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Machine learning (ML) has been well applied to studying equilibrium phase transition models, by accurately predicating critical thresholds and some critical exponents. Difficulty will be raised, however, for integrating ML into…

In this paper we present a neural network-based method for the automatic detection of phase transitions and classification of hidden percolation patterns in a (1+1)-dimensional replication process. The proposed network model is based on the…

The latest advances of statistical physics have shown remarkable performance of machine learning in identifying phase transitions. In this paper, we apply domain adversarial neural network (DANN) based on transfer learning to studying…

Recent advances in machine learning have become increasingly popular in the applications of phase transitions and critical phenomena. By machine learning approaches, we try to identify the physical characteristics in the two-dimensional…

Recently, machine learning algorithms have been used remarkably to study the equilibrium phase transitions, however there are only a few works have been done using this technique in the nonequilibrium phase transitions. In this work, we use…

In recent years, neural networks have increasingly been employed to identify critical points of phase transitions. For the tricritical directed percolation model, its steady-state configurations encompass both first-order and second-order…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…

Machine learning (ML) of phase transitions (PTs) has gradually become an effective approach that enables us to explore the nature of various PTs more promptly in equilibrium and nonequilibrium systems. Unlike equilibrium systems,…

We employ deep learning techniques to investigate the critical properties of the continuous phase transition in the majority vote model. In addition to deep learning, principal component analysis is utilized to analyze the transition. For…

Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…

The paper studies the problem of detecting and locating change points in multivariate time-evolving data. The problem has a long history in statistics and signal processing and various algorithms have been developed primarily for simple…

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that…

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…

In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with…

Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…

The application of machine learning in the study of phase transitions has achieved remarkable success in both equilibrium and non-equilibrium systems. It is widely recognized that unsupervised learning can retrieve phase transition…

Among 2D convolutional networks on point clouds, point-based approaches consume point clouds of fixed size directly. By analysis of PointNet, a pioneer in introducing deep learning into point sets, we reveal that current point-based methods…