This paper pioneers a novel approach in electromagnetic (EM) system analysis by synergistically combining Bayesian Neural Networks (BNNs) informed by Latin Hypercube Sampling (LHS) with advanced thermal–mechanical surrogate modeling within COMSOL simulations for high-frequency low-pass filter modeling. Our methodology transcends traditional EM characterization by integrating physical dimension variability, thermal effects, mechanical deformation, and real-world operational conditions, thereby achieving a significant leap in predictive modeling fidelity. Through rigorous evaluation using Mean Squared Error (MSE), Maximum Learning Error (MLE), and Maximum Test Error (MTE) metrics, as well as comprehensive validation on unseen data, the model’s robustness and generalization capability is demonstrated. This research challenges conventional methods, offering a nuanced understanding of multiphysical phenomena to enhance reliability and resilience in electronic component design and optimization. The integration of thermal variables alongside dimensional parameters marks a novel paradigm in filter performance analysis, significantly improving simulation accuracy. Our findings not only contribute to the body of knowledge in EM diagnostics and complex-environment analysis but also pave the way for future investigations into the fusion of machine learning with computational physics, promising transformative impacts across various applications, from telecommunications to medical devices.

The optimization of high-frequency circuits remains a computationally intensive task due to the need for repeated high-fidelity electromagnetic (EM) simulations. To address this challenge, we propose a novel integration of machine learning-generated inverse maps within the space mapping (SM) optimization framework to significantly accelerate circuit optimization while maintaining high accuracy. The proposed approach leverages Bayesian Neural Networks (BNNs) and surrogate modeling techniques to construct an inverse mapping function that directly predicts design parameters from target performance metrics, bypassing iterative forward simulations. The methodology was validated using a low-pass filter optimization scenario, where the inverse surrogate model was trained using electromagnetic simulations from COMSOL Multiphysics 2024 r6.3 and optimized using MATLAB R2024b r24.2 trust region algorithm. Experimental results demonstrate that our approach reduces the number of high-fidelity simulations by over 80% compared to conventional SM techniques while achieving high accuracy with a mean absolute error (MAE) of 0.0262 (0.47%). Additionally, convergence efficiency was significantly improved, with the inverse surrogate model requiring only 31 coarse model simulations, compared to 580 in traditional SM. These findings demonstrate that machine learning-driven inverse surrogate modeling significantly reduces computational overhead, accelerates optimization, and enhances the accuracy of high-frequency circuit design. This approach offers a promising alternative to traditional SM methods, paving the way for more efficient RF and microwave circuit design workflows.

Lower-fidelity electromagnetic (EM) models are widely used to reduce the computational cost of microwave filter optimization, but their practical usefulness is often assessed through response similarity, own-fidelity objective values, or nominal simulation speedup. This paper examines whether designs optimized using coarse, mesh-derived EM models remain useful when verified at higher-fidelity. A cross-fidelity study is conducted using two microstrip filter benchmarks, a low-pass filter and a band-pass filter, under a fixed simulation setup, frequency sampling, objective function, and local-search procedure, so that mesh discretization is isolated as the source of model variation. Designs independently optimized at multiple mesh levels are reevaluated across the full model hierarchy, and their degradation during fine-model verification is used as an indicator of transferability. The results show that lower-fidelity success is not necessarily preserved under finer EM evaluation. In the band-pass filter case, extra coarse and coarse models satisfy the sampled transmission mask at their own-fidelity levels but yield substantially degraded responses in the fine model, whereas an intermediate model provides a more useful starting point for refinement. Space-mapping experiments further show that coarse-to-fine response matching does not always improve the target model objective value; its benefit depends on the selected model pair and on the observed transferability of the participating models. For the examples studied, the low-pass filter could be completed using an intermediate effective fine model, whereas the band-pass filter required an intermediate-to-fine progression followed by limited fine-model refinement. These findings highlight the need to evaluate coarse EM models by the survivability of their optimized designs, not only by speed or response similarity, before using them in multifidelity microwave filter optimization.

Pixelated electromagnetic representations enable topology-free numerical exploration of microwave layouts without enforcing a predefined circuit template. This work presents a simulation-based electromagnetic modeling and analysis framework for pixelated microstrip low-pass filters within a physical footprint comparable to that of a classical stepped-impedance reference. A binary metallization encoding is embedded in a fixed microstrip domain and explored through full-wave electromagnetic optimization under consistent material, excitation, and specification conditions. The objective is not extreme miniaturization or hardware prototyping, but to assess whether topology-free pixelated layouts can produce useful low-pass responses within the same general physical scale and to analyze the structural properties of the resulting feasible layouts. Across 20 independent optimization runs, 12 specification-compliant and geometrically unique metallization layouts were identified. Aggregate analysis of 360 single-pixel perturbations reveals topology-dependent sensitivity, while finite-width regularization of ideal corner contacts preserves modeled specification compliance after refined-mesh verification, with the suitable bridge width depending on the topology. The scope is deliberately limited to full-wave EM modeling and numerical analysis; experimental fabrication and measurement are left as a subsequent validation stage. These findings support topology-free pixelated EM modeling and analysis as a route for investigating non-obvious low-pass filter layouts under comparable footprint constraints.

In this work, an initial step forward to address the development of multi-physics neural modeling is presented. The initial step consists of a prove of concept to determine if a neural network model (NN) is enough accurate to represent the bi-physical response (electrical and thermal) of a second order low-pass filter. Three different learning algorithms were used to train the neural network, being the Bayesian Regularization the model which exhibits the best generalization performance to represent the EM responses subject to changes in the circuit temperature.

Design-variable scaling is often treated as numerical preprocessing in simulation-driven optimization, although the coordinates supplied to the optimizer form part of the numerical interface to the computational model. This study quantifies the resulting implementation-level sensitivity of Nelder–Mead using two full-wave electromagnetic (EM) microwave-filter models as controlled engineering benchmarks: a three-variable low-pass filter (LPF) with comparable variable magnitudes and a five-variable band-pass filter (BPF) containing a much smaller coupling gap. For each benchmark, the physical seeds, EM model, frequency samples, sampled mask-based objective, aggregation norm, optimizer options, and evaluation budget were fixed; only the optimizer-space representation was changed. Raw physical, relative-normalized, partially scaled gap, and log-relative coordinates were compared using exact and tolerance-based success, residual violation severity, EM evaluation count, seed-level outcomes, and final-design distances. For the LPF, raw and normalized coordinates each achieved 5/15 exact successes, while log-relative coordinates achieved 4/15 with milder residual violations. For the BPF, the corresponding counts were 13/15, 13/15, 12/15, and 9/15, with the log-relative formulation producing the most severe failures. The results show that parameterization is a non-neutral component of simulation-driven optimization and should be documented and validated as part of reproducible computational-modeling workflows.