Sample flow field data generation method, model training method, flow field reconstruction method

Abstract

The present disclosure provides a method for generating sample flow field data, which relates to the field of artificial intelligence technology, and in particular to the field of deep learning and fluid mechanics technology. The specific implementation scheme is: determining the sampling space for the target object in the flow field; dividing the sampling space into multiple subspaces; determining the spatial step and time step for sampling according to the scale of the vortex in the flow field; determining the sampling point in each subspace according to the spatial step and time step; and determining the sample flow field data according to the spatiotemporal information and physical information of the sampling point in the flow field. The present disclosure also provides a method for generating sample flow field data, a training method for a deep learning model, a flow field reconstruction method, a device, an electronic device, and a storage medium.

Description

Technical Field

[0001] The present disclosure relates to the field of artificial intelligence technology, in particular to the field of deep learning and fluid mechanics technology. More specifically, the present disclosure provides a sample flow field data generation method, a deep learning model training method, a flow field reconstruction method, a device, an electronic device, a storage medium and a computer program product. Background Art

[0002] At present, artificial intelligence technology has been widely used in computer-aided engineering related fields. For example, artificial intelligence can be used to realize relevant calculations in fluid mechanics engineering applications. Summary of the invention

[0003] The present disclosure provides a sample flow field data generation method, a deep learning model training method, a flow field reconstruction method, an apparatus, an electronic device, a storage medium, and a computer program product.

[0004] According to a first aspect, a method for generating sample flow field data is provided, the method comprising: determining a sampling space for a target object in a flow field; dividing the sampling space into a plurality of subspaces; determining a spatial step and a time step for sampling according to the scale of a vortex in the flow field; determining a sampling point in each subspace according to the spatial step and the time step; and determining sample flow field data according to the spatiotemporal information and physical information of the sampling point in the flow field.

[0005] According to the second aspect, a deep learning model training method is provided, the method comprising: obtaining sample flow field data, wherein the sample flow field data is generated according to the above-mentioned sample flow field data generation method, and the sample flow field data includes spatiotemporal information and initial physical information; inputting the sample flow field data into the deep learning model to obtain target physical information of the sample flow field data; determining the loss of the deep learning model based on the relationship between the initial physical information and the target physical information, and the relationship between the spatiotemporal information and the target physical information; and adjusting the parameters of the deep learning model based on the loss.

[0006] According to the third aspect, a flow field reconstruction method is provided, which includes: obtaining discrete point data of the flow field to be reconstructed, the discrete point data including time and space information; and inputting the discrete point data into a deep learning model to obtain the velocity field and pressure field of the entire flow field to be reconstructed; wherein the deep learning model is trained according to the above-mentioned deep learning model training method.

[0007] According to a fourth aspect, a sample flow field data generating device is provided, which includes: a sampling space determination module, used to determine the sampling space for a target object in the flow field; a subspace determination module, used to divide the sampling space into multiple subspaces; a step determination module, used to determine the spatial step and time step for sampling according to the scale of the vortex in the flow field; a sampling point determination module, used to determine the sampling point in each subspace according to the spatial step and the time step; and a sample flow field data determination module, used to determine the sample flow field data according to the spatiotemporal information and physical information of the sampling point in the flow field.

[0008] According to the fifth aspect, a training device for a deep learning model is provided, which includes: a sample flow field data acquisition module, used to acquire sample flow field data, wherein the sample flow field data is generated according to the above-mentioned sample flow field data generation device, and the sample flow field data includes spatiotemporal information and initial physical information; a target physical information determination module, used to input the sample flow field data into the deep learning model to obtain the target physical information of the sample flow field data; a loss determination module, used to determine the loss of the deep learning model according to the relationship between the initial physical information and the target physical information, and the relationship between the spatiotemporal information and the target physical information; and a parameter adjustment module, used to adjust the parameters of the deep learning model according to the loss.

[0009] According to the sixth aspect, a flow field reconstruction device is provided, which includes: a discrete point data determination module, used to obtain discrete point data of the flow field to be reconstructed, the discrete point data including time and space information; and a full flow field determination module, used to input the discrete point data into a deep learning model to obtain the velocity field and pressure field of the full flow field to be reconstructed; wherein the deep learning model is trained according to the training device of the above-mentioned deep learning model.

[0010] According to the seventh aspect, an electronic device is provided, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the method provided according to the present disclosure.

[0011] According to an eighth aspect, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to cause a computer to execute the method provided according to the present disclosure.

[0012] According to a ninth aspect, a computer program product is provided, comprising a computer program, wherein the computer program is stored on at least one of a readable storage medium and an electronic device, and wherein the computer program implements the method provided according to the present disclosure when executed by a processor.

[0013] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings are used to better understand the present solution and do not constitute a limitation of the present disclosure.

[0015] Figure 1 is a schematic diagram of an exemplary system architecture to which at least one of a sample flow field data generation method, a deep learning model training method, and a flow field reconstruction method can be applied according to an embodiment of the present disclosure;

[0016] Figure 2 is a flow chart of a method for generating sample flow field data according to an embodiment of the present disclosure;

[0017] Figure 3 is a schematic diagram of a fan-shaped space according to an embodiment of the present disclosure;

[0018] Figure 4 is a flowchart of a method for training a deep learning model according to an embodiment of the present disclosure;

[0019] Figure 5 is a schematic diagram of a training method for a deep learning model according to an embodiment of the present disclosure;

[0020] Figure 6 is a flow chart of a flow field reconstruction method according to an embodiment of the present disclosure;

[0021] Figures 7A-7B is an effect diagram of flow field reconstruction according to an embodiment of the present disclosure;

[0022] Figure 8 is a block diagram of a sample flow field data generating device according to an embodiment of the present disclosure;

[0023] Fig. 9 is a block diagram of a training apparatus for a deep learning model according to an embodiment of the present disclosure;

[0024] Fig.10 is a block diagram of a flow field reconstruction device according to an embodiment of the present disclosure;

[0025] Fig.11 It is a block diagram of an electronic device according to at least one of a sample flow field data generating method, a deep learning model training method, and a flow field reconstruction method in accordance with an embodiment of the present disclosure. DETAILED DESCRIPTION

[0026] The following is a description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0027] Flow field reconstruction is an important research method in fluid mechanics. It simulates and determines the motion state of fluids through high-precision data, thus providing a scientific basis for solving various fluid mechanics problems. The core of flow field reproduction based on high-precision data is to use a large amount of experimental data and field observation data to reproduce the flow process and state of fluids through mathematical modeling and computer simulation.

[0028] Specifically, flow field reproduction mainly includes the following steps.

[0029] First, data collection. This includes collecting experimental data and field observation data. The accuracy and quantity of these data are related to the accuracy of flow field reproduction. Second, data processing. This includes data cleaning, sorting and analysis in order to extract useful information for flow field reproduction. Then, model building. This is the core step of flow field reproduction. It is necessary to establish a mathematical model based on the collected data and the theory and methods of fluid mechanics.

[0030] Next is computer simulation, which uses computers to simulate the established model to reproduce the flow process and state of the fluid.

[0031] Finally, it is the result analysis. This is to analyze the simulation results to verify the accuracy and reliability of the model. At the same time, the flow law of the fluid can be studied based on the analysis results. The flow field reproduction based on high-precision data can be used to study the basic laws of fluids and to solve practical problems, such as the design and optimization of wind power generation, aerospace, water conservancy engineering and other fields. At the same time, with the development of computer technology and data processing technology, the accuracy and efficiency of flow field reproduction have been significantly improved, and its research and application prospects are very broad.

[0032] In some examples, flow field reproduction can first use a measurement method to obtain partial data in the flow field, and then use a reconstruction method to reconstruct the entire flow field based on the measured partial data. Measurement methods include, for example, particle velocimetry, and reconstruction methods include, for example, optical flow method, Gaussian interpolation method, etc. In flow field reconstruction, optical flow method can be used to estimate the movement speed of each point in the fluid. Interpolation method can use known flow field data to determine unknown flow field data through interpolation technology.

[0033] The above-mentioned flow field reproduction methods still have some shortcomings. For example, traditional methods such as optical flow method and interpolation method have high computational complexity, large data requirements, poor generalization ability, poor robustness, poor real-time performance, and are prone to non-compliance with physical laws. Specifically, high computational complexity and large data requirements mean that the algorithm requires complex calculations and a large amount of high-precision data to obtain accurate results. In practical applications, it is usually difficult to obtain such data. Poor generalization ability means that these algorithms work well when processing specific types of flow fields, but the effect may be greatly reduced when processing other types of flow fields. Poor robustness means that for noise and outliers, a slight data error may cause the results of flow field reconstruction to deviate significantly from the actual situation. Poor real-time performance means that due to high computational complexity and large data requirements, it performs poorly in real-time flow field reconstruction. Non-compliance with physical laws means that the mass and momentum conservation of the flow field cannot be guaranteed. In addition, these algorithms are mainly used in laminar flow scenarios, and it is difficult to calculate transient turbulent scenarios under high Reynolds numbers. Among them, the Reynolds number is a dimensionless number used to characterize the flow conditions of the fluid. Low Reynolds number is laminar flow, and the fluid flow is stable. Conversely, a high Reynolds number is turbulent and the fluid flow is unstable.

[0034] Using artificial intelligence methods to reproduce flow fields provides a new solution. For example, using the Physics-Informed Neural Network (PINN) model, based on the Navier-Stokes equations, the flow field is reconstructed by solving these equations.

[0035] Model-based methods can effectively solve the above shortcomings of poor generalization, poor robustness, poor real-time performance, easy non-compliance with physical laws, and difficulty in calculating turbulent scenes. However, model-based methods also require complex calculations and a large amount of data. In practical applications, the measured flow field data is generally randomly sampled, which makes it difficult to obtain a large amount of high-precision data, resulting in poor model training results and poor flow field reproduction results.

[0036] In the technical solution of the present disclosure, the collection, storage, use, processing, transmission, provision and disclosure of user personal information involved are in compliance with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0037] In the technical solution of the present disclosure, the user's authorization or consent is obtained before obtaining or collecting the user's personal information.

[0038] Figure 1 is a schematic diagram of an exemplary system architecture to which at least one of a sample flow field data generation method, a deep learning model training method, and a flow field reconstruction method can be applied according to an embodiment of the present disclosure. It should be noted that, Figure 1What is shown is merely an example of a system architecture to which the embodiments of the present disclosure can be applied, in order to help those skilled in the art understand the technical content of the present disclosure, but it does not mean that the embodiments of the present disclosure cannot be used in other devices, systems, environments or scenarios.

[0039] like Figure 1 As shown, the system architecture 100 according to this embodiment may include terminal devices 101, 102, 103, a network 104 and a server 105. The network 104 is used to provide a medium for communication links between the terminal devices 101, 102, 103 and the server 105. The network 104 may include various connection types, such as wired and / or wireless communication links, etc.

[0040] Users can use terminal devices 101, 102, 103 to interact with server 105 through network 104 to receive or send messages, etc. Terminal devices 101, 102, 103 can be various electronic devices, including but not limited to smart phones, tablet computers, laptops, etc. Server 105 can represent a single server, or a server cluster.

[0041] At least one of the sample flow field data generation method and the flow field reconstruction method provided in the embodiments of the present disclosure can generally be executed by the terminal devices 101, 102, and 103. Accordingly, at least one of the sample flow field data generation device and the flow field reconstruction device provided in the embodiments of the present disclosure can generally be set in the terminal devices 101, 102, and 103.

[0042] The training method of the deep learning model provided in the embodiment of the present disclosure can generally be executed by the server 105. Accordingly, the training device of the deep learning model provided in the embodiment of the present disclosure can generally be set in the server 105.

[0043] In one example, terminal devices 101, 102, and 103 sample flow field data to generate sample flow field data. Server 105 obtains sample flow field data from terminal devices 101, 102, and 103, executes a training method for a deep learning model based on the sample flow field data, and obtains a trained deep learning model. The trained deep learning model can be deployed on terminal devices 101, 102, and 103, and terminal devices 101, 102, and 103 obtain new flow field data, and use the trained deep learning model to process the new flow field data to obtain full flow field data of the new flow field data. The full flow field data can also be visualized to display the flow process and state of the fluid in the flow field.

[0044] Figure 2 is a flowchart of a method for generating sample flow field data according to an embodiment of the present disclosure.

[0045] like Figure 2 As shown, the sample flow field data generating method 200 includes operations S210 to S250.

[0046] In operation S210 , a sampling space for a target object in a flow field is determined.

[0047] The flow field refers to the space occupied by the movement of fluids, which can include air and water flows. The target objects in the flow field can be movable objects such as aircraft, ships, submarines, etc., or can be obstacles such as immovable walls, facilities and equipment. The obstacles can be objects with regular shapes, such as cylinders, cubes, etc., or objects with irregular shapes.

[0048] According to an embodiment of the present disclosure, determining the sampling space includes determining a fan-shaped space for the target object in the flow field as the sampling space, wherein the center of the fan-shaped space is determined according to the position of the target object, and the radius of the fan-shaped space is determined according to the size of the target object.

[0049] For example, the target object is placed in the flow field, and the flow of the fluid around the target object is called bypass flow. A fan-shaped space can be determined behind the target object, that is, in the direction of bypass flow, as the sampling space. The center of the fan-shaped space can be the center of the target object, and the radius of the fan-shaped space can be determined according to the size of the target object. For example, if the target object is a cylinder, the center of the fan-shaped space is the center of the cylinder, and the radius of the fan-shaped space can include multiple (e.g., 10, 15, etc.) cylinder diameters.

[0050] In operation S220, the sampling space is divided into a plurality of subspaces.

[0051] According to an embodiment of the present disclosure, dividing the subspace includes determining a characteristic length according to a size of the target object; and dividing the sampling space at intervals of the characteristic length to obtain a plurality of subspaces.

[0052] The characteristic length can be selected according to the actual scenario, generally depending on the geometric size of the target object that plays a decisive role in the development of the flow field. For example, if the target object is a cylinder, the characteristic length can be the diameter of the cylinder. The sampling space can be divided into multiple subspaces in the horizontal and vertical directions with the characteristic length as the interval, and the normal of each subspace includes three directions: x, y, and z.

[0053] In operation S230 , a spatial step and a time step for sampling are determined according to the size of the vortex in the flow field.

[0054] In the scenario of high Reynolds number, the fluid flow is unstable and the flow field is turbulent. The turbulence includes vortex structures of various scales, and the scale of the vortex represents the size of the vortex in space.

[0055] According to an embodiment of the present disclosure, the size of the vortex includes at least one of the size of a large vortex for carrying and transferring energy and the size of a small vortex for energy dissipation.

[0056] The large vortex carries energy and is continuously transformed into a medium vortex. The large vortex transfers energy to the medium vortex, which is then transformed into a small vortex and transfers energy to the small vortex. Energy dissipates in the small vortex, and energy dissipation refers to energy dissipation as internal energy. The energy can be kinetic energy. There are a variety of medium vortexes of intermediate sizes between the large vortex that carries and transfers energy and the small vortex that dissipates energy, that is, the energy transfer is a cascade process.

[0057] The large vortex that carries and transfers energy can be represented by an integral length scale, which is determined by integrating the energy spectrum of turbulence. This means that the average turbulent kinetic energy of all vortices can be represented by the scale of a large vortex.

[0058] The scale of the small vortex where energy dissipation occurs is also called the energy dissipation scale or K o At the lmogorow scale, the small vortex represents the kinetic energy of the turbulence that is dissipated in the small vortex and converted into internal energy.

[0059] According to an embodiment of the present disclosure, determining the spatial step and time step for sampling includes determining the spatial step and time step based on the fact that the spatial interval of the sampling points is smaller than the scale of the vortex, and the distance the vortex flows within the time interval of the sampling points is smaller than the scale of the vortex.

[0060] One of the integral length scale and the energy dissipation scale can be selected to determine the spatial step size, and the spatial step size can be smaller than the selected scale. This is to make the sampling interval smaller than the selected scale, so as to ensure that the sampling points are sampling points in the vortex. The sampling point data of the vortex is more meaningful for the calculation of the flow field.

[0061] The vortex is flowing, so sampling also needs to consider the time step. After determining the spatial step, the time step can be determined based on the relative relationship between the spatial step and the time step. The basis for determining the time step can be to make the distance of the vortex flow within the time interval smaller than the scale of the vortex.

[0062] In operation S240 , sampling points are determined in each subspace according to the spatial step and the time step.

[0063] After determining the spatial step and time step, sampling points can be determined in each subspace. Multiple sampling points can be determined in each subspace. The spatial interval of the sampling points is smaller than the scale of the vortex. The distance the vortex flows within the time interval of the sampling points is smaller than the scale of the vortex. This can ensure that the collected sampling points are sampling points in the vortex.

[0064] In operation S250, sample flow field data is determined according to the temporal and spatial information and physical information of the sampling point in the flow field.

[0065] The spatiotemporal information of the sampling point includes spatial coordinate information and time information. The flow field is flowing and changes with time, so the flow field data is time series data, and the time information of the sampling point can be the sampling moment.

[0066] The physical information includes the velocity and pressure of the sampling point at the sampling time, and the velocity may include the velocity in the x, y, and z directions.

[0067] The sampling points and their time information and physical information constitute the sample flow field data.

[0068] The embodiments of the present disclosure determine the sampling space for the target object in the flow field, divide the sampling space into multiple subspaces, determine the time step and space step of each subspace according to the scale of the vortex in the flow field, and determine the sampling point of each subspace according to the time step and space step, so as to ensure the data sampled on the vortex, ensure the validity of the sampling point data, and at the same time ensure the uniformity and density of the sampling points, thereby improving the accuracy of the sample flow field data.

[0069] Figure 3 is a schematic diagram of a fan-shaped space according to an embodiment of the present disclosure.

[0070] like Figure 3 As shown, the target object is a cylinder, and the center of the fan-shaped space can be the center of the cylinder. The fan-shaped space is behind the target object, that is, in the direction of the bypass flow. The angle of the fan-shaped space can cover the bypass area caused by the target object, for example, it can be -30° to 30°, where the direction of 0° is parallel to the bypass flow direction.

[0071] The radius of the sector space can be multiple characteristic lengths, which are selected according to the actual scenario and application requirements. The characteristic length can be related to the size of the target object. For example, the characteristic length can be the diameter of a cylinder, and the radius of the sector space can be 15 characteristic lengths.

[0072] It should be noted that the embodiments of the present disclosure can also accurately sample points for complex geometric bodies. For example, if the target object is an irregular complex geometry, the center of the geometry can be determined as the center of the fan-shaped space. According to the size of the geometric body, the angle and radius of the fan-shaped space can be adjusted so that the fan-shaped space covers the flow area caused by the geometric body, and the sampling space can be obtained, and then the sampling space can be accurately sampled.

[0073] According to an embodiment of the present disclosure, it also includes calculating the scale of the vortex, including determining the kinetic energy and energy dissipation efficiency of the flow field according to the speed of the flow field; and calculating the scale of the vortex in the flow field according to the kinetic energy and energy dissipation efficiency.

[0074] The energy spectrum of turbulent kinetic energy can be calculated based on the average velocity of turbulence, and the above-mentioned integral length scale, that is, the scale of the large vortex, can be calculated based on the energy spectrum.

[0075] Energy dissipation efficiency indicates the rate at which the kinetic energy of a unit mass of fluid is converted into heat energy in turbulent motion per unit time. The energy dissipation efficiency can be calculated based on the velocity, density, viscosity and turbulent energy spectrum of the fluid.

[0076] The dissipation scale, i.e. the scale of the vortex, can be calculated based on the energy dissipation efficiency. The calculation formula of the dissipation scale is shown in the following formula (1).

[0077]

[0078] Among them, k represents the dissipation scale, v represents the dynamic viscosity, and ε represents the energy dissipation efficiency. Among them, k is dimensionless.

[0079] According to an embodiment of the present disclosure, determining the spatial step size according to the scale of the vortex in the flow field includes determining one of the scale of the large vortex and the scale of the small vortex as a reference scale according to the scene of the flow field; and determining the spatial step size according to the reference scale, wherein the spatial step size is smaller than the reference scale.

[0080] According to the actual scenario, one of the integral length scale and the energy dissipation scale can be used as a reference scale, and a spatial step size smaller than the reference scale can be selected.

[0081] For example, in the scenario of pursuing high efficiency, the integral length scale can be selected as the reference scale, so that the spatial step length is smaller than the integral length scale, so that the sampling point interval is smaller than the scale of the large vortex, and the data of the large vortex can be collected, which can ensure a certain accuracy and high sampling efficiency. Alternatively, in the scenario of pursuing high precision, the dissipative scale can be selected as the reference scale, so that the spatial step length is smaller than the dissipative scale, so that the sampling point interval is smaller than the scale of the small vortex, and more vortex data can be collected, making the sampling point data more refined, which can bring higher precision calculation results.

[0082] According to an embodiment of the present disclosure, determining the time step includes: determining the time step according to a relative relationship between the time step and the space step.

[0083] The Courant number represents the relative relationship between the time step and the space step, for example, the ratio of the time step to the space step. The time step is determined based on making the distance of the vortex flow within the time interval smaller than the size of the vortex.

[0084] In one example, after determining the spatial step length, the Courant number can be made less than 0.5 to calculate the spatial step length. For example, a value of the Courant number less than 0.5 is selected, and according to the relative relationship between the time step length and the spatial step length, the time step length can be equal to the product of the spatial step length and the Courant number.

[0085] Figure 4 It is a flowchart of a method for training a deep learning model according to an embodiment of the present disclosure.

[0086] like Figure 4 As shown, the deep learning model training method 400 includes operations S410 to S440.

[0087] In operation S410, sample flow field data is acquired.

[0088] The sample flow field data may be generated by the above-mentioned sample flow field data generation method. The sample flow field data is data of multiple sampling points in the flow field, and each sampling point data includes spatiotemporal information and initial physical information. The spatiotemporal information includes the spatial position coordinates and time information of the sampling point, and the initial physical information represents the initial velocity and initial pressure of the sampling point in the x, y, and z directions. The initial velocity and initial pressure may be obtained by measurement.

[0089] In operation S420, the sample flow field data is input into a deep learning model to obtain target physical information of the sample flow field data.

[0090] The deep learning model may be a physical embedded neural network model, which may include a multi-layer perceptron, an activation function, and a Navier-Stokes equation group, wherein the Navier-Stokes equation group may be used as a loss function to constrain the training of the deep learning model.

[0091] The spatiotemporal information of the sample flow field data is input into the deep learning model, and the deep learning model outputs the target physical information of the sample flow field data, which includes the target velocity and target pressure of the sampling point in the x, y, and z directions. The target velocity and target pressure are calculated and output by the model.

[0092] The Navier-Stokes equations characterize the conservation of mass and momentum in the flow field. Using the Navier-Stokes equations as a loss function to constrain the training of the neural network model can make the target velocity and target pressure of the sampling point calculated by the neural network conform to the laws of physics.

[0093] In operation S430, a loss of a deep learning model is determined according to a relationship between the initial physical information and the target physical information, and a relationship between the spatiotemporal information and the target physical information.

[0094] In operation S440, parameters of the deep learning model are adjusted according to the loss.

[0095] According to an embodiment of the present disclosure, determining the loss of a deep learning model includes inputting initial physical information and target physical information into a basic loss function to obtain a basic loss; inputting spatiotemporal information and target physical information into a loss function of a control equation to obtain a loss of the control equation; and determining the loss of the deep learning model based on the basic loss and the loss of the control equation.

[0096] The initial physical information is obtained through measurement and can be considered as real physical information. The target physical information is the output of the deep learning model. The basic loss function can be a mean square error function. The initial physical information and the target physical information are input into the mean square error function to obtain the basic loss.

[0097] The governing equations characterize the energy conservation of the flow field. For example, the governing equations include the Navier-Stokes equations. If the deep learning model is calculated accurately, the spatiotemporal information of the sample flow field data and the target physical information should conform to the physical law of energy conservation, that is, the spatiotemporal information of the sample flow field data and the target physical information satisfy the Navier-Stokes equations.

[0098] The Navier-Stokes equations are shown in the following formulas (2) to (5).

[0099]

[0100]

[0101]

[0102]

[0103] Where ν is the dynamic viscosity, (u, v, w) are the velocities in the x, y, and z directions respectively, p is the relative pressure after removing the background pressure (e.g., atmospheric pressure), and ρ is the density. The time-space information is represented as (t, x, y, z). The Navier-Stokes equations mainly characterize the conservation of mass of incompressible fluids described by Euler and the conservation of momentum under the conditions of weightless viscous incompressibility. Wherein, the above formula (2) represents the conservation of mass, and formulas (3) to (5) represent the conservation of momentum in the x, y, and z directions respectively.

[0104] The above Navier-Stokes equations can be rewritten as a function, for example, by moving the terms on both sides of the equal sign to the same side, so that the equation is equal to a function, which is used as the loss function of the Navier-Stokes equations. If the deep learning model is calculated accurately, the spatiotemporal information of the sample flow field data and the target physical information are input into the loss function, and the loss function should be 0.

[0105] The spatiotemporal information of the sample flow field data and the target physical information are input into the loss function of the Navier-Stokes equations. The difference between the value of the loss function and 0 is the loss of the Navier-Stokes equations.

[0106] The sum or weighted sum of the above basic loss and the loss of the Navier-Stokes equations can be used as the overall loss of the deep learning model. The parameters of the deep learning model can be adjusted according to the overall loss.

[0107] The embodiments of the present disclosure constrain the training of the deep learning model through the basic loss and the loss of the control equation, so that the deep learning calculation conforms to the laws of physics, improves the accuracy and precision of the deep learning model calculation, and further improves the accuracy of the flow field calculation.

[0108] Figure 5 It is a schematic diagram of a training method for a deep learning model according to an embodiment of the present disclosure.

[0109] like Figure 5 As shown, the input of the deep learning model includes spatiotemporal information (t, x, y, z), and the output includes physical information (u, v, w, p). The hidden layer of the deep learning model may include a multi-layer perceptron. The loss of the deep learning model may include the loss of the control equation, the basis loss, the loss of the initial condition, and the loss of the boundary condition.

[0110] The control equations can be Navier-Stokes equations, which are also partial differential equations. Calculating the loss of the control equations is equivalent to solving the partial differential equations. Partial differential equations have different solution methods such as direct differentiation and difference methods. The losses obtained by different solution methods may be different. Therefore, the loss of the control equations can include the loss obtained by direct differentiation and the loss obtained by difference.

[0111] The above-mentioned basic loss may include a mean square error between the initial physical data and the target physical data of the sampling point.

[0112] The loss of the initial condition may include the difference between the state of the flow field at the initial time (t=0) and the state of the flow field obtained by solution. For example, each physical quantity in the flow field at the initial time may be Fourier transformed to obtain the frequency distribution of the flow field at the initial time, and then the target physical data of the flow field currently solved may be Fourier transformed to obtain the frequency distribution of the flow field obtained by solution, and the initial condition loss may be determined based on the difference between the frequency distribution of the flow field at the initial time and the frequency distribution of the flow field obtained by solution.

[0113] Boundary conditions refer to the conditions that need to be met in order to solve the partial differential equation. As the number of training times of the deep learning model increases, the boundary conditions change. Based on the difference in the changes in the boundary conditions, the loss of the boundary conditions can be determined.

[0114] The loss of the above control equation, the basic loss, the loss of the initial condition, the loss of the boundary condition and the sum or weighted sum can be used as the overall loss to determine whether the overall loss is less than a certain threshold. If so, the model converges, otherwise the parameters of the deep learning model are adjusted.

[0115] In one example, data can be trained and learned based on the PaddlePaddle high-performance distributed deep learning framework, and optimized through the Adam (Adaptive moment estimation) optimizer and the loss function adaptation algorithm. The Adam optimizer is an optimization algorithm with an adaptive learning rate that can accelerate convergence during training.

[0116] In addition, the PaddlePaddle deep learning framework includes an automatic differentiation framework, which can accurately derive the derivative terms of partial differential equations. By quickly reducing the equation loss function, it can greatly improve the accuracy of solving the flow field, velocity and pressure, as well as the network learning efficiency.

[0117] Figure 6 is a flow chart of a flow field reconstruction method according to an embodiment of the present disclosure.

[0118] like Figure 6 As shown, the flow field reconstruction method 600 includes operations S610 to S620.

[0119] In operation S610, discrete point data of a flow field to be reconstructed is obtained.

[0120] The flow field to be reconstructed may include multiple discrete point data, which may be obtained through measurement. In order to obtain the motion process and state of the entire flow field of the reconstructed flow field, the flow field needs to be reconstructed to obtain the velocity field and pressure field of the entire flow field.

[0121] Each discrete point includes space-time information, and the space-time information includes spatial coordinate information and time information.

[0122] In operation S620, the discrete point data is input into a deep learning model to obtain a velocity field and a pressure field of the entire flow field to be reconstructed.

[0123] The deep learning model is trained according to the training method of the above deep learning model. The spatiotemporal information of discrete points is input into the trained deep learning model, and the deep learning model can output the velocity and pressure of each particle in the entire flow field in the flow field motion sequence. The particle represents a fluid element with a very small volume but a certain physical quantity in the flow field.

[0124] The velocities of all particles in the flow field constitute the velocity field, and the pressures of all particles constitute the pressure field. Therefore, based on the velocity and pressure of the fluid motion time series output by the deep learning model, the velocity field and pressure field of the entire flow field can be reconstructed.

[0125] In one example, the velocity field and pressure field of the flow field may also be visualized to show the movement process and state of the flow field.

[0126] In one example, the effect analysis of the reconstructed full flow field can also be performed to verify the effect of the reconstructed full flow field. For example, the physical quantities in the flow field to be reconstructed at the initial moment can be Fourier transformed to obtain the frequency distribution of the flow field at the initial moment. The physical quantities in the reconstructed full flow field are then Fourier transformed to obtain the frequency distribution of the reconstructed full flow field. If the frequency distribution of the flow field at the initial moment is consistent with the frequency distribution of the reconstructed full flow field, it can be determined that the reconstructed full flow field is a high-accuracy, continuous and smooth flow field that is consistent with the flow field state at the initial moment.

[0127] In one example, the frequency distribution of the reconstructed full flow field can also be compared with the frequency distribution of the flow field with an approximate Reynolds number. The approximate Reynolds number means that the Reynolds number of the reconstructed full flow field is similar to the Reynolds number of a target flow field. The Reynolds number indicates the flow stability of the flow field. The lower the Reynolds number, the more stable the flow of the fluid in the flow field. Conversely, the higher the Reynolds number, the more unstable the flow of the fluid in the flow field. If the Reynolds numbers of the two flow fields are similar, the stability of the two flow fields is comparable, and the frequency distribution characteristics are also similar. For example, the physical quantities in the reconstructed full flow field can be Fourier transformed to obtain the frequency distribution of the reconstructed full flow field. Then the physical quantities in the target flow field that is similar to the Reynolds number of the reconstructed full flow field are Fourier transformed to obtain the frequency distribution of the target flow field. If the frequency distributions of the two flow fields are consistent, it also means that the reconstructed full flow field is consistent with the actual flow field, that is, the reconstructed full flow field is highly accurate, continuous and smooth, and conforms to physical laws.

[0128] The embodiments of the present disclosure can obtain the velocity field and pressure field of the entire flow field by inputting discrete point data in the flow field to be reconstructed into a trained deep learning model, thereby realizing the reconstruction of the flow field.

[0129] Figures 7A-7B It is an effect diagram of flow field reconstruction according to an embodiment of the present disclosure.

[0130] Fig. 7A and Figure 7B They are schematic diagrams of the velocity field of the reconstructed full flow field at different angles. The velocity field can be the velocity field in the x direction at a certain moment, and the velocity in the x direction is represented by u.

[0131] like Figures 7A-7BAs shown, the target object can be a cylinder, and the fluid flows around the target object to generate a flow, which includes multiple vortex structures. The ordinate represents the velocity of the fluid in the flow field, and the velocity range of the ordinate is [-7.8*e -0.2 , 1.6*e -0.1 ]. The velocity of the fluid directly behind the target object in the x direction is close to 0, and the velocity of the fluid in the upper and lower areas directly behind the target object in the x direction is larger, close to 1.6*e -0.1 .

[0132] Figures 7A-7B The color image shown is a technical rendering. Two colors are used to represent the forward speed and the reverse speed respectively. This is to distinguish the speed of the fluid in the flow area from the speed of the fluid in other areas of the flow field, making the flow shape clearer.

[0133] Figure 8 is a block diagram of a sample flow field data generating device according to an embodiment of the present disclosure.

[0134] like Figure 8 As shown, the sample flow field data generating device 800 includes a sampling space determining module 801 , a subspace determining module 802 , a step length determining module 803 , a sampling point determining module 804 and a sample flow field data determining module 805 .

[0135] The sampling space determination module 801 is used to determine the sampling space for the target object in the flow field.

[0136] The subspace determination module 802 is used to divide the sampling space into multiple subspaces.

[0137] The step size determination module 803 is used to determine the spatial step size and time step size for sampling according to the scale of the vortex in the flow field.

[0138] The sampling point determination module 804 is used to determine the sampling points in each subspace according to the spatial step and the time step.

[0139] The sample flow field data determination module 805 is used to determine the sample flow field data according to the temporal and spatial information and physical information of the sampling point in the flow field.

[0140] The sampling space determination module 801 is used to determine a sector space for a target object in a flow field as a sampling space, wherein the center of the sector space is determined according to the position of the target object, and the radius of the sector space is determined according to the size of the target object.

[0141] The subspace determination module 802 includes a feature length determination unit and a division unit.

[0142] The characteristic length determination unit is used to determine the characteristic length according to the size of the target object.

[0143] The partitioning unit is used to partition the sampling space at intervals of characteristic length to obtain multiple subspaces.

[0144] The step length determination module 803 includes a first calculation unit, a second calculation unit and a step length determination unit.

[0145] The first calculation unit is used to determine the kinetic energy and energy dissipation efficiency of the flow field according to the velocity of the flow field.

[0146] The second calculation unit is used to calculate the scale of the vortex in the flow field according to the kinetic energy and the energy dissipation efficiency.

[0147] The step determination unit is used to determine the spatial step and the time step based on the fact that the spatial interval of the sampling points is smaller than the scale of the vortex and the distance of the vortex flow within the time interval of the sampling points is smaller than the scale of the vortex.

[0148] The step length determination unit includes a spatial step length determination subunit and a temporal step length determination subunit.

[0149] The space step determination subunit is used to determine the space step according to the scale of the vortex in the flow field, wherein the space step is smaller than the scale of the vortex.

[0150] The time step determination subunit is used to determine the time step according to the relative relationship between the time step and the space step.

[0151] According to an embodiment of the present disclosure, the size of the vortex includes at least one of the size of a large vortex for carrying and transferring energy and the size of a small vortex for energy dissipation.

[0152] The spatial step determination subunit is used to determine one of the scales of the large vortex and the small vortex as a reference scale according to the flow field scene; and determine the spatial step according to the reference scale, wherein the spatial step is smaller than the reference scale.

[0153] Fig. 9 is a block diagram of a training device for a deep learning model according to an embodiment of the present disclosure.

[0154] like Fig. 9 As shown, the training device 900 of the deep learning model includes a sample flow field data acquisition module 901, a target physical information determination module 902, a loss determination module 903 and a parameter adjustment module 904.

[0155] The sample flow field data acquisition module 901 is used to acquire sample flow field data, wherein the sample flow field data is generated according to the sample flow field data generation device, and the sample flow field data includes time-space information and initial physical information;

[0156] The target physical information determination module 902 is used to input the sample flow field data into the deep learning model to obtain the target physical information of the sample flow field data.

[0157] The loss determination module 903 is used to determine the loss of the deep learning model based on the relationship between the initial physical information and the target physical information, and the relationship between the spatiotemporal information and the target physical information.

[0158] The parameter adjustment module 904 is used to adjust the parameters of the deep learning model according to the loss.

[0159] The loss determination module includes a basic loss determination unit, a control equation loss determination unit and a model loss determination unit.

[0160] The basic loss determination unit is used to input the initial physical information and the target physical information into the basic loss function to obtain the basic loss.

[0161] The control equation loss determination unit is used to input the spatiotemporal information and the target physical information into the loss function of the control equation to obtain the loss of the control equation.

[0162] The model loss determination unit is used to determine the loss of the deep learning model according to the basic loss and the loss of the control equation.

[0163] Fig.10 is a block diagram of a flow field reconstruction device according to an embodiment of the present disclosure.

[0164] like Fig.10 As shown, the flow field reconstruction device 1000 includes a discrete point data determination module 1001 and a full flow field determination module 1002 .

[0165] The discrete point data determination module 1001 is used to obtain the discrete point data of the flow field to be reconstructed, and the discrete point data includes time and space information.

[0166] The full flow field determination module 1002 is used to input discrete point data into a deep learning model to obtain the velocity field and pressure field of the full flow field to be reconstructed.

[0167] Among them, the deep learning model is trained according to the model training device.

[0168] According to an embodiment of the present disclosure, the present disclosure also provides an electronic device, a readable storage medium and a computer program product.

[0169] Fig.11A schematic block diagram of an example electronic device 1100 that can be used to implement an embodiment of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0170] like Fig.11 As shown, the device 1100 includes a computing unit 1101, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 1102 or a computer program loaded from a storage unit 1108 into a random access memory (RAM) 1103. In the RAM 1103, various programs and data required for the operation of the device 1100 can also be stored. The computing unit 1101, the ROM 1102, and the RAM 1103 are connected to each other via a bus 1104. An input / output (I / O) interface 1105 is also connected to the bus 1104.

[0171] A number of components in the device 1100 are connected to the I / O interface 1105, including: an input unit 1106, such as a keyboard, a mouse, etc.; an output unit 1107, such as various types of displays, speakers, etc.; a storage unit 1108, such as a disk, an optical disk, etc.; and a communication unit 1109, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 1109 allows the device 1100 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0172] The computing unit 1101 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 1101 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 1101 performs the various methods and processes described above, such as at least one of the sample flow field data generation method, the training method of the deep learning model, and the flow field reconstruction method. For example, in some embodiments, at least one of the sample flow field data generation method, the training method of the deep learning model, and the flow field reconstruction method may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit 1108. In some embodiments, part or all of the computer program may be loaded and / or installed on the device 1100 via the ROM 1102 and / or the communication unit 1109. When the computer program is loaded into RAM 1103 and executed by the computing unit 1101, one or more steps of at least one of the sample flow field data generation method, the deep learning model training method, and the flow field reconstruction method described above may be performed. Alternatively, in other embodiments, the computing unit 1101 may be configured to perform at least one of the sample flow field data generation method, the deep learning model training method, and the flow field reconstruction method in any other appropriate manner (e.g., by means of firmware).

[0173] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0174] The program code for implementing the method of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0175] In the context of the present disclosure, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0176] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0177] The systems and techniques described herein may be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), and the Internet.

[0178] A computer system may include clients and servers. Clients and servers are generally remote from each other and usually interact through a communication network. The relationship of client and server is generated by computer programs running on respective computers and having a client-server relationship to each other.

[0179] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this document does not limit this.

[0180] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A method for generating sample flow field data, comprising: Determine a sampling space for a target object in the flow field; Dividing the sampling space into a plurality of subspaces; According to the scale of the vortex in the flow field, the spatial step and time step used for sampling are determined; Determine a sampling point in each of the subspaces according to the spatial step and the time step; as well as Determining sample flow field data according to the spatiotemporal information and physical information of the sampling point in the flow field; Wherein, determining the spatial step and time step for sampling according to the scale of the vortex in the flow field includes: Determining the kinetic energy and energy dissipation efficiency of the flow field according to the velocity of the flow field; Calculating the size of the vortex in the flow field according to the kinetic energy and the energy dissipation efficiency; and The spatial step and the time step are determined based on the fact that the spatial interval of the sampling points is smaller than the scale of the vortex and the distance the vortex flows within the time interval of the sampling points is smaller than the scale of the vortex.

2. The method according to claim 1, wherein: Determining the sampling space for the target object in the flow field includes: A fan-shaped space for a target object in the flow field is determined as the sampling space, wherein a center of the fan-shaped space is determined according to a position of the target object, and a radius of the fan-shaped space is determined according to a size of the target object.

3. The method according to claim 1 or 2, wherein: The dividing the sampling space into a plurality of subspaces comprises: Determining a characteristic length according to the size of the target object; and The sampling space is divided at intervals of the characteristic length to obtain the multiple subspaces.

4. The method according to claim 1, wherein: Determining the spatial step and the time step comprises: Determining the spatial step length according to the size of the vortex in the flow field, wherein the spatial step length is smaller than the size of the vortex; and The time step is determined according to the relative relationship between the time step and the space step.

5. The method according to claim 4, wherein: The size of the vortex includes at least one of the size of a large vortex for carrying and transferring energy and the size of a small vortex for energy dissipation.

6. The method according to claim 5, wherein: Determining the spatial step length according to the scale of the vortex in the flow field comprises: According to the scene of the flow field, determining one of the scale of the large vortex and the scale of the small vortex as a reference scale; and The spatial step size is determined according to the reference scale, wherein the spatial step size is smaller than the reference scale.

7. A method for training a deep learning model, comprising: Acquiring sample flow field data, wherein the sample flow field data is generated according to the method of any one of claims 1 to 6, and the sample flow field data includes spatiotemporal information and initial physical information; Inputting the sample flow field data into a deep learning model to obtain target physical information of the sample flow field data; Determining the loss of the deep learning model according to the relationship between the initial physical information and the target physical information, and the relationship between the spatiotemporal information and the target physical information; and Based on the loss, parameters of the deep learning model are adjusted.

8. The method according to claim 7, wherein: Determining the loss of the deep learning model includes: Inputting the initial physical information and the target physical information into a basic loss function to obtain a basic loss; Inputting the spatiotemporal information and the target physical information into a loss function of a control equation to obtain a loss of the control equation, wherein the control equation represents energy conservation of a flow field; and The loss of the deep learning model is determined based on the base loss and the loss of the control equation.

9. A flow field reconstruction method, comprising: Acquire discrete point data of a flow field to be reconstructed, wherein the discrete point data includes time and space information; as well as Inputting the discrete point data into a deep learning model to obtain a velocity field and a pressure field of the entire flow field to be reconstructed; Wherein, the deep learning model is trained according to any one of claims 7 to 8.

10. A sample flow field data generating device, comprising: A sampling space determination module, used to determine the sampling space for the target object in the flow field; A subspace determination module, used for dividing the sampling space into a plurality of subspaces; A step size determination module is used to determine the spatial step size and time step size for sampling according to the scale of the vortex in the flow field; A sampling point determination module, used for determining a sampling point in each of the subspaces according to the spatial step and the time step; as well as A sample flow field data determination module, used to determine the sample flow field data according to the spatiotemporal information and physical information of the sampling point in the flow field; Wherein, the step length determination module includes: A first calculation unit, used to determine the kinetic energy and energy dissipation efficiency of the flow field according to the velocity of the flow field; A second calculation unit is used to calculate the size of the vortex in the flow field according to the kinetic energy and the energy dissipation efficiency; and The step determination unit is used to determine the spatial step and the time step based on the fact that the spatial interval of the sampling points is smaller than the scale of the vortex and the distance the vortex flows within the time interval of the sampling points is smaller than the scale of the vortex.

11. The device according to claim 10, wherein: The sampling space determination module is used to determine a fan-shaped space for a target object in the flow field as the sampling space, wherein the center of the fan-shaped space is determined according to the position of the target object, and the radius of the fan-shaped space is determined according to the size of the target object.

12. The device according to claim 10 or 11, wherein: The subspace determination module comprises: a characteristic length determining unit, configured to determine the characteristic length according to the size of the target object; and The dividing unit is used to divide the sampling space into the plurality of subspaces at intervals of the characteristic length.

13. The device according to claim 10, wherein: The step length determining unit comprises: a spatial step length determination subunit, configured to determine the spatial step length according to the size of the vortex in the flow field, wherein the spatial step length is smaller than the size of the vortex; and The time step determination subunit is used to determine the time step according to the relative relationship between the time step and the space step.

14. The device according to claim 13, wherein: The size of the vortex includes at least one of the size of a large vortex for carrying and transferring energy and the size of a small vortex for energy dissipation.

15. The device according to claim 14, wherein: The spatial step length determination subunit is used to determine one of the scale of the large vortex and the scale of the small vortex as a reference scale according to the scene of the flow field; And determining the spatial step size according to the reference scale, wherein the spatial step size is smaller than the reference scale.

16. A training device for a deep learning model, comprising: A sample flow field data acquisition module, used to acquire sample flow field data, wherein the sample flow field data is generated by the device according to any one of claims 10 to 15, and the sample flow field data includes spatiotemporal information and initial physical information; A target physical information determination module, used for inputting the sample flow field data into a deep learning model to obtain target physical information of the sample flow field data; a loss determination module, configured to determine the loss of the deep learning model according to the relationship between the initial physical information and the target physical information, and the relationship between the spatiotemporal information and the target physical information; and A parameter adjustment module is used to adjust the parameters of the deep learning model according to the loss.

17. The device according to claim 16, wherein: The loss determination module comprises: A basic loss determination unit, configured to input the initial physical information and the target physical information into a basic loss function to obtain a basic loss; a control equation loss determination unit, configured to input the spatiotemporal information and the target physical information into a loss function of a control equation to obtain a loss of the control equation, wherein the control equation represents energy conservation of a flow field; and A model loss determination unit is used to determine the loss of the deep learning model based on the basic loss and the loss of the control equation.

18. A flow field reconstruction device, comprising: A discrete point data determination module, used to obtain discrete point data of a flow field to be reconstructed, wherein the discrete point data includes time and space information; as well as A full flow field determination module, used for inputting the discrete point data into a deep learning model to obtain a velocity field and a pressure field of the full flow field of the flow field to be reconstructed; Wherein, the deep learning model is trained by the device according to any one of claims 16 to 17.

19. An electronic device comprising: at least one processor; as well as a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 9.

20. A non-transitory computer-readable storage medium storing computer instructions, wherein: The computer instructions are used to cause the computer to execute the method according to any one of claims 1 to 9.

21. A computer program product, comprising a computer program, wherein the computer program is stored on at least one of a readable storage medium and an electronic device, and when the computer program is executed by a processor, the method according to any one of claims 1 to 9 is implemented.

Images