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We use deep-learning strategies to study the 2D percolation model on a square lattice. We employ standard image recognition tools with a multi-layered convolutional neural network. We test how well these strategies can characterise…
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 this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it…
Percolation is an important topic in climate, physics, materials science, epidemiology, finance, and so on. Prediction of percolation thresholds with machine learning methods remains challenging. In this paper, we build a powerful graph…
Convolutional neural networks (CNNs) have achieved remarkable performance in various fields, particularly in the domain of computer vision. However, why this architecture works well remains to be a mystery. In this work we move a small step…
Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet…
The use of machine learning techniques in classical and quantum systems has led to novel techniques to classify ordered and disordered phases, as well as uncover transition points in critical phenomena. Efforts to extend these methods to…
We investigate site percolation on a weighted planar stochastic lattice (WPSL) which is a multifractal and whose dual is a scale-free network. Percolation is typically characterized by percolation threshold $p_c$ and by a set of critical…
Cluster expansion approximates an on-lattice potential with polynomial regression. We show that using a convolutional neural network (CNN) instead leads to more accurate prediction due to the depth of the network. We construct our CNN…
We determine thresholds $p_c$ for random site percolation on a triangular lattice for neighbourhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN) and next-next-next-next-nearest (5NN)…
Nowadays, deep learning can be employed to a wide ranges of fields including medicine, engineering, etc. In deep learning, Convolutional Neural Network (CNN) is extensively used in the pattern and sequence recognition, video analysis,…
Convolutional neural networks (CNNs) have achieved superior accuracy in many visual related tasks. However, the inference process through intermediate layers is opaque, making it difficult to interpret such networks or develop trust in…
Convolutional neural networks (CNNs) can potentially provide powerful tools for classifying and identifying patterns in climate and environmental data. However, because of the inherent complexities of such data, which are often…
In this paper we introduce a new problem within the growing literature of interpretability for convolution neural networks (CNNs). While previous work has focused on the question of how to visually interpret CNNs, we ask what it is that we…
Percolation theory serves as a cornerstone for studying phase transitions and critical phenomena, with broad implications in statistical physics, materials science, and complex networks. However, most machine learning frameworks for…
This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable…
Convolutional Neural Networks (CNNs) constitute a class of Deep Learning models which have been used in the recent past to resolve many problems in computer vision, in particular optical flow estimation. Measuring displacement and strain…
Consider subcritical Bernoulli bond percolation with fixed parameter p<p_c. We define a dependent site percolation model by the following procedure: for each bond cluster, we colour all vertices in the cluster black with probability r and…
Convolutional Neural Networks (CNNs) have exhibited great performance in discriminative feature learning for complex visual tasks. Besides discrimination power, interpretability is another important yet under-explored property for CNNs. One…
Recognition algorithms based on convolutional networks (CNNs) typically use the output of the last layer as feature representation. However, the information in this layer may be too coarse to allow precise localization. On the contrary,…