Related papers: Proper Orthogonal Descriptors for Efficient and Ac…
Shape matching is a fundamental problem in computer graphics with many applications. Functional maps translate the point-wise shape-matching problem into its functional counterpart and have inspired numerous solutions over the last decade.…
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…
We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…
The projector augmented wave (PAW) method of Bl\"ochl linearly maps smooth pseudo wavefunctions to the highly oscillatory all-electron DFT orbitals. Compared to norm-conserving pseudopotentials (NCPP), PAW has the advantage of lower kinetic…
Developing reliable pseudopotentials for orbital-free density functional theory (OF-DFT), especially for transition metals, remains a significant challenge. In this study, we provide a theoretical framework for analyzing pseudization…
In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…
An analytic representation of the short-range repulsion energy in ionic systems is described that allows for the fact that ions may change their size and shape depending on their environment. This function is extremely efficient to evaluate…
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…
Metal-organic frameworks (MOFs) are an incredibly diverse group of highly porous hybrid materials, which are interesting for a wide range of possible applications. For a reliable description of many of their properties accurate…
Local atomic environment descriptors (LAEDs) are used in the materials science and chemistry communities, for example, for the development of machine learning interatomic potentials. Despite the fact that LAEDs have been extensively studied…
The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us…
Recent advancements in protein docking site prediction have highlighted the limitations of traditional rigid docking algorithms, like PIPER, which often neglect critical stochastic elements such as solvent-induced fluctuations. These…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
The Karhunen-Lo\`eve Expansion (KLE) of a stochastic process is a well understood eigenfunction expansion used widely in time series analysis, stochastic PDEs, and signal processing. Karhunen-Lo\`eve expansions have also been proven to…
The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both…
Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In a…
We analyse the spatial diversity of a multipath fading process for a finite region or curve in the plane. By means of the Karhunen-Lo\`eve (KL) expansion, this diversity can be characterised by the eigenvalue spectrum of the spatial…
In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation…
The development of next-generation molecular simulation models requires moving beyond pre-defined functional forms toward machine learning (ML) techniques that directly capture multiscale physics. Here, we demonstrate such an approach using…
Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first…