Parametric Macromodels of Digital I/O Ports

This paper addresses the development of macromodels for input and output ports of a digital device. The proposed macromodels consist of parametric representations that can be obtained from port transient waveforms at the device ports via a well established procedure. The models are implementable as SPICE subcircuits and their accuracy and efficiency are verified by applying the approach to the characterization of transistor-level models of commercial devices

Radial Structure Graph Based Mathematical for Large Distribution Networks

In the modern electrical distribution network and utility companies a steady increase in the need for high quality and safe delivery of electricity to consumers is evident, which requires an adequate distribution network, that is a network with high quality voltage and low loss of energy, with a small number of failures and equipment failure , etc. In this paper is proposed a way of representing the mathematical model of distribution networks. For calculations of energy applications, the best way for representation distribution network is in form of graph of the radial structure. By presenting the distribution network in the form of a radial structure graph, which consists of nodes and branches, possible through the use of specialized compensation algorithms for the calculation of steady state and fault analysis. Advantages of these algorithms, as compared to other algorithms are much shorter time needed for calculation and much higher accuracy of calculation results

Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, sometimes by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We review, discuss and benchmark state-of-the-art representations and relations between them, including smooth overlap of atomic positions, many-body tensor representation, and symmetry functions. For this, we use a unified mathematical framework based on many-body functions, group averaging and tensor products, and compare energy predictions for organic molecules, binary alloys and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method and hyper-parameter optimization