Related papers: Proper Orthogonal Descriptors for Efficient and Ac…
Many quantum systems admit an explicit analytic Fourier space expansion, besides the usual analytic Schrodinger configuration space representation. We argue that the use of weighted orthonormal polynomial expansions for the physical states…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
We present a formulation of proper orthogonal decomposition (POD) producing a velocity-temperature basis optimized with respect to an $H^1$ dissipation norm. This decomposition is applied, along with a conventional POD optimized with…
Experimental extraction of $\beta$-shape functions, C(W), is challenging. Comparing different experimental $\beta$-shapes to each other and to those predicted by theory in a consistent manner is difficult. This difficulty is compounded when…
We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…
Detection of abrupt spatial changes in physical properties representing unique geometric features such as buried objects, cavities, and fractures is an important problem in geophysics and many engineering disciplines. In this context,…
A major barrier to decentralized, near-patient diagnostics is the lack of a signal transduction modality that is both analytically precise and accessible at the point of care. Optical readouts remain instrument-dependent and difficult to…
The Born--Oppenheimer approximation is the standard tool for the study of molecular systems. It is founded on the observation that the energy scale of the electron dynamics in a molecule is larger than that of the nuclei. A very similar…
For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
Machine Learning (ML) approximations to Density Functional Theory (DFT) potential energy surfaces (PESs) are showing great promise for reducing the computational cost of accurate molecular simulations, but at present they are not applicable…
Unraveling a descriptor that is correlated with catalytic reactivity is essential for fast screening for the optimal catalysts for a given catalytic reaction. Herein, we propose bond-derived orbitalwise coordination number…
The rapid rise of large language models (LLMs) has unlocked many applications but also underscores the challenge of aligning them with diverse values and preferences. Direct Preference Optimization (DPO) is central to alignment but…
We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of…
This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…
We scrutinize the accuracy of the pseudopotential approximation in density-functional theory (DFT) calculations of surfaces by systematically comparing to results obtained within a full-potential setup. As model system we choose the CO…
An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…
Localized orbital-based quantum embedding, as originally formulated in the context of density matrix embedding theory (DMET), is revisited from the perspective of lattice density functional theory (DFT). An in-principle exact (in the sense…
Model reduction using the proper orthogonal decomposition (POD) method is applied to the dynamics of ferroelastic patches to study the first order square to rectangular phase transformations. Governing equations for the system dynamics are…