4D printing intelligent structure design method based on convolutional neural network

Abstract

A 4D printing intelligent structure design method based on a convolutional neural network comprises the following steps: parametric modeling and data generation: controlling finite element software through a script to construct a'material parameter field-target deformation field 'sample data set in batches; data preprocessing and geometric standardization: uniformly converting a complex design domain into a standard rectangular domain by adopting a conformal mapping technology, and realizing high-fidelity standardization of physical field data; constructing a U-Net + ResNet hybrid convolutional neural network, and combining with composite loss function training to synchronously optimize global and key region deformation prediction precision; performing standardization processing on the new design after model deployment to realize second-level high-precision deformation prediction; the physical space design is restored through inverse mapping, multi-material 4D printing manufacturing is driven, and a deformation verification closed loop is completed. According to the method, the limitation of complex geometric boundaries is broken through, the nonlinear and multi-physics field coupling characteristics of the intelligent material can be accurately represented, and the practicability of the scheme is ensured by the constructed'design-prediction-manufacturing 'integrated process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of artificial intelligence and advanced manufacturing, and particularly relates to a method for realizing 4D printing intelligent structure design based on a convolutional neural network. BACKGROUND

[0002] As a frontier branch of additive manufacturing, 4D printing technology combines smart materials (such as shape memory polymers, hydrogels, liquid crystal elastomers, etc.) with sophisticated structural design, endowing three-dimensional structures with the ability to undergo pre-programmed deformation over time (i.e., the fourth dimension) under specific external stimuli (such as temperature, humidity, light, and magnetic field). This characteristic has revolutionary application potential in soft robotics, deployable aerospace structures, customized biomedical scaffolds, and adaptive optical systems.

[0003] Currently, the core key to realizing the function of 4D printing structures lies in the "programming" design of their initial state, that is, how to accurately plan the distribution, gradient, and internal residual stress field of smart materials in space to ensure that they can produce expected and complex deformations under excitation. However, this design process faces severe challenges. Traditional methods heavily rely on the physical intuition and experience of designers, and are explored through repeated "trial and error-manufacturing-testing" cycles. This process is extremely inefficient and difficult to reach a globally optimal design solution.

[0004] To improve the scientific nature of the design, physics-based numerical simulation methods, such as finite element analysis, are introduced into the design process. Although such methods can provide high prediction accuracy, the computational cost is extremely high. A complete simulation analysis of the deformation process of a complex structure under nonlinear and multi-physical field coupling conditions often takes several hours or even days. This time cost makes it impractical to fully explore the vast design space, severely restricting the emergence of innovative designs and optimization efficiency. In addition, traditional topology optimization and shape optimization methods often face inherent difficulties such as poor convergence and easy to fall into local optimum when dealing with the strong nonlinear response of smart materials and complex boundary conditions.

[0005] In recent years, deep learning techniques, especially convolutional neural networks, have made breakthroughs in computer vision and other fields due to their powerful non-linear mapping capabilities and feature extraction abilities, providing a new paradigm for solving complex engineering problems. Although some studies have attempted to apply neural networks to structural analysis and design, these efforts have significant limitations: first, they are typically limited to simple, regular design domains (such as two-dimensional rectangles); second, they deal with linear, static mechanical problems, which are far from the complex physical characteristics involved in 4D printing, such as material nonlinearity and time-varying response; third, existing methods focus on predicting a single performance indicator and fail to form a complete "material design-performance prediction-manufacturing implementation" integrated intelligent design framework.

[0006] Specifically, the deficiencies of existing technologies mainly manifest in the following three aspects: Firstly, in terms of geometric adaptability, although traditional neural network structure optimization methods are applicable to two-dimensional or simplified two-dimensional structures, they are still mainly limited to regular shape design domains. The actual application scenarios of 4D printing structures often involve complex geometric boundaries, and the regular grid representation used by existing methods cannot accurately describe such complex geometric characteristics, resulting in limited design space.

[0007] Secondly, in terms of physical modeling capability, existing neural network models are mostly based on linear elasticity assumptions and cannot accurately represent the strong nonlinearity, time dependence, and multi-physical field coupling characteristics exhibited by 4D printing intelligent materials. Key physical phenomena such as the phase transition behavior of shape memory polymers and the swelling effect of hydrogels are not fully captured in existing models.

[0008] Finally, in terms of engineering practicality, existing research often stops at the level of performance prediction or single-objective optimization, lacking a complete workflow that directly links design results to manufacturing processes. In particular, it fails to consider the unique material distribution control and residual stress regulation of 4D printing, making it difficult to directly apply the design results to the actual manufacturing process.

[0009] To address these challenges in existing technologies, the present invention provides an innovative solution. Through a special geometric transformation method, various complex-shaped design regions are converted into standard rectangular regions, breaking the limitation of traditional methods that can only handle regular shapes. At the same time, using the strong learning ability of deep learning, this system can directly grasp the complex relationship between material distribution and final deformation without any simplifying assumptions about material properties. SUMMARY

[0010] This invention provides a 4D printing smart structure design method based on convolutional neural networks, establishing an end-to-end intelligent design framework. This framework successfully overcomes the dual challenges posed by the nonlinear behavior of complex materials and irregular geometric boundaries, providing high-precision and highly feasible design solutions for 4D printed smart structures, thus directly solving key technical problems that restrict the development of this field.

[0011] A method for designing smart structures for 4D printing based on convolutional neural networks includes the following steps: Step (1) Parametric modeling and data generation: Define the basic geometric shape of the smart structure, set the material distribution parameters and initial residual stress as adjustable input parameters, and use script to control the finite element software to generate smart structure models with different parameter combinations in batches, solve the steady-state deformation field. Different material parameters are distributed under the same residual stress and their deformation results are different. Construct a sample dataset of "material parameter field - target deformation field". Step (2) Data preprocessing and geometric standardization: Using conformal mapping technology, the complex design domains of all smart structure models in step (1) are uniformly mapped to the standard rectangular parameter domain. A uniform square grid is established in this parameter domain, and the physical field data is converted into a standardized format through interpolation algorithm to ensure information fidelity. Step (3) CNN model construction and training: Construct a U-Net+ResNet hybrid convolutional neural network with encoder and decoder, and use a composite loss function to train the standardized dataset obtained in step (2). The dataset is divided into training set, validation set and test set according to a preset ratio. The hyperparameters are dynamically adjusted until the error of the validation set meets the accuracy requirements. Step (4) Model Deployment and Deformation Prediction: Perform the same standardization process as in step (2) on the newly designed smart structure, input the material distribution parameters into the trained model, and quickly output the deformation prediction results; Step (5) 4D printing manufacturing and verification: The optimal material distribution scheme is converted back to physical space through inverse mapping, and the multi-material 4D printing equipment is driven to manufacture the solid structure. The printed model is placed in 80° hot water to measure the actual deformation and compare it with the predicted results to complete the closed-loop verification.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) Breaking through geometric boundary limitations: By using conformal mapping technology, complex design domains are uniformly converted into standard rectangular domains, which solves the problem that traditional methods can only handle regular shapes and adapts to the complex geometric boundary requirements in practical applications.

[0013] (2) Accurate characterization of complex physical properties: There is no need to make simplified assumptions about the nonlinearity, time dependence and multi-physics coupling characteristics of smart materials. The complex relationship between material distribution and deformation is directly learned through data-driven CNN models, resulting in higher prediction accuracy.

[0014] (3) Achieve integrated intelligent design: Construct an end-to-end process of "data generation-standardization-model training-prediction-manufacturing verification", directly link the design results with the 4D printing process, and consider manufacturing constraints such as material distribution control and residual stress regulation, so that the design scheme can be directly implemented.

[0015] (4) Significantly improve design efficiency: After the model is deployed, deformation prediction can be achieved in seconds. Compared with the hours to days of traditional finite element simulation, the design efficiency is improved by more than a thousand times, which can fully explore a wide design space and find the global optimal solution. Attached Figure Description

[0016] Figure 1 This is the overall flowchart of the intelligent design system of the present invention.

[0017] Figure 2 This is a schematic diagram of conformal mapping technology.

[0018] Figure 3 This is a diagram of the U-Net+ResNet hybrid convolutional neural network architecture.

[0019] Figure 4 To determine the relationship between simulation results and actual printing. Detailed Implementation

[0020] The present invention will be described in detail below with reference to specific implementation steps, so that those skilled in the art can accurately reproduce the technical solution of the present invention.

[0021] A method for designing smart structures for 4D printing based on convolutional neural networks includes the following steps: Step (1) Parametric modeling and data generation: Define the basic geometric shape of the smart structure, set the material distribution parameters and initial residual stress as adjustable input parameters, and use script to control the finite element software to generate smart structure models with different parameter combinations in batches, solve the steady-state deformation field. Different material parameters are distributed under the same residual stress and their deformation results are different. Construct a sample dataset of "material parameter field - target deformation field". Step (2) Data preprocessing and geometric standardization: Using conformal mapping technology, the complex design domains of all smart structure models in step (1) are uniformly mapped to the standard rectangular parameter domain. A uniform square grid is established in this parameter domain, and the physical field data is converted into a standardized format through interpolation algorithm to ensure information fidelity. Step (3) CNN model construction and training: Construct a U-Net+ResNet hybrid convolutional neural network with encoder and decoder, and use a composite loss function to train the standardized dataset obtained in step (2). The dataset is divided into training set, validation set and test set according to a preset ratio. The hyperparameters are dynamically adjusted until the error of the validation set meets the accuracy requirements. Step (4) Model Deployment and Deformation Prediction: Perform the same standardization process as in step (2) on the newly designed smart structure, input the material distribution parameters into the trained model, and quickly output the deformation prediction results; Step (5) 4D printing manufacturing and verification: The optimal material distribution scheme is converted back to physical space through inverse mapping, and the multi-material 4D printing equipment is driven to manufacture the solid structure. The printed model is placed in 80° hot water to measure the actual deformation and compare it with the predicted results to complete the closed-loop verification.

[0022] Preferably, in step (1) of the present invention, the material distribution parameters include Young's modulus, which ranges from 0.1 to 5 GPa; the residual stress of the target is 0.1 to 1 MPa; and the number of samples in the dataset is ≥10,000.

[0023] Preferably, in step (2) of the present invention, the size of the standard rectangular parameter domain is 103mm×253mm, the side length of the uniform square mesh is 0.2mm, and the side length of the standardized mesh is not greater than the average size of the original finite element mesh.

[0024] Preferably, in step (3) of the present invention, the encoder includes 4 downsampling stages, the decoder includes 4 upsampling stages, the original features are preserved and gradient propagation is stabilized through the residual connection mechanism, and the features extracted by the encoder are fused through the splicing operation.

[0025] Preferably, in step (3) of the present invention, the expression of the composite loss function is: The weighting coefficient α = 0.6; The mean square error loss of the global deformation field. This represents the mean square error loss of the deformation field in the key functional area.

[0026] Preferably, the present invention The calculation formula is: Where N is the total number of grid points in the analysis domain. Let i be the predicted deformation value of the i-th grid point. To correspond to the actual deformation value; The calculation formula is: Where M is the number of grid points in the key functional area. Let j be the predicted deformation value of the j-th key grid point. This corresponds to the actual deformation value.

[0027] Preferably, in step (3) of the present invention, the initial learning rate is set to 1e-4, and the dataset is divided into training set, validation set and test set in a ratio of 70:15:15.

[0028] Preferably, in step (5) of the present invention, the smart material used in the multi-material 4D printing equipment is polymer PLA and CFPLA, etc.; the target external stimulus is heated to 80°C in the verification stage.

[0029] Preferably, in step (1) of the present invention, finite element models are generated in batches and solved by Python scripts, and the data is automatically extracted and converted into a standardized image format by interpolation algorithm; in step (3), if the validation set error does not reach the threshold, the learning rate is dynamically adjusted and retraining is performed.

[0030] A 4D printing intelligent structure design method based on convolutional neural networks, the core of which lies in building a data-driven end-to-end intelligent design system. For example... Figure 1 As shown, the system fully demonstrates the complete process from parametric data generation, geometric normalization, CNN model training, deformation prediction to 4D printing verification.

[0031] Step 1: Parametric Modeling and Data Generation — Building a "Knowledge Base" Core objective: To create a dataset.

[0032] Specific plan: Parametric modeling: First, define the basic geometry of the smart structure (such as a two-dimensional sheet). Then, set its material distribution (e.g., Young's modulus and coefficient of thermal expansion in different regions) and initial residual stress as automatically adjustable input parameters.

[0033] Batch finite element analysis: The script automatically generates different combinations of input parameters, each of which defines a unique intelligent structure model.

[0034] Each model is imported into the finite element analysis software. The models have different material distributions, and their deformations are also different under the action of residual stress.

[0035] Solve for the steady-state deformation field (i.e., the displacement vector at each point) reached by each model under residual stress.

[0036] Output: A large dataset where each sample is a pair of data: {Input: material parameter field, Output: target deformation field}.

[0037] Step 2: Data Preprocessing and Geometric Standardization Core objective: To resolve the mismatch between the data generated in step one and the data format required by the CNN in step three.

[0038] Specific plans and related aspects: The problem lies in the fact that the finite element model mesh in step one is irregular and generated to fit the geometry (such as a triangular mesh), while CNNs inherently process regular, uniform pixel meshes. The two are not directly compatible.

[0039] Solution: Conformal Mapping like Figure 2 As shown, this technique maps a complex-shaped design domain onto a standard rectangle. The standardized image format consists of a dense, uniformly sized standardized square grid. To ensure that the physical information in the original finite element model is accurately preserved and transmitted, the side length of this standardized grid is carefully set to be smaller than the average side length of the original finite element grid, thereby achieving high-fidelity conversion of physical field information during interpolation.

[0040] On this standard rectangle, we construct a dense and uniform square mesh. To ensure no information is lost, this mesh is finer than the original finite element mesh.

[0041] By interpolation, all the "material parameter field" and "deformation field" data on each irregular grid in step one are converted to this unified regular grid.

[0042] Related to Step 1: This step is the "formatting" process of the data in Step 1, converting it from heterogeneous data in the physical space to homogeneous data in the computational space.

[0043] Related to step three: It provides an input format for CNNs. At this point, a material distribution is like one "picture," and its corresponding deformation field is another "picture."

[0044] Step 3: CNN Model Construction and Training Core objective: To train a neural network to learn the complex mapping relationship from "material distribution image" to "deformation field image".

[0045] Specific plan: Network construction: A hybrid architecture of U-Net + ResNet (e.g.) is adopted. Figure 3 (As shown). This convolutional neural network combines U-Net and ResNet. The encoder extracts the spatial features of the input material parameters through downsampling operations, while retaining the original features and ensuring the stability of gradient propagation by leveraging the residual connection mechanism of R. The decoder reconstructs the distribution of material parameters through upsampling operations and fuses the features extracted by the encoder through concatenation operations.

[0046] Net (encoder-decoder): It excels at capturing the contextual information of an image and achieving precise pixel-level localization, making it ideal for learning the mapping between the input field and the output field.

[0047] ResNet (Residual Connections): Solves the vanishing gradient problem in deep network training, making the network more stable, deeper, and with better performance.

[0048] Training and Key Elements: Composite Loss Function Dataset partitioning: Divide the dataset obtained in step two into three parts: training set (for learning), validation set (for parameter tuning and selecting the best model), and test set (for final evaluation).

[0049] The role and significance of loss functions: The loss function is the "command stick" of the training process, telling the network what kind of prediction is "good".

[0050] The design of the composite loss function has clear engineering significance; this loss function... It consists of two parts: the mean square error loss of the global deformation field. Mean square error loss of deformation field in key functional areas Its mathematical definition is as follows: (1) in, The aim is to ensure that the model has global consistency in predicting the deformation of the entire smart structure. The calculation formula is as follows: (2) In the formula, This represents the total number of grid points within the entire analysis domain. and The first The model's predicted deformation value at each grid point is compared with the actual deformation value from the finite element simulation.

[0051] at the same time, This is specifically designed to improve the deformation prediction accuracy of the model in areas crucial to the functional realization of 4D printed structures. Its calculation formula is as follows: (3) In the formula, The number of grid points within a predefined key functional area. and The first The model prediction and the actual value at the grid points.

[0052] Step 4: Model Deployment and Deformation Prediction Core objective: To use a trained model to quickly and accurately predict the deformation of new designs.

[0053] Specific plans and related aspects: When a completely new smart structure needs to be designed, there is no need to perform finite element simulation.

[0054] Simply take its material distribution parameters, perform the same standardization process as in step two, and input them into the trained CNN model.

[0055] The model can output high-precision deformation prediction results within seconds.

[0056] Relationship with the preceding steps: This step is the final application of the results from steps one, two, and three. Its application presupposes that the newly designed geometric shape remains consistent with the conformal mapping domain of the training data. Under this premise, the guided training of the loss function in step three ensures the high functional reliability of the prediction results here.

[0057] Step 5: 4D Printing Manufacturing and Verification Core objective: To ultimately achieve closed-loop verification from digital prediction to physical deformation through 4D printing manufacturing and experimental measurement.

[0058] Specific plan: The optimal material distribution scheme predicted by the model is transformed back to the geometry of the original physical space through inverse mapping.

[0059] Using multi-material 4D printing equipment, smart materials with different properties (such as PLA and CFPLA) are precisely laid out according to this distribution to create solid structures.

[0060] When an external stimulus (such as heating) is applied, the structure will autonomously deform according to the deformation pattern predicted by the model. By comparing the actual deformation with the model prediction, the accuracy of the entire process from design to manufacturing is verified.

[0061] Example 1: A 4D printing smart structure design method based on convolutional neural networks. Figure 4 This study reveals how the simulation model reproduces the residual stress mechanism in actual printing. A clear correspondence was established in the finite element analysis for the stress generated along the printing path in actual printing: the transverse printing path corresponds to the application of transverse residual stress, while the longitudinal path corresponds to longitudinal residual stress.

[0062] During the simulation, the model was set to be fixed at one end, and stress loads were applied for different material distributions (Young's modulus) to solve for its steady-state deformation. Finally, by automatically extracting material property (input) and displacement field (output) data for comparative analysis, it was confirmed that under the same residual stress, the difference in material distribution directly led to different deformation results.

[0063] Step 1: Parametric Modeling and Data Generation Define the basic geometric shape: based on a two-dimensional triangular sheet structure with a base of 40mm, a height of 100mm, and a thickness of 2mm; Set the input parameters: Select Young's modulus for material distribution, with a value range of 0.1-5 GPa; select the initial residual stress range of 0.1-1 MPa; Batch model generation: Using Python scripts to write ABAQUS automation interfaces, 10,000 finite element models with different parameter combinations are generated in batches. The models are divided into triangular meshes with an average mesh side length of 0.3 mm. Stimulus application and solution: Apply residual stress of 0.1-1 MPa to each model, set the boundary condition to be fixed at one end, solve the steady-state deformation field, and automatically extract the material parameter field data (Young's modulus distribution) and deformation field data (displacement of each grid point in the x and y directions) for each model. Data storage: The extracted data is stored in HDF5 format to form the original dataset.

[0064] Step 2: Data Preprocessing and Geometric Normalization Conformal mapping implementation: Conformal mapping is implemented using Python's PyTorch3D library to map the original complex design domain (50mm×100mm two-dimensional thin sheet with irregular boundaries) to a standard rectangular parameter domain of 103mm×253mm. Mesh construction: A uniform square mesh is constructed on a standard rectangular domain with a mesh side length of 0.2 mm (less than the average side length of the original finite element mesh of 0.3 mm). The total number of meshes is (103 / 0.2)×(253 / 0.2)=515×1265≈651,475 mesh points. Data interpolation and transformation: The bilinear interpolation algorithm is used to transform the material parameter field and deformation field data on the original irregular grid to a standard uniform grid, forming a standardized image format (each data field is a two-dimensional array of 515×1265 pixels) to ensure the fidelity of physical information.

[0065] Step 3: CNN Model Construction and Training Network Setup: Building a U-Net+ResNet hybrid model based on the PyTorch framework: Encoder: The input layer receives a tensor of 515×1265×2 (two channels are Young's modulus distribution and initial stress distribution, respectively); it passes through four downsampling modules in sequence (each module contains two 3×3 convolutional layers, a BatchNorm layer, a ReLU activation function, and a 2×2 max pooling layer), and the output feature map size is gradually reduced to 32×79×256; Residual connections: Add ResNet residual blocks after each downsampling module, and skip two convolutional layers through shortcut connections to avoid gradient vanishing; Decoder: The feature map size is restored to 515×1265 by passing through four upsampling modules (each module contains a transposed convolutional layer, a BatchNorm layer, and a ReLU activation function); after each upsampling module, the feature map is concatenated with the feature map of the corresponding stage of the encoder to fuse multi-scale features; Output layer: The number of feature channels is converted to 2 (corresponding to deformation displacement in the x and y directions) through a 1×1 convolutional layer, and the deformation field prediction result is output. Loss Function and Optimizer: Setting the Composite Loss Function The key functional area is set as the free end of the structure (accounting for 20% of the total number of grids); the optimizer is AdamW, with an initial learning rate of 1e-4 and a weight decay of 1e-5; Dataset partitioning: The standardized dataset is divided into a training set (7000 samples), a validation set (1500 samples), and a test set (1500 samples) in a 70:15:15 ratio. Batch gradient descent is used during training, and the batch size is set to 8. Training process: The number of training epochs is set to 100. An early stopping strategy is adopted. If the validation set loss does not decrease for 10 consecutive epochs, the learning rate is reduced to 1 / 10 of the original. If the validation set loss is lower than the preset threshold (mean squared error ≤ 1e-6), the training is terminated and the optimal model is saved.

[0066] Step 4: Model Deployment and Deformation Prediction New design input: Select a completely new complex geometry (such as a two-dimensional thin sheet with a notch, size 60mm×120mm), and define its material distribution parameters (Young's modulus 0.5-3GPa, initial stress 0-80MPa). Standardization process: The material distribution parameters of the new design are converted into a 515×1265×2 standardized tensor according to the conformal mapping and bilinear interpolation process in step 2; Deformation prediction: Input the standardized tensor into the trained CNN model. The model outputs the deformation field prediction results in the x and y directions within 0.5 seconds, saves them as a two-dimensional array format, and visualizes the deformation cloud map using Matplotlib.

[0067] Step 5: 4D Printing Manufacturing and Verification Inverse mapping transformation: Using the inverse transformation algorithm of conformal mapping, the optimal material distribution scheme output by the model is transformed from the standard rectangular domain back to the physical space of the notched two-dimensional sheet to obtain the material distribution path required for actual printing; 4D printing: The material distribution path is imported into a multi-material 4D printing device, shape memory polymers such as PLA and CFPLA are selected as printing materials, and printing parameters are set (layer height 0.3mm, printing speed 50mm / s, nozzle temperature 200℃) to manufacture solid structures; Experimental verification: The printed solid structure was fixed on the test platform, and the ambient temperature was heated to 80℃ (the target external stimulus) through the temperature control system. The temperature was maintained for 30 minutes to allow the structure to reach steady-state deformation. The actual deformation of the structure was measured using a laser scanner to obtain the displacement data in the x and y directions of each point. Results Comparison: The mean square error between the actual deformation and the model-predicted deformation was calculated. The results show that the global mean square error is ≤2e-6, and the mean square error of the key functional area is ≤1.5e-6, which meets the requirements of engineering applications and verifies the accuracy and practicality of the method of this invention.

[0068] 3. Implementation Results Description This embodiment successfully achieved end-to-end design and manufacturing of 4D-printed smart structures through specific parameter settings, equipment selection, and operational procedures. Experimental results show that the design method of this invention can accurately predict the deformation of complex geometric structures under thermal stimulation, improving design efficiency compared to traditional finite element simulation. Furthermore, the actual deformation of the printed solid structure highly matches the predicted results, verifying the scientific validity and engineering applicability of the method. Those skilled in the art can adjust parameters such as the basic geometric shape, material parameter range, and type of external stimulus according to actual application scenarios to achieve similar technical effects.

Claims

1. A method for designing intelligent structures for 4D printing based on convolutional neural networks, characterized in that, Includes the following steps: Step (1) Parametric modeling and data generation: Define the basic geometric shape of the smart structure, set the material distribution parameters and initial residual stress as adjustable input parameters, use script to control the finite element software to generate smart structure models with different parameter combinations in batches, and solve the steady-state deformation field. Different material parameters are distributed under the same residual stress and their deformation results are different. Construct a sample dataset of "material parameter field - target deformation field". Step (2) Data preprocessing and geometric standardization: Using conformal mapping technology, the complex design domains of all smart structure models in step (1) are uniformly mapped to the standard rectangular parameter domain. A uniform square grid is established in this parameter domain, and the physical field data is converted into a standardized format through interpolation algorithm to ensure information fidelity. Step (3) CNN model construction and training: Construct a U-Net+ResNet hybrid convolutional neural network with encoder and decoder, and use a composite loss function to train the standardized dataset obtained in step (2). The dataset is divided into training set, validation set and test set according to a preset ratio. The hyperparameters are dynamically adjusted until the error of the validation set meets the accuracy requirements. Step (4) Model Deployment and Deformation Prediction: Perform the same standardization process as in step (2) on the newly designed smart structure, input the material distribution parameters into the trained model, and quickly output the deformation prediction results; Step (5) 4D printing manufacturing and verification: The optimal material distribution scheme is converted back to physical space through inverse mapping, driving the multi-material 4D printing equipment to manufacture solid structures, measuring the actual deformation, and comparing it with the predicted results to complete closed-loop verification.

2. The method according to claim 1, characterized in that, In step (1), the material distribution parameters include Young's modulus, which ranges from 0.1 to 5 GPa; the target external stimulus is a uniform thermal field of 60-120℃; and the dataset has ≥10,000 samples.

3. The method according to claim 1, characterized in that, In step (2), the size of the standard rectangular parameter domain is 103mm × 253mm, the side length of the uniform square mesh is 0.2mm, and the side length of the standardized mesh is not greater than the average size of the original finite element mesh.

4. The method according to claim 1, characterized in that, In step (3), the encoder contains 4 downsampling stages and the decoder contains 4 upsampling stages. The original features are preserved and gradient propagation is stabilized through the residual connection mechanism, and the features extracted by the encoder are fused through the splicing operation.

5. The method according to claim 1, characterized in that, In step (3), the expression for the composite loss function is: The weighting coefficient α = 0.6; The mean square error loss of the global deformation field. This represents the mean square error loss of the deformation field in the key functional area.

6. The method according to claim 5, characterized in that, The calculation formula is: Where N is the total number of grid points in the analysis domain. Let i be the predicted deformation value of the i-th grid point. To correspond to the actual deformation value; The calculation formula is: Where M is the number of grid points in the key functional area. Let j be the predicted deformation value of the j-th key grid point. This corresponds to the actual deformation value.

7. The method according to claim 1, characterized in that, In step (3), the initial learning rate is set to 1e-4, and the dataset is divided into training set, validation set and test set in a ratio of 70:15:

15.

8. The method according to claim 1, characterized in that, In step (5), the multi-material 4D printing equipment uses smart materials such as PLA and CFPLA; the target external stimulus in the verification stage is heating to 80°C.

9. The method according to claim 1, characterized in that, In step (1), finite element models are generated in batches and solved using Python scripts. After the data is automatically extracted, it is converted into a standardized image format by an interpolation algorithm. In step (3), if the validation set error does not reach the threshold, the learning rate is dynamically adjusted and the training is repeated.

Images