Related papers: Rank-adaptive time integration of tree tensor netw…
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…
In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…
We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard…
We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…
Tree tensor networks, or tree-based tensor formats, are prominent model classes for the approximation of high-dimensional functions in computational and data science. They correspond to sum-product neural networks with a sparse connectivity…
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…
We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…
This paper presents a spanning tree-based genetic algorithm (GA) for the reconfiguration of electrical distribution systems with the objective of minimizing active power losses. Due to low voltage levels at distribution systems, power…
We propose a novel non-iterative domain decomposition time integrator for acoustic wave equations using a discontinuous Galerkin discretization in space. It is based on a local Crank-Nicolson approximation combined with a suitable local…
A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive…
Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable…
In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a low rank numerical method is proposed to correct the modeling…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
The Euclidean Steiner tree problem, normally posed in two dimensions, seeks to connect a set of prescribed terminal nodes by placing additional nodes, known as Steiner points, with edges connecting such nodes either to another Steiner point…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework is based on a Galerkin discretization of the underlying…