相关论文: A General Automatic Method for Optimal Constructio…

A new method to construct task graphs for \mcH-matrix arithmetic is introduced, which uses the information associated with all tasks of the standard recursive \mcH-matrix algorithms, e.g., the block index set of the matrix blocks involved…

We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce…

With the increasing popularity and accessibility of high dynamic range (HDR) photography, tone mapping operators (TMOs) for dynamic range compression are practically demanding. In this paper, we develop a two-stage neural network-based TMO…

Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including…

A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…

We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…

Molecular property optimization (MPO) problems are inherently challenging since they are formulated over discrete, unstructured spaces and the labeling process involves expensive simulations or experiments, which fundamentally limits the…

The Moody-Shapere-Wilczek's adiabatic effective Hamiltonian and Lagrangian method is developed further into the matrix effective Hamiltonian (MEH) and Lagrangian (MEL) approach to a parameter-dependent quantum system. The matrix-operator…

We introduce a Lagrangian formulation of the Density Matrix Renormalization Group (DMRG). We present Lagrangians which when minimised yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz,…

In the approaches based on matrix-product states (MPSs), such as the density-matrix renormalization group (DMRG) method, the ordering of the sites crucially affects the computational accuracy. We investigate the performance of an algorithm…

In Graph Theory a number of results were devoted to studying the computational complexity of the number modulo 2 of a graph's edge set decompositions of various kinds, first of all including its Hamiltonian decompositions, as well as the…

Hyperparameter optimization (HPO) plays a central role in the automated machine learning (AutoML). It is a challenging task as the response surfaces of hyperparameters are generally unknown, hence essentially a global optimization problem.…

Gaussian process (GP) based Bayesian optimization (BO) is a powerful method for optimizing black-box functions efficiently. The practical performance and theoretical guarantees of this approach depend on having the correct GP hyperparameter…

We present ROBO (Riemannian Overlapping Block Optimization), a distributed and parallel approach to multi-robot pose graph optimization (PGO) based on the idea of overlapping domain decomposition. ROBO offers a middle ground between…

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of…

We introduce an algorithm that is simultaneously memory-efficient and low-scaling for applying ab initio molecular Hamiltonians to matrix-product states (MPS) via the tensor-hypercontraction (THC) format. These gains carry over to Krylov…

Multiple Operator Integrals (MOIs) have played a foundational role in operator theory and functional calculus, particularly for analyzing Hermitian matrices via spectral decomposition. Conventional MOIs rely on the assumption of…

Understanding the intricate properties of one-dimensional quantum systems coupled to multiple reservoirs poses a challenge to both analytical approaches and simulation techniques. Fortunately, density matrix renormalization group-based…

As a key task in machine learning, data classification is essentially to find a suitable coordinate system to represent data features of different classes of samples. This paper proposes the mutual-energy inner product optimization method…

We propose an efficient algorithm to construct $\boldsymbol{k}\cdot \boldsymbol{p}$ effective Hamiltonians, which is much faster than the previously proposed algorithms. This algorithm is implemented in MagneticKP package. The package…