Related papers: From real materials to model Hamiltonians with den…
The automation of ab initio simulations is essential in view of performing high-throughput (HT) computational screenings oriented to the discovery of novel materials with desired physical properties. In this work, we propose algorithms and…
At early times dark matter has a thermal velocity dispersion of unknown amplitude which, for warm dark matter models, can influence the formation of nonlinear structure on observable scales. We propose a new scheme to simulate cosmologies…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer,…
Scientists and engineers rely on accurate mathematical models to quantify the objects of their studies, which are often high-dimensional. Unfortunately, high-dimensional models are inherently difficult, i.e. when observations are sparse or…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We present a first-principles approach to electronic many-body systems strongly coupled to cavity modes in terms of matter-photon one-body reduced density matrices. The theory is fundamentally non-perturbative and thus captures not only the…
Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and…
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed…
We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model which is relevant for compaction of granular materials. The computer simulations use an…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Sampling-based inference has seen a surge of interest in recent years. Hamiltonian Monte Carlo (HMC) has emerged as a powerful algorithm that leverages concepts from Hamiltonian dynamics to efficiently explore complex target distributions.…
Reconstruction of a full-space quantum Hamiltonian from its effective Feshbach's model-space avatar is shown feasible. In a preparatory step the information carried by the effective Hamiltonian is compactified using a linear algebraic…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…
Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal…