Three-dimensional rotational flow flame super-resolution reconstruction method and system based on interval diffusion normal form

Abstract

The invention discloses a three-dimensional rotational flow flame super-resolution reconstruction method and system based on an interval diffusion normal form, and the method comprises the steps: building a diffusion model for three-dimensional rotational flow flame, and constructing a diffusion process and a reverse denoising process between high-resolution data and low-resolution data; in the reverse denoising process, a three-dimensional convolutional architecture network is adopted to learn and remove noise distribution, and the residual error between the high-resolution image and the low-resolution image is used as diffusion noise; the method comprises the following steps: inputting high-resolution three-dimensional flame training data, gradually adding noise to obtain approximate low-resolution image distribution, learning a denoising process by using a physically guided gradient three-dimensional convolutional network, reconstructing high-resolution flame data, and iteratively updating network parameters; and inputting low-resolution three-dimensional flame test data into the trained model to realize high-resolution reconstruction. According to the method, high-precision super-resolution reconstruction of low-resolution three-dimensional rotational flow flame data is realized through a three-dimensional convolutional architecture network based on an interval diffusion normal form and a physical guidance gradient learning strategy.

Description

Technical Field

[0001] This invention relates to the field of intelligent fluid aerodynamics, and more specifically to a method for super-resolution reconstruction of three-dimensional swirling flames based on an interval diffusion paradigm. Background Technology

[0002] In combustion science, the study of combustion flow fields is a crucial research direction, especially the study of three-dimensional swirling flames. Due to their unique three-dimensional structure, these flames contain far more combustion information than two-dimensional images, making them an important tool for understanding the intrinsic mechanisms of combustion, assessing chemical reaction kinetics, and measuring reactant and product concentration gradients. Although current experimental techniques can obtain images of three-dimensional swirling flames, such experiments are often limited by the spatial resolution threshold of optical devices and the hardware cost of multi-camera synchronous acquisition systems. Measured data generally suffer from insufficient spatial sampling rates and blurred flow field boundaries. More importantly, dynamic interference factors such as turbulent fluctuations and thermal radiation under complex combustion conditions exacerbate the loss of detail in the flow field topology, leading to a significant increase in measurement errors of key combustion characteristic parameters. This affects the accuracy and reliability of the data, which to some extent restricts the ability to conduct in-depth analysis of combustion phenomena.

[0003] In recent years, with the development of deep learning technology, especially generative model-based deep learning methods, new solutions have been provided for scientific computing. Among them, diffusion models, with their outstanding performance in generating and reconstructing high-dimensional complex data, have become a research hotspot in the fields of computational science and machine learning. This model, by constructing an inverse denoising process for the physical field, can achieve progressive probabilistic reconstruction from low-resolution observation data to high-resolution flow field distributions. Its implicit representation learning mechanism effectively overcomes the smoothing defects of traditional interpolation algorithms for local flow field abrupt changes. This characteristic provides a theoretical basis and technical support for solving the resolution limitation problem of traditional methods in reconstructing complex physical field data. Combining diffusion models with the study of flame flow fields for super-resolution reconstruction can not only effectively improve the analytical ability of flame microstructure and dynamic behavior, but also compensate for the shortcomings of traditional experimental methods in acquiring high-resolution data, thereby promoting the understanding of combustion physics processes and downstream practical applications. Diffusion models have not only achieved good experimental results in studies combined with two-dimensional flame flow field data, but models combined with three-dimensional swirling flames have also achieved excellent indicators and generation performance in super-resolution reconstruction tasks. These works demonstrate that diffusion models have promising application prospects in this field. However, compared to two-dimensional data, the complexity of three-dimensional data places higher demands on computational resources. Furthermore, the inference process of diffusion models typically requires numerous sampling steps to gradually reconstruct the data distribution, resulting in excessively long overall inference times and low efficiency. This makes it difficult to generate high-quality reconstructed data within a reasonable timeframe, limiting its application in real-world environments. These issues urgently need to be addressed through algorithm optimization and technological improvements to enhance the model's practicality and efficiency. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm. By introducing a three-dimensional convolutional architecture network based on the interval diffusion paradigm, and combining the residuals of high- and low-resolution images as diffusion noise and decreasing weight sequence optimization information transmission, this method solves the technical problems of detail loss and low generation quality in the super-resolution reconstruction of three-dimensional swirling flame data.

[0005] The specific plan is as follows:

[0006] On the one hand, a three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm includes:

[0007] S1. Establish a diffusion model for three-dimensional swirling flames. Construct a forward diffusion process and a reverse denoising process between high and low resolution data in the diffusion model of three-dimensional swirling flames. In the reverse denoising process, a three-dimensional convolutional architecture network is used to learn, fit, and remove the distribution of noise data, and the residual between the high and low resolution images of the three-dimensional swirling flames is used as diffusion noise.

[0008] S2, high-resolution 3D flame training data is input into the diffusion model for 3D swirling flame. Noise is gradually added to the high-resolution 3D flame training data through the forward diffusion process to obtain the distribution of an approximate low-resolution image. Based on the distribution of the approximate low-resolution image, the intermediate data state of the flame containing noise is obtained. The intermediate data state of the flame containing noise is input into the reverse denoising process. The 3D convolutional architecture network with physical guided gradient learns the data distribution to remove noise during the reverse denoising process to obtain the reconstructed high-resolution 3D flame data. Based on the reconstructed high-resolution 3D flame data, the weights of the parameters of the 3D convolutional architecture network are iteratively updated to obtain the trained diffusion model of 3D swirling flame.

[0009] S3: Input the low-resolution 3D flame test data into the trained 3D swirling flame diffusion model, and obtain high-resolution 3D flame data by reconstructing the low-resolution 3D flame test data.

[0010] Furthermore, in S1, the calculation formula for the forward diffusion process is as follows:

[0011] q(x T |x HR ,x LR )=N(x T ;x HR +η 1:T r,κ 2 η T I);

[0012] r = interpolatedx LR -x HR ;

[0013] Where, x HR and x LR Represents high-resolution and low-resolution three-dimensional swirling flame temperature field data; r represents diffusion noise; κ represents the hyperparameter controlling the noise variance; I represents the identity matrix; q(x T |x HR ,x LR ) represents the complete forward diffusion process; x HR +η 1:T r represents the process of gradually adding diffused noise; T represents the parameterized Markov chain that requires T steps in the forward diffusion process; interpolated represents the interpolation operation on the data; x T This represents the noise data after T time steps; η T η represents the noise figure at step T; 1:T r represents the cumulative noise figure and diffused noise from step 1 to step T; N(x t ;x HR +η 1:T r,κ2 η T I) represents the variable x T Follows the mean x HR +η 1:T r, variance κ 2 η T I follows a normal distribution.

[0014] Furthermore, in S1, the calculation formula for the reverse denoising process is as follows:

[0015]

[0016] Where, p θ () represents the inverse denoising process for model parameter vector θ; x t This represents the three-dimensional swirling flame data at time step t; x t-1 This represents the three-dimensional swirling flame data at time step t-1; η t α represents the noise figure at step t; t Indicates the intermediate parameter, α t =η t -η t-1 κ represents the hyperparameter controlling the noise variance; t represents the corresponding time step in the denoising process.

[0017] Furthermore, a 3D convolutional architecture network with physically guided gradients learns the data distribution for noise removal during the inverse denoising process, as calculated in the following formula:

[0018]

[0019] in, For p θ (x t-1 |x t ,x LR The inverse denoising process involves adding a physical guiding gradient c to obtain a learned, noise-removed data distribution; Z is the normalization parameter. The conditional distribution is updated using gradients.

[0020] Furthermore, the process of obtaining the physical guided gradient c is as follows:

[0021] Obtain the formula for calculating the gradient of a partial differential equation:

[0022]

[0023] ξ=(ξ1,ξ2,…,ξ i )∈Ω;

[0024] Where G is the differential operator of the partial differential equation; u is the solution function of the partial differential equation, representing the distribution state of the physical field in space; ξ represents the spatial coordinate variable, in the three-dimensional case ξ=(ξ1,ξ2,ξ3) and ξ1=x, ξ2=y, ξ3=z; Ω represents the parameters of the partial differential equation; Ω represents the computational domain of the partial differential equation.

[0025] Let u = x t The physical guiding gradient c is calculated as follows:

[0026]

[0027] r t ≠0;

[0028]

[0029] Where, r t The residual is the partial differential equation.

[0030] Furthermore, the three-dimensional swirling flame data x at time step t-1 during the reverse denoising process. t-1 The calculation formula is as follows:

[0031]

[0032] Among them, f θ (c,x LR ,x t ,t) is f θ (x LR ,x t ,x LR The neural network after adding the physical guide gradient c; ∈ represents noise that follows a standard normal distribution.

[0033] Furthermore, the three-dimensional convolutional architecture network includes a downsampling module, a skip connection module, and an upsampling module:

[0034] The downsampling module performs layer-by-layer feature extraction on the three-dimensional swirling flame data. During the feature extraction process, a self-attention mechanism is introduced to enhance the perception of flame details. The feature of the three-dimensional swirling flame data that retains detailed information is obtained through a weight sequence that decreases with the number of encoding layers.

[0035] The jump connection module weighted transfers the features of the 3D swirling flame data, which retain detailed information, to the corresponding upsampling level to assist in high-resolution reconstruction;

[0036] The upsampling module performs deconvolution operations on the 3D swirling flame data features that retain detailed information passed from the skip connection module, gradually restoring the resolution of the data and obtaining reconstructed high-resolution 3D flame data.

[0037] On the other hand, a three-dimensional swirling flame super-resolution reconstruction system based on the interval diffusion paradigm includes:

[0038] The model building module is used to build a diffusion model for a three-dimensional swirling flame. It constructs a forward diffusion process and a reverse denoising process between high and low resolution data in the diffusion model of the three-dimensional swirling flame. In the reverse denoising process, a three-dimensional convolutional architecture network is used to learn and fit the distribution of noise data and remove it. The residual between the high and low resolution images of the three-dimensional swirling flame is used as the diffusion noise.

[0039] The training module is used to input high-resolution 3D flame training data into the diffusion model for 3D swirling flames. Through the forward diffusion process, noise is gradually added to the high-resolution 3D flame training data to obtain the distribution of an approximate low-resolution image. Based on the distribution of the approximate low-resolution image, the intermediate data state of the flame containing noise is obtained. The intermediate data state of the flame containing noise is input into the reverse denoising process. Through a 3D convolutional architecture network with physically guided gradients, the noise-removed data distribution is learned in the reverse denoising process to obtain reconstructed high-resolution 3D flame data. Based on the reconstructed high-resolution 3D flame data, the weights of the parameters of the 3D convolutional architecture network are iteratively updated to obtain the trained diffusion model of the 3D swirling flame.

[0040] The reconstruction module is used to input low-resolution 3D flame test data into a trained 3D swirling flame diffusion model, and obtain high-resolution 3D flame data by reconstructing the low-resolution 3D flame test data.

[0041] The present invention adopts the above technical solution and has the following beneficial effects:

[0042] (1) This invention constructs a forward diffusion and reverse denoising process to convert between high and low resolution three-dimensional swirling flame data. It uses a three-dimensional convolutional architecture network to learn and remove noise distribution, and uses the residual between high and low resolution images as diffusion noise, so that the low resolution flame image can gradually recover high resolution details, thus realizing high-precision super-resolution reconstruction of flame structure.

[0043] (2) This invention uses a three-dimensional convolutional network with physical guidance gradient to guide the model to learn a data distribution that is more in line with the actual physical laws during the reverse denoising process. It optimizes the denoising process by calculating gradients through partial differential equations, which enhances the model's understanding and processing ability of complex physical field data. It also effectively reduces the local feature smoothing problem caused by traditional interpolation algorithms and improves the authenticity and reliability of the reconstructed data.

[0044] (3) This invention integrates downsampling, skip connections and upsampling modules through a three-dimensional convolutional architecture network, and introduces a self-attention mechanism to enhance the perception of flame details. It retains as much detail information as possible during feature extraction and data recovery, and finally achieves efficient training by iteratively updating network parameters to obtain high-quality high-resolution flame data reconstruction results. Attached Figure Description

[0045] Figure 1 This is a flowchart of the three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm according to an embodiment of the present invention;

[0046] Figure 2 This is a model diagram of the three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm according to an embodiment of the present invention;

[0047] Figure 3 This is a schematic diagram of the network architecture for the reverse denoising process according to an embodiment of the present invention;

[0048] Figure 4 This is a flowchart illustrating the training and testing process according to an embodiment of the present invention.

[0049] Figure 5 This is a diagram of a three-dimensional swirling flame super-resolution reconstruction system based on the interval diffusion paradigm, according to an embodiment of the present invention. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0051] like Figure 1 As shown, the present invention provides a three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm, comprising:

[0052] S1. Establish a diffusion model for three-dimensional swirling flames. Construct a forward diffusion process and a reverse denoising process between high and low resolution data in the diffusion model of three-dimensional swirling flames. In the reverse denoising process, a three-dimensional convolutional architecture network is used to learn, fit, and remove the distribution of noise data, and the residual between the high and low resolution images of the three-dimensional swirling flames is used as diffusion noise.

[0053] Specifically, such as Figure 2 As shown, the forward diffusion stage refers to the noise addition stage of the diffusion model. Starting from a high-resolution initial data distribution, it progressively updates the state through a series of steps until it approximates the low-resolution flame data distribution. In diffusion models, forward diffusion typically involves progressively updating the probability distribution to simulate the propagation and attenuation of noise. The reverse process, based on forward diffusion, starts from data x... T We begin iterative sampling and eventually reconstruct the predicted data. To further improve the quality of the reconstructed data, we introduced low-resolution data as conditional information into the reverse process in practical applications. This allows the model to utilize more information about the original data during noise removal, thereby generating more accurate and detailed high-resolution reconstruction results.

[0054] S2, high-resolution 3D flame training data is input into the diffusion model for 3D swirling flame. Noise is gradually added to the high-resolution 3D flame training data through a forward diffusion process to obtain a distribution of an approximate low-resolution image. Based on the distribution of the approximate low-resolution image, the intermediate flame data state containing noise is obtained. The intermediate flame data state containing noise is input into the reverse denoising process. A 3D convolutional architecture network with physically guided gradients learns the data distribution to remove noise during the reverse denoising process, obtaining reconstructed high-resolution 3D flame data. Based on the reconstructed high-resolution 3D flame data, the weights of the 3D convolutional architecture network parameters are iteratively updated to obtain the trained 3D swirling flame diffusion model.

[0055] Specifically, the calculation formula for the forward diffusion process is as follows:

[0056] q(x T |x HR ,x LR )=N(x T ;x HR +η 1:T r,κ 2 η T I);

[0057] r = interpolatedx LR -x HR ;

[0058] Where r represents the diffuse noise; κ represents the hyperparameter controlling the noise variance; I represents the identity matrix; q(x T |x HR ,x LR ) represents the complete forward diffusion process; x HR +η 1:T r represents the process of gradually adding diffused noise; T represents the parameterized Markov chain that requires T steps in the forward diffusion process; interpolated represents the interpolation operation on the data; x T This represents the noise data after T time steps; η T η represents the noise figure at step T; 1:T r represents the cumulative noise figure and diffused noise from step 1 to step T; N(x T ;x HR +η 1:T r,κ 2 η TI) represents the variable x T Follows the mean x HR +η 1:T r, variance κ 2 η T I follows a normal distribution.

[0059] Specifically, the approximation in the distribution of approximate low-resolution images means x T ~N(x) LR ,κ 2 I) Follows a mean of x LR The normal distribution;

[0060] Specifically, the calculation formula for the reverse denoising process is as follows:

[0061]

[0062] Where, p θ () represents the inverse denoising process for model parameter vector θ; x t This represents the three-dimensional swirling flame data at time step t; x t-1 This represents the three-dimensional swirling flame data at time step t-1; η t α represents the noise figure at step t; t Indicates the intermediate parameter, α t =η t -η t-1 κ represents the hyperparameter controlling the noise variance; t represents the corresponding time step in the denoising process.

[0063] In this embodiment, the reverse process is based on forward diffusion, starting from data x. T We begin iterative sampling and eventually reconstruct the predicted data. In this embodiment, both training and testing include three-dimensional swirling flame data observed under different combustion chamber conditions and times. Each data set for a single condition and time contains multiple data points of different resolutions, denoted as a data unit. These data units are represented by a three-dimensional coordinate axis. Each coordinate point on this axis corresponds to the temperature, pressure, and concentration of a specific reactant at that point in the combustion chamber. High-resolution data units represent data with denser coordinate points, while low-resolution data represents units with sparser coordinate points. For example, under a specific combustion condition and time, there are multiple three-dimensional coordinate axes with different resolutions, such as 16×16×32, 32×32×64, and 64×64×128. Taking a 64×64×128 resolution data unit as an example, there are 524,288 coordinate points, each corresponding to three values ​​representing the temperature, pressure, and concentration of a specific reactant at that point in the combustion chamber. In this embodiment, two sets of data are selected and determined as high-resolution data x based on their resolution relationship.HR and low-resolution data x LR .

[0064] Specifically, to improve the quality of the reconstructed data, we introduce low-resolution data as conditional information into the reverse process in practical applications. This allows the model to utilize more information about the original data during noise removal, thereby generating more accurate and detailed high-resolution reconstruction results. The mean and variance of the 3D swirling flame data are expressed as follows:

[0065]

[0066] Used to predict x HR The neural network is represented as f θ (x t ,x LR ,t), where θ represents the parameters of the model.

[0067] Specifically, a 3D convolutional architecture network with physically guided gradients learns the data distribution for noise removal during the inverse denoising process. The calculation formula is as follows:

[0068]

[0069] in, For p θ (x t-1 |x t ,x LR Add a physical guidance gradient c, such as the temperature gradient, pressure gradient, and reactant concentration gradient of the flame field in the combustion chamber, to obtain a reverse denoising process of the data distribution for learning and removing noise; Z is the normalization parameter. The conditional distribution is updated using gradients.

[0070] Specifically, the process of obtaining the physical guided gradient c is as follows:

[0071] Obtain the formula for calculating the gradient of a partial differential equation:

[0072]

[0073] ξ=(ξ1,ξ2,…,ξ i )∈Ω;

[0074] Where G is the differential operator of the partial differential equation; u is the solution function of the partial differential equation, representing the distribution state of the physical field in space; ξ represents the spatial coordinate variable, in the three-dimensional case ξ=(ξ1,ξ2,ξ3) and ξ1=x, ξ2=y, ξ3=z; Ω represents the parameters of the partial differential equation; Ω represents the computational domain of the partial differential equation.

[0075] Let u = xt The physical guiding gradient c is calculated as follows:

[0076]

[0077] r t ≠0;

[0078]

[0079] Where, x t This represents the distribution of intermediate data at time step t during the reverse denoising process; r t For the residuals of partial differential equations, in this embodiment, this part mainly involves the acquisition of gradient values. Through mathematical derivation, the gradient components of physical gradients such as temperature gradient or concentration gradient in three-dimensional space are calculated.

[0080] Specifically, in the reverse denoising process, x at time step t-1 t-1 With gradient guidance, sampling is performed from the following normally distributed noise:

[0081]

[0082] The reverse denoising process is represented as:

[0083]

[0084] Specifically, the three-dimensional swirling flame data x at time step t-1 during the reverse denoising process, constrained by the above two conditions. t-1 The calculation formula is as follows:

[0085]

[0086] Among them, f θ (c,x LR ,x t ,t) is f θ (x LR ,x t ,x LR The neural network after adding the physical guide gradient c; ∈ represents noise that follows a standard normal distribution.

[0087] Specifically, during the network setup phase, the first step is to embed time information into the model so that it can model time itself. This helps the model learn the dynamic changes and evolution of data over time. See also Figure 3 As shown, the constructed deep learning network f θThe network architecture is based on U-Net, where each 3D residual convolutional module mainly consists of a batch normalization layer, a 3D convolution, and an activation function layer. Some downsampling and upsampling modules contain self-attention mechanism layers. To preserve the true details of the data as much as possible during model reconstruction, a set of sequences that decrease with the number of encoding layers L is designed. The fact that w1 approaches 1 helps to effectively transmit detailed data information and maintains the network's non-linearity, thereby improving the quality of model generation. The data distribution obtained in the reverse 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.

[0088] Specifically, the 3D convolutional architecture network includes mutually cooperating downsampling modules, skip connection modules, and upsampling modules:

[0089] The downsampling module performs layer-by-layer feature extraction on the three-dimensional swirling flame data. During the feature extraction process, a self-attention mechanism is introduced to enhance the perception of flame details. The feature of the three-dimensional swirling flame data that retains detailed information is obtained through a weight sequence that decreases with the number of encoding layers.

[0090] The jump connection module weighted transfers the features of the 3D swirling flame data, which retain detailed information, to the corresponding upsampling level to assist in high-resolution reconstruction;

[0091] The upsampling module performs deconvolution operations on the 3D swirling flame data features that retain detailed information passed from the skip connection module, gradually restoring the resolution of the data and obtaining reconstructed high-resolution 3D flame data.

[0092] In this embodiment, the 3D convolutional architecture uses U-Net as the main network architecture, consisting of downsampling modules, skip connection modules, and upsampling modules. The upsampling and upsampling convolutional modules are all 3D residual convolutional modules. Each 3D residual convolutional module undergoes batch normalization layer 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. To preserve the true details of the data as much as possible during model reconstruction, a set of sequences that decrease with increasing coding layer number L is designed. The fact that w1 approaches 1 helps to effectively transmit detailed data information and maintains the network's nonlinearity, thereby improving the quality of model generation. Some downsampling and upsampling modules further include 3D Swin Transformer blocks, which alternate between 3D window multi-head self-attention (3D W-MSA) and 3D shifted window multi-head self-attention (3D SW-MSA). The window is divided into M×M×M non-overlapping cubes, and the attention calculation method is as follows:

[0093]

[0094] Where B is the learnable 3D relative position bias matrix; simultaneously, multi-scale feature maps are calculated and generated in the downsampling module, as expressed by the formula:

[0095]

[0096] The skip connection module further includes an axially sparse attention layer, which calculates attention weights only along a single dimension (such as the depth axis), as follows:

[0097]

[0098] in, The AxialAttn parameter represents feature concatenation and is calculated as follows:

[0099]

[0100] The axial attention is calculated only along a single spatial dimension to balance computational efficiency with global modeling capability.

[0101] Specifically, in this embodiment, to prevent the accumulation of errors in each noise prediction step from causing deviations in the final reconstruction result, the objective function used by the model differs from that of traditional diffusion models that compare the noise predicted in the reverse denoising process with the noise added in the forward diffusion process. Instead, it utilizes the diffusion increment and coefficients designed in the forward process. The optimization is performed directly on the reconstructed flow field data generated by the model. The objective function is written in the following form:

[0102]

[0103] This method avoids the complexity and error accumulation problems caused by stepwise noise prediction, simplifies the training process, and improves the stability and accuracy of the output. To further ensure that the reconstructed 3D swirling flame data conforms to the fundamental physical laws of fluid mechanics and combustion reaction, conservation law constraints are introduced as additional loss terms. These include mass conservation and momentum conservation.

[0104] Loss due to conservation of mass:

[0105]

[0106] Where ρ represents fluid density, u represents velocity field, and t represents time.

[0107] Momentum conservation loss:

[0108]

[0109] Where ρ represents the pressure field and u represents the dynamic viscosity.

[0110] Therefore, the joint objective function is expressed as:

[0111]

[0112] Here, λ1 and λ2 represent the weight hyperparameters that can be determined through cross-validation.

[0113] S3: Input the low-resolution 3D flame test data into the trained 3D swirling flame diffusion model, and obtain high-resolution 3D flame data by reconstructing the low-resolution 3D flame test data.

[0114] Specifically, after S3, the quality of high-resolution 3D flame data is evaluated using MAE, PSNR, and SSIM, as follows:

[0115]

[0116] Where, x HR ,x SR These represent the high-resolution and super-resolution reconstructed 3D flame data, respectively. MAX x The maximum value of x in the three-dimensional data is represented by the super-resolution swirling flame x. SR With high-resolution swirling flame x HR The root mean square error, C1 and C2 represent the mean, variance, and covariance of the super-resolution and high-resolution data, respectively; C1 and C2 are constants; SSIM ranges from -1 to 1.

[0117] In this embodiment, as Figure 4As shown, during the training and testing phases, after a fixed number of steps, the quality of the reconstructed 3D flame is evaluated during the training phase. PSNR, SSIM, and MAE metrics are used to assess the difference between the reconstructed high-resolution 3D flame and the 3D flame data generated by the fine mesh. MAE is a metric used to measure the difference between two datasets, often used to evaluate the error between the model's predicted value and the true value. Its principle is to quantify the average error between two datasets by calculating the absolute value of the difference at each corresponding position and taking the average. PSNR is a metric used to measure the quality of image or audio signals, commonly used in image compression and other fields to measure signal reconstruction quality. It is based on the error between corresponding pixels, i.e., error-sensitive image quality evaluation, and its calculation formula relies on the Mean Absolute Error (MAE). SSIM, or Structural Similarity, is a metric used to measure the structural similarity between two images. It is a widely used quality assessment metric in computer vision, considering information on brightness, contrast, and structure, and is used to compare the similarity between the original image and the processed image. Through a series of quantitative and qualitative comparisons and verifications, the model demonstrates excellent performance in super-resolution reconstruction of three-dimensional swirling flame flow fields. Compared to previous models and methods, this model shows significant improvements in both performance and efficiency. It not only generates results that closely approximate high-resolution data flow and hierarchical detail, providing a valid basis for downstream tasks such as combustion diagnostics and chemical analysis, but also reduces computational resource consumption while maintaining high generation efficiency. Therefore, this model has significant practical applications.

[0118] Specifically, in this embodiment, a Markov chain is established between high-resolution and low-resolution 3D swirling flame data for a diffusion process. The residual between the high- and low-resolution 3D swirling flames is used as diffusion noise, and a set of coefficients that increases with each sampling step is designed. A forward diffusion process and a physically guided reverse denoising process are established. A 3D convolutional architecture network is defined to learn and fit the distribution of noise-removed data during the reverse denoising process. During training, noise is gradually added to the high-resolution 3D flame training data through the forward diffusion process to obtain a noise distribution approximating the low-resolution image. The obtained noise distribution is combined with the low-resolution 3D flame training data to participate in the reverse denoising process. The 3D convolutional architecture network learns the noise-removed data distribution during the reverse denoising process and gradually reconstructs the high-resolution 3D flame data in conjunction with the reverse denoising process. The physically guided gradient and mean squared error loss are calculated during the reverse denoising process, and the weights of the 3D convolutional architecture network parameters are iteratively updated. The network update is stopped according to set conditions to obtain a trained reverse denoising inference model. The low-resolution 3D flame test data is input into the completed training model to reconstruct high-resolution 3D flame data, and the quality of the reconstructed high-resolution 3D flame data is evaluated.

[0119] like Figure 5 As shown, this embodiment also discloses a three-dimensional swirling flame super-resolution reconstruction system based on the interval diffusion paradigm, characterized in that it includes:

[0120] The model building module 51 is used to build a diffusion model for a three-dimensional swirling flame. It constructs a forward diffusion process and a reverse denoising process between high and low resolution data in the diffusion model of the three-dimensional swirling flame. In the reverse denoising process, a three-dimensional convolutional architecture network is used to learn and fit the distribution of noise data and remove it. The residual between the high and low resolution images of the three-dimensional swirling flame is used as the diffusion noise.

[0121] Training module 52 is used to input high-resolution three-dimensional flame training data into the diffusion model for three-dimensional swirling flames. Through the forward diffusion process, noise is gradually added to the high-resolution three-dimensional flame training data to obtain the distribution of an approximate low-resolution image. Based on the distribution of the approximate low-resolution image, the intermediate data state of the flame containing noise is obtained. The intermediate data state of the flame containing noise is input into the reverse denoising process. Through the three-dimensional convolutional architecture network with physical guided gradient, the noise-removed data distribution is learned in the reverse denoising process to obtain the reconstructed high-resolution three-dimensional flame data. Based on the reconstructed high-resolution three-dimensional flame data, the weights of the parameters of the three-dimensional convolutional architecture network are iteratively updated to obtain the trained diffusion model of the three-dimensional swirling flame.

[0122] The reconstruction module 53 is used to input low-resolution three-dimensional flame test data into the trained three-dimensional swirling flame diffusion model, and obtain high-resolution three-dimensional flame data by reconstructing the low-resolution three-dimensional flame test data.

[0123] The specific implementation of the three-dimensional swirling flame super-resolution reconstruction system based on the interval diffusion paradigm is the same as that of the three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm, and will not be described again in this embodiment.

[0124] Although the invention has been specifically shown and described in conjunction with preferred embodiments, those skilled in the art should understand that various changes in form and detail may be made to the invention without departing from the spirit and scope of the invention as defined in the appended claims, all of which shall be within the scope of protection of the invention.

Claims

1. A method for super-resolution reconstruction of three-dimensional swirling flames based on the interval diffusion paradigm, characterized in that, include: S1. Establish a diffusion model for three-dimensional swirling flames, and construct a forward diffusion process and a reverse denoising process between high and low resolution data in the diffusion model of three-dimensional swirling flames. In the reverse denoising process, a three-dimensional convolutional architecture network is used to learn and fit the distribution of noise data and remove the noise data, and the residual between the high and low resolution images of the three-dimensional swirling flame is used as the diffusion noise. S2, high-resolution 3D flame training data is input into the diffusion model for 3D swirling flame. Noise is gradually added to the high-resolution 3D flame training data through the forward diffusion process to obtain the distribution of an approximate low-resolution image. Based on the distribution of the approximate low-resolution image, the intermediate data state of the flame containing noise is obtained. The intermediate data state of the flame containing noise is input into the reverse denoising process. The 3D convolutional architecture network with physical guided gradient learns the data distribution to remove noise in the reverse denoising process to obtain the reconstructed high-resolution 3D flame data. Based on the reconstructed high-resolution 3D flame data, the weights of the parameters of the 3D convolutional architecture network are iteratively updated to obtain the trained diffusion model of 3D swirling flame. S3: Input the low-resolution 3D flame test data into the trained 3D swirling flame diffusion model, and obtain high-resolution 3D flame data by reconstructing the low-resolution 3D flame test data.

2. The method for super-resolution reconstruction of three-dimensional swirling flames based on the interval diffusion paradigm according to claim 1, characterized in that, In S1, the calculation formula for the forward diffusion process is as follows: q(x T |x HR ,x LR )=N(x T ;x HR +η 1:T r,k 2 η T I); r=interpolatedx LR -x HR ; Where, x HR and x LR Represents high-resolution and low-resolution three-dimensional swirling flame temperature field data; r represents diffusion noise; κ represents the hyperparameter controlling the noise variance; I represents the identity matrix; q(x T |x HR ,x LR ) represents the complete forward diffusion process; x HR +η 1:T r represents the process of gradually adding diffused noise; T represents the parameterized Markov chain that requires T steps in the forward diffusion process; interpolated represents the interpolation operation on the data; x T This represents the noise data after T time steps; η T η represents the noise figure at step T; 1:T r represents the cumulative noise figure and diffused noise from step 1 to step T; N(x T ;x HR +η 1:T r,κ 2 η T I) represents the variable x T Follows the mean x HR +η 1:T r, variance κ 2 η T I follows a normal distribution.

3. The three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm according to claim 2, characterized in that, In S1, the calculation formula for the reverse denoising process is as follows: Where, p θ () represents the inverse denoising process for model parameter vector θ; x t This represents the three-dimensional swirling flame data at time step t; x t-1 This represents the three-dimensional swirling flame data at time step t-1; η t α represents the noise figure at step t; t Indicates the intermediate parameter, α t =η t -η t-1 κ represents the hyperparameter controlling the noise variance; t represents the corresponding time step in the denoising process.

4. The three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm according to claim 3, characterized in that, A 3D convolutional architecture network guided by physical gradients learns the data distribution for noise removal during the inverse denoising process. The calculation formula is as follows: in, For p θ (x t-1 |x t ,x LR The inverse denoising process involves adding a physical guiding gradient c to obtain a learned, noise-removed data distribution; Z is the normalization parameter. The conditional distribution is updated using gradients.

5. The three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm according to claim 4, characterized in that, The process of obtaining the physical guided gradient c is as follows: Obtain the formula for calculating the gradient of a partial differential equation: ξ=(ξ1,ξ2,…,ξ i )∈Ω; Where G is the differential operator of the partial differential equation; u is the solution function of the partial differential equation, representing the distribution state of the physical field in space; ξ represents the spatial coordinate variable, in the three-dimensional case ξ=(ξ1,ξ2,ξ3) and ξ1=x, ξ2=y, ξ3=z; Ω represents the parameters of the partial differential equation; Ω represents the computational domain of the partial differential equation. Let u = x t The physical guiding gradient c is calculated as follows: r t ≠0； Where, r t The residual is the partial differential equation.

6. The three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm according to claim 3, characterized in that, The three-dimensional swirling flame data x at time step t-1 during the reverse denoising process t-1 The calculation formula is as follows: Among them, f θ (c,x LR ,x t ,t) is f θ (x LR ,x t ,x LR The neural network after adding the physical guide gradient c; ∈ represents noise that follows a standard normal distribution.

7. The three-dimensional swirling flame super-resolution reconstruction method based on the interval diffusion paradigm according to claim 1, characterized in that, The three-dimensional convolutional architecture network includes a downsampling module, a skip connection module, and an upsampling module: The downsampling module performs layer-by-layer feature extraction on the three-dimensional swirling flame data. During the feature extraction process, a self-attention mechanism is introduced to enhance the perception of flame details. The feature of the three-dimensional swirling flame data that retains detailed information is obtained through a weight sequence that decreases with the number of encoding layers. The jump connection module weighted transfers the features of the 3D swirling flame data, which retain detailed information, to the corresponding upsampling level to assist in high-resolution reconstruction; The upsampling module performs deconvolution operations on the 3D swirling flame data features that retain detailed information passed from the skip connection module, gradually restoring the resolution of the data and obtaining reconstructed high-resolution 3D flame data.

8. A three-dimensional swirling flame super-resolution reconstruction system based on the interval diffusion paradigm, characterized in that, include: The model building module is used to build a diffusion model for a three-dimensional swirling flame. It constructs a forward diffusion process and a reverse denoising process between high and low resolution data in the diffusion model of the three-dimensional swirling flame. In the reverse denoising process, a three-dimensional convolutional architecture network is used to learn and fit the distribution of noise data and remove it. The residual between the high and low resolution images of the three-dimensional swirling flame is used as the diffusion noise. The training module is used to input high-resolution 3D flame training data into the diffusion model for 3D swirling flames. Through the forward diffusion process, noise is gradually added to the high-resolution 3D flame training data to obtain the distribution of an approximate low-resolution image. Based on the distribution of the approximate low-resolution image, the intermediate data state of the flame containing noise is obtained. The intermediate data state of the flame containing noise is input into the reverse denoising process. Through a 3D convolutional architecture network with physically guided gradients, the noise-removed data distribution is learned in the reverse denoising process to obtain reconstructed high-resolution 3D flame data. Based on the reconstructed high-resolution 3D flame data, the weights of the parameters of the 3D convolutional architecture network are iteratively updated to obtain the trained diffusion model of 3D swirling flames. The reconstruction module is used to input low-resolution 3D flame test data into a trained 3D swirling flame diffusion model, and obtain high-resolution 3D flame data by reconstructing the low-resolution 3D flame test data.

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