Related papers: Proper Orthogonal Descriptors for Efficient and Ac…
A method is developed for generating pseudopotentials for use in correlated-electron calculations. The paradigms of shape and energy consistency are combined and defined in terms of correlated-electron wave-functions. The resulting energy…
Let $\rho$ be a representation of a knot group (or more generally, the fundamental group of a tangle complement) into $\operatorname{SL}_2(\mathbb{C})$ expressed in terms of the Wirtinger generators of a diagram $D$. This diagram also…
The optimized-effective-potential (OEP) method is a special technique to construct local Kohn-Sham potentials from general orbital-dependent energy functionals. In a recent publication [M. Betzinger, C. Friedrich, S. Bl\"ugel, A. G\"orling,…
This paper proposes a novel orthogonal-by-construction parametrization for augmenting physics-based input-output models with a learning component in an additive sense. The parametrization allows to jointly optimize the parameters of the…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means of a Karhunen-Lo\`eve expansion. The approximation…
At the heart of the flourishing field of machine learning potentials are graph neural networks, where deep learning is interwoven with physics-informed machine learning (PIML) architectures. Various PIML models, upon training with density…
Interatomic potential models based on machine learning (ML) are rapidly developing as tools for materials simulations. However, because of their flexibility, they require large fitting databases that are normally created with substantial…
The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…
Simulations at the atomic scale provide a direct and effective way to understand the mechanical properties of materials. In the regime of classical mechanics, simulations for the thermodynamic properties of metals and alloys can be done by…
Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoretical model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of…
Machine learning interatomic potentials (MLIPs) based on a large dataset obtained by density functional theory (DFT) calculation have been developed recently. This study gives both conceptual and practical bases for the high accuracy of…
The coherent potential approximation (CPA) is extended to describe satisfactorily the motion of particles in a random potential which is spatially correlated and smoothly varying. In contrast to existing cluster-CPA methods, the present…
Scene completion refers to obtaining dense scene representation from an incomplete perception of complex 3D scenes. This helps robots detect multi-scale obstacles and analyse object occlusions in scenarios such as autonomous driving. Recent…
AI for science (AI4Science) models often suffer from discretization: learned representations remain tied to the training grid, limiting transfer across resolutions, solvers and applications. We introduce Neural Proper Orthogonal…
We visualize the Kohn-Sham kinetic energy density (KED), and the ingredients -- the electron density, its gradient and Laplacian -- used to construct orbital-free models of it, for the AE6 test set of molecules. These are compared to…
Recent advances to combine structured regression models and deep neural networks for better interpretability, more expressiveness, and statistically valid uncertainty quantification demonstrate the versatility of semi-structured neural…
Understanding how structural flexibility affects the properties of metal-organic frameworks (MOFs) is crucial for the design of better MOFs for targeted applications. Flexible MOFs can be studied with molecular dynamics simulations, whose…
In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the Localized Orthogonal Decomposition (LOD) methodology and has approximation properties independent of the regularity of the…
The quest for a formula that satisfactorily measures the effective degrees of freedom in kernel density estimation (KDE) is a long standing problem with few solutions. Starting from the orthogonal polynomial sequence (OPS) expansion for the…