Related papers: Krylov Subspace Method for Molecular Dynamics Simu…
We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes…
To leverage the redundancy between the electronic structure computed at each step of first-principles molecular dynamics, we present a data-driven modeling framework for Kohn-Sham Density Functional Theory that bypasses the explicit…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…
The procedure for simulating the nuclear magnetic resonance spectrum linked to the spin system of a molecule for a certain nucleus entails diagonalizing the associated Hamiltonian matrix. As the dimensions of said matrix grow exponentially…
Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem.…
We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific…
Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a…
A novel linear-algebraic algorithm, multiple Arnoldi method, was developed in an interdisciplinary study between physics and applied mathematics and realized one-hundred-million-atom (100-nm-scale) electronic state calculations on the K…
Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…
Approximating the ground state of many-body systems is a key computational bottleneck underlying important applications in physics and chemistry. The most widely known quantum algorithm for ground state approximation, quantum phase…
Krylov complexity is considered to provide a measure of the growth of operators evolving under Hamiltonian dynamics. The main strategy is the analysis of the structure of Krylov subspace $\mathcal{K}_M(\mathcal{H},\eta)$ spanned by the…
For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…
We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main difficulty in estimating the condition number is the estimation of…
We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…
We present a method for total energy minimizations and molecular dynamics simulations based either on tight-binding or on Kohn-Sham hamiltonians. The method leads to an algorithm whose computational cost scales linearly with the system…
We develop a novel convergence analysis of the classical deterministic block Krylov methods for the approximation of $h$-dimensional dominant subspaces and low-rank approximations of matrices $ A\in\mathbb K^{m\times n}$ (where $\mathbb…
A new approach to simulating warm and hot dense matter that combines density functional theory based calculations of the electronic structure to classical molecular dynamics simulations with pair interaction potentials is presented. The new…
In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing…