Energy-absorbing metamaterial reverse design method based on diffusion model and parameterized level set

Abstract

The invention belongs to the field of energy-absorbing metamaterial design, and particularly relates to an energy-absorbing metamaterial reverse design method based on a diffusion model and a parameterized level set. The metamaterial is generated under the condition that the required stress-strain curve is given. The diffusion model learns conditional distribution of the metamaterial of a given property, and one-to-many mapping from property to geometry is achieved. The level set representation improves the precision and design flexibility of the metamaterial topology, and ensures that the generated metamaterial has a high-quality geometrical shape. The method has the advantages of high design speed and high precision, and provides a new solution path for realizing more intelligent and customized metamaterial design.

Description

Technical Field

[0001] The invention belongs to the field of energy absorbing metamaterial design, and in particular relates to an energy absorbing metamaterial inverse design method based on a diffusion model and a parameterized level set. Background Art

[0002] Energy-absorbing materials and structures are widely used in aerospace, transportation, and human protection due to their excellent impact resistance. When designing an ideal energy-absorbing metamaterial, collision avoidance designers consider multiple criteria, including not only high energy absorption performance, but also structural stability and safety. With the desired energy absorption curve as the design goal, after determining the basic material, the distribution of the material inside the structure becomes a key design variable. Material distribution plays a vital role in optimizing the load-displacement response and energy absorption characteristics of the structure. By carefully manipulating the material distribution, designers can customize the structural behavior and enhance the energy absorption performance to achieve specific design goals and meet the desired performance standards.

[0003] The forward design method of energy-absorbing structures mainly achieves different energy absorption effects through empirical or bionic configurations. Classic energy-absorbing structures include sandwich structures, plate structures, honeycomb structures, and foam structures. Bionic design is another method to obtain structures with energy-absorbing properties by imitating the internal structure of organisms, such as designing tubular nested geometric structures inspired by the Haversian bone structure. In order to improve the energy absorption capacity of the structure, high-efficiency energy-absorbing structures are developed by modifying geometric parameters.

[0004] Inverse design methods for energy-absorbing structures can be divided into gradient-based and gradient-free methods. Gradient-based topology optimization design methods effectively meet design goals without strict material requirements. This method simplifies the design process and improves efficiency. This mature field covers a variety of methods, including solid isotropic material penalty method (SIMP), level set method (LSM), parameterized level set method (PLSM), bidirectional evolutionary structural optimization method (BESO) and mobile deformable component method (MMC). These methods require rigorous sensitivity derivation and fast convergence speed based on finite element analysis. Since the topology optimization of energy-absorbing metamaterials must consider geometric, material and contact nonlinearities, gradient-based topology optimization methods have encountered significant challenges in this field. In contrast, gradient-free design methods based on intelligent algorithms have shown good performance in solving complex multi-objective, non-convex or time-varying optimization problems that are difficult for sensitivity-based methods. The flexible model representation of intelligent algorithms improves convergence. However, due to the lack of sensitivity guidance, especially with the increase of design variables, the optimization efficiency of these algorithms is often lower than that of gradient-based algorithms.

[0005] With the rapid development of artificial intelligence (AI) technology, AI-generated content (AIGC) has had a significant impact on multiple industries such as entertainment, media, and education. Well-known AIGC tools include ChatGPT and Sora. AIGC has attracted widespread attention beyond computer science. In the field of material design, the advancement of the data-driven paradigm has greatly accelerated the exploration of inverse material design methods. From the perspective of data representation, data-driven methods for inverse design of mechanical materials can be divided into two major categories. The first category uses parametric models to represent materials and establishes agent models to explore design parameters and achieve the desired goals. In this category, the material structure is usually converted into a set of topological parameters, so that the design parameters can be effectively explored through the optimization capabilities of machine learning algorithms. The second category of data-driven design methods focuses on designing in a high-dimensional topological space rather than directly designing topological parameters. A common strategy is to divide the topological space into a series of pixels. However, the above work discretizes the design domain into variable pixel representations, resulting in jagged edges on the final topological structure, which requires further smoothing for additive manufacturing, and has not yet considered the application of AI generation to energy-absorbing metamaterial design. Furthermore, there is limited experimental validation of these methods, which affects their effectiveness and practicality in real-world applications.

[0006] This paper proposes a data-driven inverse design method for energy-absorbing metamaterials based on a diffusion model and a parameterized level set method, which can generate metamaterials and smooth, sharp boundaries based on the desired stress-strain curve. The core of the method is the diffusion model, which is suitable for learning the conditional distribution of metamaterials corresponding to the target stress-strain curve, allowing the ability to perform a one-to-many mapping to convert the desired mechanical properties into different sets of potential metamaterial topologies, while incorporating a parameterized level set function to generate topological structures with sharp boundaries. The method ensures the accuracy and efficiency of the design of energy-absorbing metamaterials, while highlighting the broad impact of integrating artificial intelligence-generated methods into material and structural design. Summary of the invention

[0007] The purpose of the present invention is to propose a design method for energy-absorbing metamaterials based on a diffusion model and a parameterized level set, aiming to overcome the difficulty of traditional methods in solving strong nonlinear problems, simplify the design process of energy-absorbing metamaterials, and provide a new solution path for achieving more intelligent and customized metamaterial design.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] The reverse design method of energy-absorbing metamaterials based on diffusion model and parameterized level set is as follows:

[0010] Step 1.1: Generate as many metamaterials as possible using a topology optimization method based on homogenization and parameterized level set method, identify boundaries using density threshold method, and effectively reduce the detected boundary data points using Ramer-Douglas-Peucker (RDP) algorithm to obtain a clear and accurate geometric representation for finite element simulation;

[0011] Step 1.2: In order to ensure the accuracy of the simulation results, a uniaxial tensile test of 304 stainless steel is carried out for constitutive parameter calibration, and the least squares method is used to identify material parameters in combination with the theory of plastic mechanics;

[0012] Step 1.3: Use finite element software to simulate the metamaterial obtained by topology optimization. The metamaterial is placed between two rigid plates. In order to avoid mutual penetration, the interaction between the plate and the structure and the self-interaction within the structure are considered. A vertical displacement is set along the y direction to simulate the compression process in a quasi-static manner and obtain the stress-strain curve when the structure is compressed.

[0013] Step 1.4: Use principal component analysis to reduce the dimension of the stress-strain curve obtained by simulation, reduce the complexity of the data by finding the principal component, and further normalize the reduced-dimensional data to eliminate the problem of the model being biased towards a certain feature due to differences between features. Finally, the metamaterial and its reduced-dimensional energy absorption curve are used as training data, of which 90% of the generated data is used for training and the remaining 10% is used for verification.

[0014] Step 2: Construct a diffusion model. The neural network architecture uses the U-Net network, initializes the network parameters, and uses the metamaterial and its energy absorption curve after dimensionality reduction as training data for iterative training in the diffusion model.

[0015] Step 3: For a trained diffusion model, given a target stress-strain curve, a family of metamaterials with target mechanical properties can be quickly generated based on the complex nonlinear mapping relationship learned by the diffusion model;

[0016] The beneficial effects of the present invention are:

[0017] 1. This paper proposes a design method for energy-absorbing metamaterials based on a diffusion model and a parameterized level set method to generate metamaterials given a desired stress-strain curve. The diffusion model learns the conditional distribution of metamaterials with given properties, achieving a one-to-many mapping from properties to geometry.

[0018] 2. The use of level set representation improves the accuracy and design flexibility of metamaterial topology, ensuring that the generated metamaterials have high-quality geometry.

[0019] 3. In summary, the present invention has the advantages of fast design speed and high precision, and provides a new solution path for realizing more intelligent and customized metamaterial design. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1(a) shows the compactly supported radial basis function of C2 continuity;

[0021] Figure 1(b) shows the partial derivatives of the C2-continuous compactly supported radial basis functions along the x-direction;

[0022] Figure 2(a) shows the design variable α;

[0023] Figure 2(b) shows the zero level set Φ of the two-dimensional level set function;

[0024] Figure 2(c) shows the clear geometric boundary obtained by the density contour method;

[0025] Figure 3(a) is a drawing of the test piece;

[0026] Figure 3(b) shows the test loading conditions;

[0027] Figure 3(c) is the true stress-strain curve. ;

[0028] Figure 4(a) shows the load condition;

[0029] Figure 4(b) shows the finite element simulation;

[0030] Figure 4(c) shows the nominal stress-strain curve;

[0031] Figure 5(a) shows the cumulative percentage of the principal components;

[0032] Figure 5(b) shows the distribution of stress data in the first and second principal component projections.

[0033] Figure 6 This is a schematic diagram of the diffusion model neural network;

[0034] Figure 7(a) is the test curve;

[0035] Figure 7(b) shows the error between the test curve and the generated curve Box plot of ;

[0036] Figure 8 (a) is test condition 1;

[0037] Figure 8 (b) is test condition 2;

[0038] Figure 8 (c) Test condition 3;

[0039] Figure 8 (d) is test condition 4;

[0040] Figure 9(a) is the interpolation curve;

[0041] Figure 9(b) shows the error between the interpolation curve and the generated curve Box plot of ;

[0042] Fig.10 (a) is interpolation curve 1;

[0043] Fig.10 (b) is interpolation curve 2;

[0044] Fig.10 (c) is interpolation curve 3;

[0045] Fig.10 (d) is interpolation curve 4;

[0046] Fig.11 (a) is interpolation curve 1;

[0047] Fig.11 (b) is interpolation curve 2;

[0048] Fig.11 (c) is interpolation curve 3;

[0049] Fig.11 (d) is the interpolation curve 4. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the technical solution of the present invention is described in detail below in combination with theoretical formulas, drawings and specific implementation cases. The technical solution adopted by the present invention is described below by examples:

[0051] Step 1.1: Introduce the process of generating metamaterial topology datasets for subsequent finite element simulations. The mathematical formulation of the topology optimization method based on homogenization and parameterized level set method is as follows:

[0052] find:α=[α1α2…α N ]

[0053]

[0054] Among them, α is the design variable, α L and α U are the lower and upper bounds of the design variables, respectively, and J is the homogenized elastic tensor E H The objective function is defined by the combination of , V is the volume constraint, and its upper limit is V max Φ is a parameterized level set function, which is approximated using a set of radial basis functions (RBFs) at each node in the entire design domain and is expressed as:

[0055]

[0056] The radial basis function sequence at each node is represented as a vector given as follows:

[0057]

[0058] In the present invention, a compactly supported radial basis function with C2 continuity is used, as shown in FIG1 , and its formula is as follows:

[0059] φ(r)=(max(0,1-r)) 4 …(4r+1)

[0060] Where r is the size of the domain of influence of the basis function at the node in the design domain. Therefore, the parameterized level set function Φ is represented by the design variable α.

[0061] H is the Heaviside function, which is expressed as:

[0062]

[0063] Where η is a small positive number introduced in the numerical process to avoid singularities, and the width of the numerical approximation of Δ is used. The elastic equilibrium equation is expressed in weak variational form, where the bilinear energy term a(u, v, Φ) and the linear load term l(v, Φ) can be expressed as:

[0064] a(u,v)=∫ Ω H(Φ)σ(u):ε(v)dΩ

[0065]

[0066] Among them, f represents body force, t represents surface force, and virtual displacement v belongs to the allowable displacement space of motion.

[0067] We systematically generated 30,000 metamaterials with volume fractions ranging from 28% to 52% by changing the initial material topology layout and volume constraints. In this study, the design variables α are uniformly distributed in the two-dimensional design domain, with 64 design variables in both the horizontal and vertical dimensions. Figure 2(a) shows the value of the design variable a at each node. Figure 2(b) shows the 0 level set corresponding to the level set function Φ. The density contour method is used for boundary detection, and the Ramer-Douglas-Peucker (RDP) algorithm is used to effectively reduce the detected boundary data points for finite element geometry modeling, as shown in Figure 2(c).

[0068] Step 1.2: To determine the mechanical properties of 304 stainless steel (304SS), a tensile specimen was designed according to GB / T 228.1-2021 standard

[59] . The tensile diagram of the specimen is shown in Figure 3(a), in units of mm.

[0069] The tensile test was carried out using a tensile testing machine, and the chuck displacement speed was set to 2 mm / min (strain rate 6.67×10 -5 s -1 ), which is consistent with the quasi-static tensile process (the strain rate is approximately 10 -5 s -1 ~10 -1 s -1 The specimen installation method is shown in Figure 3(b) to ensure accurate force-displacement data of 304SS material during the test. During the entire tensile test, a high-precision tensiometer is used to measure the axial displacement of the specimen. The collected force-displacement data is processed to obtain the true stress-strain curve:

[0070] ε=ln(1+ε N )

[0071] σ=σ N (1+ε N )

[0072] In the formula, ε N and σ N are normal strain and stress, respectively. ε and σ represent true strain and true stress, respectively. The true stress-strain is shown as the blue line in Figure 3(c). The elastic modulus E is determined by the slope of the elastic phase curve shown in Figure 3(c), which can be approximated to be 185 GPa, and the Poisson's ratio is 0.3. The present invention adopts the isotropic hardening von Mises yield function and the associated flow law. The hardening law adopts the following form:

[0073] σ y =A+B(ε p ) n

[0074] where σ y is the yield stress, ε p is the equivalent plastic strain. Where A is the initial yield stress, B is the hardening constant, and n is the dimensionless hardening exponent. According to the ASTM E8M-04 standard, the initial yield strength A is determined to be 344 MPa by the bias method (bias value is 0.2%). The least squares method is used to obtain B as 654 MPa and n as 0.61. The fitted stress-strain curve is shown in the red line in Figure 3(c). For dynamic simulation, the density is selected as 7.85×10 -9 tonne / mm 3 .

[0075] Table 1 lists all the material parameters used in the simulation

[0076]

[0077] Step 1.3: In order to save computational costs and fully demonstrate the innovation of the present invention, a single basic unit cell is used for finite element simulation. The finite element simulation process is shown in Figure 4. A two-dimensional metamaterial with a size of 10 mm × 10 mm is placed between two rigid plates. The key indicator for evaluating the effectiveness of the energy absorber requires simulating the full compression deformation behavior of the metamaterial. In this study, a quasi-static compressive strain of up to 60% was applied in the vertical direction. The deformation behavior of the two-dimensional metamaterial under quasi-static compression was simulated using the ABAQUS explicit software package. Under plane strain conditions, the CPE6M unit was used to discretize the solid part of the material, and each rigid plate was discretized using the R2D2 unit. The global seed size was set to 0.15 mm to ensure appropriate resolution and mesh size independence in the entire simulation domain. In order to prevent interpenetration, the interaction between the steel plate and the structure and the interaction within the structure were considered. For metallic materials, plastic yielding, rather than elastic buckling, is the main mechanism leading to initial structural damage. Therefore, the simulation does not consider the damage caused by buckling. The stress values ​​corresponding to the uniformly sampled strain points were obtained through compression simulation.

[0078] Step 1.4: The obtained topological structure and energy absorption curve are processed to facilitate deep neural network training. The energy absorption curve is reduced in dimension using principal component analysis. The complexity of the data is reduced by finding the principal components. As shown in Figure 5, it is obvious that the first 15 principal components have the ability to capture 99.98% of the data variance. This shows that even if the dimension is significantly reduced, most of the pivot information inherent in the data is still retained. Therefore, the original stress data is projected into a space with only 15 dimensions. Furthermore, in order to eliminate the problem of the model being biased towards a certain feature due to differences between features, the data after dimensionality reduction is normalized, which is defined as follows:

[0079]

[0080] Where Y i is the i-th value of the strain-stress curve, Y i,max and Y i,min are the i-th maximum and minimum values ​​in all strain-stress curves, respectively.

[0081] Step 1.5: Since the generated metamaterial has mirror symmetry in both horizontal and vertical directions, in order to make full use of this mirror symmetry and reduce unnecessary redundant data, we selected a quarter of the original image, that is, 32×32 pixels of metamaterial, for model training. Finally, we divided the 30,000 metamaterials and their stress-strain curves into training and validation sets, of which 90% of the generated data was used for training and the remaining 10% was used for validation.

[0082] Step 2: Construct a diffusion model. The neural network architecture uses a U-Net network with attention mechanism and group normalization, such as Figure 6 As shown in the figure, U-Net consists of three main parts: encoder, decoder and skip connection layer. The encoder compresses the input image into a low-dimensional latent space through a convolutional layer. The decoder accepts the encoded input and maps it to the original resolution. The skip connection layer connects the encoder and decoder, forming a bottleneck in the latent space, emphasizing key features and promoting bidirectional information flow. Our model mapping maps the metamaterial from 64×64 to 4×4 images. At the same time, a cross-attention mechanism is used to integrate the energy absorption curve to control the deep generation model to obtain the corresponding metamaterial according to the target energy absorption curve. Initialize the network parameters, and use the metamaterial and its energy absorption curve as training data for iterative training in the diffusion model. The selected diffusion model has 4.21 million trainable parameters, and the loss function formula is as follows

[0083]

[0084] Where ∈ is the added noise, ∈ θ is a trainable diffusion model that determines the amount of noise that should be removed in the current denoising step. Adam is used as the optimizer with a learning rate of 10 -4 , learning rate scheduling is implemented, the learning rate decays by 0.98 every 50 epochs, and a total of 2000 epochs are performed.

[0085] Step 3: Since the proposed method can learn the conditional probability distribution under given mechanical conditions, a set of metamaterials that closely match the target mechanical properties can be generated by sampling different initial noises. Four stress-strain curves in the test set are selected as generation conditions, as shown in Figure 7(a), and are put into the trained diffusion model to generate metamaterials. Subsequently, the generated metamaterials are imported into Abaqus for quasi-static loading to verify the consistency of the stress-strain curves corresponding to the generated metamaterials (referred to as generated curves) with the target curves. We adopt as a metric to quantify the error.

[0086]

[0087] Among them, Y g Indicates the generated stress-strain curve, Y t is the target stress-strain curve, and ‖·‖1 represents the L1 norm. Figure 7(b) shows the error between the generated curve and the target curve. The median error of all four target curves is less than 9%, indicating that the proposed method can accurately generate metamaterials that closely match the desired stress-strain curves.

[0088] Figure 8 The metamaterial and stress-strain curves are shown in detail. Each row represents the results generated for different conditions. In the first column, the target curve is shown in black, the curve with the lowest error in the training dataset is shown in red, and the error in the generated curve is shown in red. The smallest curve is shown in blue, generating the error in the curve The median curve is shown in green. The second column shows the metamaterial corresponding to the target curve. The third column shows the metamaterial corresponding to the curve with the smallest error in the training curve. The fourth and fifth columns show the metamaterials in the generated curve. The curves with the smallest and median errors correspond to the metamaterials. Figure 8 It can be clearly seen from the first column that the minimum error between the target curve and the generated curve Less than 5.2%. Figure 8 In (a) and (b), the minimum error in the generated curve is Smaller than the minimum error from the training dataset curve exist Figure 8 In (c) and (d), the minimum error of the generated curve is Minimum error with all curves from the training dataset This indicates that the proposed method can discover superior metamaterials within the design space. Figure 8 The generated metamaterials in the fourth and fifth columns are significantly different from the target metamaterials in the second column and the training metamaterials in the third column, which proves the powerful generation ability of the proposed method, enabling it to generate metamaterials beyond the training set. Figure 8 From the fourth and fifth columns of , it can be seen that although the curves corresponding to the generated metamaterials are similar, their metamaterial topologies are different. This observation proves that the proposed method learns the conditional distribution of metamaterials given specific mechanical properties, realizes a one-to-many mapping from properties to geometry, and generates various geometric metamaterials with the same mechanical properties.

[0089] Step 3.2: In order to evaluate the generation ability of the proposed method more deeply, we choose to select two stress-strain curves from the training data set and obtain a family of target curves by linear interpolation between the two curves. In Figure 9(a), the solid line represents the two curves selected from the training set, and the dotted line represents the interpolated curve (target curve). Figure 9(b) shows the error between the generated curve and the interpolated target curve. Box plot of the median error between the generated curve and the interpolated curve This result highlights the excellent generation capability and accuracy of the proposed method, which can effectively generate metamaterials that closely match the target curve even in complex interpolation scenarios.

[0090] Fig.10The metamaterial and its stress-strain curve under interpolation conditions are shown in detail. Each row represents the generated result of each interpolation curve. In the first column, the black line represents the target curve (interpolation curve), and the blue and green lines represent the generated curves. The minimum and median curves, represented by the green line The generated curve of the median value, the red line represents the generated The second column is the training data set. The metamaterial corresponding to the minimum value. The third column shows the error in generating the metamaterial. Metamaterials corresponding to the minimum and median values. Fig.10 The first column in shows, for some cases, the minimum error of the training curve Exceeded the minimum error for generating curves Meanwhile, the metamaterials corresponding to the second and third columns are significantly different. This finding highlights the superior generative capability of the proposed method in generating appropriate metamaterials by learning and understanding the characteristics of the target curves, thus achieving an accurate mapping from mechanical properties to metamaterial geometry.

[0091] By comparison Fig.10 In the generated metamaterials, it can be seen that as the interpolation curve changes, the adjacent metamaterials show smooth and gradual transitions rather than abrupt changes, which demonstrates the ability of the proposed method to maintain continuity and consistency when interpolating the evolution of the target stress-strain curve. This ability reflects a deep understanding of the complex relationship between metamaterials and mechanical properties and proves the reliability and stability of conditional generation. In addition, the smooth transitions produced by the proposed method help explore a wider design space, potentially leading to new metamaterial topologies with superior or unique properties, and opening up new possibilities and innovations in the field of metamaterial design.

[0092] Step 3.3: This section introduces a series of experiments to verify the performance and accuracy of the proposed method. First, the experimental samples of the metamaterial are prepared by mechanical processing. Quasi-static compression experiments are carried out using a tensile testing machine with a constant loading rate of 1 mm / min.

[0093] We select the error from the interpolation case The metamaterial corresponding to the minimum value is tested, and the experimental results are as follows Fig.11 As shown in the figure, the error between the target curve and the experimental curve is less than 12%. The experiment further verifies the effectiveness and reliability of the proposed method, highlighting its wide potential in various applications. These experiments pave the way for the integration of the model into the design and manufacturing process of the real world, promoting the development and innovation of advanced materials and structures.

Claims

1. A reverse design method for energy-absorbing metamaterials based on diffusion model and parameterized level set, characterized in that: Here are the steps: Step 1.1: Generate the metamaterial using a topology optimization method based on homogenization and parameterized level set method, identify the boundary using density threshold method, and effectively reduce the detected boundary data points using Ramer-Douglas-Peucker (RDP) algorithm to obtain a geometric representation for finite element simulation; Step 1.2: Conduct uniaxial tensile test on 304 stainless steel for constitutive parameter calibration, and combine with plastic mechanics theory to identify material parameters using the least squares method; Step 1.3: Use finite element software to simulate the metamaterial obtained by topology optimization. The metamaterial is placed between two rigid plates. A vertical displacement is set along the y direction to simulate the compression process in a quasi-static manner and obtain the stress-strain curve when the structure is compressed; Step 1.4: Use principal component analysis to reduce the dimension of the stress-strain curve obtained by simulation. By finding the principal component, the complexity of the data is reduced. The reduced-dimensional data is further normalized to eliminate the problem of the model being biased towards a certain feature due to the difference between features. Finally, the metamaterial and its reduced-dimensional energy absorption curve are used as training data, of which 90% of the generated data is used for training and the remaining 10% is used for verification. Step 2: Construct a diffusion model. The neural network architecture uses the U-Net network, initializes the network parameters, and uses the metamaterial and its energy absorption curve after dimensionality reduction as training data for iterative training in the diffusion model. Step 3: For a trained diffusion model, given a target stress-strain curve, a family of metamaterials with target mechanical properties can be quickly generated by relying on the complex nonlinear mapping relationship learned by the diffusion model.

2. The inverse design method of energy-absorbing metamaterial based on diffusion model and parameterized level set according to claim 1, characterized in that: The specific operations of step 1.1 are as follows: The mathematical expression of the topology optimization method based on homogenization and parameterized level set method is as follows: Among them, α is the design variable, α L and α U are the lower and upper bounds of the design variables, respectively, and J is the homogenized elastic tensor E H The objective function is defined by the combination of , V is the volume constraint, and its upper limit is V max Φ is a parameterized level set function, which is approximated by a set of radial basis functions (RBFs) at each node in the entire design domain and is expressed as: The radial basis function sequence at each node is represented as a vector given as follows: A compactly supported radial basis function with C2 continuity is used, and the formula is as follows: φ(r)=(max(0.1-r)) 4 …(4r+1) Where r is the size of the domain of influence of the basis function at the node in the design domain; therefore, the parameterized level set function Φ is represented by the design variable α; H is the Heaviside function, which is expressed as: Where η is a small positive number introduced in the numerical process to avoid singularities, and the width used for the numerical approximation of Δ; the elastic equilibrium equation is expressed in weak variational form, where the bilinear energy term a(u, v, Φ) and the linear load term l(v, Φ) can be expressed as: a(u,v)=∫ Ω H(Φ)σ(u):ε(v)dΩ Among them, f represents body force, t represents surface force, and virtual displacement v belongs to the allowable displacement space of motion.

3. The inverse design method of energy-absorbing metamaterial based on diffusion model and parameterized level set according to claim 1 or 2, characterized in that: The specific operations of step 1.2 are as follows: A high-precision tensiometer is used to measure the axial displacement of the specimen, and the collected force-displacement data is processed to obtain the true stress-strain curve: ε=ln(1+ε N ) s = s N (1+e N ) In the formula, ε N and σ N are the normal strain and stress, respectively; ε and σ represent the true strain and true stress, respectively.

4. The inverse design method of energy-absorbing metamaterial based on diffusion model and parameterized level set according to claim 3, characterized in that: In step 1.2, the isotropic hardening von Mises yield function is used, the associated flow law is used, and the hardening law is in the following form: s y =A+B(e p ) n where σ y is the yield stress, ε p is the equivalent plastic strain; where A is the initial yield stress, B is the hardening constant, and n is the dimensionless hardening exponent.

5. The inverse design method of energy-absorbing metamaterial based on diffusion model and parameterized level set according to claim 1 or 2, characterized in that: In step 1.4, the original stress data is projected into a space with only 15 dimensions, and the reduced-dimensional data is normalized, which is defined as follows: Where Y i is the i-th value of the strain-stress curve, Y i,max and Y i,min are the i-th maximum and minimum values ​​in all strain-stress curves, respectively.

6. The inverse design method of energy-absorbing metamaterial based on diffusion model and parameterized level set according to claim 1 or 2, characterized in that: In the step 2, the neural network architecture adopts a U-Net network with an attention mechanism and group normalization. The U-Net consists of three main parts: an encoder, a decoder, and a jump connection layer. The encoder compresses the input image into a low-dimensional latent space through a convolutional layer. The decoder accepts the encoded input and maps it to the original resolution. The jump connection layer connects the encoder and the decoder to form a bottleneck in the latent space, initializes the network parameters, and uses the metamaterial and its energy absorption curve as training data for iterative training in the diffusion model. The loss function formula is as follows: Where ∈ is the added noise, ∈ θ It is a trainable diffusion model that determines the amount of noise that should be removed in the current denoising step, using Adam as the optimizer.

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