms through point-by-point analysis of droplet profile. Decision tree demonstrates a better performance compared to Naïve Bayes (NB) classifier. Additionally, the level of surrounding humidity, as well as the time evolution of droplet base diameter and contact angle, are estimated by regression algorithms. The estimation results show promising performance for four cases of methanol droplet evolution under conditions unseen by the model, demonstrating the model’s capability to capture the complex physics underlying binary droplet evolution.

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“…Machine learning methods have emerged as powerful tools for analyzing various fluid mechanics problems ranging from turbulence modeling to phase transition [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] . For example, image processing and pattern recognition techniques have been employed to indirectly measure the target components in blood droplets after evaporation [55][56][57] .…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Real-Time Prediction for Interfacial Fluid Mechanics: Droplet Evaporation

Andalib¹,

Taira²,

Hp³

2021

Preprint

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Droplet evaporation plays crucial roles in biodiagnostics, microfabrication, and inkjet printing. Experimentally studying the evolution of a sessile droplet consisting of two or more components needs sophisticated equipment to control the vast parameter space affecting the physical process. On the other hand, non-axisymmetric nature of the problem, attributed to compositional perturbations, introduces challenges to numerical methods. In this work, droplet evaporation problem is studied from a new perspective. We analyze evolution of a sessile methanol droplet through data-driven classification and regression techniques. The models are trained using experimental data of methanol droplet evolution under various environmental humidity levels and substrate temperatures. At higher humidity levels, the interfacial tension and subsequently contact angle increase due to higher water uptake into droplet. Therefore, different regimes of evolution are observed due to adsorption-absorption and possibly condensation of water which turns the droplet into a binary system. We use classification algorithms to predict the regime of droplet with point-by-point analysis of droplet profile. Decision tree demonstrates a better performance compared to Na\text{\"i}ve Bayes (NB) classifier. Furthermore, through utilizing regression techniques, we predict the humidity level surrounding droplet as well as time evolution of macroscopic parameter (diameter or contact angle) of droplet. The prediction results show promising performance for four cases of methanol droplet evolution under conditions that are unseen by the model which demonstrates the capability of the model to capture the complex physics underlying binary droplet evolution.

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Unsupervised machine learning for detection of phase transitions in off-lattice systems. I. Foundations

Cited by 44 publications

References 48 publications

The critical temperature of the 2D-Ising model through deep learning autoencoders

The critical temperature of the 2D-Ising model through deep learning autoencoders

Data-driven time-dependent state estimation for interfacial fluid mechanics in evaporating droplets

Data-Driven Real-Time Prediction for Interfacial Fluid Mechanics: Droplet Evaporation

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