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As noticed in Ref.[1], the Ore-Powell's classical calculation of the o-Ps -> 3 gamma decay amplitude does not fulfill Low's theorem requirements for the low energy end of the photon spectrum. We reanalyze the implications of Low's theorem…
The application of Fourier analysis in combination with the Proper Orthogonal Decomposition (POD) is investigated. In this approach to turbulence decomposition, which has recently been termed Spectral POD (SPOD), Fourier modes are…
Machine-learning interatomic potential models based on graph neural network architectures have the potential to make atomistic materials modeling widely accessible due to their computational efficiency, scalability, and broad applicability.…
We have derived a new method which allows to compute the full and the Pauli reference kinetic potentials for atoms and molecules in a real space representation. This is done by applying the optimized effective potential (OEP) method to…
We present an accurate machine learning (ML) model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. The potential, named GAP-20, describes the properties of the bulk crystalline…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
The optimized effective potential (OEP) is the exact Kohn-Sham potential for explicitly orbital-dependent energy functionals, e.g., the exact exchange energy. We give a proof for the OEP equation which does not depend on the chain rule for…
Automated hyperparameter optimization (HPO) can support practitioners to obtain peak performance in machine learning models. However, there is often a lack of valuable insights into the effects of different hyperparameters on the final…
The development of interatomic potentials that can accurately capture a wide range of physical phenomena and diverse environments is of significant interest, but it presents a formidable challenge. This challenge arises from the numerous…
The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface- and nano-science. Here we…
The optimized effective potential (OEP) method is a promising technique for calculating the ground state properties of a system within the density functional theory. However, it is not widely used as its computational cost is rather high…
Deep Learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in…
Effective and accurate characterization and quantification of complex microstructure of a heterogeneous material and its evolution under external stimuli are very challenging, yet crucial to achieving reliable material performance…
We find the numerically exact partition potential for 1-D systems of interacting electrons designed to model diatomic molecules. At integer fragment occupations, the kinetic contribution to the partition potential develops sharp features in…
There has been a veritable explosion of methods and software to perform machine-learned regression on datasets of electronic energies and forces to develop high-dimensional machine learned potential energy surfaces (ML-PESs). A major, but…
A computationally efficient and accurate machine-learned (ML) interatomic potential is developed for Ti$_{n+1}$C$_n$ MXenes. With a diverse set of structures computed with density functional theory, the trained ML potential demonstrates…
Multiscale Proper Orthogonal Decomposition (mPOD) decomposes fluid flows into energy-optimal modes within prescribed frequency bands by combining Proper Orthogonal Decomposition with a multiresolution analysis (MRA). In its classical…
Chemical segregation and structural transitions at interfaces are important nanoscale phenomena, making them natural targets for atomistic modeling, yet interatomic potentials must be fit to secondary physical properties. To isolate the…
We present a benchmark designed to evaluate the predictive capabilities of universal machine learning interatomic potentials across systems of varying dimensionality. Specifically, our benchmark tests zero- (molecules, atomic clusters,…
This paper gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms…