A machine learning-based multi-layer wave-absorbing material reverse optimization design method

Abstract

The application belongs to the field of electromagnetic functional material design and computer aided engineering, and discloses a multi-layer wave-absorbing material reverse optimization design method based on machine learning. In view of the problem that the parameter space of the multi-layer wave-absorbing material design expands exponentially with the number of layers, and the time consumption of a single electromagnetic simulation is too long, so that the high-dimensional process parameters cannot be quickly reverse optimized under multi-objective constraints, the method comprises the following steps: a transmission line theory physical model is established, material and thickness parameter combinations are traversed to generate full-band reflection loss data; material types are coded as classification features, content and thickness are used as continuous numerical features, and a multi-dimensional feature vector and a training data set are constructed by splicing according to the number of layers; a neural network proxy model is trained to predict the full-band reflection loss curve; process parameters are coded as genetic algorithm gene sequences, the fitness value is calculated by decoding and inputting the proxy model in iteration, the gene bits exceeding the physical feasible region are repaired and constrained, and the optimal process parameter combination meeting the multi-objective constraints is output after multiple generations of evolution.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic functional materials design and computer-aided engineering, specifically involving a reverse optimization design method for multilayer absorbing materials based on machine learning. Background Technology

[0002] With the increasing sophistication of modern military detection methods and the widespread adoption of civilian 5G / 6G communication and electronic devices, electromagnetic pollution and military stealth issues are becoming increasingly prominent. As key functional materials capable of effectively absorbing electromagnetic waves and reducing electromagnetic radiation and reflection, absorbing materials have extremely wide-ranging applications in radar stealth coatings, electromagnetic compatibility enclosures, and microwave anechoic chambers. However, facing complex electromagnetic environments and stringent engineering requirements, simply relying on experimental trial and error is not only time-consuming and costly, but also makes it difficult to clarify the complex mapping relationship between the material's microscopic parameters and macroscopic absorption performance.

[0003] Against this backdrop, the development of computer-aided design technology has provided a completely new technical approach for the design of microwave absorbing materials. Designing microwave absorbing materials based on computer simulation is becoming the mainstream direction for both material and structural design. To support computer simulation design, existing technical solutions typically require establishing rapid evaluation methods for the electromagnetic wave absorption performance of materials based on interaction models between electromagnetic waves and multilayer materials (such as transmission line theory or S-parameter inversion theory).

[0004] Meanwhile, the emergence of various computer optimization techniques, represented by Genetic Algorithms (GA), has provided technical support for achieving multi-parameter coordinated adjustment and rapidly finding the optimal combination of multiple parameters. As a type of randomized search method derived from the evolutionary laws of biology, genetic algorithms directly operate on structural objects without the constraints of differentiation and function continuity; they possess inherent implicit parallelism and better global optimization capabilities. In the design of multilayer absorbing coatings, existing solutions often combine genetic algorithms with physical simulations. Through algorithm iteration, the optimal combination of material types, coating structures, and layer thicknesses is quickly determined. This significantly improves the design efficiency of multilayer absorbing coatings and avoids the blindness of traditional manual experience-based design.

[0005] However, the existing computer simulation-aided design and genetic optimization methods still have insurmountable technical defects and limitations, specifically:

[0006] First, traditional commercial electromagnetic simulation software (such as CST and HFSS) is extremely time-consuming, failing to meet the requirements for screening massive combinations of process parameters. In actual engineering, the performance of absorbing materials depends not only on fixed material electromagnetic parameters and thickness structure, but also on specific "preparation process conditions" (such as ball mill speed, filler content, mixing time, etc.) and the microscopic morphological differences generated during material processing. Most existing simulations can only simulate the electromagnetic response under known fixed electromagnetic parameters. If process parameters such as "speed" and "content" are to be incorporated into the design stage, a huge and extremely complex multiphysics coupling model must be established. This results in a single simulation time of minutes or even hours, making it almost impossible to find the optimal solution through wide-area trial calculations in a large-scale process parameter space, severely restricting the efficiency of engineering research and development.

[0007] Secondly, existing technologies lack the ability to perform "reverse precision optimization" for complex coupling relationships among multidimensional variables. Current designs based on genetic algorithms still rely on "forward evaluation-driven optimization." This involves first randomly or pre-setting a set of structural parameters, then using simulation software to calculate the electromagnetic performance to determine the merits of the design. However, when the design objective becomes proactive, such as specifying a target frequency band or a reflection loss threshold, and requires multi-objective coordination (e.g., "thinnest thickness," "lightest weight," "lowest density"), existing algorithms struggle to bridge the gap between physical field simulation and complex material databases. They cannot directly reverse-calculate the optimal production formula that satisfies the aforementioned multi-objective constraints, including "different material selections, different thickness combinations, different filler contents, and different manufacturing process parameters." Designers still need to rely on experience to perform secondary screening of the optimization results, lacking true targeted generation capabilities.

[0008] Especially for multilayer absorbing material systems, the increase in the number of material layers leads to an exponential growth in variables, and the electromagnetic interactions between layers become more complex. The combination of traditional physical simulation and simple genetic algorithms is not only computationally expensive, but also prone to getting trapped in local optima in the complex high-dimensional parameter space. Therefore, there is an urgent need for a technical solution that can balance the accuracy of physical calculations with the speed of machine learning prediction, and can effectively predict performance and perform reverse optimization under the multidimensional and complex coupling relationship of "fabrication process conditions - material electromagnetic parameters - macroscopic absorbing performance". Summary of the Invention

[0009] The purpose of this invention is to solve the technical problem in the design of multilayer absorbing materials where the design parameter space expands exponentially with the number of layers and the single electromagnetic simulation takes too long, making it impossible to quickly reverse-optimize high-dimensional process parameters under multi-objective constraints.

[0010] To achieve the above objectives, the present invention employs the following technical means:

[0011] This invention provides a machine learning-based reverse optimization design method for multilayer absorbing materials, comprising the following steps:

[0012] Step S1: Establish a transmission line theoretical physical model of the multilayer absorbing material, perform traversal calculations on the preset material parameter combination and thickness parameter combination, and generate full-band reflection loss data under each parameter combination; wherein, the material parameters include material type and material content, and the thickness parameter is the physical thickness of each layer of material;

[0013] Step S2: Encode the material type into a classification feature vector, and use the material content and physical thickness as continuous numerical features, splicing them according to the number of material layers to construct a multi-dimensional feature vector corresponding to each set of parameters; use the multi-dimensional feature vector as input and the corresponding full-band reflection loss data as output to construct a training dataset;

[0014] Step S3: Construct a neural network proxy model and train the neural network proxy model with the training dataset so that the neural network proxy model can predict the corresponding full-band reflection loss curve based on the input multi-dimensional feature vector;

[0015] Step S4: Encode the process parameters to be optimized into gene sequences for a genetic algorithm. The process parameters include the material type index, material content, and thickness of each layer.

[0016] In each iteration of the genetic algorithm, the gene sequence of each individual is decoded into a multi-dimensional feature vector and input into the trained neural network surrogate model to obtain the predicted full-band reflection loss curve, and the fitness value is calculated accordingly.

[0017] After the crossover and / or mutation operations in the genetic algorithm, constraints are applied to gene positions that exceed the preset physical feasible region to ensure that the evolved individuals always remain within the physical feasible region.

[0018] After multiple generations of evolution and iteration, the optimal combination of process parameters that satisfies the preset multi-objective constraints is output.

[0019] In the above scheme, the calculation process of the transmission line theoretical physical model in step S1 includes:

[0020] Step S1.1: For those containing A multilayer absorbing material with a layered structure, wherein the first layer is in close contact with a metal substrate, and the second layer is in close contact with a metal substrate. The outermost layer consists of layers, each with its own independent complex dielectric constant. Complex permeability and physical thickness Calculate the characteristic impedance of each layer of material according to the following formula. and propagation constant :

[0021]

[0022] in, The frequency of the incident electromagnetic wave The imaginary unit, At the speed of light, For layer number, ;

[0023] Step S1.2: Calculate the input impedance of the first layer based on the short-circuit boundary condition of the metal backplane:

[0024]

[0025] Step S1.3: For the first layer, The input impedance is calculated iteratively layer by layer based on the impedance transfer formula:

[0026]

[0027] Step S1.4: Based on the outermost input impedance With free space impedance Calculate the reflection coefficient and reflection loss :

[0028]

[0029] in, This is the free-space normalized wave impedance.

[0030] In the above scheme, step S1, which involves traversing the material parameter combination and thickness parameter combination using a vectorized parallel computation method, specifically includes:

[0031] The complex dielectric constant and complex permeability of all materials are preloaded into the video memory of the parallel computing unit; the coordinate grid tensor of all material combinations and thickness combinations is generated at once using the grid coordinate generation function; based on the formula of the transmission line theory physical model, vectorized impedance recursion and reflection loss calculation are performed synchronously on all parameter combinations in the coordinate grid tensor to avoid iterating through each line in a loop.

[0032] In the above scheme, step S2, the process of constructing the multidimensional feature vector, includes:

[0033] Step S2.1: For the classification characteristics of material types, a unique-heat coding method is used to classify the candidate material library. The materials are respectively mapped to lengths of The vector, where the position corresponding to the current material is set to 1, and the other positions are set to 0;

[0034] Step S2.2: For continuous numerical characteristics of material content and physical thickness, normalize the material content percentage to... The physical thickness of the interval is read directly in millimeters;

[0035] Step S2.3: For Multilayer microwave absorbing materials with a layered structure, by splicing together the unique thermal encoding vectors, material content values, and physical thickness values ​​of each layer in sequence, form a total dimension of The multidimensional feature vector;

[0036] Step S2.4: Perform Z-score normalization on the continuous numerical features in the multidimensional feature vector:

[0037]

[0038] in, These are the original continuous numerical eigenvalues. The mean of all samples on this feature dimension. The standard deviation of all samples on this feature dimension. These are the standardized feature values.

[0039] In the above scheme, in step S2, the training dataset is stored in HDF5 hierarchical data format, specifically including:

[0040] A scalable dataset is created in the HDF5 file using a block-based storage method to store the multidimensional feature vectors and the corresponding full-band reflection loss data; the mean value in the Z-score normalization process is then processed. Standard deviation The material list and feature dimension information are stored as attributes of the HDF5 file in an integrated manner to ensure data processing consistency between the model training and deployment phases.

[0041] In the above scheme, in step S3, the neural network proxy model is a deep residual fully connected network, the structure of which includes:

[0042] The input layer, with dimensions consistent with the length of the multidimensional feature vector, encodes the material preparation properties into a high-dimensional dense feature vector;

[0043] The hidden layer adopts a multi-layer fully connected structure with the width increasing first and then decreasing, and a residual block is inserted at the layer with the largest width. The residual block contains a first linear layer, a first batch of normalized layers, a GELU activation function layer, a Dropout layer, a second linear layer, and a second batch of normalized layers connected in sequence, and the input of the residual block is added to the output of the second batch of normalized layers through a skip connection.

[0044] Output layer, dimension and number of frequency sampling points in the target frequency band Consistent, used for one-time output of the entire frequency band To meet the requirements of high-precision evaluation across a wide bandwidth, the 1-18 GHz frequency band is uniformly discretized into 201 frequency sampling points, and a multi-task regression head is constructed to directly map the predicted reflection loss value corresponding to each frequency point.

[0045] In the above scheme, the training process in step S3 adopts the following strategy:

[0046] The loss function used is the Huber loss function;

[0047] The optimizer uses the AdamW optimizer with weight decay.

[0048] The training process employs automatic mixed-precision training, performing some calculations in the forward and backward propagation as half-precision floating-point numbers;

[0049] The learning rate scheduling adopts a pre-set warm-start cycle followed by a cosine annealing strategy for decay.

[0050] Set an early stopping mechanism to stop training and save the optimal model weights when the validation set loss no longer decreases within a preset number of rounds.

[0051] In the above scheme, step S4, the encoding and constraint processing of the gene sequence includes:

[0052] for A multilayer microwave absorbing material with a layered structure, wherein the gene sequence is encoded as ["material"1"index","content"1,"thickness"1,"material"2"index","content"2,"thickness"2,"...,"material"x"index","content"x,"thickness"x]], totaling... One gene locus;

[0053] After the crossover and / or mutation operations in the genetic algorithm, a constraint repair operation is performed on each gene position: the value of each gene position is checked to see if it falls within the preset physical feasible range. If the value of a gene position exceeds its corresponding physical feasible range, the value of the gene position is reset to a random valid integer within the physical feasible range, so that all evolved individuals are always within the physical feasible range.

[0054] In the above scheme, step S4, the calculation of the fitness value includes:

[0055] Based on the full-band reflection loss curve output by the neural network proxy model, it is detected whether the reflection loss is less than the preset reflection loss threshold within the target frequency band set by the user.

[0056] For individuals whose reflection loss is less than the reflection loss threshold within the target frequency band, their fitness value is assigned the opposite of the minimum reflection loss value within the target frequency band, and the individual is stored in the qualified archive.

[0057] For individuals that do not meet the conditions, a fitness value is assigned as the sum of a preset maximum penalty value and the individual's minimum reflection loss value across the entire frequency band, so that the individual is eliminated in evolutionary selection.

[0058] In the above scheme, step S4, where the output of the optimal combination of process parameters satisfying preset multi-objective constraints includes:

[0059] After the genetic algorithm completes all iterations, all qualified individuals stored in the qualified archive are sorted according to the following two dimensions:

[0060] First sorting dimension: Sort by the total thickness of the multilayer absorbing materials from smallest to largest, and output the top layers with the smallest total thickness. One option is recommended as the thinnest thickness option;

[0061] Second sorting dimension: Sort by minimum reflection loss value within the target frequency band from largest to smallest, and output the top values ​​with optimal reflection loss. The following schemes are recommended as the optimal reflection loss schemes;

[0062] Each recommended scheme includes specific process parameter values ​​for the material type, material content, and physical thickness of each layer.

[0063] Because the present invention employs the above-mentioned technical means, it has the following beneficial effects:

[0064] 1. Achieve "second-level" response for predicting the performance of absorbing materials and reverse-engineering processes, greatly improving R&D efficiency.

[0065] This invention constructs a closed-loop system of "physically driven generation of massive data → data-driven training of neural networks → neural network-driven acceleration of genetic reverse optimization." Using a Deep Residual Fully Connected Network (DeepResMLP) surrogate model, forward prediction speed reaches millisecond levels, representing a speed improvement of several orders of magnitude compared to traditional commercial electromagnetic simulation software (such as CST), which requires minutes or even hours for a single simulation. In the reverse optimization stage, a trained neural network replaces the physical engine as the fitness evaluation function of the genetic algorithm, enabling the genetic algorithm to complete a global search of thousands of individuals and hundreds of generations of evolution within tens to hundreds of seconds, directly outputting a process formula that meets multiple objective constraints (specified bandwidth, minimum thickness, optimal reflection loss, etc.). Traditional methods rely on manual trial and error or parameter scanning, which is impractical in terms of time when facing the exponentially expanding combination space of multi-layered structures (e.g., nearly 70 million combinations for a three-layered structure). This invention transforms the originally infeasible search problem into an engineering-feasible and efficient solution, significantly accelerating the research and development process of novel absorbing materials.

[0066] 2. High accuracy in positive prediction, closely matching the actual physical values.

[0067] This invention employs HuberLoss as the loss function, combined with the AdamW optimizer, weight decay, mixed precision training (AMP), Warmup and cosine annealing learning rate scheduling, and early stopping mechanism, to fully guarantee the accuracy and generalization ability of the neural network training. Experimental data from Example 1 show that, under the two-layer structure, the model achieves high R-values ​​on the test set. 2 The R value is above 0.98, and the RMSE is below 0.4 dB; in the three-layer structure of Example 2, R 2 The accuracy is above 0.99, and the RMSE is below 0.04 dB. The experimental conditions and methods described above have been detailed in step 3 of the specific implementation plan (based on the PyTorch framework, automatic mixed-precision training, HuberLossδ=0.1, AdamW optimizer, weight decay, 300 epochs of training, etc.). This accuracy indicates that the neural network surrogate model can replace the physical computing engine with extremely high fidelity, providing a reliable evaluation basis for subsequent genetic optimization and ensuring the effectiveness of the recommended process parameters.

[0068] 3. Overcomes the "curse of dimensionality" problem in the optimization of traditional multilayer absorbing materials, and possesses extremely strong multilayer expansion capability.

[0069] This invention features a versatile and decoupled architecture. The physics calculation engine, based on the recursive formulas of transmission line theory, naturally supports recursive calculations of any number of layers N. Feature engineering employs a linear accumulation method (vector dimension = N × (M + 2)), and the genetic algorithm's gene encoding expands synchronously and linearly, both unrestricted by the number of layers. Experimental data from Example 1 (two-layer) and Example 2 (three-layer) fully validate the scalability of this invention. Taking the three-layer structure as an example, the number of combinations of 41 different material thicknesses increased from 900 in the two-layer model (single-layer thickness 0.1mm–3.0mm, step size 0.1mm) to 1000 (single-layer thickness 0.1mm–1.0mm, step size 0.1mm), and the number of material combinations increased from 1681 to 68921, with a total of nearly 70 million combinations. Faced with such a vast search space, this invention's GPU-based tensor-parallel physics engine can complete the accurate calculation of all data in approximately 5 minutes, while traditional CST simulations, estimated at 1 second per calculation, would take approximately 2.2 years. This fully demonstrates the significant computational advantage of the physics engine of this invention over traditional simulation methods when dealing with multi-layered high-dimensional combinations.

[0070] 4. Directly output engineering process parameters that conform to physical preparation constraints, rather than only providing theoretical optimal values.

[0071] This invention innovatively introduces a multi-dimensional strong constraint repair operator into the gene encoding of genetic algorithms. Addressing the physical limitations of material preparation in actual scientific research and production (such as the requirement that specific material content can only be prepared within a certain percentage range, or the existence of process limits on thickness), the constraint repair operator can automatically reset illegal genes to valid random integers after crossover and mutation operations, ensuring that all search domains remain within the physically feasible domain. The tabular data output in Examples 1 and 2 (Tables 1 to 4) directly provide specific process parameters for preparation on the machine, such as the material serial number, content percentage, and thickness of the bottom / middle / top layers, solving the pain point that traditional optimization algorithms often output theoretically infeasible solutions or require extensive post-processing corrections.

[0072] 5. Enable personalized solution recommendations under multi-objective constraints to meet diverse engineering needs.

[0073] This invention considers both "full-band target compliance" and "minimal reflection loss" in a multi-objective fitness function, and stores qualified individuals in a "qualified archive." After the genetic algorithm iteration is complete, the archive is sorted according to the two dimensions of "thinnest thickness" and "optimal reflection loss," and the Top 10 solutions are recommended to the user. Tables 1 to 4 of Examples 1 and 2 show that the system can simultaneously provide a lightweight solution with a thickness of only 1.8mm but an RL of -13.27dB (ranked 1 in Table 1) and a high-performance solution with a total thickness of 2.9mm but an RL of -30.83dB (ranked 1 in Table 2) from the same batch of optimization results, allowing users to flexibly choose based on the priorities of weight, thickness, or stealth performance for their actual equipment. This multi-objective, multi-alternative output mode better meets the trade-off decision-making needs in engineering practice and has higher practical value than traditional methods that only provide a single optimal solution. Attached Figure Description

[0074] Figure 1 This is a simplified flowchart of the present invention. Detailed Implementation

[0075] The embodiments of the present invention will be described in detail below. Although the present invention will be described and illustrated in conjunction with some specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, any modifications or equivalent substitutions made to the present invention should be covered within the scope of the claims of the present invention.

[0076] Furthermore, to better illustrate the present invention, numerous specific details are set forth in the following detailed embodiments. Those skilled in the art will understand that the present invention can be practiced without these specific details.

[0077] This invention provides a method for predicting and reverse-optimizing the performance of multilayer absorbing materials based on a physics-data hybrid approach. This method can not only predict the reflection loss of any multilayer absorbing structure in seconds, but also utilize a trained neural network surrogate model combined with a genetic algorithm to accurately reverse-generate fabrication process parameters (material type, content, thickness, etc.) under multiple objective constraints (such as specified bandwidth, minimum thickness, minimum density, and optimal RL). Although this embodiment uses a double-layer absorbing coating as an example, the overall technical framework and algorithm logic described in this invention are fully applicable to any multilayer material system and any combination of material electromagnetic parameters, including single-layer, double-layer, and even three-layer (N-layer) materials.

[0078] The specific implementation of this invention includes the following four core steps:

[0079] Step S1: Fast physical calculation engine for multilayer absorption performance based on transmission line theory (generating large-scale data)

[0080] This step serves as the physical basis for multilayer absorption and is used to replace traditional commercial electromagnetic simulation software such as CST, enabling "second-level" rapid solutions for different combinations of electromagnetic parameters under massive process parameters.

[0081] 1. Establish a universal physical model for arbitrarily multilayered absorbing materials:

[0082] Set the free space wave impedance as (Normalized), the speed of light is c = 3 × 10⁸ m / s. For a microwave absorbing material with an N-layer structure (the Nth layer is the outermost layer, and the first layer is in close contact with the metal substrate), each layer has an independent complex dielectric constant. Complex permeability and physical thickness (Unit: meter). Characteristic impedance Z of each layer of material. i and propagation constant k i The calculation formula is:

[0083]

[0084] in is the frequency of the incident electromagnetic wave (unit: Hz), and j is the imaginary unit.

[0085] 2. Establish the multi-layer iterative input impedance and reflection loss calculation equations:

[0086] According to transmission line theory, since the first layer is in close contact with the metal backplate (considered a short circuit), its input impedance is:

[0087]

[0088] For the nth layer (n≥2), iterate layer by layer based on the impedance propagation formula:

[0089]

[0090] Finally, the input impedance of the outermost layer (the Nth layer) This is the input impedance of the entire structure. Calculate the reflection coefficient of this structure. With reflection loss RL (unit: dB):

[0091]

[0092] 3. GPU-based large-scale tensor parallel computing:

[0093] To avoid significant Python loop overhead when traversing massive material combinations (e.g., material A is close to the metal, material B is far from the metal, and meshes of different thicknesses), this method utilizes PyTorch to construct tensor matrices and deploys them on a GPU for batch computation. By pre-loading all material electromagnetic parameters into GPU memory and using torch.meshgrid (which generates coordinate grid tensors for parameter combinations), tens of thousands of thickness and material combinations are simultaneously vectorized for computation.

[0094] Step S2: Construction of multidimensional feature dataset (normalization and HDF5 storage)

[0095] To ensure that the neural network model can simultaneously handle categorical attributes (material type) and continuous numerical attributes (thickness, content) and enable the training process to converge quickly, this step constructs a multidimensional feature dataset.

[0096] 1. Analysis of multi-dimensional process and structural features:

[0097] This invention extracts all combinations of process parameters affecting microwave absorption performance as vectorized features. Taking a double-layer structure as an example, it involves six variables: bottom layer material, bottom layer content, bottom layer thickness, top layer material, top layer content, and top layer thickness. Material type (classification feature): One-hot encoding is used to map material types to high-dimensional sparse vectors. If there are M types of materials in the equipment's material library, material A is mapped to a vector of length M, with corresponding positions set to 1 and the rest to 0. Material content and thickness (continuous features): The actual content percentage (0%~100% normalized to 0.0~1.0) and thickness value (unit: mm) are directly read.

[0098] 2. Feature assembly and data standardization:

[0099] Concatenate all the above features into a complete input vector. For an x-layer structure, the total dimension of the vector is... (That is, each layer contains M-dimensional one-hot encoding, 1-dimensional content, and 1-dimensional thickness, for a total of x layers). The mean μ and standard deviation σ of all samples are calculated, and Z-score standardization is performed on all continuous numerical features:

[0100]

[0101] 3. Data partitioning and high-efficiency HDF5 storage:

[0102] Due to the extremely large number of samples generated (up to tens of millions across multiple layers), this invention employs a hierarchical data storage architecture in HDF5 format. A scalable dataset is created within the HDF5 file, using a chunked storage method to support concurrent read and write operations. Simultaneously, hyperparameters such as the mean, standard deviation, material list, and feature dimensions of the standardizer are stored as attributes (attrs) within the HDF5 file, ensuring complete consistency in data processing during subsequent model training and deployment.

[0103] Step S3: Construct a deep residual fully connected neural network forward surrogate model (data-driven training)

[0104] This step utilizes the massive dataset generated in step 2 to train a high-precision neural network proxy model that can replace the physical calculation engine, enabling millisecond-level inference of the absorption performance spectrum curves of unknown material combinations (forward prediction of RL from 1 to 18 GHz).

[0105] 1. Construct a Deep Residual Fully Connected Network (DeepResMLP):

[0106] To address the gradient vanishing and overfitting problems that traditional multilayer perceptrons (MLPs) easily encounter when fitting high-dimensional features, this invention constructs a deep neural network that includes residual connections.

[0107] Input layer: The dimension is the same as the feature vector length in step 2.

[0108] Hidden layers: A strategy of gradually increasing width is adopted. The specific hidden layer node design for layer x is [512, 1024, 1024, 1024, 512]. When the network depth reaches a layer width of 1024, a residual block is inserted. The residual block contains "linear layer > batch normalization (BatchNorm) > GELU activation function > Dropout > linear layer > batch normalization", and the input of the residual block is directly added to the output of the block (SkipConnection), which promotes good gradient propagation in deep networks.

[0109] Output layer: The output dimension is consistent with the number of points K of the target frequency band (e.g., 1~18GHz, step 0.1GHz, 201 frequency points), and outputs the predicted reflection loss (RL) value of the entire frequency band at one time.

[0110] 2. Hybrid precision training and learning rate strategy:

[0111] Loss function: HuberLoss (δ=0.1) is used, which is highly robust to outliers and balances the sensitivity of mean squared error with the stability of absolute error.

[0112] Optimizer: The AdamW optimizer is used, along with weight decay to prevent the model from overfitting the training set.

[0113] Training acceleration: By utilizing PyTorch's Automatic Mixed Precision (AMP) training, some calculations in the forward and backward propagation are performed using float16 half-precision floating-point numbers, which significantly saves GPU memory and improves training speed.

[0114] Learning rate scheduling: A warm-up of 5 epochs is used first, followed by cosine annealing to adjust the learning rate, allowing the model to converge to the global optimum more smoothly. An early stopping mechanism is also set up: when the validation set loss exceeds 40 epochs and no longer decreases, training is stopped and the optimal model weights are saved.

[0115] Step S4: Reverse optimization using a genetic algorithm based on a neural network surrogate model.

[0116] This step is the core engineering application of this invention. Unlike traditional optimization methods that can only perform "forward trial and error," this invention directly utilizes a trained neural network to replace the physics engine, constructing a high-speed genetic algorithm search space to reverse-engineer the optimal preparation process based on the user-defined target threshold.

[0117] 1. Gene coding and constraint repair:

[0118] An individual's "genes" consist of a set of integers. Taking layer x as an example, the gene sequence is: [Material 1 index, content 1 percentage (integer), thickness 1 grid index, material 2 index, content 2 percentage (integer), thickness 2 grid index, ..., material x index, content x percentage (integer), thickness x grid index].

[0119] Multidimensional strong constraint handling: To address the physical limitations of material preparation in actual scientific research and production, a constraint repair operator is introduced. For example, if the content of material 1 is set to be physically feasible only within the range of 50% to 90%, and if a randomly generated crossover or mutation produces 50% of the genes, the constraint repair operator will automatically reset it back to a valid random integer within the range, ensuring that all search domains are within the physically feasible domain.

[0120] 2. Multi-objective fitness function design:

[0121] When evaluating each generation of the population, the genes are directly decoded into feature vectors and input into the neural network trained in step 3 for millisecond-level RL curve prediction.

[0122] Constraint Judgment and Penalty: First, check whether the predicted RL curve is less than the "RL threshold (e.g. -10dB)" within the user-defined "target frequency band range (e.g., 8-12GHz)".

[0123] Fitness assignment logic: For individuals that meet the full-band requirements: Fitness = −min(RLband), that is, the more negative the minimum RL value within the bandwidth (the better the absorption), the better the fitness, and they are stored in the "qualified archive". For individuals that do not meet the requirements: assign a very large penalty value (such as 100), plus the individual's minimum RL value, to ensure that they are naturally eliminated in the evolution.

[0124] Multi-objective candidate output: After the genetic algorithm iteration is completed, all schemes in the "qualified archive" are sorted in multiple dimensions. Two sets of data are generated: "Top 10 Thinnest Scheme" and "Top 10 Best RL Scheme". After sorting, specific bottom material, content, and thickness, as well as top material, content, and thickness, are directly recommended to the user.

[0125] 3. Genetic operations accelerate convergence:

[0126] The population size was set at 4000, and the number of generations was set at 800. Tournament selection was used, combined with single-point crossover and dynamic mutation (mutation rate of 0.15). Since the inference engine is a pre-trained neural network, a single computation only takes milliseconds, and the total computation time of the 800-generation genetic algorithm is usually only tens of seconds, achieving "second-level genetic optimization".

[0127] Extended explanation: Applicability to N layers of materials with arbitrary multilayer structures and arbitrary electromagnetic parameters.

[0128] The core of this invention lies in the universality and decoupling of its architectural design. Although the above embodiments use a "two-layer" structure (first layer and second layer) for detailed data feature engineering and genetic coding, the underlying logic of the entire technical solution does not have an inherent limitation on the number of material layers, specifically reflected in:

[0129] The physics calculation engine is not limited by the number of layers: the input impedance iteration formula in step S1 Supports N-level recursive calculations. To calculate a three-layer structure, simply use torch.meshgrid(d1,d2,d3) to generate the 3D thickness combination when building the thickness mesh; the remaining electromagnetic parameter calculation code can be completely reused.

[0130] Feature vector and neural network input dimension adaptation: The feature concatenation in step S2 is a linear accumulation based on the number of material layers. If extended to 3 layers, the feature vector dimension becomes 3×M+6 (three independent thermal layers + three layer thicknesses + three layer contents). In step S3, only the hyperparameters of the neural network input_dim need to be adjusted according to the change in input dimension to achieve transfer training of the multi-layer architecture without changing the main structure of the network.

[0131] Linearization of genetic algorithm gene encoding: In step S4, the gene sequence length only needs to be extended to [material 1, content 1, thickness 1, material 2, content 2, thickness 2, ..., material N, content N, thickness N]. With the corresponding constraint repair and crossover mutation operators, this invention can be directly used to guide the optimization of process parameters for any number of microwave absorbing material layers.

[0132] This invention constructs a highly efficient, accurate, and multi-material, multi-layer scalability intelligent design closed-loop system for absorbing materials by "generating massive amounts of data through physical means > training neural networks through data > accelerating genetic reverse optimization through neural networks".

[0133] Example 1: Intelligent Design and Backward Optimization of Double-Layer Absorbing Material (N=2)

[0134] This embodiment takes a two-layer absorbing coating structure as an example, which includes a bottom layer (closely attached to the metal) and a top layer (incident end).

[0135] Physics engine configuration and data generation:

[0136] Material library: Prepare 18 kinds of microwave absorbing materials (such as ferrite series and different spherical series). Different contents of each material correspond to different electromagnetic parameters, forming a database of electromagnetic parameters under different rotation speeds and contents.

[0137] Thickness grid: The thickness of a single layer ranges from 0.1mm to 3.0mm, with a step size of 0.1mm. Each single layer offers 30 thickness options.

[0138] Data scale: A database of 41 electromagnetic parameters (including electromagnetic parameters under different material contents) composed of 18 different materials is arranged in an ordered two-layer structure, resulting in 41 × 41 = 1681 material combinations; thickness combinations are 30 × 30 = 900. The physics engine generates a total of 1681 × 900 = 1,512,900 RL curve data. With GPU acceleration, the entire calculation can be completed in just tens of seconds, which is thousands of times more efficient than traditional CST simulation.

[0139] 2. Data normalization and network training:

[0140] Input features: The feature vector dimension of the two-layer structure is 2×M+4 (i.e., M types of materials, bottom layer heat insulation + bottom layer content + bottom layer thickness + M types of materials, top layer heat insulation + top layer content + top layer thickness).

[0141] Training parameters: The input dimension of the Deep Residual Network (DeepResMLP) is automatically adapted, the hidden layer structure is set to [512,1024,1024,1024,512], and the output layer dimension is set to 201 (corresponding to 1~18GHz, step size 0.085GHz).

[0142] Training Results: Using HuberLoss for up to 300 epochs of training, the model achieved R0 on the test set. 2 With an accuracy of over 0.98 and an RMSE of less than 0.4dB, this demonstrates that the proxy model has replaced physical calculations with extremely high precision.

[0143] 3. Reverse optimization and multi-objective evaluation:

[0144] User requirements: Target bandwidth set at 6–16 GHz, requiring full-band reflection loss RL < −11 dB.

[0145] Genetic algorithm parameters: population size 4000, number of generations 800, mutation rate 0.15.

[0146] Optimization results: The system completed the search within tens of seconds. For "thinnest thickness" and "lowest RL," the algorithm calculated and output the material thickness, content, and preparation parameters for each layer. The ranking of the thinnest thickness corresponds to Table 1, and the ranking of the lowest RL corresponds to Table 2.

[0147] Table 1 shows the ranking of the thinnest outputs.

[0148]

[0149] Table 2 Lowest RL Ranking

[0150]

[0151] Example 2: Broadband Prediction and Backward Optimization of Three-Layer Absorbing Material (N=3)

[0152] This embodiment is illustrated using a three-layer absorbing coating structure. The three-layer structure, due to its richer "impedance gradient" design space, is often used to solve broadband absorption problems. However, this leads to an exponential explosion in the search space. This embodiment demonstrates the computational advantage of this invention when dealing with ultra-large-scale combinations.

[0153] 1. The challenges and performance of high-dimensional calculations in physics engines:

[0154] Model extension: The physics engine is not limited by the number of layers. Simply modify the thickness mesh generation in step S1 to torch.meshgrid(d1,d2,d3) to calculate the combination of three dimensions simultaneously.

[0155] The data volume has increased dramatically: the electromagnetic parameter database for the aforementioned 41 materials (including electromagnetic parameters under different material contents) is still used. The thickness range for a single layer is set to 0.1mm~1.0mm, and the thickness range for three layers is 0.3mm~3.0mm, with a step size of 0.1mm.

[0156] Number of material combinations: 41 × 41 × 41 = 68921;

[0157] Number of thickness combinations: 10×10×10=1000.

[0158] The physics engine generated a total of 68,921 × 1,000 = 68,921,000 (nearly 70 million) RL curve data points.

[0159] Technical Performance Comparison: For conventional CST simulations, even assuming a simulation is completed every second, calculating these 70 million combinations would take 2.2 years (unrealistic). However, the GPU physics calculation engine based on this invention, thanks to its vectorized non-cyclic characteristics, can complete the precise physical calculation of these nearly 70 million basic data points in just about 5 minutes, providing training data for subsequent machine learning.

[0160] 2. Transfer learning and network adaptation:

[0161] Feature expansion: The feature concatenation dimension of the three-layer structure is automatically adjusted to 3×M+6. Only input_dim needs to be changed during neural network initialization; the residual architecture of the main network does not need to be altered during training.

[0162] Training parameters: The input dimension of the Deep Residual Network (DeepResMLP) is automatically adapted, the hidden layer structure is set to [1024,2048,4096,2048,1024], and the output layer dimension is set to 201 (corresponding to 1~18GHz, step size 0.085GHz).

[0163] Training Results: Using HuberLoss for up to 300 epochs of training, the model achieved R0 on the test set. 2 With a score above 0.99 and an RMSE below 0.04dB, this demonstrates that the proxy model has replaced physical calculations with extremely high accuracy.

[0164] 3. Constraint Repair and Broadband Optimization:

[0165] User objective: To set a wider bandwidth requirement of 8–12 GHz, with RL < −10 dB within this band.

[0166] Gene encoding expansion: The genetic algorithm automatically expands the gene sequence to [bottom layer material, bottom layer content, bottom layer thickness, middle layer material, middle layer content, middle layer thickness, top layer material, top layer content, top layer thickness]. The original constraint repair operator automatically applies to the three newly expanded gene positions to ensure that the search does not deviate from the actual physical production boundary.

[0167] Optimization results: The genetic algorithm can find multiple optimal thickness and material formulation combinations from nearly 70 million combinations within seconds, fully satisfying the requirements of wide bandwidth (8-12GHz) and low threshold (<-10dB), and directly output the engineering parameters that can be fabricated. The ranking of the thinnest thickness corresponds to Table 3, and the ranking of the lowest RL corresponds to Table 4.

[0168] Table 3 shows the ranking of the thinnest output thickness.

[0169]

[0170] Table 4 Outputs the lowest RL ranking

[0171]

[0172] Because the present invention adopts the above-described solution, it has the following characteristics:

[0173] Feature 1: Based on a three-level linkage closed-loop architecture of "physical computing engine → neural network agent → genetic algorithm optimization".

[0174] This invention organically combines physics-driven (transmission line theory GPU batch computation), data-driven (deep residual network training), and intelligent optimization (genetic algorithm reverse search) to form an end-to-end intelligent design system for microwave absorbing materials. Traditional methods either only perform forward simulation (such as CST) or only perform simple parameter scanning, without forming a closed-loop linkage among the three. In the three-level architecture of this invention, the output of each level serves as the input of the next level. The physics engine provides training data for the neural network, and the neural network provides a rapid fitness evaluation function for the genetic algorithm, ultimately achieving automatic mapping from a "massive combination space" to "optimal process parameters".

[0175] Feature 2: A GPU-based tensor parallelism-based method for "second-level" physical calculations of multilayer absorbing materials

[0176] Leveraging the tensor computation capabilities of deep learning frameworks such as PyTorch, the complex permittivity and permeability parameters of all materials are pre-loaded into GPU memory. The `torch.meshgrid` method generates coordinate grid tensors for all material and thickness combinations in a single operation. Based on transmission line theory formulas, fully vectorized batch impedance recursion and reflection loss calculations are performed, completely avoiding Python-level loop overhead. The computational complexity of this method does not linearly deteriorate with the number of material types or layers, enabling the rapid generation of tens of millions or even billions of samples.

[0177] Feature 3: A universal transmission line recursive calculation model applicable to any N-layer structure

[0178] Based on the recursive formula of transmission line theory, it naturally supports recursive calculation of any number of layers N; the boundary conditions of the metal backplate (the first layer is regarded as a short circuit) are set; each layer is independently assigned complex numbers ε, μ and thickness d, the parameters are completely decoupled and do not depend on any specific material system.

[0179] Feature 4: A method for constructing multidimensional feature vectors for multilayer absorbing materials with mixed-type features (classification, continuity)

[0180] One-hot encoding is used for material types, which are mapped to M-dimensional sparse vectors; material content (percentage) and thickness (mm) are directly used as continuous numerical features; features are concatenated layer by layer, with each layer contributing M+2-dimensional features, for a total dimension of N×(M+2); Z-score standardization is performed on continuous features, and the standardization parameters (mean μ, standard deviation σ) are stored in the same file as the dataset.

[0181] Feature 5: A hierarchical storage and hyperparameter integrated management method for massive absorbing material datasets based on HDF5 format.

[0182] The HDF5 hierarchical data architecture is adopted to store massive RL curve data in a chunked manner; it supports concurrent read and write; hyperparameters such as normalizer parameters (mean, standard deviation), material list, and feature dimensions are stored together as attributes (attrs) of the HDF5 file to ensure the consistency of data processing during the training and deployment phases.

[0183] Feature 6: Deep Residual Fully Connected Network (DeepResMLP) Architecture for Spectral Prediction of Absorbing Materials

[0184] The input layer dimension is adaptive (consistent with the feature vector length); a "wide-then-deep" hidden layer structure design is adopted (e.g., [512, 1024, 1024, 1024, 512] or [1024, 2048, 4096, 2048, 1024]); a residual block is inserted in the layer with the largest width (e.g., a 1024-dimensional layer), which contains a "linear layer → BatchNorm → GELU → Dropout → linear layer → BatchNorm" structure, and a skip connection is introduced; the output layer outputs the RL prediction values ​​of the entire frequency band (e.g., 201 frequency points) at once, instead of predicting point by point.

[0185] Feature 7: Hybrid precision training and adaptive optimization strategy combination applied to spectral prediction of absorbing materials

[0186] The loss function uses HuberLoss (δ adjustable, preferably 0.1); the optimizer uses AdamW+ weight decay; automatic mixed precision training (AMP) is used, with some calculations using float16 half precision; the learning rate uses a joint scheduling strategy of "Warmup" and "Cosine Annealing"; an early stopping mechanism is set, and training stops if the validation set loss does not decrease after exceeding a preset number of epochs (e.g., 40 epochs).

[0187] Feature 8: Genetic reverse optimization method for process parameters of absorbing materials based on neural network surrogate model

[0188] The process parameters to be optimized are encoded as integer gene sequences [material 1 index, content 1, thickness 1, material 2, content 2, thickness 2, ...]. Individuals in each generation of the population are directly decoded into feature vectors and input into the neural network to obtain full-band RL prediction curves, which are used to replace physical simulation as the basis for fitness evaluation. The millisecond-level inference speed of the neural network is used to achieve rapid iteration of large-scale populations (e.g., 4000 individuals) × multiple generations of evolution (e.g., 800 generations).

[0189] Feature 9: Multidimensional Strong Constraint Repair Operator for Physical Constraints in Materials Preparation

[0190] For each layer of material, a physically feasible range is set for the content, thickness and other process parameters (e.g., a material can only be prepared in the range of 50% to 80%). After the crossover and mutation operations of the genetic algorithm, it is automatically detected whether each gene position falls into the legal range. Illegal gene positions are automatically reset to random legal integers within the range to ensure that all evolved individuals are always within the physically feasible domain.

[0191] Feature 10: A multi-objective fitness assessment and multi-dimensional scheme ranking output method based on a "qualified archive".

[0192] The fitness function employs a dual-judgment system: First, it checks whether the predicted RL curves are all less than a set threshold (e.g., -10dB) within the target frequency band. For qualified individuals, the fitness is calculated as -min(RL_band) (the more negative the minimum value, the better the fitness), and they are stored in the "qualified archive". For unqualified individuals, a maximum penalty value (e.g., 100) is assigned plus the individual's minimum RL, allowing them to be naturally eliminated during evolution. After the iteration, the qualified archive is sorted according to two dimensions: "thinnest total thickness" and "optimal RL (global / in-band)", and TopN (e.g., Top10) candidate solutions are output.

[0193] Feature 11: A general framework for gene coding and genetic operations that supports linear expansion of any number of layers N.

[0194] The length of the gene sequence is linearly positively correlated with the number of layers N (3N gene positions); when the number of material layers increases, only a new [material index, content, thickness] triplet needs to be appended to the end of the gene sequence; genetic operators such as crossover, mutation, and constraint repair automatically act on all extended gene positions without the need to redesign the algorithm logic. Combining feature 3 (the N-layer versatility of the physics engine) and feature 4 (the N-layer linear accumulation of feature vectors), a complete N-layer expansion technology solution is formed.

Claims

1. A reverse optimization design method for multilayer absorbing materials based on machine learning, characterized in that, Includes the following steps: Step S1: Establish a transmission line theoretical physical model of the multilayer absorbing material, perform traversal calculations on the preset material parameter combination and thickness parameter combination, and generate full-band reflection loss data under each parameter combination; wherein, the material parameters include material type and material content, and the thickness parameter is the physical thickness of each layer of material; Step S2: Encode the material type into a classification feature vector, and use the material content and physical thickness as continuous numerical features, splicing them according to the number of material layers to construct a multi-dimensional feature vector corresponding to each set of parameters; use the multi-dimensional feature vector as input and the corresponding full-band reflection loss data as output to construct a training dataset; Step S3: Construct a neural network proxy model and train the neural network proxy model with the training dataset so that the neural network proxy model can predict the corresponding full-band reflection loss curve based on the input multi-dimensional feature vector; Step S4: Encode the process parameters to be optimized into gene sequences for a genetic algorithm. The process parameters include the material type index, material content, and thickness of each layer. In each iteration of the genetic algorithm, the gene sequence of each individual is decoded into a multi-dimensional feature vector and input into the trained neural network surrogate model to obtain the predicted full-band reflection loss curve, and the fitness value is calculated accordingly. After the crossover and / or mutation operations in the genetic algorithm, constraints are applied to gene positions that exceed the preset physical feasible region to ensure that the evolved individuals always remain within the physical feasible region. After multiple generations of evolution and iteration, the optimal combination of process parameters that satisfies the preset multi-objective constraints is output.

2. The method according to claim 1, characterized in that, In step S1, the calculation process of the transmission line theoretical physical model includes: Step S1.1: For those containing A multilayer absorbing material with a layered structure, wherein the first layer is in close contact with a metal substrate, and the second layer is in close contact with a metal substrate. The outermost layer consists of layers, each with its own independent complex dielectric constant. Complex permeability and physical thickness Calculate the characteristic impedance of each layer of material according to the following formula. and propagation constant : in, The frequency of the incident electromagnetic wave The imaginary unit, At the speed of light, For layer number, ; Step S1.2: Calculate the input impedance of the first layer based on the short-circuit boundary condition of the metal backplane: Step S1.3: For the first layer, The input impedance is calculated iteratively layer by layer based on the impedance transfer formula: Step S1.4: Based on the outermost input impedance With free space impedance Calculate the reflection coefficient and reflection loss : in, This is the free-space normalized wave impedance.

3. The method according to claim 2, characterized in that, In step S1, the traversal calculation of the material parameter combination and thickness parameter combination adopts a vectorized parallel calculation method, specifically including: The complex dielectric constant and complex permeability of all materials are preloaded into the GPU's memory; the coordinate grid tensor of all material combinations and thickness combinations is generated at once using the grid coordinate generation function; based on the formula of the transmission line theory physical model, vectorized impedance recursion and reflection loss calculation are performed synchronously on all parameter combinations in the coordinate grid tensor to avoid iterating through each line in a loop.

4. The method according to claim 1, characterized in that, In step S2, the process of constructing the multidimensional feature vector includes: Step S2.1: For the classification characteristics of material types, a unique-heat coding method is used to classify the candidate material library. The materials are respectively mapped to lengths of The vector, where the position corresponding to the current material is set to 1, and the other positions are set to 0; Step S2.2: For continuous numerical characteristics of material content and physical thickness, normalize the material content percentage to... interval; Step S2.3: For Multilayer microwave absorbing materials with a layered structure, by splicing together the unique thermal encoding vectors, material content values, and physical thickness values ​​of each layer in sequence, form a total dimension of The multidimensional feature vector; Step S2.4: Perform Z-score normalization on the continuous numerical features in the multidimensional feature vector: in, These are the original continuous numerical eigenvalues. The mean of all samples on this feature dimension. The standard deviation of all samples on this feature dimension. These are the standardized feature values.

5. The method according to claim 4, characterized in that, In step S2, the training dataset is stored in HDF5 hierarchical data format, specifically including: A scalable dataset is created in the HDF5 file using a block-based storage method to store the multidimensional feature vectors and the corresponding full-band reflection loss data; the mean value in the Z-score normalization process is then processed. Standard deviation The material list and feature dimension information are stored as attributes of the HDF5 file in an integrated manner to ensure data processing consistency between the model training and deployment phases.

6. The method according to claim 1, characterized in that, In step S3, the neural network proxy model is a deep residual fully connected network, the structure of which includes: The input layer, with dimensions consistent with the length of the multidimensional feature vector, encodes the material preparation properties into a high-dimensional dense feature vector; The hidden layer adopts a multi-layer fully connected structure with the width increasing first and then decreasing, and a residual block is inserted at the layer with the largest width. The residual block contains a first linear layer, a first batch of normalized layers, a GELU activation function layer, a Dropout layer, a second linear layer, and a second batch of normalized layers connected in sequence, and the input of the residual block is added to the output of the second batch of normalized layers through a skip connection. Output layer, dimension and number of frequency sampling points in the target frequency band Consistent, used for one-time output of the entire frequency band Predicted reflection loss values ​​at each frequency point.

7. The method according to claim 6, characterized in that, In step S3, the training process employs the following strategy: The loss function used is the Huber loss function; The optimizer uses the AdamW optimizer with weight decay. The training process employs automatic mixed-precision training, performing some calculations in the forward and backward propagation as half-precision floating-point numbers; The learning rate scheduling adopts a pre-set warm-start cycle followed by a cosine annealing strategy for decay. Set an early stopping mechanism to stop training and save the optimal model weights when the validation set loss no longer decreases within a preset number of rounds.

8. The method according to claim 1, characterized in that, In step S4, the encoding and constraint processing of the gene sequence includes: for A multilayer microwave absorbing material with a layered structure, wherein the gene sequence is encoded as ["material"1"index","content"1,"thickness"1,"material"2"index","content"2,"thickness"2,"...,"material"x"index","content"x,"thickness"x]], totaling... One gene locus; After the crossover and / or mutation operations in the genetic algorithm, a constraint repair operation is performed on each gene position: the value of each gene position is checked to see if it falls within the preset physical feasible range. If the value of a gene position exceeds its corresponding physical feasible range, the value of the gene position is reset to a random valid integer within the physical feasible range, so that all evolved individuals are always within the physical feasible range.

9. The method according to claim 8, characterized in that, In step S4, the calculation of the fitness value includes: Based on the full-band reflection loss curve output by the neural network proxy model, it is detected whether the reflection loss is less than the preset reflection loss threshold within the target frequency band set by the user. For individuals whose reflection loss is less than the reflection loss threshold within the target frequency band, their fitness value is assigned the opposite of the minimum reflection loss value within the target frequency band, and the individual is stored in the qualified archive. For individuals that do not meet the conditions, a fitness value is assigned as the sum of a preset maximum penalty value and the individual's minimum reflection loss value across the entire frequency band, so that the individual is eliminated in evolutionary selection.

10. The method according to claim 9, characterized in that, In step S4, the optimal combination of process parameters that satisfies the preset multi-objective constraints includes: After the genetic algorithm completes all iterations, all qualified individuals stored in the qualified archive are sorted according to the following two dimensions: First sorting dimension: Sort by the total thickness of the multilayer absorbing materials from smallest to largest, and output the top layers with the smallest total thickness. One option is recommended as the thinnest thickness option; Second sorting dimension: Sort by minimum reflection loss value within the target frequency band from largest to smallest, and output the top values ​​with optimal reflection loss. The following schemes are recommended as the optimal reflection loss schemes; Each recommended scheme includes specific process parameter values ​​for the material type, material content, and physical thickness of each layer.

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