Three-dimensional swirling flame super-resolution reconstruction method based on physically guided diffusion model

Abstract

The application discloses a three-dimensional rotational flow flame super-resolution reconstruction method based on a physical guidance diffusion model, and comprises the following steps: low-resolution and high-resolution three-dimensional rotational flow flame data acquisition is performed by adopting a laser Doppler test technology and cooperating with laser Doppler particle analysis software; high-resolution three-dimensional flame is continuously superimposed with Gaussian noise along with the growth of step number, and random noise data is obtained; in a backward denoising process based on a physical gradient guide, low-resolution three-dimensional flame data is taken as an initial condition, a three-dimensional network is built to fit noise distribution to be removed in the backward denoising process, and a high-resolution three-dimensional image is reconstructed in combination with physical gradient guidance of a partial differential equation in a backward training process; after iteration is stopped, the performance of the model is evaluated by using corresponding indexes. The application reduces the time consumed by multiple iterations, improves the reconstruction efficiency, saves the calculation resources, and the reconstructed high-resolution three-dimensional flame has good details.

Description

Technical Field

[0001] This invention relates to the field of intelligent fluid aerodynamics, specifically to a three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model. Background Technology

[0002] One of the most important applications of combustion research is the internal combustion engine, whose combustion chamber is the source of heat to drive the turbine, converting thermal energy into mechanical energy, thus allowing the engine to operate. Flame stability at high speeds is based on ensuring that at least a portion of the flame is stably fixed to the burner. Incorporating swirl can improve flame stability by increasing residence time. Another benefit of using swirl to stabilize the flame is the production of a compact flame with a higher quality recirculation level than a non-swirl configuration, improving the efficiency of the power system.

[0003] Three-dimensional swirling flames offer multiple perspectives for observing turbulence, providing a more comprehensive view of combustion reactions than simply observing two-dimensional slices or planar measurements. Analyzing combustion flames within internal combustion engines can significantly aid in their design and improvement. Obtaining a clear image of the flame distribution within the combustion chamber is crucial. However, limitations in the number of sensors, hardware costs, and optical accessibility in confined spaces restrict the acquisition of high-resolution three-dimensional flame images. Acquiring high-resolution three-dimensional images solely through sensors is prohibitively expensive; therefore, a method is needed to capture clear swirling flames with rich edge information.

[0004] Applying deep learning methods for flame reconstruction is an efficient and innovative approach to intelligent scientific research. When studying flames, especially when analyzing the relative motion between objects and flames, deep learning provides a powerful tool for a more comprehensive and accurate understanding of flame dynamics. This method not only solves complex aerodynamic problems that are difficult to handle with traditional methods, but also continuously adapts and improves the model during the learning and optimization process, thus better adapting to diverse flame behaviors.

[0005] 3D super-resolution reconstruction is a computer vision technique that aims to improve the resolution and detail of low-resolution 3D images by analyzing and processing them, thereby generating higher-quality, high-resolution 3D images. This technique has wide applications in various fields, including medical 3D imaging and geological exploration. With the rapid development of deep learning and neural network technologies, significant progress has been made in the field of 3D super-resolution.

[0006] In super-resolution tasks, low-resolution images often suffer from detail loss due to sampling and sensor limitations. Diffusion models, by simulating the propagation and attenuation of noise and learning the correlation between pixels in an image, flexibly adapt to various image sizes and structures. This allows them to better preserve the structure and details of the original image when increasing resolution, which helps to restore details in flames. Diffusion models also exhibit a certain degree of robustness in dealing with adversarial noise and distortion, making them more robust to problems in different types of flames. Summary of the Invention

[0007] In real combustion tests, due to factors such as high temperature and the accuracy of measurement sensors, both high-resolution and low-resolution three-dimensional swirling flames will have certain disturbances or noise. The cost required to generate high-resolution three-dimensional swirling flame data through sensors is huge. Therefore, this invention proposes a reconstruction method that can directly reconstruct low-resolution three-dimensional flames into super-resolution three-dimensional flames.

[0008] The present invention adopts the following technical solution:

[0009] A method for super-resolution reconstruction of three-dimensional swirling flames based on a physically guided diffusion model includes:

[0010] The data acquisition process involves using laser Doppler testing technology in conjunction with laser Doppler particle analysis software to acquire swirling flame data, resulting in low-resolution 3D flame training data, low-resolution 3D flame test data, and high-resolution 3D flame training data.

[0011] The steps for constructing a diffusion model and a noise prediction network are as follows: establish a forward diffusion process and a physically guided backward denoising process; define a three-dimensional convolutional architecture network to learn and fit the distribution of noise-removed data during the backward denoising process.

[0012] The training process involves progressively adding noise to the high-resolution 3D flame training data through a forward diffusion process to obtain a random noise distribution. This random noise distribution is then combined with the low-resolution 3D flame training data to participate in the backward denoising process. The 3D convolutional architecture network learns the noise-removed data distribution during the backward denoising process and gradually reconstructs the high-resolution 3D flame data in conjunction with the backward denoising process. The physical guidance gradient and mean squared error loss are calculated during the backward denoising process, and the weights of the 3D convolutional architecture network parameters are iteratively updated. The network update is stopped according to the set conditions to obtain the trained backward denoising inference model.

[0013] The testing procedure involves inputting low-resolution 3D flame test data and random noise into a trained backward denoising inference model to reconstruct high-resolution 3D flame data, and then evaluating the quality of the reconstructed high-resolution 3D flame data.

[0014] Preferably, in the steps of constructing the diffusion model and noise prediction network, the forward diffusion process is specifically implemented as follows:

[0015] Probability distribution of high-resolution 3D flame training data The noise addition method and the forward diffusion process are as follows:

[0016]

[0017]

[0018] in, Indicates x during the forward diffusion process m The three-dimensional conditional probability data distribution of flames, x m By x m-1 Obtained by adding noise; This indicates that the added noise is Gaussian noise; β m ∈(0,1) represents the variance used in each step, which increases continuously as the forward diffusion process progresses, making the final x... T The distribution of is random noise; I represents the identity matrix; To represent the complete forward diffusion process, using high-resolution 3D flame training data x0 as a condition, a flame data distribution x1 to x2 with added noise is generated step by step. T T represents a Markov chain that requires T steps of parameterization for the forward diffusion process.

[0019] Preferred flame data distribution form x after adding noise m It is expressed as follows:

[0020]

[0021] The forward diffusion process can be represented as follows:

[0022]

[0023] Among them, a m =1-β m , γ m This is represented as step a at step m. i The product of the two, the distribution form of the flame data after adding noise x m The high-resolution 3D flame training data x0 and the corresponding m steps are sampled, which are x0 and random noise. A linear combination of .

[0024] Preferably, in the diffusion model and noise prediction network construction steps, the specific implementation of the backward denoising process is as follows:

[0025] The backward denoising process is combined with a conditional generation method, starting with random noise composed of a series of Gaussian distributions parameterized by a neural network. Each step of the backward denoising process is achieved through x... m The reasoning yields x m-1 conditional probability distribution Design a backward denoising process for a 3D convolutional architecture network containing neural networks. Fitted probability distribution Since super-resolution reconstruction is a conditional generation task, it uses... To fit the backward denoising process;

[0026] As an initial condition, the backward denoising process without the addition of the physical guiding gradient c is represented as follows:

[0027]

[0028] Where y represents low-resolution 3D flame training data; For the backward denoising process, sampling begins with random noise. The backward denoising process combines the noise with the low-resolution 3D flame training data to generate high-resolution 3D flame data. In this process, only the high-resolution 3D flame data is noise-free, so the data distribution in the backward denoising process is a Gaussian noise distribution. Guided by the low-resolution 3D flame training data, x is generated. m-1 The mean μ of the data distribution θ (y,x m m) and standard deviation σ θ (y,x m In the backward denoising process, a three-dimensional convolutional architecture network is introduced to form the final backward denoising inference model.

[0029] Preferably, the mean μ θ (y,x m m) and standard deviation σ θ (y,x m ,m) represents the following:

[0030]

[0031]

[0032] Wherein, the mean is determined by f θ (y,x m The neural network constructed from (m) is used for learning, but the physical guiding gradient c has not yet been added as guidance; the variance is a fixed value at each time step m. In the backward denoising process, only the mean of the noise distribution needs to be learned; the distribution form x of the noisy flame data in step m is derived in the backward denoising process. m-1 The formula is as follows:

[0033]

[0034] Preferably, the update process after adding gradient guidance is as follows:

[0035]

[0036] in, For the reason The gradient c is derived from the physical guidance gradient; Z is the normalization parameter; b is a constant. Gradient update conditional distribution.

[0037] Preferably, the process for obtaining the physical guided gradient c is as follows:

[0038] Obtain the formula for calculating the gradient of a partial differential equation:

[0039]

[0040] Where G is the differential operator of the PDE equation; u(ξ) is the solution of the above equation; Ω represents the parameters of the equation; Ω represents the computational domain of the partial differential equation.

[0041] Let u = x m The following formula is obtained:

[0042]

[0043]

[0044] Where, x m This represents the intermediate data distribution format for the backward denoising process; r m The residual is the partial differential equation.

[0045] Preferably, x in the backward denoising process m-1 With gradient guidance, sampling is performed from the following normally distributed noise:

[0046]

[0047] The backward denoising process is represented as:

[0048]

[0049] The above two constraints are used to derive the noisy flame data distribution form x in the m-th step of the backward denoising process. m-1 The formula is as follows:

[0050]

[0051] Among them, f θ (c,y,x m,m) is f θ (y,x m For a network with added physical guiding gradient c, the backward denoising process involves predicting noise. The noise prediction error is formulated as follows:

[0052]

[0053] Where p is the normal form of the gradient function being calculated; f θ A 3D convolutional architecture network is constructed to predict the noise distribution at each stage.

[0054] Preferably, the three-dimensional convolutional architecture uses U-Net as the main network architecture, consisting of downsampling modules, connection modules, and upsampling modules. The upsampling and upsampling convolutional modules are all three-dimensional residual convolutional modules. Each three-dimensional residual convolutional module undergoes batch normalization layer processing, is calculated using a corresponding activation function, and then input into the three-dimensional convolutional module before being output to the next batch normalization layer. Some downsampling and upsampling modules include self-attention mechanism layers.

[0055] Preferably, the quality of the reconstructed image is evaluated using MSE, PSNR, and SSIM, as follows:

[0056]

[0057]

[0058]

[0059] Where I(i,j,k) represents low-resolution 3D flame test data; N(i,j,k) represents reconstructed high-resolution 3D flame data; a, b, and d are the length, width, and depth of the 3D data, respectively; MAX I μ is the maximum pixel value in the 3D image. I With μ N σ represents the mean pixel values ​​of I(i,j,k) and N(i,j,k), respectively; I 2 and σ N 2 σ represents the variance of the pixel values ​​of I(i,j,k) and N(i,j,k), respectively; IN C1 and C2 are constants; SSIM ranges from -1 to 1.

[0060] The beneficial effects of this invention are as follows:

[0061] The diffusion model of this invention helps generate high-quality, detailed images, providing quality assurance for super-resolution reconstruction of 3D flame data. The addition of physical guide gradients helps maintain physical consistency during super-resolution reconstruction. Combined with physical gradients, the backward denoising inference model is better able to understand the structure and texture in the image and can effectively fuse physical gradient information at different scales and directions. It can better reconstruct the swirling flame details inside the combustion chamber and generate more realistic and accurate high-resolution images.

[0062] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the three-dimensional swirling flame super-resolution reconstruction method based on the physical guided diffusion model of the present invention is not limited to the embodiments. Attached Figure Description

[0063] Figure 1 This is a flowchart of the three-dimensional swirling flame super-resolution reconstruction method based on a physical guided diffusion model according to an embodiment of the present invention;

[0064] Figure 2 This is a schematic diagram of data acquisition according to an embodiment of the present invention;

[0065] Figure 3 This is a schematic diagram of the forward diffusion process according to an embodiment of the present invention;

[0066] Figure 4 This is a schematic diagram of the backward denoising process with added physical guidance in an embodiment of the present invention;

[0067] Figure 5 This is the network structure for predicting noise distribution in an embodiment of the present invention;

[0068] Figure 6 This is a detailed flowchart of the training and testing process according to an embodiment of the present invention. Detailed Implementation

[0069] To make the objectives and technical solutions of this invention clearer, the invention will be further described below with reference to the accompanying drawings and examples. It should be understood that the examples described herein are for illustrative purposes only and are not intended to limit the invention.

[0070] The three-dimensional swirling flame within the combustion chamber offers multiple perspectives for observing turbulence, providing a more comprehensive view of the combustion response than simply observing two-dimensional slices or planar measurements. Previous methods for observing three-dimensional swirling flames primarily employed a combination of computers and sensors, using the computer to process and project signals from the sensors to determine the flow structure of the three-dimensional swirling flame.

[0071] However, due to limitations in the number of sensors, hardware costs, and optical accessibility in space-constrained environments, the high-resolution 3D flames that can be imaged are limited and costly. Therefore, it is necessary to propose a method that can directly reconstruct low-resolution 3D flames into ultra-high-resolution 3D flames.

[0072] See Figure 1 As shown, the three-dimensional swirling flame super-resolution reconstruction method based on the physical guidance diffusion model includes a data acquisition step S101, a diffusion model and noise prediction network construction step S102, a training step S103, and a testing step S104. Specifically, it can be divided into a data acquisition stage, a forward diffusion stage, a backward denoising stage with physical guidance, network construction, and training and testing, which will be carried out in sequence below.

[0073] When an internal combustion engine is working, it is necessary to observe and analyze the distribution of the swirling flame inside the combustion chamber. Due to the presence of swirling motion, the flame is usually spiral or ring-shaped. The more combustion details, the better it can assist in the subsequent design and improvement of the internal combustion engine. This method is applied here.

[0074] For details, see Figure 2 As shown, during the data acquisition phase, laser Doppler testing technology was employed. A standard dual-channel laser Doppler measurement configuration was used for data acquisition. An ion continuous laser was used, and the receiving optical element consisted of a fixed-focal-length lens. A receiving angle between 25° and 30° was used, and the two laser beams were focused above the inlet plane to avoid reflection from the bottom of the burner. A traverse system was used to collect data on the burner volume. Fixed samples were collected at each measurement location according to the set acquisition time. Laser Doppler particle analysis software was used for data acquisition.

[0075] The complexity of Doppler measurements stems from the flow restriction imposed by the square casing, which reflects and disperses the laser light near the wall, resulting in noise and disturbance in the acquired data, affecting the acquisition of flame edge information. This disturbed and unclear flame data is designated as low-resolution data, while clean data with clear edge information is designated as high-resolution data. The low-resolution data is further divided proportionally into low-resolution 3D flame training data and low-resolution 3D flame test data; the high-resolution data serves as high-resolution 3D flame training data.

[0076] See Figure 3 As shown, the forward diffusion stage refers to the random noise generation stage of the diffusion model. Starting from a high-resolution initial data distribution, it gradually updates the state through a series of steps until the final random noise distribution is reached. In diffusion models, forward diffusion typically involves progressively updating the probability distribution to simulate the propagation and attenuation of noise.

[0077] First, high-resolution data for the forward diffusion process is obtained, with the original data distribution as follows: The forward diffusion process is a parameterized Markov chain that requires T steps. Each step is obtained by adding noise to the data from the previous step, resulting in the joint distribution of the Markov chain as follows:

[0078]

[0079] The forward diffusion process with x0 as the initial condition, x m Given the data distribution at step m, since the data distribution after x1 is related to the previous data distribution, the formula for the forward diffusion process can be obtained as follows:

[0080]

[0081] in, For distribution x m In x m-1 The probability distribution under the condition that, where This indicates that the added noise is sampled from Gaussian noise, with a variance β. t The values ​​are predefined at different time steps and gradually increase as T increases. Noise is used. Distribution x at any time t It can be calculated from x0, let The formula is as follows:

[0082]

[0083] Where, x m It is a linear combination of x0 and random noise ∈. The above formula represents the overall forward diffusion process, and the final data distribution of the forward diffusion process can be obtained from the formula above.

[0084] See the physically-guided backward denoising stage. Figure 4 As shown, this is achieved by performing a backward operation based on forward diffusion. The goal of this backward denoising process is to reconstruct a high-resolution image from the image after noise propagation and evolution by combining the low-resolution data distribution. From random noise x t It begins by consisting of a series of Gaussian distributions parameterized by a neural network.

[0085] The backward denoising process is combined with a conditional generation method, starting with random noise composed of a series of Gaussian distributions parameterized by a neural network. Each step of the backward denoising process requires passing through x... m The reasoning yields x m-1 conditional probability distribution However, it cannot be directly accessed via x. m Calculate xm-1 Based on the probability distribution, design a backward denoising process using a 3D convolutional neural network architecture. Fitted probability distribution Since super-resolution reconstruction is a conditional generation task, it uses... To fit the backward denoising process, y represents low-resolution 3D flame data as an initial condition. At this point, the physical guiding gradient c has not yet been added, and the following formula is derived:

[0086]

[0087] in, For the backward denoising process, sampling begins with random noise. y represents a low-precision data distribution guide label provided in the initial backward denoising stage. The backward denoising process combines the noise with the low-resolution 3D flame data to generate high-resolution 3D flame data. In this process, only the high-resolution 3D flame data is noise-free, so the data distribution in the backward denoising process is a Gaussian noise distribution. x is generated under the conditional guidance of the low-resolution 3D flame data. m-1 The mean μ of the data distribution θ (y,x m m) and standard deviation σ θ (y,x m The backward denoising process requires the support of a three-dimensional convolutional neural network architecture to form the final generative model.

[0088]

[0089] The obtained mean is given by f θ (y,x m The neural network constructed from m is used for learning. At this point, the physical gradient c has not yet been incorporated as guidance, and the variance is a fixed value, requiring no further learning from the network. In each backward step, based on the current state and the information learned by the model, simulated noise is removed at each step through the network f. θ The learned noise distribution is used to obtain x during the backward denoising process. m-1 The distribution can be obtained from the following formula.

[0090]

[0091] The above shows the data distribution obtained under low-resolution 3D flame data with initial conditions. To more closely approximate the real data distribution and enrich it with interpretable physical meaning, corresponding physical gradients are added as training constraints. Partial differential equations cover parameters such as fluid velocity, density, and pressure. Flames are usually caused by combustion, which involves physical processes such as heat conduction and mass transfer. Fluid motion can be described using partial differential equations. Assume the partial differential equations are in the following form:

[0092]

[0093] Among them, G is the differential operator of the PDE equation, u(ξ) is the solution of the above equation, Θ is the parameter of the equation, such as viscosity in fluid mechanics, etc., and Ω is the computational domain of the partial differential equation. Let u = x m , x m is the data distribution at time m, and r m is the residual of the PDE equation, which is used to evaluate the accuracy of the data distribution form in the backward denoising process, and the following formula can be obtained.

[0094]

[0095]

[0096] Adding gradient guidance in the backward denoising process can be expressed by the following formula

[0097]

[0098] Among them, is changed from adding physical guidance c, where m < T, Z is the normalization parameter, c is the guidance condition, and b is a constant. Gradient update conditional distribution. Using the method of variational inference, it can be judged that when there is gradient guidance in the backward denoising process, from μ θ (x m ), σ θ (x m ) the corresponding mean and standard deviation μ, σ can be obtained, then x<...> m-1 can be written as the following formula.

[0101]

[0102] Repeat the steps of backward denoising, and gradually perform the operations of backward and forward diffusion until the required restoration effect is achieved or the stop criterion is satisfied. The noise prediction error formula for model update is as follows.

[0103]

[0104] P is the norm of the calculated gradient function, fIt should be noted that there seems to be some incomplete or unclear parts in the original text (such as the ellipsis in ID=40), but the translation is carried out as accurately as possible according to the existing content.​​​​​​θ The constructed deep learning network is used to predict the noise distribution at each stage, where ∈ represents Gaussian noise, m represents the noise distribution at time m, y represents the initial low-resolution 3D flame condition, and c represents the physical guidance gradient condition.

[0105] In the network construction phase, the first step is to embed time information into the model so that the model can model time. This helps the model learn the dynamic changes and evolution of data over time. Based on the step T required by the Markov chain, an embedding function is designed. This function transforms the time step T into a fixed-dimensional vector. The time embedding t∈[0,T] can be added to the model input or combined with the model's hidden layer representation. By incorporating the time embedding into the model, the model can better capture the evolution and correlation of data over time. The time embedding can be represented by the following formula.

[0106]

[0107] Here, l is an integer representing the index or code of the temporal embedding, typically starting from 0, indicating the starting point of the time step; T is the time step required for the forward diffusion process, which is also the period of the temporal embedding; and sin and cos are sine and cosine functions, respectively. These are periodic functions used to introduce periodic patterns into the temporal embedding.

[0108] See Figure 5 As shown, the constructed deep learning network f θ Using U-Net as the main network architecture, unlike previous architectures, 3D residual convolution is applied as the main module because the flame data is three-dimensionally distributed. See the deep learning network f shown in 5(a). θ It mainly consists of a downsampling module, a linking module, and an upsampling module, as shown in 5(b). Each three-dimensional residual convolution module is mainly composed of a batch standard normalization layer, a three-dimensional convolution, and an activation function layer. Some downsampling and upsampling modules contain a self-attention mechanism layer.

[0109] The data distribution obtained in the backward denoising stage is input into the deep learning network f. θ The data is processed by the batch normalization layer in each module. After being calculated by the corresponding activation function, it is input into the 3D convolution module and then input into the next batch normalization layer. The initial condition y mentioned above is combined with the input data and distributed into each batch normalization layer, so that the network can better utilize the conditional distribution to learn how to remove noise.

[0110] A self-attention mechanism layer is added to some downsampling and upsampling modules. The calculation formula for the self-attention mechanism is as follows:

[0111]

[0112] Where Q is the query matrix, representing the information of the current position, used for comparison with other positions; K is the key matrix, representing the information of other positions, used for comparison with the query; and V is the numerical matrix, containing the actual numerical information of the corresponding position. This is a standardization factor, where k k This normalization factor, representing the dimension of the bond, is used to make the dot product QK. T The numerical range of these values ​​will not be too large, which helps to maintain the stability of the gradient; This part of the calculation determines the weight of each position, representing the degree of attention the current position pays to other positions. The Softmax function ensures that the sum of these weights is 1.

[0113] See Figure 6 As shown, during the training and testing phases, after a fixed number of steps, the quality of the 3D flame reconstructed by the model at this point is evaluated. The differences between the reconstructed high-resolution 3D flame and the 3D flame data generated by the fine mesh are evaluated using PSNR, SSMI, and MSE metrics.

[0114] MSE (Mean Slightest Error) is a metric used to measure the difference between two data points, often employed to assess the error between model predictions and actual values. It works by calculating the square of the difference at each corresponding position and averaging the results to quantify the average error between the two data points.

[0115] PSNR is a metric used to measure the quality of image or audio signals. It is commonly used in image compression and other fields to measure the quality of signal reconstruction. It is based on the error between corresponding pixels, i.e., it is an error-sensitive image quality evaluation. Its calculation formula relies on the mean square error (MSE) for definition. Based on the characteristics of three-dimensional data, we define it as follows:

[0116]

[0117] Where I(i,j,d) is the original 3D image, N(i,j,k) is the generated 3D image, abc is the length, width, and depth of the 3D data, and MAX is the maximum value. I This represents the maximum possible pixel value in the 3D image.

[0118] SSIM, or Structural Similarity, is a metric used to measure the structural similarity between two images. It's a widely used quality assessment metric in computer vision, considering brightness, contrast, and structure to compare the similarity between the original and processed images. Its calculation formula is as follows:

[0119]

[0120] Where I(i, j, k) represents low-resolution 3D flame test data; N(i, j, k) represents reconstructed high-resolution 3D flame data; a, b, and d represent the length, width, and depth of the 3D data, respectively; MAX I μ is the maximum pixel value in the 3D image. I With μ N σ represents the mean pixel values ​​of I(i,j,k) and N(i,j,k), respectively; I 2 and σ N 2 Let σ be the variance of the pixel values ​​of I(i,j,k) and N(i,j,k), respectively; IN C1 and C2 are constants; SSIM ranges from -1 to 1.

[0121] After training using the above method is completed, Figure 6 The test phase shown demonstrates how Doppler particle analysis software effectively captures the overall structure of the swirling flame during combustion in the combustion chamber. It reconstructs the three-dimensional swirling flame, which contains disturbances and has unclear boundaries. This method can accurately reproduce the overall structural distribution and flame edge details of a real swirling flame without laser reflection or noise disturbance without requiring excessive precision measuring equipment and testing time. This provides assistance for the internal combustion analysis of internal combustion engines, and is fast and efficient.

[0122] It should be understood that those skilled in the art can make improvements and modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model, characterized in that, include: The data acquisition process involves using laser Doppler testing technology in conjunction with laser Doppler particle analysis software to acquire swirling flame data, resulting in low-resolution 3D flame training data, low-resolution 3D flame test data, and high-resolution 3D flame training data. The steps for constructing a diffusion model and a noise prediction network are as follows: establish a forward diffusion process and a physically guided backward denoising process; define a three-dimensional convolutional architecture network to learn and fit the distribution of noise-removed data during the backward denoising process. The training process involves gradually adding noise to the high-resolution 3D flame training data through a forward diffusion process to obtain a random noise distribution. This random noise distribution is then combined with the low-resolution 3D flame training data to participate in the backward denoising process. The 3D convolutional architecture network learns the noise-removed data distribution during the backward denoising process and gradually reconstructs the high-resolution 3D flame data by combining it with the backward denoising process. Calculate the physical guidance gradient and mean squared error loss during the backward denoising process, and iteratively update the weights of the 3D convolutional architecture network parameters. Stop the network update according to the set conditions to obtain the trained backward denoising inference model. The testing procedure involves inputting low-resolution 3D flame test data and random noise into a trained backward denoising inference model to reconstruct high-resolution 3D flame data, and then evaluating the quality of the reconstructed high-resolution 3D flame data. The update process after adding gradient guidance during backward denoising is as follows: （1）； in, For the reason The gradient c is derived from the physical guidance gradient; Z is the normalization parameter. Gradient update conditional distribution; The process of obtaining the physical guided gradient c is as follows: Obtain the formula for calculating the gradient of a partial differential equation: （2）； in, For the differential operator of the PDE equation; This is the solution to equation (2) above; These are the parameters of the equation; Let be the computational domain of the partial differential equation; make = The following formula is obtained: （3）； （4）； in, This represents the intermediate data distribution format in the backward denoising process; The residuals of the partial differential equation; In the backward denoising process With gradient guidance, sampling is performed from the following normally distributed noise: （5）； in, Indicates generation The mean of the data distribution; This represents the corresponding standard deviation; Represents the identity matrix; The distribution of noisy flame data in the m-th step is derived in the backward denoising process using the two constraints of equations (5) and (1) above. The formula is as follows: （6）； in, Indicates random noise. for After adding the physical guiding gradient c, the backward denoising process in the network is a process of predicting noise. The prediction error formula for the noise is as follows: （7）； in, This is the normal form of the calculated gradient function; A three-dimensional convolutional architecture network was constructed to predict the noise distribution at each stage; This represents high-resolution 3D flame training data; This represents low-resolution 3D flame training data.

2. The three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model according to claim 1, characterized in that, In the construction steps of the diffusion model and noise prediction network, the specific implementation of the forward diffusion process is as follows: For the probability distribution of high-resolution three-dimensional flame training data The noise addition method and the forward diffusion process are as follows: （8）； （9）； in, Indicating the forward diffusion process The three-dimensional conditional probability data distribution of flames. Depend on Obtained by adding noise; This indicates that the added noise is Gaussian noise; The variance used at each step increases continuously as the forward diffusion process progresses, leading to the final... The distribution is random noise; Representing the complete forward diffusion process using high-resolution 3D flame training data As a condition, a flame data distribution with added noise is gradually generated. ; This represents a parameterized Markov chain that requires T steps in the forward diffusion process.

3. The three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model according to claim 2, characterized in that, Flame data distribution after adding noise It is expressed as follows: （10）； The forward diffusion process can be represented as follows: （11）； in, , This represents each step up to the m-th step. The product of High-resolution 3D flame training data Sampling is performed in the corresponding m steps. and random noise A linear combination of .

4. The three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model according to claim 2, characterized in that, The specific implementation of the backward denoising process in the diffusion model and noise prediction network construction steps is as follows: The backward denoising process is combined with a conditional generation method, starting with random noise composed of a series of Gaussian distributions parameterized by a neural network. Each step of the backward denoising process... Reasoning conditional probability distribution Design a backward denoising process for a 3D convolutional architecture network containing neural networks. Fitted probability distribution Since super-resolution reconstruction is a conditional generation task, it uses... To fit the backward denoising process; As an initial condition, the backward denoising process without the addition of the physical guiding gradient c is represented as follows: (12); in, For the backward denoising process, sampling begins with random noise. The backward denoising process combines the noise with the low-resolution 3D flame training data to generate high-resolution 3D flame data. In this process, only the high-resolution 3D flame data is noise-free, so the data distribution during the backward denoising process is a Gaussian noise distribution. Guided by the low-resolution 3D flame training data, the process generates... The mean of the data distribution with standard deviation In the backward denoising process, a three-dimensional convolutional architecture network is introduced to form the final backward denoising inference model.

5. The three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model according to claim 4, characterized in that, mean with standard deviation It is expressed as follows: （13）； （14）； Among them, the mean is from The constructed neural network is learned, but at this point, the physical guiding gradient c has not yet been added as guidance; the variance is for each... For a fixed value at a given time, in the backward denoising process, only the mean of the noise distribution needs to be learned; the derivation of the first... Noisy flame data distribution The formula is as follows: （15）。 6. The three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model according to claim 1, characterized in that, The described 3D convolutional architecture uses U-Net as its main network architecture and consists of downsampling modules, connection modules, and upsampling modules. Both the upsampling and upsampling convolutional modules are 3D residual convolutional modules. Each 3D residual convolutional module undergoes batch normalization processing, is calculated using a corresponding activation function, and then input into the 3D convolutional module before being output to the next batch normalization layer. Some downsampling and upsampling modules include self-attention mechanism layers.

7. The three-dimensional swirling flame super-resolution reconstruction method based on a physically guided diffusion model according to claim 1, characterized in that, The quality of the reconstructed image is evaluated using MSE, PSNR, and SSIM, as follows: （16）； （17）； （18）； in, This represents low-resolution 3D flame test data; For reconstructing high-resolution 3D flame data; For the length, width, and depth of the three-dimensional data; The maximum pixel value in the 3D image; and They are respectively and The average pixel value; They are respectively and The variance of pixel values; The covariance of pixel values; and It is a constant; the value of SSIM ranges from -1 to 1.

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