相关论文: Importance truncation in non-perturbative many-bod…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…
We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…
Quasiparticle self-consistent many-body perturbation theory (MBPT) methods that update both eigenvalues and eigenvectors can calculate the excited-state properties of molecular systems without depending on the choice of starting points.…
In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on…
Full tensor gravity (FTG) devices provide up to five independent components of the gravity gradient tensor. However, we do not yet have a quantitative understanding of which tensor components or combinations of components are more important…
To understand the dynamics of quantum many-body systems, it is essential to study excited eigenstates. While tensor network states have become a standard tool for computing ground states in computational many-body physics, obtaining…
Real-time nonequilibrium Green functions (NEGF) have been very successful to simulate the dynamics of correlated many-particle systems far from equilibrium. However, NEGF simulations are computationally expensive since the effort scales…
Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N^2) memory. However, in its grid-based least-squares…
Nonequilibrium Green's functions provide a powerful framework for studying quantum many-body dynamics including the laser-induced dynamics in solids. The Non-Equilibrium Systems Simulation package (NESSi) offers an efficient platform for…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
Strongly-coupled Quantum Field Theories (QFTs) are ubiquitous in high energy physics and many-body physics, yet our ability to do precise computations in such systems remains limited. Hamiltonian Truncation is a method for doing…
Exact diagonalization (ED) is an essential tool for exploring quantum many-body physics but is fundamentally limited by the exponentially-scaled computational complexity. Here, we propose tensor network variational diagonalization (TNVD),…
As the demand for user privacy grows, controlled data removal (machine unlearning) is becoming an important feature of machine learning models for data-sensitive Web applications such as social networks and recommender systems.…
A method for solving the shell-model eigenproblem in a severely truncated space, spanned by properly selected correlated states obtained by partitioning the full configuration space, is proposed. The method describes in a practically exact…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
Open quantum systems provide a conceptually simple setting for the exploration of collective behavior stemming from the competition between quantum effects, many-body interactions, and dissipative processes. They may display dynamics…
We present a collection of methods to simulate entangled dynamics of open quantum systems governed by the Lindblad equation with tensor network methods. Tensor network methods using matrix product states have been proven very useful to…
Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…
To find deterministic solutions to the transient $S_N$ neutron transport equation, iterative schemes are typically used to treat the scattering (and fission) source terms. We explore the one-cell inversion iteration scheme to do this on the…