相关论文: Interpolating moving least-squares methods for fit…
Transition intensities for small molecules such as water and CO$_2$ can now be computed with such high accuracy that they are being used to systematically replace measurements in standard databases. These calculations use high accuracy ab…
This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…
We have tested the original interaction-strength-interpolation (ISI) exchange-correlation functional for main group chemistry. The ISI functional is based on an interpolation between the weak and strong coupling limits and includes…
In a series of recent publications of the author, three interpolation procedures, denoted IMPE, IMMPE, and ITEA, were proposed for vector-valued functions $F(z)$, where $F : \C \to\C^N$, and their algebraic properties were studied. The…
This paper proposes a novel location information aided multiple intelligent reflecting surface (IRS) systems. Assuming imperfect user location information, the effective angles from the IRS to the users are estimated, which is then used to…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of…
A method is presented for generating a good initial guess of a transition path between given initial and final states of a system without evaluation of the energy. An objective function surface is constructed using an interpolation of…
We resolve the long-standing controversy over the surface energy of simple metals: Density functional methods that require uniform-electron-gas input agree with each other at many levels of sophistication, but not with high-level correlated…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an…
A wide variety of integral inequalities (IIs) have been developed and studied for the stability analysis of distributed parameter systems using the Lyapunov functional approach. However, no unified mathematical framework has been proposed…
Machine learning interatomic potentials (MLIPs) are routinely used to model diverse atomistic phenomena, yet parameterizing them to accurately capture solid-state phase transformations remains difficult. We present error metrics and…
Data approximation is essential in fields such as geometric design, numerical PDEs, and curve modeling. Moving Least Squares (MLS) is a widely used method for data fitting; however, its accuracy degrades in the presence of discontinuities,…
The rapid emergence of universal Machine Learning Interatomic Potentials (uMLIPs) has transformed materials modeling. However, a comprehensive understanding of their generalization behavior across configurational space remains an open…
Machine learning interatomic potentials (MLIPs) are used to estimate potential energy surfaces (PES) from ab initio calculations, providing near quantum-level accuracy with reduced computational costs. However, the high cost of assembling…
The role of numerical accuracy in training and evaluating neural network-based potential energy surfaces is examined for different experimental observables. For observables that require third- and fourth-order derivatives of the total…
The advent of 6G is expected to enable many use cases which may rely on accurate knowledge of the location and orientation of user equipment (UE). The conventional localization methods suffer from limitations such as synchronization and…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
Simulations of single- and multi-species compressible flows with shock waves and discontinuities are conducted using a weighted compact nonlinear scheme (WCNS) with a newly developed sixth order localized dissipative interpolation. In…