Related papers: Machine Learning Topological Invariants with Neura…

Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…

We employ a convolutional neural network to explore the distinct phases in random spin systems with the aim to understand the specific features that the neural network chooses to identify the phases. With the energy spectrum normalized to…

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…

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…

Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…

Invariances to translations have imbued convolutional neural networks with powerful generalization properties. However, we often do not know a priori what invariances are present in the data, or to what extent a model should be invariant to…

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…

Efficient and automated classification of phases from minimally processed data is one goal of machine learning in condensed matter and statistical physics. Supervised algorithms trained on raw samples of microstates can successfully detect…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

Many-body topological quantum states host exotic quantum phenomena and lie at the forefront of developing next-generation quantum technologies. Recently emerged neural network wavefunction methods have established themselves as a powerful…

The computational complexity of calculating phase diagrams for multi-parameter models significantly limits the ability to select parameters that correspond to experimental data. This work presents a machine learning method for solving the…

We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the…

Databases compiled using ab-initio and symmetry-based calculations now contain tens of thousands of topological insulators and topological semimetals. This makes the application of modern machine learning methods to topological materials…

The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…

We employ a machine learning technique for an estimate of the topological charge $Q$ of gauge configurations in SU(3) Yang-Mills theory in vacuum. As a first trial, we feed the four-dimensional topological charge density with and without…

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in…

We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced…

Topology and machine learning are two actively researched topics not only in condensed matter physics, but also in data science. Here, we propose the use of topological data analysis in unsupervised learning of the topological phase…

We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. Using a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum, we sample wave…

Examples of non-hermitian quantum systems admitting topological insulator phase are presented in one, two and three space dimensions. All of these non-hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity is maintained…