We study the first-order flocking transition of birds flying in low-visibility conditions by employing three different representative types of neural network (NN) based machine architectures that are trained via either an unsupervised approach called learning by confusion or a widely used supervised approach. We find that after the training via either the unsupervised approach or the supervised one, all of these three different representative types of NNs, namely, the fully-connected NN, the convolutional NN, and the residual NN, are able to successfully identify the first-order flocking transition point of this nonequilibrium many-body system. This indicates that NN based machine can be employed as a promising generic tool to investigate rich physics in scenarios associated to first-order phase transitions and nonequilibrium many-body systems.
We study the first-order flocking transition of birds flying in low-visibility conditions by employing three different representative types of neural network (NN) based machine architectures that are trained via either an unsupervised approach called learning by confusion or a widely used supervised approach. We find that after the training via either the unsupervised approach or the supervised one, all of these three different representative types of NNs, namely, the fully-connected NN, the convolutional NN, and the residual NN, are able to successfully identify the first-order flocking transition point of this nonequilibrium many-body system. This indicates that NN based machine can be employed as a promising generic tool to investigate rich physics in scenarios associated to first-order phase transitions and nonequilibrium many-body systems.
We develop the neural network based “learning from regression uncertainty” approach for the automatic detection of phases of matter in nonequilibrium active systems. Taking the flocking phase transition of self-propelled active particles described by the Vicsek model for example, we find that after training a neural network for solving the inverse statistical problem, i.e. for performing the regression task of reconstructing the noise level from given samples of such a nonequilibrium many-body complex system’s steady state configurations, the uncertainty of regression results obtained by the well-trained network can actually be utilized to reveal possible phase transitions in the system under study. The noise level dependence of regression uncertainty is assumed to be in a non-trivial M-shape, and its valley appears at the critical point of the flocking phase transition. By directly comparing this regression-based approach with the widely-used classification-based “learning by confusion” and “learning with blanking” approaches, we show that our approach has practical effectiveness, efficiency, good generality for various physical systems across interdisciplinary fields, and a greater possibility of being interpretable via conventional notions of physics. These approaches can complement each other to serve as a promising generic toolbox for investigating rich critical phenomena and providing data-driven evidence on the existence of various phase transitions, especially for those complex scenarios associated with first-order phase transitions or nonequilibrium active systems where traditional research methods in physics could face difficulties.
The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning techniques. Using the axial next-nearest-neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbor interactions can learn to identify a new type of phase occurring when next-nearest-neighbor interactions are introduced. All our results rely on few- and low-dimensional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.
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 application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or the ensemble of correlators sampled in Monte Carlo simulations. Here we introduce a gener- alization of supervised machine learning approaches that allows to accurately map out phase diagrams of inter- acting many-body systems without any prior knowledge, e.g. of their general topology or the number of distinct phases. To substantiate the versatility of this approach, which combines convolutional neural networks with quantum Monte Carlo sampling, we map out the phase diagrams of interacting boson and fermion models both at zero and finite temperatures and show that first-order, second-order, and Kosterlitz-Thouless phase transitions can all be identified. We explicitly demonstrate that our approach is capable of identifying the phase transition to non-trivial many-body phases such as superfluids or topologically ordered phases without supervision.
Machine learning has become increasingly popular as a computational tool in all aspects of science and the private sector, however its application as an additional computational physics tool has only recently began to gain traction. This thesis aims to study the application of supervised and unsupervised neural networks to computational classical statistical physics problems, focusing on what is learned and\nwhether it is a useful tool for these applications. Supervised neural networks are used to distinguish between the different phases of four different models, containing a second-order phase-transition (PT), infinite-order PT, and both in close proximity to one another, as well as a model without a PT but with frustration. Different iterations of the restricted Boltzmann machine (RBM), a type of unsupervised neural\nnetwork, are trained on the one- and two-dimensional Ising model. The neural network is able to differentiate between the different phases only if the PT is clearly discernible from the input configurations. It is too crude a tool to differentiate between two close subsequent PTs. It is concluded that application of neural networks to detect PTs in classical statistical physics models where an intuition for the PT exists, holds no advantage over alternative conventional computational methods. This thesis concludes that restrictions placed on the RBM, such that the RBM has translation\ninvariance, still allow the restricted RBMs to learn the magnetisation really well, while two-spin correlations are learned less well. Surprisingly, the block Gibbs sampling of the restricted RBMs is better behaved than for the unrestricted RBM, as can be explained using an analysis of the trained weight-matrix.
We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were previously found to be efficient in classifying phases and locating phase transitions of various basic model systems. In order to rationalize the emergence of the classification process and for identifying any underlying physical quantities, it is feasible to examine the weight matrices and the convolutional filter kernels that result from the learning process of such shallow networks. Furthermore, we demonstrate how the learning-by-confusing scheme can be used, in combination with a simple threshold-value classification method, to diagnose the learning parameters of neural networks. In particular, we study the classification process of both fully-connected and convolutional neural networks for the two-dimensional Ising model with extended domain wall configurations included in the low-temperature regime. Moreover, we consider the two-dimensional XY model and contrast the performance of the learning-by-confusing scheme and convolutional neural networks trained on bare spin configurations to the case of preprocessed samples with respect to vortex configurations. We discuss these findings in relation to similar recent investigations and possible further applications.