相关论文: GCA-$\mathcal{H}^2$ matrix compression for electro…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
We design a quantum molecular dynamics method for strongly correlated electron metals. The strong electronic correlation effects are treated within a real-space version of the Gutzwiller variational approximation (GA), which is suitable for…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
We implement, optimize, and validate the linear-scaling Kubo-Greenwood quantum transport simulation on graphics processing units by examining resonant scattering in graphene. We consider two practical representations of the Kubo-Greenwood…
We review the recent optimizations of gravitational $N$-body kernels for running them on graphics processing units (GPUs), on single hosts and massive parallel platforms. For each of the two main $N$-body techniques, direct summation and…
Graph classification is crucial in network analyses. Networks face potential security threats, such as adversarial attacks. Some defense methods may trade off the algorithm complexity for robustness, such as adversarial training, whereas…
We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both…
This paper presents a hierarchical low-rank decomposition algorithm assuming any matrix element can be computed in $O(1)$ time. The proposed algorithm computes rank-revealing decompositions of sub-matrices with a blocked adaptive cross…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
Dense kernel matrices $\Theta \in \mathbb{R}^{N \times N}$ obtained from point evaluations of a covariance function $G$ at locations $\{ x_{i} \}_{1 \leq i \leq N} \subset \mathbb{R}^{d}$ arise in statistics, machine learning, and numerical…
Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank…
The heteroscedastic probabilistic principal component analysis (PCA) technique, a variant of the classic PCA that considers data heterogeneity, is receiving more and more attention in the data science and signal processing communities. In…
In the field of biological research, it is essential to comprehend the characteristics and functions of molecular sequences. The classification of molecular sequences has seen widespread use of neural network-based techniques. Despite their…
In recent years, compressed sensing (CS) based image coding has become a hot topic in image processing field. However, since the bit depth required for encoding each CS sample is too large, the compression performance of this paradigm is…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
In a recent paper, J. Chem. Phys. 162, 214101 (2025), a novel approach for the rigidification of a molecular cluster was proposed, in which starting with an all-atom (AA) potential, a coarse-grained (CG) potential for the associated cluster…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation…
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
A typical optimization of customized accelerators for error-tolerant applications such as multimedia, recognition, and classification is to replace traditional arithmetic units like multipliers and adders with the approximate ones to…