Physical guide infrared thermal imaging data enhancement method for composite material defect detection
By combining a physical-guided dual-encoder method with a thermal conduction model and a convolutional autoencoder, the problems of blurred defect boundaries and low signal-to-noise ratio in infrared thermal imaging technology are solved, achieving high-precision detection of defects in composite materials. This method is applicable to infrared thermal imaging detection under various excitation conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-16
- Publication Date
- 2026-03-13
AI Technical Summary
Existing infrared thermal imaging technology suffers from problems such as blurred defect boundaries, low signal-to-noise ratio, and insufficient thermal contrast between defects and background in composite material defect detection, making it difficult to consistently improve detection consistency and accuracy. Furthermore, deep learning models lack accurate simulation of actual physical phenomena when dealing with complex physical processes.
A physically guided dual encoder method is adopted, which combines a thermal conduction model with a convolutional autoencoder. By using feature difference and principal component thermal imaging methods, background information is weakened, thereby improving the accuracy of defect detection.
It significantly improves the detection accuracy and reliability of internal defects in composite materials, and can clearly identify and locate defects without the need for manual thresholding and empirical filtering. It is suitable for infrared thermal imaging detection under various excitation conditions.
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Figure CN121660906A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of defect detection technology in industrial processes, and specifically to a physical-guided infrared thermal imaging data enhancement method for detecting defects in composite materials. Background Technology
[0002] Carbon fiber reinforced polymer (CFRP) composites, for example, are widely used in aerospace, automotive, and wind power industries due to their lightweight, high strength, and corrosion resistance. However, due to the complex structure and manufacturing process of CFRP, defects such as interlaminar delamination, porosity, and cracks may occur within the material, often posing a potential threat to its mechanical properties and safety. Therefore, defect detection in CFRP materials is crucial to ensure structural safety and reliability. Non-destructive testing (NDT) techniques, as a means of assessing the internal quality of materials without damaging them, have become the standard method for evaluating the health of composite materials in industry.
[0003] Non-destructive testing (NDT) technology encompasses a variety of methods, including ultrasonic testing, X-ray testing, and infrared thermography. Among these, infrared thermography has been widely used in defect detection of carbon fiber composite materials due to its non-contact, real-time imaging, and ease of operation. It can quickly identify potential defects by detecting differences in thermal conductivity caused by internal defects on the material surface, and it has significant advantages, especially in detecting defects on the surface and near the surface layer.
[0004] Although infrared thermal imaging is widely used in nondestructive testing of composite materials, existing acquisition processes and imaging mechanisms introduce a series of objective limitations: First, due to the influence of thermal diffusion and the spatial resolution of the imaging system, defect boundaries are prone to diffusion blurring; second, sensor noise, differences in surface emissivity, and environmental drift combine to result in a low signal-to-noise ratio; third, under pulsed excitation conditions, short-duration high-energy input causes significant spatiotemporal inhomogeneity in the temperature field, leading to insufficient thermal contrast between defects and the background. Traditional methods such as filtering, background subtraction, and empirical thresholding rely on artificial parameters and prior assumptions, which have limited adaptability to different materials, thicknesses, and excitation conditions, making it difficult to consistently improve defect detectability and characterization consistency.
[0005] With the rise of deep learning technology, the application of infrared thermal imaging in defect detection has gradually entered a new stage. Deep learning models, especially structures such as convolutional neural networks, can automatically extract high-level features from thermal imaging images, thereby significantly improving the accuracy and robustness of defect identification. Deep learning, through its end-to-end training method, avoids the complexity and limitations of traditional feature extraction. However, when dealing with complex physical problems, deep learning often relies on large amounts of data for pattern recognition, but struggles to effectively combine physical laws with data simulation. This results in a lack of accurate simulation and explanation of actual physical phenomena in many engineering applications, especially in tasks involving physical processes such as heat conduction.
[0006] To address this, this invention proposes a physically guided dual-encoder infrared thermal imaging data enhancement (DEPIT) defect detection method. This method integrates a heat conduction model into a convolutional autoencoder, capturing defect features and enhancing thermophysical properties, significantly improving the accuracy and reliability of infrared thermal imaging data processing. The dual-encoder architecture suppresses background information in the latent space, while the decoder reconstructs the thermal response to improve defect detection accuracy. Subsequently, principal component thermal imaging (PCT) is applied to the reconstructed sequence to extract the principal components with the highest contribution to construct a defect saliency map, achieving dimensionality reduction, noise reduction, and feature focusing. Through this process, internal defects in composite materials can be clearly identified and located without the need for manual thresholding and empirical filtering, significantly improving detection accuracy and meeting the engineering application requirements described in the invention patent. Summary of the Invention
[0007] The technical solution adopted by this invention to solve its technical problem is:
[0008] This invention proposes a physically guided infrared thermal imaging data enhancement method for composite defect detection, the method comprising the following steps:
[0009] Step 1: Acquisition of Infrared Thermal Imaging Defect Image Dataset
[0010] A pulse-excited infrared thermal imaging method is used to apply short-pulse transient thermal excitation to the sample under test. During the cooling phase after the excitation ends, an infrared camera continuously acquires thermal images of the sample surface temperature field at a preset frame rate. The acquired thermal image data is stored in a three-dimensional thermal image matrix in a computer system and organized into the raw dataset used for subsequent processing.
[0011] Step 2: Image Preprocessing
[0012] The three-dimensional thermal image matrix obtained in step 1 is reshaped into a two-dimensional matrix. The data is normalized according to the image sequence, and the amplitude is uniformly mapped to [0,1] to reduce the influence of background non-uniformity and improve the training efficiency and stability of the subsequent model. The normalization is used to unify the dimensions and magnitudes of different samples and different frames. The normalized thermal image sequence is used as the standard input for subsequent processing and model training.
[0013] Step 3: Construct a physically guided dual-encoder data augmentation model
[0014] The normalized thermal image sequence obtained in step 2 and the background thermal image sequence fitted based on the thermal conduction physical model are input into the defect-aware encoder and background encoder, respectively, to extract the corresponding spatiotemporal features. The two features are mapped to the same latent space, and feature difference is performed to obtain a background-free defect representation. The differenced features are then input into the decoder for reconstruction, resulting in an enhanced thermal image sequence with prominent defect responses. To reduce data redundancy and facilitate comparative analysis, dimensionality reduction is performed in the image dimension. Principal component thermal imaging is preferred, retaining several key thermal images to achieve image compression and saliency representation of defects.
[0015] Furthermore, the process of step 1 is as follows:
[0016] Step 1.1: Infrared Thermal Imaging System Configuration and Data Acquisition
[0017] The infrared thermal imaging system consists of a pulse-excited flash lamp, an infrared camera, a sample to be tested, and a computer with infrared thermal imaging software installed. The pulse excitation device and the camera are synchronized via trigger control and parameter settings are completed according to preset pulse energy and frame rate. During acquisition, a pulsed transient heating is applied to the sample. After excitation terminates, a cooling phase begins, during which the infrared camera continuously records the temporal evolution of the sample surface temperature field at a preset frame rate. The computer processes multiple frames of thermal images as input for subsequent processing.
[0018] Step 1.2: Preparation of defective samples and data composition
[0019] This invention employs a resin transfer molding process to composite carbon fiber sheets with epoxy resin to create defect samples. Subsequently, the infrared thermal imaging system described in step 1.1 is used to acquire data under uniform excitation and acquisition parameters. The obtained thermal image sequence consists of T thermal images, with a single frame resolution of H×W pixels. A three-dimensional thermal image data matrix of size T×H×W is constructed using a computer as input for subsequent processing and analysis.
[0020] Furthermore, the process of step 2 is as follows:
[0021] Step 2.1: Unfolding the 3D matrix
[0022] The thermal image sequence acquired by the infrared thermal imaging system is organized into a three-dimensional matrix of size T×H×W, where H and W are the image height and width, and T is the number of frames. The three-dimensional matrix is expanded with pixels as samples and time as features to obtain a two-dimensional matrix X of size T×N, where N=H×W.
[0023] Step 2.2: Normalization of the two-dimensional matrix
[0024] To reduce background inhomogeneity and improve model training efficiency, a row-wise normalization strategy is adopted for the two-dimensional matrix in step 2.1: for each row of data in the matrix (specifically each image), the minimum value min(x) of that row is calculated. i ) and the maximum value max(x) i This allows for a linear mapping of the row's amplitude to a uniform range, thus ensuring consistency in the dimensions and magnitudes of different pixel samples over time. The specific formula is as follows: ;
[0025] Linearly map it to the interval [0,1], where x i Let X be the pixel in the i-th row. This is the result after normalization.
[0026] Furthermore, step 3 is as follows:
[0027] Step 3.1: Constructing a physical model
[0028] Building a physical model requires the coordinates x, y, z, and time t of the spatial infrared thermal imaging data, with the output being the predicted grayscale value u. In actual infrared thermal imaging experiments, since the infrared camera can only record the temperature of the sample surface (i.e., the temperature at z=0), the model only needs to consider the two-dimensional coordinates (x, y) and time t. To address the issue that the infrared camera only records surface temperature, the boundary conditions at the x and y boundaries are considered, ignoring the boundary in the z direction. Furthermore, subsequent experiments are expanded using the following heat conduction formula: ;
[0029] in, , k is the thermal conductivity coefficient, c is the specific heat capacity, and ρ is the density. Assuming that in equation (2) It does not change with z and can be estimated using initial conditions. Therefore, the physical model in the experiment was modified to two feedforward neural networks. Feedforward neural network one (NN1) is used to calculate the relationship between the input and u, while feedforward neural network two (NN2) is used to calculate... .
[0030] In infrared thermal imaging experiments, the focus is primarily on the cooling process of the sample surface. It is assumed that heat transfer mainly occurs within the test sample, and heat exchange between the sample and its surroundings is negligible. Then, Ω represents the entire domain. This represents the boundary. Subsequently, the boundary conditions can be expressed as: ;
[0031] Where m is the unit normal to the boundary, and .
[0032] Physical constraints are typically derived from the governing equations (such as partial differential equations) and boundary and initial conditions of the problem. In practical infrared thermal imaging problems, constraints can be imposed during model training using Fourier's law and its boundary conditions. According to formula (2), the partial differential equations in the model... This can be summarized as follows: ;
[0033] in, Represents the residuals of the governing equations. , , If the model is trained by minimizing the prediction loss using the PINN loss function, then the prediction loss will be lost. pred Partial differential loss pde and boundary loss LOSS bc It can be represented as: ;
[0034] Where u pred u is the predicted value of NN1. ture This is the normalized thermal image data. N is the set of thermal image data collected in the infrared thermal imaging experiment. This represents the number of pixels randomly selected for model training along the boundary between x and y. In summary, the loss function of the PINN model is LOSS. total This can be summarized as follows: ;
[0035] Here, θ and β are hyperparameters used to balance the weights of various losses in the overall optimization.
[0036] Step 3.2: Construct a dual-encoder autoencoder model
[0037] The reconstructed background information and the features of the original heatmap are encoded separately. Background removal is achieved by feature subtraction in the hidden layer, and image reconstruction is then completed in a single decoder. The core idea is to use two encoders in the hidden layer stage to extract features from the original heatmap and the reconstructed background image respectively, and then perform subtraction in the hidden layer before feeding them into a single decoder for reconstruction. One encoder uses the original heatmap I... raw As input, local texture and global structural features of the image are extracted through multiple convolutional layers (or fully connected layers) to obtain the feature vector F. raw Another encoder reconstructs the background image I. bg As input, a multi-layer network structure is also used to extract background features, resulting in the feature vector F. bg After obtaining F raw With F bg Then, subtraction is performed in the hidden layer to obtain the feature representation after background removal. The residual feature F after subtraction is then processed. res The input is a single decoder, which consists of multiple deconvolution layers to reconstruct the image and finally output the background-suppressed image R. de Theoretically, this image should primarily contain information about the defect area, with background interference significantly reduced. Specifically, it can be represented as: ;
[0038] Where, σ raw , σ bg and τ de W represents the activation functions of the original encoder, background encoder, and decoder, respectively; raw W bg W de b represents the weights of the two encoders and decoders, respectively; raw b bg b de R represents the weights of the two encoders and decoders; de This represents the final decoding result with background suppression.
[0039] The model is trained by minimizing the reconstruction error to learn a low-dimensional representation of the data. Then, the reconstructed image data N is obtained by extracting the decoder results. n ×N x N y Expand it into N n Zhang N x ×N y Thermal images were used for observation. However, since the number of reconstructed images was the same as the original images, feature extraction methods were further employed to control the number of images within a certain range, facilitating further observation by researchers.
[0040] Step 3.3: Data Dimensionality Reduction and Visualization Processing
[0041] Since the number of reconstructed images is the same as the original sequence, to facilitate analysis and comparison, the reconstruction results in step 3.2 are reduced to 6 images using the commonly used principal component thermal imaging method. These 6 images are then visualized to obtain thermal images containing defect information.
[0042] The technical concept of this invention is as follows:
[0043] An autoencoder network with dual encoders is constructed, and physical priors are used to process thermal images: the original infrared image and a background image fitted according to a physical model are input into the corresponding encoders to extract features. Differentiation is performed in the latent space of the autoencoder to weaken background components unrelated to defects, and the enhanced image is obtained after decoding and reconstruction. Principal component analysis is then performed on the reconstructed data, and the most representative principal components are extracted for defect saliency and discrimination. This method can effectively suppress background interference caused by environmental factors and non-uniform heating, improve defect contrast, and is applicable to infrared thermal imaging detection of composite materials under various excitation conditions such as pulse and phase-locked loop, and can be implemented on a general-purpose computing platform.
[0044] The beneficial effects of this invention are mainly reflected in the following aspects: This invention proposes a physically guided dual-encoder data enhancement method for infrared thermal imaging detection of composite defects. Through the joint design of physical prior constraints and dual-encoder differential mechanism, it achieves accurate background removal and significant defect enhancement of thermal image sequences. 1) Feature subtraction is performed in the shared latent space to significantly weaken irrelevant components such as background and noise, reducing the influence of irrelevant factors on defect detection; 2) Single decoder reconstruction enhances the response of weak defects while preserving edges and details, improving detection accuracy; 3) Combining principal component thermal imaging methods to reduce the dimension reduction and compression of image data reduces redundant frames and manual interpretation workload, facilitating rapid screening in engineering applications. Attached Figure Description
[0045] Figure 1 This is a flowchart of the algorithm of the present invention;
[0046] Figure 2 This is a schematic diagram of the model structure of the present invention;
[0047] Figure 3 This is a distribution map of defect locations in the dataset of this invention;
[0048] Figure 4 This is the data augmentation visualization result of the method of the present invention;
[0049] Figure 5 This is the data dimensionality reduction visualization result of the method of this invention. Detailed Implementation
[0050] The present invention will now be further described with reference to the accompanying drawings.
[0051] Reference Figures 1-5 A physically guided dual encoder data augmentation method for infrared thermal imaging detection of defects in composite materials includes the following steps:
[0052] Step 1: Acquisition of Infrared Thermal Imaging Defect Image Dataset
[0053] Step 1.1: Resin was injected into the fiber preform composed of stacked fiber layers under vacuum pressure. The experimental sample consisted of 20 fiber layers of 0.395 mm each. To study the defect characteristics of infrared thermal imaging, polytetrafluoroethylene inserts with different geometries were strategically placed at different depths in different layers during the layup process. Three typical defect configurations were designed: (1) trapezoidal insert (marked as C) with parallel base edges of 5 mm (top edge) and 15 mm (bottom edge); (2) circular insert (B) with a radius of 20 mm; (3) rhomboid insert (A) with four equal 20 mm sides.
[0054] Step 1.2: Data was acquired using infrared thermal imaging technology. The acquired images consisted of 73 425×617 data points.
[0055] (2) Image preprocessing
[0056] Step 2.1: Expand the acquired three-dimensional matrix (73×425×617) into a two-dimensional matrix (73×262225).
[0057] Step 2.2: Process the data according to the normalization formula.
[0058] Step 3: Build and train a physically guided dual-encoder data augmentation model
[0059] Step 3.1: Establish a physically guided dual-encoder data augmentation model. Feedforward Neural Network 1 (NN1) consists of an input layer with three neurons, eight hidden layers each with thirty neurons, and an output layer. Feedforward Neural Network 2 (NN2) includes an input layer with three neurons, two hidden layers each with twenty neurons, and an output layer. The training process utilized 100,000 data points selected from the complete dataset. The learning rate was set to 0.001. In the autoencoders of the dual encoders, except for the last layer of the decoder which uses a sigmoid function, the rest use ReLU functions.
[0060] Step 3.2: Input the normalized data into the model for training. Select the Adam optimizer to optimize the parameters, and finally save the trained model.
[0061] Step 3.3: Obtain the trained model and the decoder reconstruction result.
[0062] Step 3.3: After obtaining the reconstruction results in Step 3.2, perform dimensionality reduction using commonly used principal component thermal image analysis.
[0063] Step 3.4: Data visualization. Visualize and analyze the dimensionality reduction results obtained in Step 3.3.
[0064] To evaluate the effectiveness of the proposed method, a metric is needed to quantitatively assess the quality of the results. This invention uses the contrast-to-noise ratio (CNR), a metric commonly used for quantitative assessment of defects in thermal images. Its calculation formula is as follows: ;
[0065] Where, m def and m in These are the average pixel values of the defective and non-defective regions in the thermal image, respectively, σ in The standard deviation of pixel values in the non-defective region is denoted as CNR. CNR reflects the contrast between the defective and non-defective regions; the higher the CNR value, the stronger the defect identification capability of the method. Table 1 compares the CNR values of different defects in the original thermal image with those after principal component thermal image analysis processed by the model of this invention. The results show that the method of this invention has a strong defect identification capability.
[0066] Table 1. Comparison of CNR values for different defects before and after data processing ;
[0067] The comparison results above show that the defect detection performance of the present invention using PCT is far superior to that of the original image using traditional PCT. This invention proposes a physically guided infrared thermal imaging data enhancement method for composite material defect detection, improving the accuracy of defect identification and localization.
[0068] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.
Claims
1. A physically guided infrared thermal imaging data enhancement method for composite defect detection, characterized in that, Includes the following steps: Step 1) Obtaining the infrared thermal imaging defect image dataset: A transient thermal excitation is applied to the sample to be tested, and the temporal changes of the temperature field on the sample surface are continuously recorded during the cooling phase. The obtained raw thermal images are stored in the computer system in the form of a three-dimensional matrix to form the raw dataset. Step 2) Image preprocessing: The three-dimensional thermal image obtained in step 1) is reshaped into a two-dimensional matrix, and normalization processing is performed sequentially according to the image sequence to obtain a normalized thermal image sequence. Step 3) Construct a physically guided dual-encoder data augmentation model: The normalized thermal image sequence obtained in step 2) and the background thermal image sequence fitted based on the thermal conduction physical model are respectively input into the corresponding encoder to extract features. The two features are aligned in the shared latent space of the autoencoder and differential operation is performed to suppress background components unrelated to defects. Then the differential result is input into the decoder for reconstruction to obtain an enhanced thermal image that highlights the defect information. Dimensionality reduction methods are used to reduce the number of images, making comparative analysis easier.
2. The physical-guided infrared thermal imaging data enhancement method for composite defect detection as described in claim 1, characterized in that, The process of step 1 is as follows: Step 1.1: Infrared Thermal Imaging System Configuration and Data Acquisition The infrared thermal imaging system includes a pulse-excited flash lamp, an infrared camera, a sample to be tested, and a computer with infrared thermal imaging software installed. During the acquisition process, pulsed transient heating is applied to the sample to be tested. During its cooling phase, the infrared camera continuously records the change of the sample surface temperature field over time at a preset frame rate. The computer receives and stores the thermal image sequence, thereby obtaining time-series data composed of several frames of thermal images. Step 1.2: Preparation of defective samples and data composition The defect sample is made of carbon fiber sheet and epoxy resin using a resin transfer molding process, and data is acquired through the infrared thermal imaging system to obtain T thermal images. Each image has a resolution of H×W pixels, and the data is aggregated by a computer to form a three-dimensional thermal image data matrix with a size of T×H×W for subsequent processing and analysis.
3. The method for enhancing physically guided infrared thermal imaging data for detecting defects in composite materials as described in claim 2, characterized in that, The process of step 2 is as follows: Step 2.1: Unfolding the 3D matrix The thermal image sequence acquired by the infrared thermal imaging system is organized into a three-dimensional matrix of size T×H×W, where H and W are the image height and width, and T is the number of frames; The three-dimensional matrix is expanded using pixels as samples and time as a feature to obtain a two-dimensional matrix X of size T×N, where N=H×W; Step 2.2: Normalization of the two-dimensional matrix Perform row-wise normalization on the two-dimensional matrix X: for the i-th row x of X i Calculate its minimum value min(x) i ) and the maximum value max(x) i ), and according to ; Linearly map it to the interval [0,1], where This is the result after normalization.
4. The physical-guided infrared thermal imaging data enhancement method for composite defect detection as described in claim 1, characterized in that, The process of step 3 is as follows: Step 3.1: Constructing a physical model A physical model for heat conduction is established with spatial coordinates and time as independent variables and image grayscale as dependent variable. The model input includes three-dimensional spatial coordinates (x, y, z) and time t, and the output is the predicted surface grayscale u. Since actual infrared thermal imaging only acquires sample surface information, only the corresponding boundary conditions are set for the x and y boundaries, and the boundary constraints in the z direction are ignored. The solution is based on the heat conduction control equation and is expanded. Combined with the above boundary conditions, the gray field prediction results are obtained and used as the physical prior for subsequent differential enhancement. Step 3.2: Construct a dual-encoder autoencoder model Reconstructed background thermal image I bg Compared with the original thermal image I raw The corresponding encoders are input separately, and the corresponding features are extracted under the action of multi-layer convolutional modules. The two features are scale-aligned in the shared latent space, and then difference is performed to achieve background term elimination, obtaining residual features F mainly composed of defect responses. res The residual features are input into a single decoder, and recovered step by step through deconvolution or upsampling to complete the thermal image reconstruction and output the background-suppressed result image I. rec As a result, background interference in the output image is significantly reduced, and defective areas are highlighted. The specific calculation formula is as follows: ; Among them, F raw With F bg These represent the feature vectors of the original data and background information obtained through two encoders, respectively; σ raw , σ bg and τ de W represents the activation functions of the original encoder, background encoder, and decoder, respectively; raw W bg W de b represents the weights of the two encoders and decoders, respectively; raw b bg b de R represents the weights of the two encoders and decoders; de This represents the final decoding result with background suppression. The network is trained by minimizing the reconstruction error, enabling the model to learn a low-dimensional representation of the thermal image sequence in the latent space. After training, the decoder output is extracted to obtain a result of size N. n ×N x N y Reconstructed data; Step 3.3: Data Dimensionality Reduction and Visualization Processing The reconstruction results are subjected to dimensionality reduction and feature selection. Principal component thermal imaging is used to select representative principal components as objects for subsequent observation and evaluation. Then, the selected representative principal components are visualized to obtain the result image containing defect information.
5. The method for enhancing physically guided infrared thermal imaging data for detecting defects in composite materials as described in claim 1, characterized in that, The process of solving the heat conduction control equation in step 3.1, and then combining it with the above boundary conditions to obtain the grayscale field prediction result, is as follows: Expanding the heat conduction formula: ; in, k is the thermal conductivity coefficient, c is the specific heat capacity, and ρ is the density; Assuming in equation (6) It does not change with z, and z is estimated using initial conditions; two feedforward neural networks are used, where feedforward neural network NN1 is used to calculate the relationship between the input and u, and feedforward neural network NN2 is used to calculate ; Assuming heat transfer occurs within the test sample and heat exchange between the sample and the surrounding environment is negligible, then Ω represents the entire domain. The boundary is represented; subsequently, the boundary conditions are expressed as: ; Where m is the unit normal to the boundary, and ; According to formula (6), the partial differential equations in the model In summary: ; in, Represents the residuals of the governing equations. , , ; If the model is trained by minimizing the prediction loss using the PINN loss function, then the prediction loss will be lost. pred Partial differential loss pde and boundary loss LOSS bc They are represented as follows: ; Among them, u pred u is the predicted value of NN1. ture These are normalized thermal image data, where N is the set of thermal image data collected in the infrared thermal imaging experiment. This indicates the number of pixels randomly selected for model training at the boundary between x and y. In summary, the loss function of the PINN model is LOSS. total In summary: ; Here, θ and β are hyperparameters used to balance the weights of various losses in the overall optimization.