High-dimensional Design Space Research Articles

Hydrodynamic Shape Optimization of a Naval Destroyer by Machine Learning Methods

This paper explores the integration of advanced machine learning (ML) techniques within simulation-based design optimization (SBDO) processes for naval applications, focusing on the hydrodynamic shape optimization of the DTMB 5415 destroyer model. The use of unsupervised learning for design-space dimensionality reduction, combined with supervised learning through active learning-based multi-fidelity surrogate modeling, allows for significant improvements in computational efficiency while addressing complex, high-dimensional design spaces. By applying these ML techniques to both single- and multi-objective optimizations, aimed at minimizing resistance and enhancing seakeeping performance, the proposed framework demonstrates its practical value in hydrodynamic design. This approach provides a scalable and efficient solution, reducing the reliance on high-fidelity simulations while accelerating the optimization process, without substantial modifications to existing toolchains. A design-space dimensionality reduction of approximately 70% is achieved, reducing the design variables from 22 to 7 while retaining 95% of the original geometric variance. Additionally, computational cost reductions of 65% to 98% are observed, compared to using the full design space and high-fidelity simulations only.

Jet mixing optimization using a bio-inspired evolution of hardware and control

Jet mixing is a critical factor in various engineering applications, influencing pollutant dispersion, chemical processes, medical treatments, and combustion enhancement. Hitherto, jet mixing has typically been optimized by either passive or active control techniques. In this experimental study, we combine simultaneous optimization of active control with 12 inward-pointing minijets and a tuneable nozzle exit shape commanded by 12 stepper motors. Jet mixing is monitored at the end of the potential core with an array of 7 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} 7 Pitot tubes. This high-dimensional actuation space is conquered with Particle Swarm Optimization through Targeted, Position-Mutated Elitism. Our results underscore the significant impact of combining control techniques, illustrating the complex interactions of both passive and active control on jet flow dynamics. The mixing area of the combined control optimization is 4.5 times larger than the area of the unforced state. This mixing increase significantly outperforms the effect of shape optimization of the nozzle alone. Our study points at the potential of optimization in high-dimensional design spaces for shapes as well as passive and active control—leveraging the rapid development of flow control hardware and the increasingly powerful tools of artificial intelligence for optimization.

Efficient multi-objective optimization and operational analysis of amine scrubbing CO2 capture process with artificial neural network

Amine scrubbing processes for post-combustion CO2 capture have been extensively studied and significantly improved via various novel designs. However, the amine scrubbers implemented nowadays were usually not optimized according to a number of different evaluation criteria. This is often due to the fact that, for high dimensional design spaces, the rigorous simulation runs needed to facilitate process optimization always calls for huge numbers of simulation software accesses and overwhelming iterative calculations. Therefore, in this study, the well-trained surrogate model was adopted to replace its rigorous counterpart for the purpose of ensuring efficient optimization runs in practical applications. In current study, two objectives, i.e., the specific equivalent work and the CO2 capture level, were both rapidly and effectively optimized in various practical scenarios with different flue gas CO2 concentrations. The corresponding operational parameters and utility consumptions were also easily obtained without additional effort. The computation results obtained so far showed that the proposed surrogate-assisted approach can be utilized to significantly reduce the computational load in practice.

Nacelle optimisation through multi-fidelity neural networks

PurposeAerodynamic shape optimisation is a complex problem usually governed by transonic non-linear aerodynamics, a high dimensional design space and high computational cost. Consequently, the use of a numerical simulation approach can become prohibitive for some applications. This paper aims to propose a computationally efficient multi-fidelity method for the optimisation of two-dimensional axisymmetric aero-engine nacelles.Design/methodology/approachThe nacelle optimisation approach combines a gradient-free algorithm with a multi-fidelity surrogate model. Machine learning based on artificial neural networks (ANN) is used as the modelling technique because of its ability to handle non-linear behaviour. The multi-fidelity method combines Reynolds-averaged Navier Stokes and Euler CFD calculations as high- and low-fidelity, respectively.FindingsRatios of low- and high-fidelity training samples to degrees of freedom of nLF/nDOFs = 50 and nHF/nDOFs = 12.5 provided a surrogate model with a root mean squared error less than 5% and a similar convergence to the optimal design space when compared with the equivalent CFD-in-the-loop optimisation. Similar nacelle geometries and aerodynamic flow topologies were obtained for down-selected designs with a reduction of 92% in the computational cost. This highlights the potential benefits of this multi-fidelity approach for aerodynamic optimisation within a preliminary design stage.Originality/valueThe application of a multi-fidelity technique based on ANN to the aerodynamic shape optimisation problem of isolated nacelles is the key novelty of this work. The multi-fidelity aspect of the method advances current practices based on single-fidelity surrogate models and offers further reductions in computational cost to meet industrial design timescales. Additionally, guidelines in terms of low- and high-fidelity sample sizes relative to the number of design variables have been established.

Multifidelity Methodology for Reduced-Order Models with High-Dimensional Inputs

In the early stages of aerospace design, reduced-order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multifidelity, parametric, and nonintrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction—employing proper orthogonal decomposition and model-based active subspace—with multifidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE 2822 airfoil and the 3D NASA CRM wing, assessing various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity principal component–active subspace (PCAS) method, our multifidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design.

Unidirectional Transmission Metasurfaces with Topological Continuity Generated from High-dimensional Design Space.

With the growing demand for nanodevices, there is a concerted effort to improve the design flexibility of nanostructures, thereby expanding the capabilities of nanophotonic devices. In this work, a Laplacian-weighted binary search (LBS) algorithm is proposed to generate a unidirectional transmission metasurface from a high-dimensional design space, offering an increased degree of design freedom. The LBS algorithm incorporates topological continuity based on the Laplacian, effectively circumventing the common issue of high structural complexity in designing high-dimensional nanostructures. As a result, metasurfaces developed using the LBS algorithm in a high-dimensional design space exhibit reduced complexity, which is advantageous for experimental fabrication. An all-dielectric metasurface with unidirectional transmission, designed from the high-dimensional space using the LBS method, demonstrated the successful application of these design principles in experiments. The metasurface exhibits high optical performance on unidirectional transmission in measurements by a high-resolution angle-resolved micro-spectra system, achieving forward transmissivity above 90% (400-700 nm) and back transmissivity below 20% (400-500 nm) within the targeted wavelength range. This work provides a feasible approach for advancing high-dimensional metasurface applications, as the LBS design method takes into account topological continuity during experimental processing. Compared to traditional direct binary search (DBS) methods, the LBS method not only improves information processing efficiency but also maintains the topological continuity of structures. Beyond unidirectional transmission, the LBS-based design method has generality and flexibility to accommodate almost all physical scenarios in metasurface design, enabling a multitude of complex functions and applications.

Electrothermal Coupling Methodologies and Their Influence on the Optimization of Aircraft Electric Motors

This work presents a fully coupled electrothermal motor analysis and optimization framework, where the motor’s electromagnetic performance depends on its temperature distribution, and the temperature distribution simultaneously depends on its electromagnetic performance. Notably, we analytically compute derivatives through this nonlinear, multidisciplinary analysis using coupled adjoints, which enables the exploration of high-dimensional design spaces. We demonstrate the framework on a series of optimization problems that investigate the effect of feedback coupling and serve to highlight the framework’s utility and flexibility. Furthermore, our results indicate that modeling the motor’s electrothermal coupling is critical to accurate performance prediction. We show that designs optimized using a feedforward-coupled model are found to be either infeasible or nonoptimal under the fully coupled feedback analysis; both conditions are unacceptable for aircraft applications, in which performance is critical.

Reduced-order modelling for real-time physics-based variation simulation enhanced with adaptive sampling and optimized interpolation

AbstractManufacturing industries require a right-first-time paradigm to remain competitive. Variation simulation (VS) is a key tool to predict variation of the final shape of flexible assemblies, allowing to reduce defects and waste. VS models involving compliant sheet-metal parts commonly integrate physics-based simulation with statistical approaches (usually Monte Carlo simulation). Although increasingly used as a backbone of synthesis techniques for (stochastic) optimization of assembly systems, the main roadblock of VS methods is the intense computational costs due to time-intensive simulations and high-dimensional design space. Driven by the need of time reduction, this paper presents an innovative real-time physics-based VS model of assembly systems with compliant sheet-metal parts. The proposed methodology involves a non-intrusive reduced-order model (niROM), empowered by a novel adaptive sampling procedure for dataset generation, and a cross-validation-based optimized radial basis function (RBF) formulation for interpolation. Demonstrated through two case studies—(i) a remote laser welding operation to predict mechanical distortions, with two input parameters, and (ii) the assembly of an aircraft vertical stabilizer with five input parameters—the methodology achieves accurate real-time results, with up to a 43% improvement in accuracy compared to traditional sampling techniques. Findings highlight the critical influence of the sampling strategy and the number of input parameters on ROM accuracy. Better results are reached by employing adaptive sampling in combination with optimum RBF, which additionally disengages the user from the choice of the interpolation settings. This study unlocks new avenues in the field of variation simulation and dimensional/quality monitoring by narrowing the gap between any advanced CAE solver and VS models with real-time physics-based simulations.

A dynamic aggregation strategy enhanced efficient global optimization algorithm for solving high-dimensional turbomachinery design problems

ABSTRACT To address challenges effectively in turbomachinery design optimization involving high-dimensional ( d ≥ 30 ) expensive black-box problems, a dedicated Efficient Global Optimization (EGO) algorithm is proposed with dynamic aggregation. This specialized approach efficiently navigates optimization tasks with limited sample evaluations. Specifically, the Dynamic Aggregate Efficient Global Optimization (DA-EGO) algorithm decomposes the original high-dimensional design space into low-dimensional subspaces for efficient surrogate-based optimization search, and the optimal solutions of subspaces are combined as an elite-point for the global search. Most importantly, the subspace variables are updated in each iteration, according to the variable interaction analyses in the sub- and full-spaces. The perturbation method and the analysis of variance are used to detect variable interactions. After being validated on 21 benchmark functions ranging from 30 to 90 dimensions, the DA-EGO is used for the optimization of a transonic compressor rotor with 28 variables and a multi-stage compressor optimization with 60 variables. With the above, the effectiveness of the proposed algorithm is well demonstrated.

Surrogate-assisted differential evolution using manifold learning-based sampling for high- dimensional expensive constrained optimization problems

To address the challenges of high-dimensional constrained optimization problems with expensive simulation models, a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling (SADE-MLS) is proposed. In SADE-MLS, differential evolution operators are executed to generate numerous high-dimensional candidate points. To alleviate the curse of dimensionality, a Manifold Learning-based Sampling (MLS) mechanism is developed to explore the high-dimensional design space effectively. In MLS, the intrinsic dimensionality of the candidate points is determined by a maximum likelihood estimator. Then, the candidate points are mapped into a low-dimensional space using the dimensionality reduction technique, which can avoid significant information loss during dimensionality reduction. Thus, Kriging surrogates are constructed in the low-dimensional space to predict the responses of the mapped candidate points. The candidate points with high constrained expected improvement values are selected for global exploration. Moreover, the local search process assisted by radial basis function and differential evolution is performed to exploit the design space efficiently. Several numerical benchmarks are tested to compare SADE-MLS with other algorithms. Finally, SADE-MLS is successfully applied to a solid rocket motor multidisciplinary optimization problem and a re-entry vehicle aerodynamic optimization problem, with the total impulse and lift to drag ratio being increased by 32.7% and 35.5%, respectively. The optimization results demonstrate the practicality and effectiveness of the proposed method in real engineering practices.

A process-structure-property model via physics-based/data-driven hybrid methods for freeze-cast porous ceramics in Si3N4-Si2N2O case system

For the engineering applications of freeze-cast porous ceramics, the demand targets are often multiple and competing, which is a challenging problem to seek a Nash equilibrium in the high-dimensional design space. An accurate and robust quantification of process-structure-property correlations would provide an effective path to find the set of Pareto optimal materials for one specific need. In this work, using porous Si3N4-Si2N2O ceramics as the model materials, a hybrid model for the quantitative design of the microstructure and mechanical properties is developed from four physics-based process-microstructure models with sintering, solidification, phase transformation and grain growth kinetic theories, and the subsequent data-driven structure-property model utilizing a machine learning method, artificial neural network (ANN). The SHapely Additive exPlanations (SHAP) analysis is further introduced to interpret the ANN model and mathematically identify the contribution of each microstructure feature descriptor toward target mechanical property outputs. These results present a systematic understanding of the process-structure-property relationships through the hybrid model, guiding the optimal design of the freeze-cast porous ceramics with required microstructures and mechanical properties.

Large-scale sandwich structures optimization using Bayesian method

Benefiting from advanced features like high stiffness-to-weight ratios, sandwich structures are widely used in aerospace for primary and secondary structures. As tasks grow more complex and structures increase in scale, high-dimensional design spaces inevitably arise. Optimizing large-scale sandwich structures efficiently and intelligently presents certain challenges. Additionally, functional requirements and constraints, such as thermal deformation, should be fully considered in the design of practical structures like solar arrays, which involve a large expensive analysis and make the problem more complicated. This paper proposes to use efficient Bayesian optimization with the active subspace (AC) method to address this type of problem. The active subspace method, combined with the adaptive kriging and global sensitivity analysis (GSA), is employed for dimension reduction and reconstructing the design space. Then the structure is optimized within the reconstructed design space using the efficient Bayesian method. The proposed optimization strategy is applied to a case study of solar array with sandwich panels, demonstrating that the developed framework is feasible and effective for structural optimization of large-scale sandwich structures.

Navigating the Expansive Landscapes of Soft Materials: A User Guide for High-Throughput Workflows.

Synthetic polymers are highly customizable with tailored structures and functionality, yet this versatility generates challenges in the design of advanced materials due to the size and complexity of the design space. Thus, exploration and optimization of polymer properties using combinatorial libraries has become increasingly common, which requires careful selection of synthetic strategies, characterization techniques, and rapid processing workflows to obtain fundamental principles from these large data sets. Herein, we provide guidelines for strategic design of macromolecule libraries and workflows to efficiently navigate these high-dimensional design spaces. We describe synthetic methods for multiple library sizes and structures as well as characterization methods to rapidly generate data sets, including tools that can be adapted from biological workflows. We further highlight relevant insights from statistics and machine learning to aid in data featurization, representation, and analysis. This Perspective acts as a "user guide" for researchers interested in leveraging high-throughput screening toward the design of multifunctional polymers and predictive modeling of structure-property relationships in soft materials.

CFD-based design optimization of ducted hydrokinetic turbines

Hydrokinetic turbines extract kinetic energy from moving water to generate renewable electricity, thus contributing to sustainable energy production and reducing reliance on fossil fuels. It has been hypothesized that a duct can accelerate and condition the fluid flow passing the turbine blades, improving the overall energy extraction efficiency. However, no substantial evidence has been provided so far for hydrokinetic turbines. To investigate this problem, we perform a CFD-based optimization study with a blade-resolved Reynolds-averaged Navier–Stokes (RANS) solver to explore the design of a ducted hydrokinetic turbine that maximizes the efficiency of energy extraction. A gradient-based optimization approach is utilized to effectively deal with the high-dimensional design space of the blade and duct geometry, with gradients being calculated through the adjoint method. The final design is re-evaluated through higher-fidelity unsteady RANS (URANS) simulations. Our optimized ducted turbine achieves an efficiency of about 54% over a range of operating conditions, higher than the typical 46% efficiency of unducted turbines.

Optimizing graded metamaterials via genetic algorithm to control energy transmission

Optimization of functionally graded metamaterial arrays with a high dimensional and continuous geometric design space is cumbersome and could be accelerated via machine learning tools. Mechanical metamaterials can manipulate acoustic or ultrasonic waves by introducing significant dispersive and attenuative effects near their natural frequency. In this work, functionally graded structures are designed and optimized to combine the energy attenuation performance of multiple unit cells with varying frequency responses and to reduce the interlayer mismatch effects. Optimization through genetic algorithms avoids many local minima related to high dimensionality of the design space, but requires many iterations. A reduced order model (ROM) is applied, which can reproduce the transmission response traditionally calculated with FEM in a fraction of the time. Pairing GA and the ROM together, an array of 6 unit cells (with a total of 18 independent geometric design variables) is optimized to have stop bands with extended width and sharper boundaries. Symmetric functionally graded structures are determined to have optimal geometric configurations. Measured 3D printed features are projected onto the ROM solutions to quantify the effect of printing uncertainty on array performance. Repeatability error of ±20μm is determined to reduce the mean depth of the transmission stop band by a factor of 102 and introduce small shifts in center frequency and band width. Proposed methods to improve the resolution of accessible points in the ROM space, reduce sensitivity to geometric uncertainty, and add design freedom include introducing out-of-plane perforations and varying constituent materials using tunable filled resin systems.

Shape-Informed Dimensional Reduction in Airfoil/Hydrofoil Modeling

Parametric models have been widely used in pertinent literature for reconstructing, modifying and representing a wide range of airfoil and/or hydrofoil profile geometries. Design spaces corresponding to these models can be exploited for modeling and profile-shape optimization under various performance criteria. Accuracy requirements, along with the need for modeling local features, often lead to high-dimensional design spaces that hinder the process of shape optimization and design through analysis. In this work, we propose a shape-informed dimensional reduction approach that attempts to tackle this deficiency by producing low-dimensional latent design spaces that can be efficiently used in shape representation and optimization. Furthermore, geometric moments are introduced in an attempt to cost-effectively capture analysis-relevant information that is generally expensive to produce. Specifically, geometric integral properties, although intrinsic features of the shape, are quite commonly related to performance indicators employed in performance optimization and therefore provide a cost-effective physics-informed component in the description of the design in the latent space. To this end, we employ the generalized Karhunen-Loève expansion to produce a shape- and physics-informed subspace retaining the highest possible geometric variance and robustness, that is, a lack of invalid designs. At the same time, a series of shape discretizations, encoding the foil’s shape profile, are examined with regard to their effect on the resulting latent space’s quality and efficiency. Our results demonstrate a significant reduction in the dimensionality of the original design space while maintaining a high representational capacity and a large percentage of valid geometries that facilitate fast convergence to optimal solutions in performance-based optimization.

An Efficient Hybrid Multi-Objective Optimization Method Coupling Global Evolutionary and Local Gradient Searches for Solving Aerodynamic Optimization Problems

Aerodynamic shape optimization is frequently complicated and challenging due to the involvement of multiple objectives, large-scale decision variables, and expensive cost function evaluation. This paper presents a bilayer parallel hybrid algorithm framework coupling multi-objective local search and global evolution mechanism to improve the optimization efficiency and convergence accuracy in high-dimensional design space. Specifically, an efficient multi-objective hybrid algorithm (MOHA) and a gradient-based surrogate-assisted multi-objective hybrid algorithm (GS-MOHA) are developed under this framework. In MOHA, a novel multi-objective gradient operator is proposed to accelerate the exploration of the Pareto front, and it introduces new individuals to enhance the diversity of the population. Afterward, MOHA achieves a trade-off between exploitation and exploration by selecting elite individuals in the local search space during the evolutionary process. Furthermore, a surrogate-assisted hybrid algorithm based on the gradient-enhanced Kriging with the partial least squares(GEKPLS) approach is established to improve the engineering applicability of MOHA. The optimization results of benchmark functions demonstrate that MOHA is less constrained by dimensionality and can solve multi-objective optimization problems (MOPs) with up to 1000 decision variables. Compared to existing MOEAs, MOHA demonstrates notable enhancements in optimization efficiency and convergence accuracy, specifically achieving a remarkable 5–10 times increase in efficiency. In addition, the optimization efficiency of GS-MOHA is approximately five times that of MOEA/D-EGO and twice that of K-RVEA in the 30-dimensional test functions. Finally, the multi-objective optimization results of the airfoil shape design validate the effectiveness of the proposed algorithms and their potential for engineering applications.

Aerodynamic Optimization Framework for a Three-Dimensional Nacelle Based on Deep Manifold Learning-Assisted Geometric Multiple Dimensionality Reduction

As a core component of an aero-engine, the aerodynamic performance of the nacelle is essential for the overall performance of an aircraft. However, the direct design of a three-dimensional (3D) nacelle is limited by the complex design space consisting of different cross-section profiles and irregular circumferential curves. The deep manifold learning-assisted geometric multiple dimensionality reduction method combines autoencoders (AE) with strong capabilities for non-linear data dimensionality reduction and class function/shape function transformation (CST). A novel geometric dimensionality reduction method is developed to address the typical constraints of nacelle parameterization. Low-dimensional latent variables are extracted from the high-dimensional design space to achieve a parametric representation of 3D nacelle manifolds. Compared with traditional parametric methods, the proposed geometric dimensionality reduction method improves the accuracy and efficiency of geometric reconstruction and aerodynamic evaluation. A multi-objective optimization framework is proposed based on deep manifold learning to increase the efficiency of 3D nacelle design. The Pareto front curves under drag divergence constraints reveal the correlation between the geometry distribution and the surface isentropic Mach number distribution of 3D nacelles. This paper demonstrates the feasibility of the proposed geometric dimensionality reduction method for direct multi-objective optimization of 3D nacelles.

A reinforcement learning approach to airfoil shape optimization

Shape optimization is an indispensable step in any aerodynamic design. However, the inherent complexity and non-linearity associated with fluid mechanics as well as the high-dimensional design space intrinsic to such problems make airfoil shape optimization a challenging task. Current approaches relying on gradient-based or gradient-free optimizers are data-inefficient in that they do not leverage accumulated knowledge, and are computationally expensive when integrating Computational Fluid Dynamics (CFD) simulation tools. Supervised learning approaches have addressed these limitations but are constrained by user-provided data. Reinforcement learning (RL) provides a data-driven approach bearing generative capabilities. We formulate the airfoil design as a Markov decision process (MDP) and investigate a Deep Reinforcement Learning (DRL) approach to airfoil shape optimization. A custom RL environment is developed allowing the agent to successively modify the shape of an initially provided 2D airfoil and to observe the associated changes in aerodynamic metrics such as lift-to-drag (L/D), lift coefficient (Cl) and drag coefficient (Cd). The learning abilities of the DRL agent are demonstrated through various experiments in which the agent’s objective-maximizing L/D, maximizing Cl or minimizing Cd-as well as the initial airfoil shape are varied. Results show that the DRL agent is able to generate high performing airfoils within a limited number of learning iterations. The strong resemblance between the artificially produced shapes and those found in the literature highlights the rationality of the decision-making policy learned by the agent. Overall, the presented approach demonstrates the relevance of DRL to airfoil shape optimization and brings forward a successful application of DRL to a physics-based aerodynamics problem.

Performance Optimization Engineering of Multicomponent Absorbing Materials Based on Machine Learning.

Multicomponent materials are microwave-absorbing (MA) materials composed of a variety of absorbents that are capable of reaching the property inaccessible for a single component. Discovering mostly valuable properties, however, often relies on semi-experience, as conventional multicomponent MA materials' design rules alone often fail in high-dimensional design spaces. Therefore, we propose performance optimization engineering to accelerate the design of multicomponent MA materials with desired performance in a practically infinite design space based on very sparse data. Our approach works as a closed-loop, integrating machine learning with the expanded Maxwell-Garnett model, electromagnetic calculations, and experimental feedback; aiming at different desired performances, Ni surface@carbon fiber (NiF) materials and NiF-based multicomponent (NMC) materials with target MA performance were screened and identified out of nearly infinite possible designs. The designed NiF and NMC fulfilled the requirements for the X- and Ku-bands at thicknesses of only 2.0 and 1.78 mm, respectively. In addition, the targets regarding S, C, and all bands (2.0-18.0 GHz) were also achieved as expected. This performance optimization engineering opens up a unique and effective way to design microwave-absorbing materials for practical application.