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We present a machine-learning method for predicting sharp transitions in a Hamiltonian phase diagram by extrapolating the properties of quantum systems. The method is based on Gaussian Process regression with a combination of kernels chosen…

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…

Recently, Deep Convolutional Neural Network (DCNN) has achieved tremendous success in many machine learning applications. Nevertheless, the deep structure has brought significant increases in computation complexity. Largescale deep learning…

In this paper, we present two deep learning-based hybrid data-driven reduced order models for the prediction of unsteady fluid flows. The first model projects the high-fidelity time series data from a finite element Navier-Stokes solver to…

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…

In recent years, machine learning has been adopted to complex networks, but most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition…

Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high…

The classification of phases and the detection of phase transitions are central and challenging tasks in diverse fields. Within physics, it relies on the identification of order parameters and the analysis of singularities in the free…

This paper proposes a deep neural network approach for predicting multiphase flow in heterogeneous domains with high computational efficiency. The deep neural network model is able to handle permeability heterogeneity in high dimensional…

Nonlinear dynamical systems exposed to changing forcing can exhibit catastrophic transitions between alternative and often markedly different states. The phenomenon of critical slowing down (CSD) can be used to anticipate such transitions…

Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral…

We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function. The key property of differential Gaussian…

Many natural and man-made systems are prone to critical transitions -- abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal (EWS) for critical transitions by learning generic…

Machine-learning techniques are evolving into a subsidiary tool for studying phase transitions in many-body systems. However, most studies are tied to situations involving only one phase transition and one order parameter. Systems that…

We present a deep neural network for a model-free prediction of a chaotic dynamical system from noisy observations. The proposed deep learning model aims to predict the conditional probability distribution of a state variable. The Long…

Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the…

Most deep learning models are based on deep neural networks with multiple layers between input and output. The parameters defining these layers are initialized using random values and are "learned" from data, typically using stochastic…

Around a glass transition, the dynamics of a supercooled liquid dramatically slow down, exhibited by caging of particles, while the structural changes remain subtle. In alternative to recent machine learning studies searching for structural…

Understanding the semantic characteristics of the environment is a key enabler for autonomous robot operation. In this paper, we propose a deep convolutional neural network (DCNN) for the semantic segmentation of a LiDAR scan into the…

Phase-field models have been widely used to investigate the phase transformation phenomena. However, it is difficult to solve the problems numerically due to their strong nonlinearities and higher-order terms. This work is devoted to…