Irregular sampling shear layer flow field prediction method and system based on improved depth operator network

Abstract

The invention relates to an irregular sampling shear layer flow field prediction method based on an improved DeepONet, and the method comprises the steps: S1, constructing a data set covering typical flow characteristics of a shear layer through numerical simulation or experimental measurement; s2, designing and executing a non-uniform sampling strategy according to the characteristic of non-uniform speed change in the shear layer flow field to obtain a non-uniform sampling flow field data set for network training; s3, constructing and training an NFNO-DeepONet network architecture by using the non-uniform sampling flow field data set, constructing an NFNO structure with an irregular input processing capability by the network through NDFT, and combining the NFNO structure with the backbone network to form the NFNO-DeepONet neural network architecture so as to predict and model a shear layer velocity field of irregular sampling; and S4, inputting an initial condition of a to-be-predicted flow field obtained based on simulation or an experiment into the trained NFNO-DeepONet network, and executing a prediction task to obtain a prediction result. Effective modeling of non-uniform sampling data is realized, and flexible regional sampling is supported to optimize calculation efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of fluid dynamics and deep learning, and particularly relates to an irregular sampling shear layer flow field prediction method and system based on an improved DeepONet. BACKGROUND

[0002] Flow field prediction is a key problem in the field of fluid mechanics, and has wide and important value in engineering applications such as aircraft design, climate simulation, combustion control, etc. Among numerous flow field problems, shear layer flow is a typical flow structure with obvious physical characteristics and engineering significance. Shear layer is commonly found at the interface between high-speed fluid and low-speed fluid, and there is a sharp velocity gradient and unstable structure inside, which is the main occurrence area of turbulent flow development, boundary layer separation, etc.

[0003] Traditional numerical simulation methods such as finite element method and finite difference method gradually expose problems such as large computational overhead, poor generalization ability and sensitivity to grid quality in high-dimensional complex geometric problems, real-time prediction and data sparse scenes. In recent years, flow field prediction methods based on neural networks have developed rapidly and shown strong expression ability and generalization performance. However, existing neural network-based flow field prediction methods generally rely on regular and uniform grid sampling structure as a prerequisite assumption. In real engineering applications, especially in shear layer prediction tasks, input data often presents non-uniform and irregular distribution characteristics, which significantly reduces the performance of existing models, and even cannot be adapted.

[0004] Therefore, there is an urgent need for a flow field prediction method that can not only retain the expression ability of neural networks, but also effectively handle non-uniform grid sampling data to meet the modeling needs of complex regions such as shear layer. SUMMARY

[0005] To solve the problems existing in the prior art, the application provides an irregular sampling shear layer flow field prediction method and system based on an improved DeepONet. The specific scheme is as follows:

[0006] An irregular sampling shear layer flow field prediction method based on an improved DeepONet, the method comprising:

[0007] S1, constructing a data set covering typical flow characteristics of shear layer through numerical simulation or experimental measurement;

[0008] S2, designing and executing a non-uniform sampling strategy according to the characteristic of non-uniform velocity change in the shear layer flow field, to obtain a non-uniform sampling flow field data set for network training;

[0009] S3. Construct and train the NFNO-DeepONet network architecture using a non-uniformly sampled flow field dataset. The network constructs an NFNO structure with the ability to process irregular inputs through NDFT, and combines it with the backbone network to form the NFNO-DeepONet neural network architecture to predict and model the velocity field of the irregularly sampled shear layer.

[0010] S4. Input the initial conditions of the flow field to be predicted, obtained from simulation or experiment, into the trained NFNO-DeepONet network, execute the prediction task, and obtain the prediction results.

[0011] Further, step S1 includes the following steps:

[0012] Step 1.1: Determine the typical physical scenarios of shear layer flow, including free shear layer, boundary layer separation, and laminar transition types, and set different initial conditions and boundary parameters to cover representative shear layer flow structures;

[0013] Step 1.2: Generate velocity field data of the flow field using numerical simulation methods, or obtain velocity distribution data of the real flow field using experimental methods to form a shear layer velocity field sample set;

[0014] Step 1.3: Standardize, transform coordinates and unify size of the generated velocity field samples to build a dataset with a unified format. Each sample contains the initial conditions of the velocity field, the predicted target field after 1 second, and spatial location coordinate information, which serve as the basis for subsequent non-uniform sampling and network training.

[0015] Further, step S2 includes the following steps:

[0016] Step 2.1: Perform preliminary analysis on the constructed velocity field data samples, calculate the spatial gradient distribution of the velocity field in each sample, identify regions with drastic local velocity changes and regions with gentle overall changes, and divide the regions by extracting statistical features of the velocity gradient or setting thresholds;

[0017] Step 2.2: Based on the region division results, formulate a non-uniform sampling strategy; implement high-density sampling in regions with drastic changes to capture local flow characteristics; and implement low-density sampling in regions with gentle changes to reduce redundant data and computational resource consumption.

[0018] Step 2.3: Based on the above sampling strategy, spatial sampling is performed in each velocity field sample to extract the set of non-uniformly distributed coordinate points and their corresponding velocity values, and to construct a dataset containing multiple regions with different sampling densities for training the neural network.

[0019] Further, step S3 includes the following steps:

[0020] Step 3.1: Replace the original branch network in DeepONet with NFNO to process non-uniformly sampled inputs and generate feature representations that match the backbone network;

[0021] Step 3.2: Retain the backbone network in the original DeepONet structure, and use a multi-layer fully connected neural network to encode the position coordinates of each target point to be predicted, and output a spatial feature vector;

[0022] Step 3.3: Perform a dot product operation between the frequency domain feature vector output by the branch network and the spatial feature vector output by the backbone network to obtain the velocity field output at the predicted position after 1 second, thus realizing the prediction from the non-uniform initial velocity field to the future velocity field.

[0023] Step 3.4: Use the non-uniformly sampled velocity field dataset obtained in S2 to train the constructed NFNO-DeepONet network. During training, the initial velocity field is used as the network input, and the target is the true velocity value of the predicted position after 1 second. The network parameters are updated by minimizing the error between the predicted value and the true value.

[0024] Further, step 3.1 includes the following steps:

[0025] Step 3.1.1: Receive the coordinates of the non-uniformly sampled points and their corresponding initial velocity values ​​of the flow field to form the input data;

[0026] Step 3.1.2: Perform dimensionality upscaling on the input data using a fully connected neural network to obtain a high-dimensional feature representation for frequency domain modeling;

[0027] Step 3.1.3: Perform the NDFT operation on the upgraded feature representation to map it from the time domain to the frequency domain;

[0028] Step 3.1.4: Perform a linear transformation on the extracted spectral information in the frequency domain;

[0029] Step 3.1.5: Restore the linearly transformed spectral data back to the time domain using the inverse NDFT;

[0030] Step 3.1.6: Repeat steps 3.1.3 to 3.1.5 to form a multi-layer frequency domain modeling structure. The obtained results are then subjected to dimensionality reduction using a fully connected neural network.

[0031] Step 3.1.7: Perform average pooling on the dimensionality-reduced output to make its dimension consistent with the dimension of the backbone network output vector, thus forming the final output of the branch network.

[0032] Further, step S4 includes the following steps:

[0033] Step 4.1: Import the initial condition data of the flow field to be predicted, including the spatial coordinate points obtained by non-uniform sampling and their corresponding initial velocity values, as the network input;

[0034] Step 4.2: Input the initial conditions into the trained NFNO-DeepONet network, and then perform dot product operations through the respective encodings of the branch networks and the backbone network to output the prediction results;

[0035] Step 4.3: Obtain the predicted value of the velocity field after 1 second, including the velocity at each location point in the two-dimensional space.

[0036] The present invention also relates to an irregular sampling shear layer flow field prediction system based on an improved DeepONet, comprising a computer module that applies the above-described method.

[0037] Advantages

[0038] (1) This invention achieves effective modeling of non-uniformly sampled data: This invention introduces NDFT to replace the traditional FFT, constructs an NFNO network structure with the ability to process irregular inputs, and embeds it into the branch network of DeepONet, which effectively breaks through the limitation of existing neural network models on regular grids and improves the modeling accuracy and adaptability under non-uniform sampling conditions.

[0039] (2) This invention supports flexible sampling of regions to optimize computational efficiency: This invention includes an adaptive sampling strategy based on the characteristics of the velocity change of initial conditions, which performs high-density sampling in regions with drastic changes and sparse sampling in regions with gentle changes, thereby significantly reducing redundant calculations while ensuring prediction accuracy and improving overall modeling efficiency and utilization of computing resources. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the present invention;

[0041] Figure 2 This is a schematic diagram of the typical initial conditions for shear flow according to the present invention;

[0042] Figure 3 This is a schematic diagram of the sampling strategy formulated by the present invention based on the initial conditions of the shear flow;

[0043] Figure 4 This is a schematic diagram of the NFNO-DeepONet network structure in this invention;

[0044] Figure 5 This is a schematic diagram comparing the flow field prediction results obtained by the method of this invention with the reference results. Detailed Implementation

[0045] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0046] like Figure 1 As shown, the present invention provides a method for predicting irregular sampling shear layer flow fields based on an improved DeepONet, comprising the following steps:

[0047] Step 1: Construct a dataset covering typical flow characteristics of the shear layer through numerical simulation or experimental measurement.

[0048] Step 1.1: Based on the typical characteristics of shear layer flow, select representative physical scenarios for modeling, including free shear layers, boundary layer separation, laminar transition, and other types. Set different initial velocity distributions, boundary conditions, perturbation parameters, and other conditions for each type of scenario to cover multiple shear layer morphologies, thereby improving the diversity and generalization ability of the training data.

[0049] Step 1.2: Generate velocity field samples using numerical simulation; or collect velocity distribution data of real flow fields through experiments. All samples contain the two-dimensional velocity distribution at a certain initial moment, that is, the initial conditions of the flow field and the corresponding velocity field after a fixed delay of 1 second, forming training sample pairs.

[0050] Step 1.3: Preprocess the velocity field samples obtained from simulation or experiment, including velocity normalization, coordinate standardization, and size unification. All samples are converted to a uniform spatial resolution and coordinate range through interpolation or cropping. Each sample ultimately contains three types of data: the initial velocity field, the target velocity field after 1 second, and the corresponding two-dimensional coordinate position array, serving as the foundation dataset for subsequent non-uniform sampling and network training.

[0051] Step 2: To address the non-uniform velocity variation in the shear layer flow field, a non-uniform sampling strategy is designed and implemented to obtain a non-uniform sampled flow field dataset for network training.

[0052] like Figure 2 As shown, a typical initial condition for shear flow is provided. To improve the model's ability to model key regions and increase computational efficiency, this invention designs a non-uniform sampling strategy based on velocity gradients to generate the non-uniform sampled flow field dataset required for training. Specifically, it includes the following steps:

[0053] Step 2.1: Analyze the velocity field dataset constructed in Step 1 and calculate the spatial gradient distribution of the velocity field in each sample. Estimate the rate of velocity change at each location point using the first-order difference or smooth gradient operator. Further, based on statistical characteristics such as the maximum gradient magnitude, mean, and standard deviation, or by setting a fixed threshold, divide the flow field into regions with drastic velocity changes and regions with gradual velocity changes.

[0054] Step 2.2: Based on the above region division results, formulate a non-uniform sampling strategy. The specific sampling strategy is as follows: Figure 3 As shown, Figure 3 The black horizontal lines represent the selected sampling locations. High-density sampling is used in areas with drastic velocity changes to capture local flow characteristics in detail; low-density sampling is used in areas with slow changes to avoid redundant information, thus achieving a balance between focusing on key areas and saving computational resources.

[0055] Step 2.3: Execute a sampling strategy on each velocity field sample to extract a set of two-dimensional coordinate points and their corresponding initial velocity values, constructing training samples with non-uniform spatial distribution characteristics. The resulting non-uniform sampled flow field dataset contains multiple regions with different sampling densities and retains information such as initial conditions, target velocity field, and coordinate positions, which can be used for training neural network models.

[0056] Step 3: Construct and train the NFNO-DeepONet network architecture using a non-uniformly sampled flow field dataset.

[0057] To achieve accurate prediction of the velocity field of the shear layer under irregular sampling, this embodiment constructs an improved neural network architecture based on the DeepONet structure, namely NFNO-DeepONet. This network architecture replaces the traditional FFT with NDFT, constructs an NFNO module, and completely replaces the branch networks in the original DeepONet. Combined with the original backbone network, it forms a deep learning operator structure capable of processing non-uniformly sampled data. The network architecture of NFNO-DeepONet is as follows: Figure 4 As shown, the specific steps include:

[0058] Step 3.1: Replace the branch networks in DeepONet with the NFNO module to handle non-uniformly sampled inputs and generate feature representations with the same dimensionality as the backbone network output. Its specific structure is as follows:

[0059] Step 3.1.1: Receive coordinate points of non-uniform sampling and the corresponding initial velocity values ​​of the flow field This constitutes the input data;

[0060] Step 3.1.2: Set the initial velocity value of the flow field Feed into a fully connected neural network We perform an up-dimensional mapping to obtain a high-dimensional feature representation for frequency domain modeling.

[0061] Step 3.1.3: Perform the NDFT operation on the upgraded feature representation to map it from the time domain to the frequency domain;

[0062] Step 3.1.4: Perform a linear transformation on the extracted spectral data in the frequency domain;

[0063] Step 3.1.5: Restore the linearly transformed spectral data back to the time domain using the inverse NDFT;

[0064] Step 3.1.6: Repeat steps 3.1.3 to 3.1.5 several times to form a multi-layer Fourier layer structure, and pass the final output through a fully connected neural network. Perform dimensionality reduction;

[0065] Step 3.1.7: Perform average pooling on the dimensionality-reduced output. This ensures that the dimension of the branch network matches the dimension of the output vector of the backbone network, forming the final output of the branch network. .

[0066] Step 3.2: The backbone network retains the original DeepONet structure and uses a multi-layer fully connected neural network to receive the two-dimensional coordinates of the target point to be predicted. It outputs the spatial feature vector related to the location of that point. , for subsequent fusion.

[0067] Step 3.3: Convert the frequency domain feature vector generated by the branch network Spatial feature vectors generated by the backbone network The velocity field of the target point is predicted after 1 second by fusing the data through dot product operations. This enables the prediction of future velocity fields from non-uniform initial velocity fields.

[0068] Step 3.4: Train the constructed NFNO-DeepONet network using the non-uniform sampled velocity field dataset generated in Step 2. During training, the initial velocity field is used as input, and the actual velocity value at the corresponding location after 1 second is used as the supervision target. The mean squared error (MSE) loss function is adopted, and the network parameters are updated by backpropagation using the Adam optimizer. After training, the model has the ability to predict the evolution of the corresponding velocity field from any non-uniform initial conditions, and is suitable for flow field modeling tasks in complex regions such as shear layers.

[0069] Step 4: Input the initial conditions of the flow field to be predicted, obtained from simulation or experiment, into the trained NFNO-DeepONet network, execute the prediction task, and output the prediction results. This includes the following steps:

[0070] Step 4.1: Import the initial condition data for the flow field to be predicted. The initial conditions are sampled in a non-uniform manner and include a set of spatial coordinate points. and its corresponding initial velocity value , as input data for the network;

[0071] Step 4.2: Input the initial condition data described above into the trained NFNO-DeepONet neural network model. The branch network performs frequency domain modeling on the input data and generates frequency domain feature vectors, while the backbone network encodes the coordinates of the location to be predicted to generate spatial feature vectors. Finally, the two are fused through a dot product operation to complete the velocity prediction at the relevant location.

[0072] Step 4.3: Figure 5 It includes the predicted target velocity field after 1 second and a comparison with the reference result. Experiments have verified that the prediction accuracy of the network model trained in this invention is above 94%.

[0073] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for predicting irregularly sampled shear layer flow fields based on an improved DeepONet, characterized in that, The method includes: S1. Construct a dataset covering typical flow characteristics of the shear layer through numerical simulation or experimental measurement; S2. To address the non-uniform velocity variation in the shear layer flow field, a non-uniform sampling strategy is designed and implemented to obtain a non-uniform sampled flow field dataset for network training. S3. Construct and train the NFNO-DeepONet network architecture using a non-uniformly sampled flow field dataset. The network constructs an NFNO structure with the ability to process irregular inputs through NDFT, and combines it with the backbone network to form the NFNO-DeepONet neural network architecture to predict and model the velocity field of the irregularly sampled shear layer. S4. Input the initial conditions of the flow field to be predicted, obtained from simulation or experiment, into the trained NFNO-DeepONet network, execute the prediction task, and obtain the prediction results.

2. The irregular sampling shear layer flow field prediction method based on improved DeepONet according to claim 1, characterized in that, S1 includes the following steps: Step 1.1: Determine the typical physical scenarios of shear layer flow, including free shear layer, boundary layer separation, and laminar transition types, and set different initial conditions and boundary parameters to cover representative shear layer flow structures; Step 1.2: Generate velocity field data of the flow field using numerical simulation methods, or obtain velocity distribution data of the real flow field using experimental methods to form a shear layer velocity field sample set; Step 1.3: Standardize, transform coordinates and unify size of the generated velocity field samples to build a dataset with a unified format. Each sample contains the initial conditions of the velocity field, the predicted target field after 1 second, and spatial location coordinate information, which serve as the basis for subsequent non-uniform sampling and network training.

3. The irregular sampling shear layer flow field prediction method based on improved DeepONet according to claim 1, characterized in that, S2 includes the following steps: Step 2.1: Perform preliminary analysis on the constructed velocity field data samples, calculate the spatial gradient distribution of the velocity field in each sample, identify regions with drastic local velocity changes and regions with gentle overall changes, and divide the regions by extracting statistical features of the velocity gradient or setting thresholds; Step 2.2: Based on the region division results, formulate a non-uniform sampling strategy; implement high-density sampling in regions with drastic changes to capture local flow characteristics; and implement low-density sampling in regions with gentle changes to reduce redundant data and computational resource consumption. Step 2.3: Based on the above sampling strategy, spatial sampling is performed in each velocity field sample to extract the set of non-uniformly distributed coordinate points and their corresponding velocity values, and to construct a dataset containing multiple regions with different sampling densities for training the neural network.

4. The irregular sampling shear layer flow field prediction method based on improved DeepONet according to claim 1, characterized in that, S3 includes the following steps: Step 3.1: Replace the original branch network in DeepONet with NFNO to process non-uniformly sampled inputs and generate feature representations that match the backbone network; Step 3.2: Retain the backbone network in the original DeepONet structure, and use a multi-layer fully connected neural network to encode the position coordinates of each target point to be predicted, and output a spatial feature vector; Step 3.3: Perform a dot product operation between the frequency domain feature vector output by the branch network and the spatial feature vector output by the backbone network to obtain the velocity field output at the predicted position after 1 second, thus realizing the prediction from the non-uniform initial velocity field to the future velocity field. Step 3.4: Use the non-uniform sampling velocity field dataset obtained in S2 to train the constructed NFNO-DeepONet network; During training, the initial velocity field is used as the network input, and the target is the actual velocity value of the predicted position after 1 second. The network parameters are updated by minimizing the error between the predicted value and the actual value.

5. The irregular sampling shear layer flow field prediction method based on improved DeepONet according to claim 4, characterized in that, Step 3.1 includes the following steps: Step 3.1.1: Receive the coordinates of the non-uniformly sampled points and their corresponding initial velocity values ​​of the flow field to form the input data; Step 3.1.2: Perform dimensionality upscaling on the input data using a fully connected neural network to obtain a high-dimensional feature representation for frequency domain modeling; Step 3.1.3: Perform the NDFT operation on the upgraded feature representation to map it from the time domain to the frequency domain; Step 3.1.4: Perform a linear transformation on the extracted spectral information in the frequency domain; Step 3.1.5: Restore the linearly transformed spectral data back to the time domain using the inverse NDFT; Step 3.1.6: Repeat steps 3.1.3 to 3.1.5 to form a multi-layer frequency domain modeling structure. The obtained results are then subjected to dimensionality reduction using a fully connected neural network. Step 3.1.7: Perform average pooling on the dimensionality-reduced output to make its dimension consistent with the dimension of the backbone network output vector, thus forming the final output of the branch network.

6. The irregular sampling shear layer flow field prediction method based on improved DeepONet according to claim 1, characterized in that, S4 includes the following steps: Step 4.1: Import the initial condition data of the flow field to be predicted, including the spatial coordinate points obtained by non-uniform sampling and their corresponding initial velocity values, as the network input; Step 4.2: Input the initial conditions into the trained NFNO-DeepONet network, and then perform dot product operations through the respective encodings of the branch networks and the backbone network to output the prediction results; Step 4.3: Obtain the predicted value of the velocity field after 1 second, including the velocity at each location point in the two-dimensional space.

7. A flow field prediction system for irregular sampling shear layer based on an improved DeepONet, characterized in that, It includes a computer module that applies the method described in any one of claims 1-6.

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