Related papers: Thick-Restart Block Lanczos Method for Large-Scale…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…
${\mathcal H}\Phi$ [$aitch$-$phi$] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the…
A method of truncating the large shell model basis is outlined. It relies on the order given by the unperturbed energies of the basis states and on the constancy of their spreading widths. Both quantities can be calculated by a simple…
In this work, we have developed a multiscale computational algorithm to couple finite element method with an open source molecular dynamics code --- the Large scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) --- to perform…
The complex scaling method is commonly used to describe decaying states, but its applications are limited because the Hamiltonian operator must contain only relative coordinates. This has hindered the use of complex scaling in models…
Quantum Monte Carlo methods find fruitful application in large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in a fluctuating one-body field;…
We introduce a novel training methodology named zELO, which optimizes retrieval performance via the analysis that ranking tasks are statically equivalent to a Thurstone model. Based on the zELO method, we use unsupervised data in order…
The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…
The computation and memory costs of large language models kept increasing over last decade, which reached over the scale of 1T parameters. To address the challenges from the large scale models, model compression techniques such as low-rank…
We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a…
Current widely-used approaches to calculate spectral functions using the density-matrix renormalization group in frequency space either necessarily include an artificial broadening (correction-vector method) or have limited resolution…
We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This…
This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
In calculations of heavy-atom molecules with the shape-consistent Relativistic Effective Core Potential (RECP), only valence and some outer-core shells are treated explicitly, the shapes of spinors are smoothed in the atomic core regions…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of cancer pose significant computational challenges. Coupling discrete cell-based models…
Convergence analysis of block iterative solvers for Hermitian eigenvalue problems and the closely related research on properties of matrix-based signal filters are challenging, and attract increasing attention due to their recent…
We summarize our recent efforts to develop the Density Matrix Renormalization Group (DMRG) method into a practical truncation strategy for large-scale nuclear shell model calculations. Following an overview of the essential features of the…