Uncertainty-guided ensemble self-training for semi-supervised flow field reconstruction

Abstract

This invention discloses a semi-supervised flow field reconstruction method guided by uncertainty and employing ensemble self-training. The method includes: acquiring multiple labeled and unlabeled data sets; constructing multiple first deep learning models with different initialization parameters, and a second deep learning model with the same initialization parameters; training the multiple first deep learning models using the labeled data; acquiring the complete flow field and its corresponding uncertainty for each unlabeled data set using the trained first deep learning models, and calculating the uncertainty weights corresponding to the uncertainties; pre-training the second deep learning model using the unlabeled data, the corresponding complete flow field, and the uncertainty weights; and retraining the second deep learning model using the labeled data. This method enables the acquisition of a high-precision deep learning model using a small amount of labeled data, reducing the cost of flow field reconstruction and improving its accuracy.

Description

Technical Field

[0001] This invention relates to the field of flow field reconstruction technology, and more specifically to a semi-supervised flow field reconstruction method based on uncertainty-guided integrated self-training. Background Technology

[0002] In practical engineering applications, understanding the state of a physical system is crucial for its monitoring, control, analysis, and design, and is also a prerequisite for building a digital twin system. One key issue in understanding the state of a physical system is reconstructing its global flow field using measurement data from a limited number of sensors within the system. For example, several sensors can be deployed on the surface of an aircraft or within a fluid flow domain to acquire partial state information of the physical system, and this partial information can be used to reconstruct the velocity field, pressure field, and other flow fields of the entire physical system. However, in practical applications, directly using partial observation data to solve the inverse problem to reconstruct the global flow field is usually quite difficult, rarely yielding accurate reconstruction results, and incurring extremely high computational costs.

[0003] With the continuous development of deep learning technology, data-driven methods, represented by deep learning, have demonstrated excellent performance in various flow field reconstruction applications by learning from historical data to reconstruct the global flow field. Existing deep learning-based flow field reconstruction methods construct deep learning models, train them with a large amount of labeled sample data including finite measurement point data within the flow field and their corresponding complete flow fields, and then use the trained deep learning model for flow field reconstruction.

[0004] However, since real data of the complete flow field is difficult to obtain, labeled sample data is usually obtained through physical simulation experiments and / or numerical calculations. The acquisition of each labeled sample data requires a lot of computing resources and time. Existing deep learning-based flow field reconstruction methods require a large amount of labeled sample data, resulting in extremely high computational costs. Summary of the Invention

[0005] To address some or all of the technical problems existing in the prior art, this invention provides a semi-supervised flow field reconstruction method based on uncertainty-guided integrated self-training.

[0006] The technical solution of the present invention is as follows:

[0007] An uncertainty-guided integrated self-training semi-supervised flow field reconstruction method is provided, the method comprising:

[0008] Acquire multiple labeled data and multiple unlabeled data, wherein the labeled data includes state observation values ​​of multiple set measuring points in the flow field and their corresponding complete flow field, and the unlabeled data includes state observation values ​​of multiple set measuring points in the flow field;

[0009] Construct multiple first deep learning models with different initial model parameters, and a second deep learning model with initial model parameters;

[0010] The labeled data is used to train multiple first deep learning models to fit the mapping relationship between the state observation values ​​of multiple set measurement points in the flow field and the complete flow field.

[0011] The complete flow field and its corresponding uncertainty corresponding to each unlabeled data are obtained by using multiple first deep learning models that have been trained, and the uncertainty weights corresponding to the uncertainty are calculated.

[0012] The unlabeled data and its corresponding complete flow field and uncertainty weights are used to pre-train the second deep learning model to fit the mapping relationship between the state observations of multiple set measurement points in the flow field and the complete flow field;

[0013] The labeled data is used to retrain the second deep learning model to fit the mapping relationship between the state observations of multiple set measurement points in the flow field and the complete flow field.

[0014] In some possible implementations, training the first deep learning model using the labeled data includes:

[0015] The first deep learning model is trained by taking the state observations of multiple set measurement points in the flow field from the labeled data as input and the complete flow field from the labeled data as output.

[0016] In some possible implementations, the first deep learning model is trained by taking the state observations of multiple designated measurement points within the flow field in the labeled data as input and the complete flow field in the labeled data as output, including the following steps:

[0017] Step S301: Input the state observation values ​​of multiple set measurement points in the flow field from the multiple labeled data into the first deep learning model in sequence to obtain the predicted flow field output by the first deep learning model;

[0018] Step S302: Compare the predicted flow field output by the first deep learning model with the complete flow field in the labeled data, and calculate the prediction accuracy of the first deep learning model.

[0019] Step S303: Determine whether the prediction accuracy obtained at least twice consecutively is greater than a preset accuracy threshold. If yes, use the current first deep learning model as the first deep learning model that has completed training. If no, calculate the preset loss function, update the parameters of the first deep learning model using the preset loss function, and return to step S301.

[0020] In some possible implementations, the loss function during training of the first deep learning model is:

[0021]

[0022] Where N represents the number of labeled data points, and Ω represents the area of ​​the flow field. Let x represent the state at a point x in the complete flow field of the i-th labeled data set. Let x represent the state at a certain point x in the predicted flow field output by the first deep learning model corresponding to the i-th labeled data.

[0023] In some possible implementations, the complete flow field corresponding to the unlabeled data is determined using the following formula:

[0024]

[0025] The uncertainty corresponding to the complete flow field is determined using the following formula:

[0026]

[0027] Among them, y p This represents the complete flow field corresponding to unlabeled data, and n represents the number of the first deep learning models. U represents the predicted flow field output by the i-th first deep learning model corresponding to the unlabeled data. p It indicates uncertainty.

[0028] In some possible implementations, the uncertainty weights are calculated using the following formula:

[0029] W = 1 - Norm(U p )

[0030] Where W represents the uncertainty weight, Norm(U p ) indicates that uncertainty U p Normalize to the interval [0,1].

[0031] In some possible implementations, the second deep learning model is pre-trained using the unlabeled data and its corresponding complete flow field and uncertainty weights, including:

[0032] The second deep learning model is trained by taking the state observation values ​​of multiple set measurement points in the flow field of the unlabeled data and the uncertainty weights corresponding to the unlabeled data as inputs and the complete flow field corresponding to the unlabeled data as outputs.

[0033] In some possible implementations, the second deep learning model is trained by taking the state observations of multiple set measurement points in the flow field of the unlabeled data and the uncertainty weights corresponding to the unlabeled data as inputs, and the complete flow field corresponding to the unlabeled data as outputs, including the following steps:

[0034] Step S501: The state observation values ​​of multiple set measurement points in the flow field of the multiple unlabeled data and the uncertainty weights corresponding to the unlabeled data are sequentially input into the second deep learning model to obtain the predicted flow field output by the second deep learning model;

[0035] Step S502: Compare the predicted flow field output by the second deep learning model with the complete flow field corresponding to the unlabeled data, and calculate the prediction accuracy of the second deep learning model.

[0036] Step S503: Determine whether the prediction accuracy obtained in at least two consecutive steps is greater than the preset accuracy threshold. If yes, use the current second deep learning model as the second deep learning model that has completed pre-training. If no, calculate the preset loss function, update the parameters of the second deep learning model using the preset loss function, and return to step S501.

[0037] In some possible implementations, the loss function during pre-training of the second deep learning model is:

[0038]

[0039] Where M represents the number of unlabeled data points, Ω represents the area of ​​the flow field, and W... j (x) represents the uncertainty weight at a point x in the complete flow field corresponding to the j-th unlabeled data. Let x represent the state at a point x in the complete flow field corresponding to the j-th unlabeled data. Let x represent the state at a certain point x in the predicted flow field output by the second deep learning model corresponding to the j-th unlabeled data.

[0040] In some possible implementations, retraining the second deep learning model using the labeled data includes:

[0041] The second deep learning model is trained by taking the state observations of multiple set measurement points in the flow field of the labeled data as input and the complete flow field in the labeled data as output.

[0042] The main advantages of the technical solution of this invention are as follows:

[0043] The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method of the present invention can obtain a deep learning model with high prediction accuracy using a small amount of labeled data, significantly reducing the need for labeled data for model training, effectively reducing the computation time and computational resources required to obtain training data, reducing the cost of flow field reconstruction, and improving the accuracy of flow field reconstruction. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart of an uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to an embodiment of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0047] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0048] Consider a two-dimensional discrete flow field Γ, which can be described by the following partial differential governing equations:

[0049]

[0050] Among them, w x Let f represent the state vector at a point x in the flow field Γ, which is determined by the parameter θ and time t. The parameter θ represents the known parameter in the governing equation determined by the flow field system, and f represents the nonlinear equation that controls the flow field Γ.

[0051] In practical engineering, due to the complexity of physical systems, the complete state w of a physical system is usually unknown. However, the state of a physical system at a finite number of points can be observed by deploying sensors and other detection instruments. Therefore, if a(t; θ) is taken as the observed state at a certain location and time t in the physical system, the goal of the flow field reconstruction task is to reconstruct the complete state w(t; θ) of the physical system based on the finite observed state a(t; θ). This process can be expressed as:

[0052] w(t;θ)=F(a(t;θ))

[0053] in, a y Let represent the observation state of the y-th measurement point, Λ represent the set of measurement points, and F represent the reconstruction model to be constructed.

[0054] As shown in the formula above, once the reconstruction model is determined, inputting the acquired observation states into the reconstruction model will yield the complete flow field corresponding to the observation states output by the reconstruction model. Accordingly, the accuracy and efficiency of flow field reconstruction mainly depend on the accuracy of the reconstruction model and the time required to construct the reconstruction model.

[0055] Therefore, refer to Figure 1 An embodiment of the present invention provides a semi-supervised flow field reconstruction method guided by uncertainty and integrated self-training, the method comprising the following steps S1-S6:

[0056] Step S1: Obtain multiple labeled data and multiple unlabeled data. The labeled data includes the state observation values ​​of multiple set measuring points in the flow field and their corresponding complete flow field. The unlabeled data includes the state observation values ​​of multiple set measuring points in the flow field.

[0057] In one embodiment of the present invention, a simulation model of a physical system can be constructed, and multiple physical simulation experiments can be conducted based on the simulation model to obtain labeled data of multiple state observations of multiple set measurement points within the flow field and their corresponding complete flow fields. Multiple physical simulation experiments can also be conducted to obtain unlabeled data of multiple state observations of multiple set measurement points within the flow field. Alternatively, sensors can be deployed at multiple set measurement points in the actual physical system to collect the state of the measurement points. Based on the state observations collected by multiple sensors at a certain moment, the finite element analysis method can be used to simulate and calculate the corresponding complete flow field at the current state observation value, thus obtaining a set of state observations of multiple set measurement points within the flow field and their corresponding complete flow field. Furthermore, based on the state observations collected by multiple sensors at multiple different moments, the finite element analysis method can be used to simulate and calculate the corresponding complete flow field, thus obtaining multiple sets of state observations of multiple set measurement points within the flow field and their corresponding complete flow fields. Finally, by collecting the state of the measurement points using sensors, multiple sets of state observations collected by multiple sensors at multiple different moments can be obtained as unlabeled data of multiple state observations of multiple set measurement points within the flow field.

[0058] Of course, if the physical system has corresponding historical data, it is possible to directly obtain labeled data of multiple state observations of multiple set measuring points in the flow field and their corresponding complete flow field, as well as unlabeled data of multiple state observations of multiple set measuring points in the flow field.

[0059] In one embodiment of the present invention, the amount of unlabeled data is greater than the amount of labeled data.

[0060] Step S2: Construct multiple first deep learning models with different initial model parameters, and a second deep learning model with initial model parameters.

[0061] In one embodiment of the present invention, the first deep learning model and the second deep learning model can employ convolutional neural networks. By training the first and second deep learning models, the deep learning models can learn the physical laws in the data, thereby obtaining a neural network with strong generalization ability, which can achieve rapid prediction of the complete flow field of a physical system. Essentially, the deep learning model is a surrogate model.

[0062] In one embodiment of the present invention, the structures of the first deep learning model and the second deep learning model can be determined firstly, and then the first deep learning model can be randomly initialized multiple times to determine the model parameters, resulting in multiple first deep learning models with different initialized model parameters. Then, the second deep learning model can be randomly initialized once to determine the model parameters, resulting in a second deep learning model with initialized model parameters.

[0063] In order to improve training efficiency and ensure the prediction accuracy of the trained model, the first deep learning model and the second deep learning model have the same structure.

[0064] Step S3: Use labeled data to train multiple first deep learning models to fit the mapping relationship between the state observation values ​​of multiple set measurement points in the flow field and the complete flow field.

[0065] In one embodiment of the present invention, training a first deep learning model using labeled data includes:

[0066] The first deep learning model is trained by taking the state observations of multiple set measurement points in the flow field from the labeled data as input and the complete flow field from the labeled data as output.

[0067] Specifically, in one embodiment of the present invention, the state observation values ​​of multiple set measurement points in the flow field of the labeled data are used as input, and the complete flow field in the labeled data is used as output to train a first deep learning model, including the following steps:

[0068] Step S301: Input the state observation values ​​of multiple set measurement points in the flow field from multiple labeled data into the first deep learning model in sequence to obtain the predicted flow field output by the first deep learning model.

[0069] In one embodiment of the present invention, the state observation values ​​of multiple set measurement points in the flow field in the labeled data are input from the input end of the first deep learning model, processed sequentially by the parameters of each layer in the first deep learning model, and output from the output end of the first deep learning model. The information output from the output end is the predicted flow field corresponding to the state observation values ​​of multiple set measurement points in the flow field.

[0070] Step S302: Compare the predicted flow field output by the first deep learning model with the complete flow field in the labeled data, and calculate the prediction accuracy of the first deep learning model.

[0071] In one embodiment of the present invention, the prediction accuracy can be obtained by calculating the ratio of the difference between the predicted flow field corresponding to each labeled data and the complete flow field in the labeled data and the complete flow field. The average value of all ratios can be used as the prediction accuracy.

[0072] Furthermore, since each point in a complete flow field has a corresponding state value, in order to facilitate data processing and subsequent calculations, the flow field can be divided into multiple regions, and the state value of a set point in a region can be used as the state value of that region. The state of the entire flow field can be represented by the states of the multiple regions.

[0073] Step S303: Determine whether the prediction accuracy obtained in at least two consecutive steps is greater than the preset accuracy threshold. If yes, use the current first deep learning model as the first deep learning model that has completed training. If no, calculate the preset loss function, update the parameters of the first deep learning model using the preset loss function, and return to step S301.

[0074] In one embodiment of the present invention, when training the first deep learning model, the corresponding loss function is set as follows:

[0075]

[0076] Where N represents the number of labeled data points, and Ω represents the area of ​​the flow field. Let x represent the state at a point x in the complete flow field of the i-th labeled data set. Let x represent the state at a certain point x in the predicted flow field output by the first deep learning model corresponding to the i-th labeled data.

[0077] Furthermore, in one embodiment of the present invention, gradient descent is used to optimize and update the parameters of the first deep learning model. Specifically, the chain rule is first used to differentiate the parameters with respect to the loss function, and then the parameters are updated using the differentiation result and a preset learning rate.

[0078] Specifically, the parameters of the first deep learning model can be updated using the following formula:

[0079]

[0080] Where θ1 represents the parameter set of the first deep learning model, Δ[·] represents the optimizer, and η represents the learning rate. The optimizer can be, for example, Adam or SGD, and the learning rate needs to be preset to control the speed of parameter updates.

[0081] Step S4: Use multiple first deep learning models that have been trained to obtain the complete flow field and its corresponding uncertainty for each unlabeled data, and calculate the uncertainty weight corresponding to the uncertainty.

[0082] In one embodiment of the present invention, unlabeled data is input into multiple first deep learning models that have completed training, and the predicted flow field corresponding to the unlabeled data output by each first deep learning model is obtained. The average value of the predicted flow fields output by multiple first deep learning models is used as the pseudo label corresponding to the current unlabeled data, that is, the complete flow field corresponding to the current unlabeled data.

[0083] Furthermore, uncertainty is often used to reflect the magnitude of noise in the model prediction results. Since multiple first deep learning models can obtain multiple different predicted flow fields for the same data sample, in one embodiment of the present invention, the variance of the predicted flow field is used to quantify uncertainty.

[0084] Specifically, the complete flow field corresponding to the unlabeled data is calculated and determined using the following formula:

[0085]

[0086] Among them, y p This represents the complete flow field corresponding to unlabeled data, and n represents the number of the first deep learning models. This represents the predicted flow field output by the i-th first deep learning model corresponding to the unlabeled data.

[0087] The uncertainty corresponding to the predicted complete flow field is calculated and determined using the following formula:

[0088]

[0089] Among them, U p This represents the uncertainty corresponding to the predicted complete flow field.

[0090] Furthermore, in one embodiment of the present invention, the uncertainty is normalized to the interval [0,1], and the uncertainty weight is calculated based on the normalization result.

[0091] Specifically, the uncertainty weights are calculated using the following formula:

[0092] W = 1 - Norm(U p )

[0093] Where W represents the uncertain weight, Norm represents the normalization process, and Norm(U p ) indicates that uncertainty U p Normalize to the interval [0,1].

[0094] Step S5: Use unlabeled data and its corresponding complete flow field and uncertainty weights to pre-train the second deep learning model to fit the mapping relationship between the state observations of multiple set measurement points in the flow field and the complete flow field.

[0095] In one embodiment of the present invention, a second deep learning model is pre-trained using unlabeled data and its corresponding complete flow field and uncertainty weights, including:

[0096] The second deep learning model is trained by taking the state observations of multiple set measurement points in the flow field from the unlabeled data and the uncertainty weights corresponding to the unlabeled data as inputs, and the complete flow field corresponding to the unlabeled data as outputs.

[0097] Specifically, in one embodiment of the present invention, the state observation values ​​of multiple set measurement points in the flow field of unlabeled data and the uncertainty weights corresponding to the unlabeled data are used as inputs, and the complete flow field corresponding to the unlabeled data is used as output to train a second deep learning model, including the following steps:

[0098] Step S501: Input the state observation values ​​of multiple set measurement points in the flow field from multiple unlabeled data and the uncertainty weights corresponding to the unlabeled data into the second deep learning model in sequence to obtain the predicted flow field output by the second deep learning model.

[0099] In one embodiment of the present invention, the state observation values ​​of multiple set measurement points in the flow field in the unlabeled data and the uncertainty weights corresponding to the unlabeled data are input from the input end of the second deep learning model, processed sequentially by the parameters of each layer in the second deep learning model, and output from the output end of the second deep learning model. The information output from the output end is the predicted flow field corresponding to the state observation values ​​of multiple set measurement points in the flow field.

[0100] Step S502: Compare the predicted flow field output by the second deep learning model with the complete flow field corresponding to the unlabeled data, and calculate the prediction accuracy of the second deep learning model.

[0101] In one embodiment of the present invention, the prediction accuracy can be obtained by calculating the ratio of the difference between the predicted flow field output by the second deep learning model corresponding to each unlabeled data and the complete flow field corresponding to the unlabeled data and the complete flow field. The average value of all ratios can be used as the prediction accuracy.

[0102] Step S503: Determine whether the prediction accuracy obtained in at least two consecutive steps is greater than the preset accuracy threshold. If yes, use the current second deep learning model as the second deep learning model to complete the pre-training. If no, calculate the preset loss function, update the parameters of the second deep learning model using the preset loss function, and return to step S501.

[0103] In one embodiment of the present invention, when pre-training the second deep learning model, the corresponding loss function is set as follows:

[0104]

[0105] Where M represents the number of unlabeled data points, Ω represents the area of ​​the flow field, and W... j (x) represents the uncertainty weight at a point x in the complete flow field corresponding to the j-th unlabeled data. Let x represent the state at a point x in the complete flow field corresponding to the j-th unlabeled data. Let x represent the state at a certain point x in the predicted flow field output by the second deep learning model corresponding to the j-th unlabeled data.

[0106] In one embodiment of the present invention, according to the loss function set above, during the pre-training of the second deep learning model, the location region is weighted according to the uncertainty of each location region in the complete flow field corresponding to the unlabeled data. Location regions with greater uncertainty are assigned smaller weights, and location regions with less uncertainty are assigned larger weights. This enables the second deep learning model to learn more location regions with less noise and ignore location regions with greater noise, thereby avoiding the influence of noise on the model during the learning process and further improving the prediction accuracy of the trained model.

[0107] Furthermore, in one embodiment of the present invention, gradient descent is used to optimize and update the parameters of the second deep learning model. Specifically, the chain rule is first used to differentiate the parameters with respect to the loss function, and then the parameters are updated using the derivative and a preset learning rate. The specific parameter update formula can refer to the parameter update formula of the first deep learning model described above, and will not be repeated here.

[0108] Step S6: The second deep learning model is retrained using labeled data to fit the mapping relationship between the state observations of multiple set measurement points in the flow field and the complete flow field.

[0109] In one embodiment of the present invention, retraining a second deep learning model using labeled data includes:

[0110] The pre-trained second deep learning model is trained by taking the state observations of multiple set measurement points in the flow field from the labeled data as input and the complete flow field from the labeled data as output.

[0111] Specifically, in one embodiment of the present invention, the state observation values ​​of multiple set measurement points in the flow field of the labeled data are used as input, and the complete flow field in the labeled data is used as output to train the pre-trained second deep learning model, including the following steps:

[0112] Step S601: Input the state observation values ​​of multiple set measurement points in the flow field from multiple labeled data into the pre-trained second deep learning model in sequence to obtain the predicted flow field output by the second deep learning model.

[0113] In one embodiment of the present invention, the state observation values ​​of multiple set measurement points in the flow field in the labeled data are input from the input end of the second deep learning model, processed sequentially by the parameters of each layer in the second deep learning model, and output from the output end of the second deep learning model. The information output from the output end is the predicted flow field corresponding to the state observation values ​​of multiple set measurement points in the flow field.

[0114] Step S602: Compare the predicted flow field output by the second deep learning model with the complete flow field in the labeled data, and calculate the prediction accuracy of the second deep learning model.

[0115] In one embodiment of the present invention, the prediction accuracy can be obtained by calculating the ratio of the difference between the predicted flow field output by the second deep learning model corresponding to each labeled data and the complete flow field in the labeled data and the complete flow field. The average value of all ratios is used as the prediction accuracy.

[0116] Step S603: Determine whether the prediction accuracy obtained in at least two consecutive steps is greater than the preset accuracy threshold. If yes, use the current second deep learning model as the second deep learning model to complete the retraining. If no, calculate the preset loss function, update the parameters of the second deep learning model using the preset loss function, and return to step S601.

[0117] In one embodiment of the present invention, when retraining the second deep learning model, the corresponding loss function is set as follows:

[0118]

[0119] Where N represents the number of labeled data points, and Ω represents the area of ​​the flow field. Let x represent the state at a point x in the complete flow field of the i-th labeled data set. This represents the state at a point x in the predicted flow field output by the second deep learning model corresponding to the i-th labeled data.

[0120] Furthermore, in one embodiment of the present invention, gradient descent is used to optimize and update the parameters of the second deep learning model. Specifically, the chain rule is first used to differentiate the parameters with respect to the loss function, and then the parameters are updated using the derivative and a preset learning rate. The specific parameter update formula can refer to the parameter update formula of the first deep learning model described above, and will not be repeated here.

[0121] Furthermore, in one embodiment of the present invention, the method further includes:

[0122] Step S7: Reconstruct the flow field using the completed second deep learning model.

[0123] Specifically, after retraining the second deep learning model, the state observation values ​​of multiple set measurement points in the flow field are input into the second deep learning model to obtain the corresponding complete flow field, thereby completing the flow field reconstruction.

[0124] An embodiment of the present invention provides a semi-supervised flow field reconstruction method with uncertainty-guided integrated self-training that can obtain a deep learning model with high prediction accuracy using a small amount of labeled data. This significantly reduces the need for labeled data for model training, effectively reduces the computation time and resources required to obtain training data, lowers the cost of flow field reconstruction, and improves the accuracy of flow field reconstruction.

[0125] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Additionally, the terms "front," "back," "left," "right," "upper," and "lower" in this document refer to the placement shown in the accompanying drawings.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A semi-supervised flow field reconstruction method guided by uncertainty and employing self-training, characterized in that, include: Acquire multiple labeled data and multiple unlabeled data, wherein the labeled data includes state observation values ​​of multiple set measuring points in the flow field and their corresponding complete flow field, and the unlabeled data includes state observation values ​​of multiple set measuring points in the flow field; Construct multiple first deep learning models with different initial model parameters, and a second deep learning model with initial model parameters; The labeled data is used to train multiple first deep learning models to fit the mapping relationship between the state observation values ​​of multiple set measurement points in the flow field and the complete flow field. The complete flow field and its corresponding uncertainty corresponding to each unlabeled data are obtained by using multiple first deep learning models that have been trained, and the uncertainty weights corresponding to the uncertainty are calculated. The unlabeled data and its corresponding complete flow field and uncertainty weights are used to pre-train the second deep learning model to fit the mapping relationship between the state observations of multiple set measurement points in the flow field and the complete flow field; The labeled data is used to retrain the second deep learning model to fit the mapping relationship between the state observations of multiple set measurement points in the flow field and the complete flow field.

2. The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to claim 1, characterized in that, Training the first deep learning model using the labeled data includes: The first deep learning model is trained by taking the state observations of multiple set measurement points in the flow field from the labeled data as input and the complete flow field from the labeled data as output.

3. The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to claim 2, characterized in that, The first deep learning model is trained by taking the state observations of multiple designated measurement points in the labeled data as input and the complete flow field in the labeled data as output, including the following steps: Step S301: Input the state observation values ​​of multiple set measurement points in the flow field from the multiple labeled data into the first deep learning model in sequence to obtain the predicted flow field output by the first deep learning model; Step S302: Compare the predicted flow field output by the first deep learning model with the complete flow field in the labeled data, and calculate the prediction accuracy of the first deep learning model. Step S303: Determine whether the prediction accuracy obtained at least twice consecutively is greater than a preset accuracy threshold. If yes, use the current first deep learning model as the first deep learning model that has completed training. If no, calculate the preset loss function, update the parameters of the first deep learning model using the preset loss function, and return to step S301.

4. The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to claim 3, characterized in that, When training the first deep learning model, the loss function is: Where N represents the number of labeled data points, and Ω represents the area of ​​the flow field. Let x represent the state at a point x in the complete flow field of the i-th labeled data set. Let x represent the state at a certain point x in the predicted flow field output by the first deep learning model corresponding to the i-th labeled data.

5. The semi-supervised flow field reconstruction method based on uncertainty-guided integrated self-training according to any one of claims 1-4, characterized in that, The complete flow field corresponding to unlabeled data is determined using the following formula: The uncertainty corresponding to the complete flow field is determined using the following formula: Among them, y p This represents the complete flow field corresponding to unlabeled data, and n represents the number of the first deep learning models. U represents the predicted flow field output by the i-th first deep learning model corresponding to the unlabeled data. p It indicates uncertainty.

6. The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to claim 5, characterized in that, The uncertainty weights are calculated using the following formula: W=1-Norm(U p ) Where W represents the uncertainty weight, Norm(U p ) indicates that uncertainty U p Normalize to the interval [0,1].

7. The semi-supervised flow field reconstruction method with uncertainty-guided integrated self-training as described in claim 1 or 6, characterized in that, The second deep learning model is pre-trained using the unlabeled data and its corresponding complete flow field and uncertainty weights, including: The second deep learning model is trained by taking the state observation values ​​of multiple set measurement points in the flow field of the unlabeled data and the uncertainty weights corresponding to the unlabeled data as inputs and the complete flow field corresponding to the unlabeled data as outputs.

8. The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to claim 7, characterized in that, The second deep learning model is trained by taking the state observations of multiple set measurement points in the flow field of the unlabeled data and the uncertainty weights corresponding to the unlabeled data as inputs, and the complete flow field corresponding to the unlabeled data as outputs, including the following steps: Step S501: The state observation values ​​of multiple set measurement points in the flow field of the multiple unlabeled data and the uncertainty weights corresponding to the unlabeled data are sequentially input into the second deep learning model to obtain the predicted flow field output by the second deep learning model; Step S502: Compare the predicted flow field output by the second deep learning model with the complete flow field corresponding to the unlabeled data, and calculate the prediction accuracy of the second deep learning model. Step S503: Determine whether the prediction accuracy obtained in at least two consecutive steps is greater than the preset accuracy threshold. If yes, use the current second deep learning model as the second deep learning model that has completed pre-training. If no, calculate the preset loss function, update the parameters of the second deep learning model using the preset loss function, and return to step S501.

9. The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to claim 8, characterized in that, When pre-training the second deep learning model, the loss function is: Where M represents the number of unlabeled data points, Ω represents the area of ​​the flow field, and W... j (x) represents the uncertainty weight at a point x in the complete flow field corresponding to the j-th unlabeled data. Let x represent the state at a point x in the complete flow field corresponding to the j-th unlabeled data. Let x represent the state at a certain point x in the predicted flow field output by the second deep learning model corresponding to the j-th unlabeled data.

10. The uncertainty-guided integrated self-training semi-supervised flow field reconstruction method according to claim 1 or 9, characterized in that, Retraining the second deep learning model using the labeled data includes: The second deep learning model is trained by taking the state observations of multiple set measurement points in the flow field of the labeled data as input and the complete flow field in the labeled data as output.

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