Related papers: Efficient tensor network algorithm for layered sys…

We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…

The proposed method extends upon the representational output of semantic instance segmentation by explicitly including both visible and occluded parts. A fully convolutional network is trained to produce consistent pixel-level embedding…

We develop and benchmark a technique for simulating excitation spectra of generic two-dimensional quantum lattice systems using the framework of projected entangled-pair states (PEPS). The technique relies on a variational ansatz for…

We develop tangent space methods for projected entangled-pair states (PEPS) that provide direct access to the low-energy sector of strongly-correlated two-dimensional quantum systems. More specifically, we construct a variational ansatz for…

Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow joint modeling of spatiotemporal features. These networks have improved performance of video and volumetric image analysis, but have been limited in size due to…

Among 2D convolutional networks on point clouds, point-based approaches consume point clouds of fixed size directly. By analysis of PointNet, a pioneer in introducing deep learning into point sets, we reveal that current point-based methods…

We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions (2D). To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction…

We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…

We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to…

We present a 2D bosonization duality using the language of tensor networks. Specifically, we construct a tensor network operator (TNO) that implements an exact 2D bosonization duality. The primary benefit of the TNO is that it allows for…

In this paper, we calculate entanglement in the isotropic Heisenberg model in a magnetic field on a two-dimensional rectangular zig-zag lattice in the strong rung-coupling limit, using the one-dimensional XXZ model as a proxy. Focusing on…

The norms or expectation values of infinite projected entangled-pair states (PEPS) cannot be computed exactly, and approximation algorithms have to be applied. In the last years, many efficient algorithms have been devised -- the corner…

This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…

3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…

We propose a novel algorithm with a modified Tucker decomposition for tensor network that allows for efficiently and precisely calculating the ground state and thermodynamic properties of two-dimensional (2D) quantum spin lattice systems,…

Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels.…

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…