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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…
Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a new technique based on the…
Data analysis that uses the output of topological data analysis as input for machine learning algorithms has been the subject of extensive research. This approach offers a means of capturing the global structure of data. Persistent homology…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
We study in this paper global properties, mainly of topological nature, of attractors of discrete dynamical systems. We consider the Andronov-Hopf bifurcation for homeomorphisms of the plane and establish some robustness properties for…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
In this paper, we exploit minimal sensing information gathered from biologically inspired sensor networks to perform exploration and mapping in an unknown environment. A probabilistic motion model of mobile sensing nodes, inspired by motion…
The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram. Computing persistence diagrams is often the…
We discuss the identification of attracting sets using combinatorial multivector fields (CMVF) from Conley-Morse-Forman theory. A CMVF is a dynamical system induced by the action of a continuous dynamical system on a phase space…
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…
We report an experimental demonstration of a machine learning approach to identify exotic topological phases, with a focus on the three-dimensional chiral topological insulators. We show that the convolutional neural networks---a class of…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Networks built to model real world phenomena are characeterised by some properties that have attracted the attention of the scientific community: (i) they are organised according to community structure and (ii) their structure evolves with…
This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (or repeller), which could be seen as the union of compact…