Related papers: Application of symbolic programming for atomic man…
Nonlinear mixed effects modeling is a powerful tool when analyzing data from several entities in an experiment. In this paper, we present NLMEModeling, a package for mixed effects modeling in Wolfram Mathematica. NLMEModeling supports mixed…
Atomic probe tomography (APT), based on the work of Erwin Mueller, is able to generate three-dimensional chemical maps in atomic resolution. The required instruments for APT have evolved over the last 20 years from an experimental to an…
We demonstrate the use of symbolic regression in deriving analytical formulas, which are needed at various stages of a typical experimental analysis in collider phenomenology. As a first application, we consider kinematic variables like the…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
Modelling the cosmic large-scale structure can be done through numerical N-body simulations or by using perturbation theory. Here, we present an N-body approach that effectively implements a multi-step forward model based on Lagrangian…
In this work, we present a general purpose deep neural network package for representing energies, forces, dipole moments, and polarizabilities of atomistic systems. This so-called recursively embedded atom neural network model takes both…
In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting…
We develop a package of numerical simulations implemented in MATLAB to solve complex many-body quantum systems. We focus on widely used examples that include the calculation of the magnetization dynamics for the closed and open Ising model,…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
The QMol-grid package provides a suite of routines for performing quantum-mechanical simulations in atomic and molecular systems, currently implemented in one spatial dimension. It supports ground- and excited-state calculations for the…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
This paper discusses the algorithms and implementations of three Mathematica packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
Molecular dynamics (MD) simulations provide detailed insight into atomic-scale mechanisms but are inherently restricted to small spatio-temporal scales. Coarse-grained molecular dynamics (CGMD) techniques allow simulations of much larger…
One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schr\"{o}dinger equations of the system. But…
The Minkowski operators (addition and substraction of sets in vectorial spaces) has been extensively used for Computer Graphics and Image Processing to represent complex shapes. Here we propose to apply those mathematical concepts to extend…
SchNetPack is a versatile neural networks toolbox that addresses both the requirements of method development and application of atomistic machine learning. Version 2.0 comes with an improved data pipeline, modules for equivariant neural…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
Modern atomic physics applications in science and technology pose ever higher demands on the precision of computations of properties of atoms and ions. Especially challenging is the modeling of electronic correlations within the…
This paper describes an algorithmic system called SQT for the computer simulation of a wide class of quantum experiments on entangled particles. SQT maintains a hidden internal state for each particle and it provides an initialization…