Related papers: Volume extrapolation via eigenvector continuation
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general…
Simulations of quantum systems in finite volume have proven to be a useful tool for calculating physical observables. Such studies to date have focused primarily on understanding the volume dependence of binding energies, from which it is…
Variational autoencoders (VAEs) are a popular generative model used to approximate distributions. The encoder part of the VAE is used in amortized learning of latent variables, producing a latent representation for data samples. Recently,…
As deep Variational Auto-Encoder (VAE) frameworks become more widely used for modeling biomolecular simulation data, we emphasize the capability of the VAE architecture to concurrently maximize the timescale of the latent space while…
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot…
A modular, maintainable and extensible particle beam simulation architecture is presented. Design considerations for single particle, multi particle, and rms envelope simulations (in two and three dimensions) are outlined. Envelope…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
Variational quantum eigensolvers (VQEs) are successful algorithms for studying physical systems on quantum computers. Recently, they were extended to the measurement-based model of quantum computing, bringing resource graph states and their…
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Here, by making use of the FTvN systems framework introduced by…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
We reconsider the procedure of calculation of fermion-boson vertices and numerical solution of Bethe-Salpeter equations, used in non-local extensions of dynamical mean-field theory. Because of the frequency dependence of vertices, finite…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum mechanical systems. By choosing particle-in-a-box…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…
We consider the problem of enabling robust range estimation of eigenvalue decomposition (EVD) algorithm for a reliable fixed-point design. The simplicity of fixed-point circuitry has always been so tempting to implement EVD algo- rithms in…
Generating large volume hydrodynamical simulations for cosmological observables is a computationally demanding task necessary for next generation observations. In this work, we construct a novel fully convolutional variational auto-encoder…