Machine Learning methodologies for the design of RF/MW systems: challenges, and opportunities

Prof. Tom Dhaene

Ghent University (Belgium)

Advances in manufacturing and growing demands for higher signal bandwidths are pushing RF and microwave systems toward millimeter-wave frequencies and miniaturized electronics. Accurate modeling of critical non-ideal effects—such as crosstalk, reflection, and coupling—poses major challenges. Traditional CAD-based simulations often prove costly when exploring large design spaces. Machine learning now plays a key role by providing data-efficient methods for optimization, sensitivity, and variability analysis. This talk presents fundamentals of deep learning and Bayesian inference, demonstrating how they address design complexity and accelerate innovation.

You can find more information about Tom Dhaene here: https://sumo.ilabt.imec.be/home/members/tdhaene

"Efficient Quasi-Newton Finite Element Formulations for Computational Electromagnetics"

Prof Manfred Kaltenbacher

Institute of Fundamentals and Theory in Electrical Engineering, TU Graz, Austria

Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses Quasi-Newton updates locally, at every material point, to construct appropriate linearizations of the material behaviour during the nonlinear iterations. The resulting scheme shows similar fast convergence as the Newton-method but, like the fixed-point methods, does not require derivative information of the underlying material law. As a consequence, the method can be used for the efficient solution of models with hysteresis which involve non-smooth material behaviour.

"Volumetric Spline Geometries for Finite Elements in Simulation and Optimization of Electric Machine"

L. Blumrich⁽¹⁾, Y. Burkhardt⁽¹⁾, C. Geuzaine⁽²⁾, B. Marussig⁽³⁾, S. Schöps⁽⁴⁾, M. Wiesheu⁽⁴⁾

(1) Electrical Drive Systems, Technical University of Darmstadt, 64289 Darmstadt, Germany

(2) Montefiore Institute, University of Liège, B-4000 Liège, Belgium

(3) Institute of Applied Mechanics, Technical University of Graz, 8010 Graz, Austria

(4) Computational Electromagnetics Group, Technical University of Darmstadt, 64289 Darmstadt, Germany

During design optimization, geometry modifications pose challenges for mesh generation. We propose a method that combines spline-based representations with an automated structured mesh generation. The approach provides a reduction in the computational complexity compared to conventional meshing techniques, while allowing for seamless integration of geometric changes into the mesh. The concept is implemented in Gmsh and GetDP.

"Model Order Reduction Techniques for Electric Machine Modeling"

Michael Müller

University of West Bohemia, Univerzitni 26, 306 14 Pilsen, Czech Republic

In times where the world becomes more and more complex so do simulations. Solving models analytically is only possible for sufficient small input which only covers the solutions of real applications. As soon as more complicated models are used the computational complexity is the limiting factor. It can be either the required memory or the needed time to solve such models, both not acceptable to an alternative. Yet, to solve mathematical models of numerical simulations to a satisfying level one method yields promising results: model order reduction (MOR). The goal of MOR is to approximate the input-to-output behaviour ∥y - y'∥ ≪ 1 while reducing the number of system states and differential equations r ≪ n

"Multi-Objective Optimization Of A Permanent Magnet Brushless DC Motor Using Whale Optimization Algorithm"

Ł. Knypiński, K. Kasprzak

Poznan University of Technology, Institute of Electrical Engineering and Electronics, Piotrowo 3a, 60 – 965 Poznań, Poland

In this paper, the algorithm and computer script for the multi-objective optimization of permanent magnet brushless DC motors for propulsion of electric vehicles have been developed. The optimization procedure was based on the whale optimization algorithm. The optimization procedure was tested using the selected benchmark function. The mathematical model of the outer-rotor BLDC motor was developed. The designed motor is described by four design variables. The multiobjective compromise function contains two functional parameters of the designed motor: efficiency and total mass of materials used in the construction of the motor. Selected optimization results are presented and discussed.

"An Efficient Multi-Fidelity Bayesian Optimization Method For Electromagnetic Metasurface Absorber Design"

N. Chen⁽¹⁾, S. Yang⁽¹⁾ and J. Sykulski⁽²⁾

(1) College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

(2) Electronics and Computer Science, University of Southampton, SO17 1BJ Southampton, U.K.

To tackle the challenges of nonlinearity, multimodality, and computational intensity in optimizing an electromagnetic (EM) metasurface (MS) absorber for radio frequency energy harvesting (RFEH), we propose multi-fidelity Bayesian optimization (BO) method. By integrating a multi-path lower confidence bound (LCB) prescreening and an adaptive sample-replacement strategy, the proposed BO method ensures robust exploration and efficient design, avoiding premature convergence and maintaining compact training datasets. Benchmark test results confirm its high accuracy and fast convergence, while practical applications demonstrate substantial improvements in accuracy and efficiency in RFEH MS absorber design.

"Finite Element Models For Computing The AC Resistance Of Milliken Conductors"

A. Piwonski⁽¹⁾, J. Dular⁽²⁾, R. S. Rezende⁽¹⁾, R. Schuhmann⁽¹⁾

(1) Theoretische Elektrotechnik, Technische Universität Berlin, Berlin, Germany

(2) TE-MPE-PE, CERN, Geneva, Switzerland

Milliken conductors are a common design choice for the inner conductors of AC high voltage power cables. Determining their AC resistance numerically is a challenge due to the arising multiscale problem (strand diameter vs. pitch length of the strand layers vs. pitch length of the segments). We propose a finite element model that takes advantages of helicoidal symmetries and homogenization techniques.

"Open Source Software for Coupled Field Simulation"

M. Kaltenbacher⁽¹⁾, D. Mayrhofer⁽¹⁾, E. Museljic⁽¹⁾, K. Roppert⁽¹⁾, F. Toth⁽²⁾, F. Wein⁽³⁾

(1) Institute of Fundamentals and Theory in Electrical Engineering, TU Graz, Austria

(2) Institute of Mechanics and Mechatronics, TU Wien, Austria

(3) Department of Mathematics, Friedrich-Alexander-Universitat Nurnberg (FAU), Germany

The open source software openCFS is a finite element-based multi-physics modeling and simulation tool available for Linux, Windows and macOS. With about 20 years of research-driven development, the core of openCFS is used in scientific research and industrial application. The modeling strategy focuses on physical fields and their respective couplings.

"Numerical Simulation Of Hydrogels For Cartilage Tissue Engineering Using Opensource Software"

A.R. Farooqi⁽¹⁾, L.V. Che⁽¹⁾, U. van Rienen^(1)(2)(3)

(1) Institute of General Electrical Engineering, University of Rostock, Germany

(2) Department Life, Light & Matter, University of Rostock, Germany

(3) Department of Ageing of Individuals and Society, Interdisciplinary Faculty, University of Rostock, Germany

Articular hyaline cartilage covers articulating bone surfaces in diarthroidal joints of the human body. Despite the availability of palliative and surgical treatment options, they cannot fully regenerate damaged tissue at a defect site. Cartilage tissue engineering using electrical stimulation of hydrogel samples has been proven to be an effective strategy. The current study deals with a simulation model of electrosensitive hydrogels for cartilage tissue engineering. The simulations are performed using the open-source high-performance finite element software NGSolve. The aim is to analyse different quantities, including ionic concentrations, electric potential, and electric conductivity in a hydrogel sample and the surrounding medium.

"AGROS - Software For Physical Fields Simulations"

P. Karban, D. Pánek, J. Kaska

University of West Bohemia, Czech Republic

Agros is an open-source software designed for physical simulations. The aim of this contribution is to present features of a new version of this software. It discuss the architecture of the software, used third party codes, basic principles of scripting and possibilities of solving optimization tasks.

"Partitioned Multirate Simulation Of Electromagnetic-Thermal Problems Using The Precice Library / Open source"

M. Wiesheu⁽¹⁾, K. Roppert⁽²⁾, B. Rodenberg⁽³⁾, I. Cortes Garcia⁽⁴⁾ and S. Schöps⁽¹⁾

(1) Computational Electromagnetics Group, Technical University of Darmstadt, 64289 Darmstadt, Germany

(2) Institute of Fundamentals and Theory in Electrical Engineering, Technical University of Graz, 8010 Graz, Austria

(3) TUM School of Computation, Information and Technology, Technical University of Munich, 85748 Garching, Germany

(4) Department of Mechanical Engineering, Eindhoven University of Technology, 5600MB, The Netherlands

This work explores the possibilities of using the library preCICE to couple different tools to solve electrothermal problems with multirate behavior. Exemplary results are shown for coupled simulation of a 2D transformer example.

"Closed-Form Solution For Zero-Volt Loop Electromagnetic Energy Conversion In Non-Linear Switched Reluctance Machines"

A. Stuikys⁽¹⁾, J.K. Sykulski⁽²⁾

(1) RETORQ Motors Ltd., United Kingdom

(2) Electronics and Computer Science, University of Southampton, SO17 1BJ Southampton, U.K.

The non-linear switched reluctance (SR) machine energy conversion optimization is a challenging computational task due to the non-linearly varying current and torque and numerous design and operating parameters. Zero-volt loop (ZVL) control method of the SR machine is an effective method of operation that optimizes torque production and minimizes the magnetic and the switching losses. This paper presents simple and rapid energy optimization computation method that enables accurate search of ZVL of a given SR machine design.

"Multi-Physics Drive Cycle Performance Computation Of Electric Machines Using FEA"

Kourosh Heidarikani, Pawan Kumar Dhakal, Roland Seebacher, Annette Muetze

Electric Drives and Power Electronic Systems Institute, Graz University of Technology, Austria

This works explores the modelling and computational challenges of finite element based electromagneticthermal coupled drive cycle performance analysis. Two laboratory scale motors are used as application cases: a 70 W 7000 rpm permanent magnet synchronous motor (PMSM) and a 4.4 kW 1430 rpm induction motor (IM). Multi-physics computations are performed for each individual operating point of the drive cycle, including a 2D electromagnetic finite element model directly coupled with a 3D thermal finite element model.

"Stepper Motor Position Control With Optimal Compensation"

M. PAWLAK, S. STĘPIEŃ

Institute of Automatic Control and Robotics, Poznan University of Technology, Poland

The paper presents, a modelling and control design methodology as the concept is proposed to design of high-performance optimal drive systems for stepper motor device. The paper deals with a nonlinear model of electric stepper motor and solution of the new intelligent/optimal position control problem with optimal energy compensation for the motor. The paper also proofs that energy delivered and energy lost can be significantly decreased employing optimal compensation, keeping the same motor dynamics.

"Front-Loading The Design Process For Electromagnetic Devices"

D.A.Lowther⁽¹⁾⁽²⁾, A.Akbari⁽¹⁾

(1) McGill University, Canada

(2) Siemens DISW, Belgium

The design of electromagnetic devices often involves a basic sizing system, to provide a fast suggestion of the structure needed, followed by a multi-physics analysis of the performance. This is a computationally expensive task and can take significant engineering time. If an issue is found with the device performance, it can often mean a significant redesign. Machine learning can be used to enhance the sizing process to provide an initial design along with an estimate of the multi-physics performance accelerating the design process and reducing the probability of a significant redesign.

"A Comparison Of Machine Learning Approaches And Classical Numerical Methods For The Resolution Of Electromagnetic Problems"

S. Barmada⁽¹⁾, S. Dodge⁽¹⁾, A. Formisano⁽²⁾

(1) DESTEC, University of Pisa, Italy

(2) DI, University of Campania “Luigi Vanvitelli”, Aversa (CE), Italy

Machine Learning (ML) is getting more and more present as an alternative computing approach for the numerical analysis of electromagnetic fields. On the other hand, specialised methods like Finite Elements (FEM) [1] or Boundary Elements (BEM) [2] proved to be quite effective in terms of accuracy and computational burden, yet requiring ad-hoc modelling for each different problem. In this contribution we propose a comparison among different ML approaches with some classical approaches in terms of accuracy, time to obtain the result, and generalization capabilities.

"Physics-Informed Neural Networks for Modelling Problems with Material Interfaces"

Sina Toghranegar, Hussain Kazmi, Geert Deconinck, Ruth V. Sabariego

Department of Electrical Engineering (ESAT), KU Leuven, EnergyVille, 3001 Leuven, Belgium

This paper examines the use of Physics-Informed Neural Networks (PINNs) for solving electromagnetic interface problems, with a particular focus on scenarios involving two distinct materials with differing electromagnetic properties and a shared interface. A representative test case involving concentric disks with differing permeabilities is employed to solve Poisson’s equation for the z-component of the magnetic vector potential. The results generated by the PINN are compared to those obtained using the Finite Element Method (FEM) with errors typically below 3.3%. The findings indicate that PINNs are wellsuited for tackling the complexities associated with electromagnetic modeling involving interfaces.

"Machine Learning For Reduced Order Modeling Of Nonlinear Inductors"

Matteo Zorzetto⁽¹⁾, Riccardo Torchio⁽¹⁾⁽²⁾, Francesco Lucchini⁽¹⁾, Paolo di Barba⁽³⁾,

Maria Evelina Mognaschi⁽³⁾, Michele Forzan⁽¹⁾, Fabrizio Dughiero⁽¹⁾

(1) Department of Industrial Engineering, Università degli Studi di Padova, Via Gradenigo 6/A, 35131, Padova, Italy

(2) Department of Information Engineering, Università degli Studi di Padova, Via Gradenigo 6/B, 35131, Padova, Italy

(3) Department of Electrical, Computer, and Biomedical Engineering, University of Pavia, Pavia 27100, Italy

This paper explores the integration of the Proper Orthogonal Decomposition (POD) algorithm with machine learning to develop a non-intrusive reduced-order model for a nonlinear inductor. Using the Finite Element Method (FEM), an axisymmetric model of a nonlinear inductor is constructed and a dataset consisting of the magnetic vector potential's spatial distribution for different current values is collected. POD is applied to reduce the dataset's dimensionality, while machine learning establishes a mapping between the inputs and the reduced state vector. The resulting surrogate model significantly increases computational efficiency with minimal accuracy loss.

"Multi-Criteria Shape Design Of IPM Motors For Electric Vehicle Traction Based On Machine-Learning Models"

P. Di Barba, M.E. Mognaschi

Dept. of Electrical, Computer and Biomedical Engineering, University of Pavia, Italy

In the paper, the optimal shape design of an Interior Permanent Magnet (IPM) motor is performed considering both running and cogging torque as design criteria. The genetic algorithm NSGA-II is used, based on surrogate models for the objective function evaluations. Specifically, feed-forward, shallow Neural Networks are used, showing good results in terms of accuracy and reduction of computational costs.

"Deep Learning Models For Electric Vehicle Motors: A Transfer Learning Approach"

P. Di Barba, M.E. Mognaschi

Dept. of Electrical, Computer and Biomedical Engineering, University of Pavia, Italy

In the paper, the transfer learning technique is applied to Deep Neural Networks (DNNs) used as surrogate model for the evaluation of an Interior Permanent Magnet (IPM) motor performances. Specifically, the cogging torque is considered, with constraints on the running torque. Several ways of applying transfer learning are investigated and the results are given in terms of accuracy and reduction of computational costs.

"Optimization Of FGM-Application In HVDC GIL Based On Deep Neural Network"

H. Hensel, M. Clemens

University of Wuppertal, Germany

In HVDC GIL high electric field stress, resulting from space charge accumulation due to DC condition, may ap-pear. Functional graded materials (FGM) are a field control technique to reduce the intensity of the electric field. FGM is realized by a spatial distribution of the electric conductivity in the spacer material by filler particles. In this work, an optimized spatial distribution of the electric conductivity in the spacer material is investigated by numerical simulation and by utilizing a deep neural network (DNN), in order to homogenize the electric field distribution optimally and to decrease the maximum electric field. The results show a decisive reduction of the electric field.

"Hysteresis Model Of Ferromagnetic Material Based On The Deep Operator Neural Network"

Ziqing Guo, Ruth V. Sabariego

Dept. of Electrical Engineering, KU Leuven, Campus EnergyVille, Belgium

In this digest, the deep operator network (DeepONet) is used to model the nonlinear hysteretic behaviour of ferromagnetic materials. We first generate a set of BHcurves (with H, the magnetic field and B, the magnetic flux density) by means of the Jiles-Atherton model to train, validate and test the deep neural operator network. The constructed model is validated by comparing the predicted B values and the hysteresis losses with reference values. Attention is paid to feasibility and accuracy.

"Electromagnetic Time Reversal For Partial Discharge Localisation In DC Systems"

A. Ragusa⁽¹⁾⁽²⁾, H. Sasse⁽¹⁾, A. Duffy^(1),(2), W. H. Siew⁽³⁾, M. Given⁽³⁾

(1) De Montfort University, Leicester, United Kingdom

(2) The Institute of Marine Engineering (INM) - The Italian National Research Council (CNR), Rome, Italy

(3) The University of Strathclyde, Glasgow, United Kingdom

The paper analyses the possibility of using electromagnetic time reversal (EMTR) with transmission-line matrix (TLM) numerical method to locate partial discharges (PD) in DC power systems, introducing the open challenges with PDs in DC systems.

"Analysis of trapped modes in beam pipes of accelerating cavity modules"

Sosoho-Abasi Udongwo⁽¹⁾, Shahnam Gorgi Zadeh⁽³⁾, Ursula van Rienen⁽¹⁾⁽²⁾

(1) Institut fur Allgemeine Elektrotechnik, Universitat Rostock, Rostock, Germany,

(2) Department Life, Light & Matter, Universitat Rostock, D-18051 Rostock, Germany,

(3) CERN, Geneva, Switzerland

This contribution investigates an important aspect of the design of particle accelerators, i.e., the behaviour of the geometric shunt impedance, R/Q, as a function of the beam pipe length for eigenmodes formed within the beam pipes connecting the cavities in a module. The study employs both analytical and numerical approaches to characterise these dependencies, providing an understanding of how R/Q varies with the geometric parameters. Analytical formulas are derived and validated by comparison with numerical solutions. The results highlight optimal performance - minimised impedance - for certain beam pipe length-to-radius ratios.

"Implementation of an Edge-Based H-Formulation in the Nonlinear Magnetostatic Case"

Lukas D. Domenig, Klaus Roppert, and Manfred Kaltenbacher

Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Graz, Austria

This paper deals with the usage of a magnetic field oriented formulation that is derived from a mixed formulation using the penalty method, which reduces the problem to one partial differential equation. To achieve accurate results the occurring penalty factor has to be chosen properly. For this reason, a rule to select this parameter is developed for linear and nonlinear material laws. It is shown that it yields good results when compared to measurements provided by the TEAM problem 13.

"Comparison Of Different Modeling Approaches For Graphene Field-Effect Transistors"

Philippe Peter, Mario Kupresak, Jasmin Smajic, Juerg Leuthold

Institute of Electromagnetic Fields (IEF), ETH Zurich, Switzerland

This work compares two different static approaches to model carrier concentrations in graphene. First, a drift-diffusion based model that approximates 1-D quasi-Fermi levels in the graphene channel (M1). Second, an equilibrium model that expresses carrier concentrations directly as a function of the electric potential (M2). The comparison shows that M1 and a 1-D version of M2 produce the same results at equilibrium. For a non-equilibrium case, deviating results are obtained. The 1-D models assume that carrier concentrations are constant across the thickness of graphene. The work examines the effect of this assumption, by comparing the results of a 1-D and a full 2-D version of M2 at equilibrium. The obtained results are validated against existing literature.

"Measurenment And Analysis Of The Magnetostriction Of Oriented And Non-Oriented Electrical Steel Sheets"

Tao Chen, Qingxin Yang, Changgeng Zhang, Yongjian Li

Hebei University of Technology, China

Magnetostriction is an important cause of vibration and noise in transformer operation. It is of great significance to measure and study the magnetostriction of electrical steel sheet for transformer design, optimization and vibration and noise reduction. In this paper, a single sheet tester is set up to measure the alternating magnetostrictive characteristics of a single sheet sample of electrical steel with laser interferometer. Further, the variation trend of magnetostriction with magnetization frequency is also studied.

"Extracting Lumped-Element Parameters from a Finite Element Three-Phase Transformer Model – A Practical Approach"

A. Sauseng, M. Kaltenbacher, and K. Roppert

Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Graz, Austria

This contribution focuses on a lumped-element parameter extraction of a finite-element three-phase transformer model. The two-dimensional transformer model is simulated using the A-formulation in the finite-element solver OPENCFS. The lumped-element model is based on modified nodal analysis and utilizes Hopkinson’s analogy to derive a magnetic equivalent circuit. The core in both approaches is described using a saturation function. The parameter extraction of the finite-element model for the lumped element model is discussed practically, and the simulation results are compared.

"Hybrid Approach Based On Tensor Decomposition For Model Order Reduction Applied To Motor Diagnosis"

Ze Guo^(1)(2)(3), Zuqi Tang⁽¹⁾

(1)Univ. Lille, Arts et Métier Institute of Technology, Centrale Lille, Junia, ULR 2697-L2EP, F-59000 Lille, France

(2)Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China

(3)University of Chinese Academy of Sciences, Beijing 100190, China

In this work, a hybrid model order reduction (MOR) approach is proposed for nonlinear multi-parameter magnetostatic problems applied to motor diagnostics, considering various operating conditions and fault scenarios. The proposed approach leverages tensor decomposition to construct both the reduced basis and the nonlinear term, demonstrating superior performance compared to classical methods.

"Efficient Computation Of Circulating Currents In Electrical Machines Based On Existing Models"

S. Schirrmacher, M. Henke

ebm-papst Mulfingen GmbH & Co. KG, Germany

In the design of high-speed electrical machines with parallel strand windings, circulating currents must be considered. This paper presents a method that utilizes existing Finite Element Analysis (FEA) models, combined with additional static FEA, to solve the voltage equation. The results show that this approach achieves sufficient accuracy while significantly reducing computation time compared to transient FEA with fully modelled strands.

"Modeling Of Power Cables Using CLN Method"

W. Chen, S. Clénet, T. Henneron, F. Colas

Univ. Lille, Arts et Metiers Institute of Technology, Centrale Lille, Junia, ULR 2697 - L2EP, Lille, France

The Cauer Ladder Network (CLN) method can generate a reduced model based on an equivalent electrical circuit from a finite element magnetoquasistatic problem. In this study, the CLN method has been used to construct a cascaded pi model of a system composed of two HVDC cables. A comparison of the generated model with ElectroMagnetic Transient (EMT) software shows that the proposed method leads to accurate results and seems to be more stable at low frequencies.

"Accurate Identification Of BH-Loops From Measurement Using Wide Ring Specimen"

T. Matsuo

Kyoto University, Japan

An analytical formulation is developed for identifying the hysteretic property of magnetic material from the measured current-flux property of a ring specimen. A computational example shows that the proposed method can reconstruct the hysteretic property more accurately than conventional approximations.

"Electrically Small Magneto-Electric Antennas For Shielding Efficiency Quantification In IC-Stripline Emission Tests"

Thomas Bauernfeind and Dominik Kreindl

Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Austria

Shielding of unwanted electromagnetic emissions of ICs is vital for a proper electromagnetic compatibility (EMC) of the IC with other electronic based devices in close proximity. Due to high integration densities large metallic shielding caps are impractical. Hence, other shielding measures have to be developed. In order to quantify the shielding efficiency (SE) of the developed methods specific test configurations are needed. In the present work, finite element method-based investigations on electrically small magneto-electric antennas are conducted which should be used for shielding-efficiency tests.

"Electromagneto-Quasistatic Versus Full Maxwell Models For Low- And Middle-Frequency Field Problems"

M. Clemens⁽¹⁾, M.-L. Henkel⁽¹⁾, M. Günther⁽¹⁾ and S. Schöps⁽²⁾

(1)IMACM, University of Wuppertal, 42119 Wuppertal, Germany

(2)Computational Electromagnetics Group, Technical University of Darmstadt, 64289 Darmstadt, Germany

This paper provides a discussion of the applications of electromagneto-quasistatic (EMQS) field formulations of Darwin-type, where radiation effects are neglected, and the regular full Maxwell field formulations with respect to their usability in low- and middle-frequency field problems. It is shown that both types of formulation result in ill-conditioned systems of equations, where aspects of numerical stability and solver efficiency are affected.