Machine learning dynamical phase transitions in complex networks

Abstract

Recent years have witnessed a growing interest in using machine learning to predict and identify critical dynamical phase transitions in physical systems (e.g., many body quantum systems). The underlying lattice structures in these applications are generally regular. While machine learning has been adopted to complex networks, most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition point associated with dynamical processes on complex networks thus stands out as an open and significant problem. Here we develop a framework combining supervised and unsupervised learning, incorporating proper sampling of training data set. In particular, using epidemic spreading dynamics on complex networks as a paradigmatic setting, we start from supervised learning alone and identify situations that degrade the performance. To overcome the difficulties leads to the idea of exploiting confusion scheme, effectively a combination of supervised and unsupervised learning. We demonstrate that the scheme performs well for identifying phase transitions associated with spreading dynamics on homogeneous networks, but the performance deteriorates for heterogeneous networks. To strive to meet this challenge leads to the realization that sampling the training data set is necessary for heterogeneous networks, and we test two sampling methods: one based on the hub nodes together with their neighbors and another based on k-core of the network. The end result is a general machine learning framework for detecting phase transition and accurately identifying the critical transition point, which is robust, computationally efficient, and universally applicable to complex networks of arbitrary size and topology. Extensive tests using synthetic and empirical networks verify the virtues of the articulated framework, opening the door to exploiting machine learning for understanding, detection, prediction, and control of complex dynamical systems in general.

Machine learning methods trained on simple models can predict critical transitions in complex natural systems

“…ML models are able to automatically capture statistical characteristics by identifying and learning hidden patterns in data (Pathak et al 2018), making them ideally suited to detecting warning signals. Indeed, ML has been used to classify phases of matter, study phase behavior, detect phase transitions, and predict chaotic dynamics (Scandolo 2019, Van Nieuwenburg et al 2017, Canabarro et al 2019, Zhao and Fu 2019, Pathak et al 2018, whilst supervised learning algorithms such as artificial neural networks have been used to study second-order phase transitions, especially the Ising model (Morningstar and Melko 2017, Cossu et al 2019, Ni et al 2019, Giannetti et al 2019. However, thus far machine learning tools have not been used to classify the most common transitions seen in ecological, financial, and climatic systems -catastrophic (i.e., firstorder or discontinuous) and non-catastrophic (i.e., second-order or continuous) transitions (Martín et al 2015).…”

Direct detection of plasticity onset through total-strain profile evolution

“…The application of modern statistical methods to identify transitions between phases with well-defined order parameters in materials has become quite common [5]. The recent theme in the physics and engineering communities is the application of machine learning methods so that the identification of a precise characterization parameter is avoided and automatic detection is achieved [6][7][8][9][10][11][12][13]. However, the absence of detailed knowledge may lead to overfitting artifacts and unsuccessful machine learning training.…”

Mapping distinct phase transitions to a neural network

“…Within these developments machine learning has critically influenced the domain of statistical mechanics, particularly in the study of phase transitions [3,4]. A wide range of machine learning techniques, including neural networks [5][6][7][8][9][10][11][12][13][14][15][16][17], diffusion maps [18], support vector machines [19][20][21][22] and principal component analysis [23][24][25][26][27] have been implemented to study equilibrium and non-equilibrium systems. Transferable features have also been explored in phase transitions, including modified models through a change of lattice topology [3] or form of interaction [28], in Potts models with a varying odd number of states [29], in the Hubbard model [6], in fermions [5], in the neural network-quantum states ansatz [30,31] and in adversarial domain adaptation [32].…”