The transfer learning of a neural network is one of its most outstanding aspects, and has given supervised learning with neural networks a prominent place in data science. Here we explore this feature in the context of strongly interacting many-body systems. By means of case studies, we show the potential of this deep learning technique to detect phases and their transitions in frustrated spin systems, using dense and convolutional neural networks. In addition, we explore a recently-introduced technique, which is at the middle point of supervised and unsupervised learning. It consists in evaluating the performance of a neural network which has been deliberately 'confused' during its training. To properly demonstrate the capability of the 'confusion' and transfer learning techniques, we apply them to a paradigmatic model of frustrated magnetism in two dimensions, to determine its phase diagram and compare it with high-performance Monte Carlo simulations.The transfer learning of a neural network is one of its most outstanding aspects, and has given supervised learning with neural networks a prominent place in data science. Here we explore this feature in the context of strongly interacting many-body systems. By means of case studies, we show the potential of this deep learning technique to detect phases and their transitions in frustrated spin systems, using dense and convolutional neural networks. In addition, we explore a recently-introduced technique, which is at the middle point of supervised and unsupervised learning. It consists in evaluating the performance of a neural network which has been deliberately 'confused' during its training. To properly demonstrate the capability of the 'confusion' and transfer learning techniques, we apply them to a paradigmatic model of frustrated magnetism in two dimensions, to determine its phase diagram and compare it with high-performance Monte Carlo simulations.

Sep 1, 20202 citations

Machine Learning of Frustrated Classical Spin Models

Ce Wang, Hui Zhai

Bulletin of the American Physical SocietyMar 6, 201810 citations

Feedforward Neural Networks for Quantum Frustrated Magnets

Dmitrii Kochkov, Bryan K. Clark

Bulletin of the American Physical SocietyMar 9, 20180 citations

Minimal Training Set for Training a Successful CNN: A Case Study of the Frustrated J 1- J 2 Ising Model on the Square Lattice

Shang-Wei Li, Yuan-Heng Tseng, Ming-Che Hsieh +1 more

Abstract The minimal training set to train a working convolutional neural network (CNN) is explored in detail. The model under consideration is the frustrated $J_1$ - $J_2$ Ising model on the square lattice. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest neighboring couplings, respectively. We train the CNN using the configurations of $g \stackrel{\text{def}}{=} J_2/|J_1| = 0.7$ and employ the resulting CNN to study the phase transition of $g = 0.8$ . We find that this transfer learning is successful. In particular, only configurations of two temperatures, one below and one above the critical temperature $T_c$ of $g=0.7$ , are needed to accurately determine the $T_c$ of $g=0.8$ . However, it may be subtle to use this strategy for the training. Specifically, for the model under consideration, due to the inefficiency of the single spin-flip algorithm used in sampling the configurations in the low-temperature region, the two temperatures associated with the training set should not be too far away from the $T_c$ of $g=0.7$ . Otherwise, the performance of the obtained CNN is not of high quality, and hence cannot determine the $T_c$ of $g=0.8$ accurately. For the model under consideration, we also uncover the condition for training a successful CNN when only configurations of two temperatures are considered as the training set.Abstract The minimal training set to train a working convolutional neural network (CNN) is explored in detail. The model under consideration is the frustrated $J_1$-$J_2$ Ising model on the square lattice. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest neighboring couplings, respectively. We train the CNN using the configurations of $g \stackrel{\text{def}}{=} J_2/|J_1| = 0.7$ and employ the resulting CNN to study the phase transition of $g = 0.8$. We find that this transfer learning is successful. In particular, only configurations of two temperatures, one below and one above the critical temperature $T_c$ of $g=0.7$, are needed to accurately determine the $T_c$ of $g=0.8$. However, it may be subtle to use this strategy for the training. Specifically, for the model under consideration, due to the inefficiency of the single spin-flip algorithm used in sampling the configurations in the low-temperature region, the two temperatures associated with the training set should not be too far away from the $T_c$ of $g=0.7$. Otherwise, the performance of the obtained CNN is not of high quality, and hence cannot determine the $T_c$ of $g=0.8$ accurately. For the model under consideration, we also uncover the condition for training a successful CNN when only configurations of two temperatures are considered as the training set.

arXiv:2504.19795Progress of Theoretical and Experimental PhysicsOct 23, 20252 citations

Recent advances in the study of frustrated magnetism with Neural-Network quantum states

Kenny Choo, Titus Neupert, Giuseppe Carleo

APSJan 1, 20190 citations

Neural Network Method for Calculation of the Curie Point of the Two-Dimensional Ising Model

Alena Korol, K. V. Nevedev, Vitalii Yu. Kapitan

The authors describe a method for determining the critical point of a second order phase transitions using a convolutional neural network based on the Ising model on a square lattice. Data for training and analysis were obtained using Monte Carlo simulations. The neural network was trained on the data corresponding to the low-temperature phase, that is a ferromagnetic one and high-temperature phase, that is a paramagnetic one, respectively. After training, the neural network analyzed input data from the entire temperature range: from 0.1 to 5.0 (in dimensionless units J) and determined the Curie point Tc.The authors describe a method for determining the critical point of a second order phase transitions using a convolutional neural network based on the Ising model on a square lattice. Data for training and analysis were obtained using Monte Carlo simulations. The neural network was trained on the data corresponding to the low-temperature phase, that is a ferromagnetic one and high-temperature phase, that is a paramagnetic one, respectively. After training, the neural network analyzed input data from the entire temperature range: from 0.1 to 5.0 (in dimensionless units J) and determined the Curie point Tc.

Siberian Journal of PhysicsSep 11, 20220 citations

Abstract The minimal training set to train a working convolutional neural network (CNN) is explored in detail. The model under consideration is the frustrated

J_1

J_2

Ising model on the square lattice. Here

J_1 < 0

and

J_2 > 0

are the nearest and next-to-nearest neighboring couplings, respectively. We train the CNN using the configurations of

g \stackrel{\text{def}}{=} J_2/|J_1| = 0.7

and employ the resulting CNN to study the phase transition of

g = 0.8

. We find that this transfer learning is successful. In particular, only configurations of two temperatures, one below and one above the critical temperature

T_c

g=0.7

, are needed to accurately determine the

T_c

g=0.8

. However, it may be subtle to use this strategy for the training. Specifically, for the model under consideration, due to the inefficiency of the single spin-flip algorithm used in sampling the configurations in the low-temperature region, the two temperatures associated with the training set should not be too far away from the

T_c

g=0.7

. Otherwise, the performance of the obtained CNN is not of high quality, and hence cannot determine the

T_c

g=0.8

accurately. For the model under consideration, we also uncover the condition for training a successful CNN when only configurations of two temperatures are considered as the training set.