Future connected vehicles require antennas that remain reliable under service-dependent electromagnetic requirements and time-varying in-cabin loading. This paper presents a passenger-aware reduced-order digital twin for slice-aware fluidic reconfigurable automotive antennas. Its computational contribution is a confidence-aware prediction-and-state-selection framework that couples conductive-fluid antenna states, snapshot based reduced prediction, passenger-induced dielectric loading, explicit acceptance/defer rules, and service-dependent state se lection. The active slice is mapped to impedance, bandwidth, realized gain, angular coverage, pattern stability, and, where applicable, isolation and envelope correlation. Validation uses eight fluidic states, four passenger scenarios, and 41 frequency samples. Within the sampled interpolation domain, the method yields a reflection-coefficient RMSE of 0.19 dB, a radiation-pattern RMSE of 0.31 dB, and pattern correlation above 0.99. Extrapolative, experimental, real-time, and hardware-robustness claims are not made. Runtime acceleration is not quantified because reproducible hardware metadata and raw solver logs were unavailable.
Electromagnetic (EM) inverse synthesis of pixelated antennas is a high-dimensional discrete problem that maps desired impedance and radiation responses to a fabrication-ready binary metallization layout. This paper introduces Multi-Response-to-Patch (MR2P), a conditional binary-diffusion framework that directly generates one-bit microstrip patch layouts from heterogeneous EM response specifications. Unlike full-wave or surrogate-assisted optimization pipelines that require a new search for each target, MR2P samples a binary layout through a single response-conditioned reverse process. The framework consists of a Multi-Response Encoder (MRE), pre-trained by a Multi-Response Masked AutoEncoder to embed broadband reflection coefficients $|S_{11}|$ and frequency-wise $X$- and $Y$-polarized beam patterns into a unified latent sequence, and a Binary Diffusion Model (BDM), which denoises Bernoulli noise into a $32\times 32$ metal/void layout under cross-attention conditioning. Because the reverse process is defined directly on binary variables, no post-hoc thresholding is required. MR2P is trained on $24~\mathrm{k}$ HFSS-labeled one-bit layouts and evaluated by closed-loop full-wave re-simulation of generated layouts. Ablation studies verify the importance of the MRE pretraining, while artificial wideband and triple-band targets, nearest-neighbor comparisons, and a fabricated multi-response example demonstrate threshold-free, fabrication-ready inverse synthesis from quantitative EM specifications.
With the rapid advancement of high-speed digital communication technology, signal integrity (SI) issues in high speed links have become increasingly prominent. To address the high computational complexity and low simulation efficiency of traditional electromagnetic simulation methods in multi-topology and multi-parameter scenarios, this paper proposes a surrogate modeling approach based on a hybrid model integrating Graph Attention Networks (GAT), Deep Neural Networks (DNN), and Long Short-Term Memory (LSTM) networks. First, this method utilizes GAT to extract global features from the topological structures and physical parameters of key link components, including drivers, packages, and channels. Subsequently, the DNN module performs nonlinear fusion of global features from the three components, forming a unified global representation that characterizes the electrical properties of the entire high-speed link. Finally, the global representation of the link is input into the LSTM network alongside the differential excitation waveform, enabling high-precision prediction of the transient differential response for high-speed links. Experimental results demonstrate that the proposed model achieves prediction accuracy comparable to traditional circuit simulation methods while significantly reducing computational cost. Compared with existing machine learning based surrogate models, this approach effectively alleviates the limitations of fixed topologies and parameters, providing a highly accurate, efficient, and scalable modeling pathway for SI analysis, design space exploration, and simulation acceleration in high speed links.
The inaugural article in JMMCT's “Explaining the Unexplained” series raised a fundamental question about DC power transmission: is it transmitted by electromagnetic waves, like AC power? Its authors believe so; they believe that DC waves exist, even though this may seem difficult to accept due to the absence of electromagnetic coupling at zero frequency. The present paper aims to contribute to finding a comprehensive answer to this challenging question, considering separately the cases of wireless and wired transmission systems, and examining DC and quasi-DC electromagnetic fields, in the context of classical electromagnetism. Based on Maxwell's equations, we show, theoretically, that quasi DC wave propagation and quasi-AC wave propagation are absolutely similar when it comes to wired systems (transmission lines), but not so in the case of wireless systems (antenna radiation) that are unable to support quasi-DC waves. The presence or absence of electric charges, at rest or in motion, in the space between the energy source and the energy receiver is key to this discussion.
Electromagnetic (EM) analysis of interconnected transmission-line networks (TLNs) with intricate topologies is challenging. While conventional electromagnetic topology (EMT) -based methods can characterize EM responses, they are limited to simple networks composed of single conductors and heavily rely on manual, expertise-driven matrix construction, which restricts their scalability. To address these issues, we propose the Hierarchical Graph-Electromagnetic Topology (HG-EMT) method that bridges automated EM modeling with rigorous EM computation. First, a hierarchical graph representation is introduced to encapsulate the network topology, multi-conductor coupling mechanisms, and the mapping between physical transmission lines and EMT tubes, enabling concise and mathematically tractable modeling. Second, by integrating the graph model with EMT theory, a programmable EM computation workflow is established in which topological information is automatically extracted to determine the elements and assembly sequence of the governing matrix equations, e.g., Baum-Liu-Tesche equations. This eliminates extensive expert intervention and transforms EM analysis from a manual process into a programmatic procedure. Simulation results from representative case studies verify the accuracy and efficiency of the proposed method. This work provides a robust foundation for next generation of specialized simulation tools capable of handling large-scale and complex interconnected systems.
Computational electromagnetics (CEM) is employed to numerically solve Maxwell's equations, and it has very important and practical applications across a broad range of disciplines, including biomedical engineering, nanophotonics, wireless communications, and electrodynamics. The main limitation of existing CEM methods is that they are computationally demanding. Our work introduces a leap forward in the integration of numerical modeling with deep learning frameworks by proposing an original solution of Maxwell's equations that is grounded on message passing on graphs. Specifically, we demonstrate that the update equations derived by discretizing Maxwell's partial differential equations can be innately expressed as a two-layer graph neural network (GNN) with static and pre-determined edge weights. Given this intuition, a straightforward way to numerically solve Maxwell's equations entails simple message passing between the graph's nodes, yielding a significant computational time gain, while preserving the same accuracy as conventional transient CEM methods. Ultimately, our work supports the efficient and precise emulation of electromagnetic wave propagation with GNNs, and more importantly, we anticipate that a similar treatment can be generalized to systems of partial differential equations arising in other scientific disciplines.
Full-wave electromagnetic simulation is essential in the semiconductor and packaging industry, for the design and signal integrity analysis of high-speed interconnects and integrated passive components. These applications often entail broadband simulations of multiscale structures from DC to millimeter-wave frequencies, which requires the accurate modeling of conductor losses and the skin effect, and poses a substantial challenge to computational techniques. The boundary element method is an appealing candidate to address this challenge, because it offers a two-dimensional representation of a three-dimensional problem using a surface integral formulation of Maxwell's equations. However, this often comes at the cost of ill-conditioned matrices at low frequencies and for multiscale structures. In this work, a new boundary element formulation is developed, where the underlying surface integral equations are inherently valid from statics to full-wave electrodynamics. A discretization scheme is proposed which leads to a system of equations that (a) is immune to low-frequency breakdown and solvable from exactly DC to millimeter-wave frequencies, even for multiscale geometries, (b) models the skin effect rigorously, and (c) does not require a barycentric refinement or intermediate matrix factorization, unlike existing methods. Realistic and representative numerical examples drawn from the target application areas demonstrate the accuracy and effectiveness of the proposed method.
Theoretical modeling of Rydberg atom-based microwave sensors is often limited by the high computational cost of the density matrix formalism (DMF), especially when resolving transient dynamics in Doppler-broadened vapor cells. We introduce an efficient direct time-domain numerical framework based on the Monte Carlo Wave Function (MCWF) method for Doppler-broadened Rydberg-atom simulations. By incorporating the Doppler effect as a stochastic initialization parameter within individual quantum trajectories, our approach naturally captures thermal broadening, thereby avoiding explicit velocity-grid integration in the MCWF calculation. This reformulates the propagation from a density-matrix representation whose state dimension scales quadratically with the number of levels to a trajectory-based wave-function representation with linear state dimension for each propagated trajectory. We demonstrate that this framework achieves nearly one order of magnitude reduction in runtime under comparable AT-splitting extraction accuracy, while maintaining agreement with the DMF results for the considered observables. The method is further applied to representative time-domain signal-recovery scenarios, including baseband symbol recovery for 8-ary amplitude-shift keying (8-ASK) signals. This work provides a scalable tool for designing and optimizing next-generation Rydberg quantum receivers.
In this paper, a neural network method is proposed for better estimation of simulation material parameters. Such improved estimations increase the accuracy of EM simulations. Estimating simulation material parameters from an electrical response is an ill-posed problem since multiple parameter combinations can exhibit almost the same electrical response. Such problems can be more effectively addressed by specific neural network topologies, such as tandem neural networks. Hence, a solution following this approach is proposed. As an example, the substrate model parameters of the cascaded T-resonators and the Beatty resonator are estimated using their scattering parameters. The proposed approach supports a wide range of microwave structures through a structure-independent training data generation process. As an alternative to the proposed tandem neural network that combines convolutional, transposed convolutional and fully connected neural networks, a second tandem neural network employing only fully connected neural networks was also realized as a reference model and the performance of the two is compared. The performance of the two is evaluated using synthetic test data obtained from EM simulations. The mean squared error of the proposed model is approximately $0.5 \times 10^{-3}$, which is significantly lower than that of the reference model. The proposed method can be applied to measurement-based modeling, de-embedding fixture effects at high frequencies, production lot monitoring, among others.
We introduce rank-limiting strategies to optimize tensor-train decompositions for three-dimensional finite-difference time-domain simulations using the relationship between the tensors and their specific dimensionality. These include the use of hard caps on the inner ranks of the tensor train decomposition and the use of a group rounding algorithm taking into account all field components simultaneously. Several numerical examples are considered to verify the efficacy of the proposed optimization strategies.
This paper proposes a regularization-augmented physics-informed neural network (RAPINN) framework based on the volume integral equation (VIE) for electromagnetic inverse scattering problems. By incorporating the VIE, the scattered field is evaluated through the Green's function, allowing the neural networks to reconstruct the total field only inside the domain of interest and reducing the computational burden for far-field problems. To avoid repeated forward solves, the inverse problem is reformulated as an optimal-control-inspired physics-constrained optimization problem. For each inverse problem, a complex-valued field module and a real-valued contrast module are jointly optimized through the data-equation and state-equation residuals, replacing explicit matrix inversion with residual-based optimization. The resulting vanilla PINN framework achieves accuracy comparable to NN-based inversion with lower computational cost. To improve robustness in challenging cases, squared total-variation-like (squared TV) smoothness regularization and Tikhonov regularization are further incorporated into the PINN loss to form RAPINN. By introducing prior information on the scatterer, these explicit regularization terms complement the implicit constraints imposed by the physics residuals and help mitigate unstable reconstructions produced by the vanilla PINN in high-contrast and noisy scenarios. Numerical results show that RAPINN provides more stable and accurate reconstructions than conventional methods and vanilla PINN in the tested cases.
Thermal effects pose a significant challenge to the electromagnetic transmission and circuit-level performance of compact radio-frequency (RF) modules based on advanced packaging technology. To address the limitations of conventional thermal-electrical coupling analysis methods and thermal-management approaches for RF integrated modules, this paper presents an algorithm-assisted modeling (AAM)-based thermal-electromagnetic-circuit coupling analysis method and package-level heat-dissipation layout designs for a fan-out wafer-level packaging (FOWLP)-based frequency-modulated continuous-wave (FMCW) RF module. First, an FOWLP-based FMCW RF module is developed as the analysis platform. Then, the proposed AAM-based method introduces the nonuniform temperature distribution into the electromagnetic and circuit-level analysis of the RF module. The results show that, as the ambient temperature increases, the S-parameter curves exhibit more pronounced fluctuations, and the reduction in intermediate-frequency signal-to-noise ratio (SNR) calculated by the AAM-based method relative to the uniform-temperature model also increases. Finally, three horizontal heat-dissipation layouts based on through-mold via (TMV) chips and solder-ball arrays are designed and evaluated. Without changing the original package dimensions, the proposed layouts improve both thermal and system-level RF performance. The hybrid layout reduces the maximum temperature and the area exceeding 40(degrees)C by 6.0% and 52.2%, respectively. The uniform layout provides the largest improvements in transmit power and intermediate-frequency SNR, with increases of 2.93dB and 1.51dB, respectively.
Accurate electromagnetic (EM) modeling of electronic package structures is critical for signal and power integrity analysis, yet full-wave simulations on fine meshes are often computationally expensive. Deep learning and neural network models have recently attracted considerable attention as alternative solutions. However, with the continuous expansion of the design space in advanced packaging, conventional surrogate architectures such as FCNNs, CNNs, and RNNs start to exhibit limitations in scalability. Therefore, in this paper, we propose two vision-based transformer models that eliminate the need for design parameters and leverage self-attention mechanism for efficient package-level EM and multi-physics simulation. The first framework employs a Vision Transformer (ViT) to directly predict frequency-domain responses (S-parameters) from structural images of the package. By capturing global spatial dependencies through self-attention, the ViT-based model achieves high accuracy while significantly reducing computational cost compared to conventional EM solvers. The second framework introduces a transformer-based super-resolution neural network designed for multiphysics co-simulation scenarios. Specifically, a physical structure is simulated with a coarse mesh using an EM solver to provide power input to the thermal solver, which subsequently generates low-resolution temperature profile images. The super-resolution neural network then refines these results to produce high-resolution temperature distributions, akin to those obtained through numerical simulations with a fine mesh. Various numerical examples are simulated to validate the capability and improvement of the proposed method.
Accurate modeling of radiofrequency (RF) coils is essential for reliable electromagnetic (EM) field simulations in magnetic resonance imaging (MRI). This study evaluates the numerical accuracy of higher-order surface basis functions for RF coil simulation within the surface-volume integral equation (SVIE) framework. Graglia-Wilton-Peterson (GWP) basis functions and quadratic curvilinear triangular discretization elements replace the conventional Rao-Wilton-Glisson (RWG) basis functions and flat triangular elements used to approximate the coil currents. SVIE simulations show that the solver based on GWP achieves up to two orders of magnitude lower error in the electric field distribution within the coil load for coils without open edges, while no significant performance improvements were observed for coils with open edges. These results demonstrate that higher-order formulations are needed for accurate RF coil modeling in certain scenarios.
Deep learning has greatly advanced metasurface design by overcoming the slow, inefficient and experience-driven limitations of traditional numerical simulations. However, inverse design of metasurface arrays for electromagnetic scattering control in the frequency-space domain entails significantly higher degrees of freedom, which leads to increased computational complexity and prohibitive full-wave simulation costs. To address this, we integrate universal Huygens scattering into a deep learning framework to build a fast simulation surrogate. This physics-informed approach accelerates optimization while circumventing solution ambiguity. Through a two-stage inverse design strategy, multi-objective optimization is decomposed to lower computational burden and reduce inter-objective trade-offs. Our method supports the realization of arbitrary scattering profiles with high design flexibility. Experimentally, the designed metasurface achieves 7.6-29.8 dB RCS reduction at normal incidence over 3.7-18 GHz (131.8% bandwidth) and maintains over 6 dB average reduction within +/- 30 degrees in two orthogonal planes. This work establishes an efficient route to inversely design broadband, wide-angle scattering-controlling metasurface arrays.
Deep-learning-based electromagnetic solvers are often constrained by their reliance on large training datasets and the challenge of maintaining physical consistency. This paper presents a physics-constrained deep image prior (PcDIP) framework for electromagnetic forward modeling that leverages low-resolution pre-computed field distributions. The method embeds discretized governing equations into the loss function, enabling physics-consistent field reconstruction through unsupervised optimization. A dual-channel architecture is employed to represent the real and imaginary components of complex fields, and a residual-based stopping criterion is introduced to ensure automatic and stable convergence. Simulation experiments involving scatterers with a wide range of material properties demonstrate the effectiveness of the proposed framework for forward modeling of scattering problems. The generalization capability of PcDIP is further validated using two realistic models. Compared with the previous DIP-based forward modeling approach and conventional iterative solvers, PcDIP achieves higher computational accuracy and faster convergence. These results indicate that the proposed framework provides a practical and efficient solution for rapid electromagnetic forward modeling in real-world applications.
This paper introduces, for the first time, a scalable and interpretable genetic programming (GP)-based surrogate modeling approach within an explainable AI framework for the synthesis of Printed Ridge Gap Waveguide (PRGW) unit cells. The proposed approach targets stop-band frequencies ranging from 3 to 300 GHz. The dataset is initially generated using full-wave electromagnetic simulations and augmented using a conditional generative adversarial network (cGAN) to enrich the feature space and scale the dataset to approximately one million samples. The cGAN is used exclusively during data preparation. Leveraging the augmented dataset, a GP-based surrogate model is constructed and expressed as a closed-form analytical relationship that maps the desired stop-band frequency and substrate material properties to the corresponding PRGW unit-cell dimensions. The proposed method improves reliability, significantly reduces computational time, and demonstrates superior performance compared with conventional trial-and-error procedures and traditional machine learning techniques in terms of mean squared error (MSE), mean absolute error (MAE), and efficiency. Experimental validation is performed through the design, fabrication, and measurement of two PRGW-based waveguides targeting Internet of Space (12-16 GHz) and mid-band 5G (3-4 GHz) applications. The measured results confirm the effectiveness of the proposed GP-based surrogate modeling framework for automated RF and microwave component and subsystem design.
In this paper, the terminal responses of twisted-wire pairs (TWPs) in complex platforms are obtained using field-wire-circuit co-simulation approach for multiscale electromagnetic analysis. The proposed method mainly combines the three-dimensional (3D) full-wave conformal finite-difference time-domain (CFDTD) method, the one-dimensional (1D) FDTD scheme for transmission line equations, and the state variable method for arbitrary terminals. First, the 3D full-wave FDTD combined with metallic conformal method is employed to compute the electromagnetic fields in PEC shielding cavities or automotive environments, where the magnetic-field updating equations on edge grids adjacent to metallic boundaries are modified. Then, a high-precision interpolation algorithm is used to obtain the electric-field components required for constructing the equivalent distributed sources along the TWPs, while the cables are not explicitly included in the full-wave simulation. Last, 1D FDTD method is applied to calculate the voltages and currents along the TWPs, and the terminal responses are solved together with the state variable representation of the terminal circuits. The proposed hybrid FDTD method naturally integrates the interactions among electromagnetic fields, cables, and terminal circuits. Numerical examples demonstrate that the results obtained by the proposed approach agree well with those from 3D full-wave simulations and CST Cable Studio co-simulation, confirming the accuracy and reliability of the proposed method. Moreover, the proposed hybrid method can apply larger mesh size to correctly calculate the terminal response of the TWPs, and the simulation time is greatly reduced.
Computer models can benefit the development of devices containing microwave plasma by clarifying the physical processes of the relevant system. Traditional multiphysics modeling is of limited help due to complex methodology, ambiguous interpretation of the results, and excessive computational resources. However, modeling the electromagnetic processes responsible for initiating and maintaining the plasma can be of great importance. Recently, a key step in developing this approach was made, linking modeling parameters of the plasma with operational parameters of the system, such as power, type of gas, and pressure. In this paper, we present an experimental verification of this approach for a previously developed high-power plasma limiter. In a Finite-Difference Time Domain (FDTD) model of the device, the plasma is characterized by the plasma frequency, which is defined via an established relationship between electron density and power; and the collision frequency, which is calculated for a given gas and pressure inside the plasma cell. A small discrepancy between the measured and simulated transmission coefficients is attributed to uncertainty in the model input data, which inherits any uncertainty in the conditions of the experiment. The presented simulation results, not readily obtained using other multiphysics tools, provide additional insight into the behavior and functionality of the power limiter. It is suggested, based on the results of this endeavor, that FDTD simulations combined with the proposed plasma modeling approach may serve as a practical and informative tool for the analysis and design of microwave plasma devices.
Frequency Selective Surface (FSS) radomes have become increasingly crucial in modern radar systems due to their excellent band-pass characteristics and ability to reduce radar cross-section (RCS). The accurate simulation of the conformal radome requires large computational resources due to their electrically large size and complex geometric structure. In this article, an efficient finite element modeling method based on the first principles of symmetry is proposed, applying it to the electromagnetic simulation of conformal FSS radomes exemplified by C-N rotational symmetry. Utilizing projection operators from group theory, the method decomposes excitations into sub-excitations that adhere to the symmetry. This approach is versatile, extending beyond single rotational symmetry to accommodate any spatial symmetries and their combinations, thus surpassing the discrete Fourier expansion method's capabilities. The technique significantly reduces the degrees of freedom (DOFs) to 1/N of the original size, thus enhancing computational efficiency and simplifying geometric modeling and mesh complexity. With the proposed method, key metrics of conformal radomes, such as the RCS and transmittance/reflectance, can be effectively evaluated, thus supporting the design of conformal FSS radomes with arbitrary high rotational symmetry.
