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Several forms for constructing novel physics‐informed neural‐networks (PINNs) for the solution of partial‐differential‐algebraic equations (PDAEs) based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype for demonstration. The present work is a natural extension of our review paper (Vu‐Quoc and Humer, CMES‐Comput Modeling Eng Sci, 137(2):1069–1343, 2023) aiming at both experts and first‐time learners of both deep learning and PINN frameworks, among which the open‐source DeepXDE (DDE; SIAM Rev, 63(1):208–228, 2021) is likely the most well documented framework with many examples. Yet, we encountered some pathological problems (time shift, amplification, static solutions) and proposed novel methods to resolve them. Among these novel methods are the PDE forms, which evolve from the lower‐level form with fewer unknown dependent variables (e.g., displacements, slope, finite extension) to higher‐level form with more dependent variables (e.g., forces, moments, momenta), in addition to those from lower‐level forms. Traditionally, the highest‐level form, the balance‐of‐momenta form, is the starting point for (hand) deriving the lowest‐level form through a tedious (and error prone) process of successive substitutions. The next step in a finite element method is to discretize the lowest‐level form upon forming a weak form and linearization with appropriate interpolation functions, followed by their implementation in a code and testing. The time‐consuming tedium in all of these steps could be bypassed by applying the proposed novel PINN directly to the highest‐level form. We also developed a script based on JAX, the High Performance Array Computing library. For the axial motion of elastic bar, while our JAX script did not show the pathological problems of DDE‐T (DDE with TensorFlow backend), it is slower than DDE‐T. Moreover, that DDE‐T itself being more efficient in higher‐level form than in lower‐level form makes working directly with higher‐level form even more attractive in addition to the advantages mentioned further above. Since coming up with an appropriate learning‐rate schedule for a good solution is more art than science, we systematically codified in detail our experience running optimization (network training) through a normalization/standardization of the network‐training process so readers can reproduce our results. [ABSTRACT FROM AUTHOR]

We propose a method to determine the effective parameters for toroidal cores. We have found the method effective in generating the initial flux-magnetomotive-force curve, as well as minor and major flux-MMF loops for a wide range of commercial toroids, using three commercial power manganese-zinc (MnZn) ferrites. In the method, a material-dependent function is used to approximate the initial magnetization curve. Material-independent, geometry-dependent expressions are then derived for the effective parameters. We compare initial-magnetization-based [l.sub.e] and [A.sub.e] with those published by core producers. Index Terms--Ferrites, ferrimagnetic materials, magnetic cores, magnetic hysteresis, soft magnetic materials.

In this letter, we characterize the temperature dependence of the parameters of a frequency-dependent hysteresis model from room temperature to the Curie temperature, at different field amplitude and frequency. Empirical formulas based on power, rational, and gamma functions are suggested for the thermal variations to facilitate the use of the hysteresis model in computer-aided design. We demonstrate a parameter extraction procedure and provide experimental data for a commercial MnZn power ferrite magnetized up to 0.4 T, between 10 kHz and 1 MHz, and between 25 [degrees] C and 225 [degrees]C. Index Terms--Ferrimagnetic materials, ferrites, high-temperature effects, hysteresis, magnetic cores.

We present a methodology for modeling hysteresis in bulk manganese-zinc (MnZn) power ferrites, over the practical ranges of amplitude and frequency, at room temperature. Starting from an existing static hysteresis model (such as Basso-Bertotti's), nonlinear algebraic relationships and linear ordinary differential equations are synthesized and strategically embedded in the static model to achieve satisfactory fit between predicted and measured dynamic hysteresis loops. Two model parameters, [f.sub.rev] and [f.sub.irr], define the cutoff frequencies of the reversible and irreversible processes. We have demonstrated the modeling methodology for a commercial MnZn power ferrite, magnetized up to 0.4 T at frequencies between 10 kHz and 1 MHz. Index Terms--Complex permeability, domain-wall dynamics, dynamic hysteresis modeling, MnZn power ferrites.

Hysteresis-based effective parameters ([l.sub.eHys] and [A.sub.eHys]) are described that are extracted from minor and major loop measurements, and are thus more suitable for computations involving these loops. For three commercial power ferrites, formulae are given for [l.sub.eHys] and [A.sub.eHys] of toroids with radius ratio [k.sub.r] between 0.2 and unity.

Basso and Bertotti's physics-based, yet simple, static hysteresis model is brought to the power electronic community as an alternative for simulation of magnetic components embedded in a power electronic converter. The model is reviewed and its equations cast in application/simulation-oriented forms. It is then revised to better characterize the very soft saturation behavior of commercial power manganese--zinc (MnZn) ferrites. The procedures to extract the model parameters from voltage and current measurements are described. The improved models have been verified against experimental data for major and minor hysteresis loops of three commercial power ferrites. Index Terms--Domain-wall, hysteresis modeling, power MnZn ferrites, preisach model, soft magnetic materials.

As the size of the semiconductor devices is getting smaller with advanced technology, self-heating effects in power semiconductor devices are becoming important. An electrothermal simulation of complete power electronic systems that include Si chips, thermal packages, and heat sinks is essential for an accurate analysis of the behavior of these systems. This paper presents a rational approach to construct thermal circuit networks equivalent to a discretization of the heat equation by the finite element method. Elemental thermal circuit networks are developed, which correspond to the linear and cubic Hermite elements in the 1-D case, to the triangular and rectangular elements in the 2-D case, and to the tetrahedral and cube elements in the 3-D case. These thermal circuit networks are to be connected to the electrical networks of power electronic systems to provide complete electrothermal models that can be conveniently used in any circuit simulator package. Verification examples are presented to demonstrate the accuracy of the proposed formulation.

To increase the efficiency of the electrothermal simulation of power electronic circuits and devices, model reduction techniques are applied to develop reduced thermal circuit models of Si chips, thermal packages, and heat sinks. Both the Modal Superposition method and a Component Mode Synthesis method are presented together with a model error estimation and a Ritz vector method. An alternative method for substructuring is also included. The reduced thermal circuit models are verified and implemented in the SABER circuit simulator. The electrothermal model of a full-bridge converter is simulated employing the proposed approach, and the results discussed.

A strategy for accurately determining thermodynamic phenomenological models over all phases of ferroelectric and ferroelastic materials by semi-infinite optimization is suggested. The elastic Gibbs function is shown as a truncated Taylor series of the polarization vector components, whose coefficients are unknown functions of temperature. The unknown coefficients are obtained empirically. The models accurately compute the ferroelectric properties such as phase transitions, spontaneous polarization and permittivity over a wide temperature range.

A new theory of sandwich beams/one-dimensional plates explains the shear deformation and minute rotations in all layers admitted through the beams. The three different layers passing through these geometrically perfect sandwich beams show variability, both in the thickness and length, thus permitting ply drop-off. When the beam deformation is restricted to planar deformation, the motion of a particular cross-section becomes identical to that of a multibody system having three rigid joints linked together by means of fringes.

The Galerkin projection of the equilibrium equations of geometrically exact sandwich beams satisfy the continuity of displacements across layers. The finite rotation and the shear deformation in each layer can be calculated from the equations. The modelling of sandwich structures can be done with ply drop-off for multilayered structures, variable layer lengths and thicknesses. The shear deformation of each layer can be calculated by assuming straight layered cross-section of the deformed beam.

Hysteresis-based effective parameters (leHys and AeHys) are described, that lire extracted from minor and major loop measurements, and are thus more suitable for computations involving these loops. For three commercial power ferrites, formulae are given for leHysand AeHys of toroids with radius ratio kr between 0.2 and unity. [ABSTRACT FROM AUTHOR]

Discusses a rational formulation of thermal circuit models for electrothermal simulation. Use of model reduction techniques; Modal superposition method; Circuit configuration; Model error estimation; Error norm; Ritz vector approach.

Presents an approach to construct thermal circuit networks equivalent to a discretization of the heat equation by the finite element method. Formulation of circuit elements; Coupled electrothermal equations; Resemblance of thermal and circuit systems; Area coordinate; Conductive terms.