System, method and application for solving velocity potential field based on physical information gated loop

Abstract

The present invention belongs to the technical field of machine learning, and discloses a system, method and application for solving a velocity potential field based on a physical information gated loop. The system includes a physical information gated loop unit that operates in parallel on different servers, and the physical information gated loop unit includes a high-dimensional spatiotemporal domain decomposition module, a backward time slice association module, and a dual neural network solution module. The present invention reasonably utilizes time association information, and for divided high-speed fields and low-speed fields, calculations are completed separately by different servers and then combined into a complete velocity potential field, so that fast flow velocity prediction can be achieved through the present invention.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning, and in particular relates to a system, method and application for solving velocity potential field based on physical information gated loop. Background Art

[0002] Physical information neural network is a scientific machine learning technology used to solve problems involving partial differential equations. Physical information neural network approximates the solution of partial differential equations by training the neural network to minimize the loss function, including the terms reflecting the initial conditions and boundary conditions along the boundary of the space-time domain, and the residual of the partial differential equation at the selected point in the domain (called the collocation point). As a deep learning network, it is essentially a gridless technology. Given an input point, it generates an estimated solution of the differential equation at that point after training. Based on an unsupervised strategy, it does not require labeled data, previous simulation or experimental results. It finds the solution of partial differential equations by converting the problem of directly solving the control equation into a loss function optimization problem. The specific working principle is to integrate the mathematical model into the network and add the residual term in the control equation to the loss function. The residual term is used as a penalty term to limit the space of acceptable solutions. The specific implementation method is to add the difference before and after the iteration of the physical equation to the loss function of the neural network, so that the physical equation is also involved in the training process. Therefore, the neural network optimizes both the network's own loss function and the difference of each iteration of the physical equation during the training iteration, and finally makes it fully constrained by physical information.

[0003] The Benney-Luke equation has a wide range of application values ​​in the fields of oceanography, hydrodynamics and wave theory. In order to more accurately describe the characteristics of water wave motion, Yuan Chunxin et al. proposed a modified Benney-Luke equation (abbreviated as mBL equation), which adjusts the nonlinear terms of the Benney-Luke equation to make it more in line with the actual situation. These correction terms can better capture the nonlinear behavior and interaction effects of waves and improve the accuracy of the model.

[0004] The mBL equation has a complex form, and its high-order partial derivatives and complex boundary conditions make it more difficult to solve. The traditional physical information neural network has poor solving effect, mainly because it has the following problems:

[0005] (1) It is difficult to solve high-dimensional complex partial differential equations. High-dimensional partial differential equations often exhibit complex structures and high-order derivatives. Their complexity makes it extremely difficult to solve them effectively. When solving high-dimensional partial differential equations, physical information neural networks often find it difficult to obtain exact solutions to the problem due to their approximate solution characteristics. This inaccuracy leads to error accumulation in solving high-dimensional partial differential equations, making it very difficult to obtain accurate solutions. During the training process, deep neural networks incorporate the physical information of partial differential equations through automatic differentiation. When the equation form is complex, there are many spatial and temporal partial derivatives and high-order partial derivatives that need to be calculated, which greatly increases the cost and time required for training. In addition, high-dimensional input data further increases the difficulty of training, making the entire solution process more difficult.

[0006] (2) Unable to capture the temporal correlation of partial differential equations. Physical information neural networks only use simple deep neural networks, which cannot handle the temporal correlation of partial differential equations and cannot capture the different dynamic evolutions in time. They treat all input variables equally and do not distinguish between spatial positions and time slices. However, the spatial positions and time slices of partial differential equations often differ by several orders of magnitude in terms of data volume, which results in the inability to pass information from the previous time slice to the next time slice. Summary of the invention

[0007] In view of the shortcomings of the prior art, the present invention provides a system, method and application for solving the velocity potential field based on physical information gated loop. According to the characteristics of the mBL equation, the following three aspects are designed for improvement: (1) Optimization of solving high-dimensional complex partial differential equations: The high-dimensional time-space domain decomposition module decomposes the overall velocity potential field in the time-space domain, divides the spatial domain into two parts: the high-speed field and the low-speed field, and constructs the overall velocity potential field as a time series of spatial positions, thereby reducing the complexity of the overall velocity potential field. (2) Capturing the temporal correlation of partial differential equations: The backward time slice association module changes the backbone network of the physical information neural network into a gated loop unit, and passes the information of the previous time slice to the subsequent time slice in the form of a hidden state, so as to better capture the temporal correlation of the partial differential equation. (3) Balancing the temporal feature information of data: The dual neural network solution module solves through an additional deep neural network, which enhances the extraction of data features. At the same time, by weighted addition with the solution results of the gated loop unit, the temporal correlation degree in the data loss is balanced, so that the data loss of each time slice can make more reasonable use of the temporal correlation information.

[0008] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0009] The method for solving the velocity potential field based on physical information gated loop includes the following steps:

[0010] Step S1, normalization of mBL equation:

[0011] Firstly, the velocity potential field of the fluid is spatially divided, and then the mBL equation is normalized according to the regular shape of the velocity potential field. By setting the equation coefficients, initial conditions and boundary conditions of the normalized mBL equation, a velocity potential field with a regular shape is obtained.

[0012] Step S2: high-dimensional spatiotemporal domain decomposition:

[0013] The input overall velocity potential field is first decomposed in the time domain to obtain a velocity potential field with time as a sequence, and then decomposed in the space domain to obtain a high-speed field with time as a sequence and a low-speed field with time as a sequence;

[0014] Step S3, time slice backward correlation calculation:

[0015] The time series data constructed after the processing in step S2 is divided into time steps along the time axis direction, and input into the gated recurrent unit. The gated recurrent unit is used to realize the backward transmission of physical information of different time slices. The input of each gated recurrent unit includes two parts: the input data of the current time slice and the hidden state of the backward transmission of the previous time slice. After the gated recurrent unit is calculated, the output of the number of time slices is obtained, and finally all the outputs are merged into the time series output;

[0016] Step S4: Solve the dual neural network and calculate the loss:

[0017] First, an additional deep neural network is used to solve the velocity potential field at each time step and calculate the loss. Then, the loss of each time slice when the gated recurrent unit in step S3 solves the velocity potential field is calculated, and the loss of each time slice is summed to obtain the overall loss. Finally, the weighted sum of the losses of the deep neural network and the gated recurrent unit is taken to obtain the total data loss.

[0018] Step S5, high-speed field and low-speed field are calculated in parallel to solve the overall velocity potential field:

[0019] For the divided high-speed field and low-speed field, the calculations are completed separately by different servers and then combined into a complete overall velocity potential field.

[0020] Furthermore, the high-dimensional spatiotemporal domain decomposition in step S2 is specifically that the time domain decomposition is as follows: the input data is sorted into time series data of x*y*t, where x and y represent the spatial position of a spatial point, and t represents time. The data of each time slice is respectively passed into the gated recurrent unit for solution, that is, the velocity potential field processed by each gated recurrent unit contains x*y*1 solutions, thereby achieving decomposition in the time domain and obtaining a velocity potential field with time as a sequence;

[0021] The spatial domain decomposition is as follows: for different time slices, the speed threshold of this time slice is obtained by taking the minimum value of the speed potential value of all spatial points in MATLAB; for each time slice, the speed potential field is divided into a high-speed field and a low-speed field according to the set speed threshold, thereby obtaining a high-speed field with time as a sequence and a low-speed field with time as a sequence.

[0022] Furthermore, step S3 specifically divides the time series data x*y*t constructed after the processing of step S2 by time steps along the time axis direction to obtain t slices X1, X2, ..., X1, each with a size of x*y*1. t , input gated recurrent unit, after calculation, output time slice number t output , ,……, , merged into a time series output, represented as , , ,……, are the velocity potential values ​​corresponding to t time slices respectively;

[0023] When the gated recurrent unit processes data, it sets is the input data of the current time slice, is the hidden state of the previous time slice, which contains the physical information of the previous time slice. is the hidden state passed to the next time slice, is a candidate hidden state, It is the reset gate. It is the update gate. is the sigmoid function, and tanh is the tanh function;

[0024] The calculation formulas for the reset gate and update gate are as follows:

[0025] (3);

[0026] (4);

[0027] in Indicates that the hidden state h of the previous time slice is t-1 and the input of the current time slice To connect, W r , b r , W z , b z are all learnable weights and bias terms;

[0028] Candidate hidden states The calculation formula is as follows:

[0029] (5);

[0030] ⊙ represents element-by-element multiplication, W and b are learnable weights and bias terms;

[0031] The formula for updating the hidden state is as follows:

[0032] (6);

[0033] When updating the hidden state, according to the update gate Control the hidden state of the previous time slice and candidate hidden states The reset gate determines which information of the past hidden state is ignored, and the update gate determines the weight between the past hidden state and the candidate hidden state. Through these gating mechanisms, the gated recurrent unit can selectively retain and forget information, update the hidden state, and pass the physical information of the current time slice backward to the next time slice.

[0034] Further, in step S4, for the deep neural network, input spatial data ( , ), the velocity potential value can be obtained by solving each time step through the deep neural network , the mean square error can be obtained ;MSE_ξ D For the gated recurrent unit, the input data X is automatically divided into t X i , X i = (x, y, t), i = 1,2,......,t, after passing through the gated recurrent unit, the output velocity potential value , the mean square error can be obtained ; Solve the mean square error of the current time slice, add up the losses of each time slice, and get the overall loss; weighted sum of the two losses to get the total velocity potential loss , the formula is as follows:

[0035] (7);

[0036] (8);

[0037] (9);

[0038] Among them, α is the weight parameter, is the velocity potential value solved by the pseudo-spectral method, N is the number of input spatial points, including the initial points and boundary points;

[0039] The velocity potential obtained by the gated recurrent unit After automatic differentiation, it becomes multiple first-order partial derivatives and second-order partial derivatives. Multiple partial derivatives are substituted into the normalized mBL equation formula in step 1 to become the solution sequence f; velocity potential value , the first-order partial derivative of the velocity potential with respect to time , Substitute the value of a time slice in the solution sequence f into equations (11) and (12) to solve the mean square error of the current time slice, and add up the loss of each time slice to get the overall loss; where, is the first-order partial derivative of the velocity potential with respect to time obtained by the pseudo-spectral method,

[0040] (10);

[0041] (11);

[0042] (12);

[0043] in, represents the first-order partial derivative of the velocity potential with respect to time, represents the solution sequence, Represents the first-order partial derivative error of the velocity potential value, Represents the error in the equation.

[0044] Furthermore, in step S5, the formula for parallel calculation of different servers is as follows:

[0045] (13);

[0046] (14);

[0047] (15);

[0048] in, represents the sequence of velocity potential values ​​of the overall velocity potential field to be solved, represents the velocity potential value sequence of the high-speed field to be solved, represents the velocity potential value sequence of the low-velocity field to be solved, represents the dual neural network solution of high-speed field, and HFs represents the high-speed field sequence; represents the dual neural network solution of the low-speed field, LFs represents the low-speed field sequence, including the initial field, the initial point and the boundary points in the initial field, Depend on and Taking the union we get, and Have the same structure.

[0049] Furthermore, the method for solving the velocity potential field based on physical information gated loop, the overall loss function includes three parts: the total velocity potential value loss solved by the deep neural network and the gated loop unit, the loss of the first-order time partial derivative, and the loss of the equation value.

[0050] The present invention also provides a system for solving velocity potential field based on physical information gated loop, which is used to implement the method for solving velocity potential field based on physical information gated loop as described above, wherein the system includes a physical information gated loop unit that operates in parallel on different servers, and the physical information gated loop unit includes a high-dimensional space-time domain decomposition module, a backward time slice association module, and a dual neural network solution module; the physical information gated loop unit includes a high-dimensional space-time domain decomposition module, a backward time slice association module, and a dual neural network solution module; the high-dimensional space-time domain decomposition module is used to perform high-dimensional space-time domain decomposition, the backward time slice association module is used to perform time slice backward association calculation, and the dual neural network solution module is used to perform dual neural network solution and calculate loss; for the divided high-speed field and low-speed field, the calculations are completed separately by different servers and then combined into a complete overall velocity potential field.

[0051] The present invention also provides an application of a system for solving velocity potential fields based on physical information gated loops for simulating flow fields. Specifically, by using the method for solving velocity potential fields based on physical information gated loops as described above, the velocity potential field is solved and a fluid flow field simulation visualization image is output.

[0052] The present invention also provides an application of a system for solving velocity potential fields based on physical information gated loops, which is used to predict flow rate, analyze and predict fluid behavior. Specifically, by using the method for solving velocity potential fields based on physical information gated loops as described above, the velocity potential field is solved, and the velocity of the fluid at any point in the flow field is determined based on the velocity potential field, the flow velocity of the fluid under specific conditions is predicted, and then the fluid behavior is predicted.

[0053] Compared with the prior art, the present invention has the following advantages:

[0054] First, the optimization solution of high-dimensional complex partial differential equations is realized. The high-dimensional time-space domain decomposition module normalizes the mBL equation, decomposes the overall velocity potential field in the time-space domain, and divides the spatial domain into two parts: the high-speed field and the low-speed field, which is convenient for parallel solution and improves computational efficiency. The overall velocity potential field is constructed as a time series of spatial positions, and the time dimension is converted into time-related information transmitted in a hidden state. Data containing only spatial position information is constructed to facilitate deep neural network solution, reducing the complexity of solving the overall velocity potential field.

[0055] Second, the capture of the temporal correlation of partial differential equations is realized. The backward time slice association module changes the backbone network of the physical information neural network into a gated recurrent unit, and transmits the information of the previous time slice to the subsequent time slice in the form of a hidden state. Each gated recurrent unit only needs to calculate the spatial information of the current time step and then combine it with the temporal information in the hidden state, which greatly improves the computational efficiency. At the same time, the information transmitted backward is processed reasonably and selectively through the gating mechanism, and the temporal information is successfully added to the data loss and the physical equation loss, which better captures the temporal correlation of partial differential equations and has better solution effect and interpretability.

[0056] Third, the balance of data time feature information is achieved: the dual neural network solution module obtains time correlation by solving the velocity potential field sequence data through the gated recurrent unit, and enhances the extraction of data features through an additional deep neural network solution. At the same time, the deep neural network solution result is weightedly added with the gated recurrent unit solution result, which balances the degree of time correlation in the data loss while not affecting the loss of the physical equation to obtain all the time information, thereby achieving a more reasonable use of time correlation information for the data loss of each time slice.

[0057] In summary, the present invention solves through a gated recurrent unit. The input of each time slice to be solved not only contains the physical information of the current time slice, but also contains the physical information transmitted from the previous time slice in the form of a hidden state. At the same time, an additional deep neural network is used to balance the time-related information in the data loss. Finally, the high-speed field and the low-speed field are solved in parallel, and the overall velocity potential field is output.

[0058] Fourth, the method of the present invention can be used to predict flow velocity, predict, simulate and analyze fluid flow field, and predict fluid behavior with fast calculation speed and high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0060] Figure 1 It is a schematic diagram of a high-dimensional spatiotemporal domain decomposition module of the present invention;

[0061] Figure 2 It is a schematic diagram of a backward time slice association module of the present invention;

[0062] Figure 3 It is a schematic diagram of a dual neural network solution module of the present invention;

[0063] Figure 4 It is a schematic diagram of the velocity potential field of the mBL equation of the present invention in a partial time slice;

[0064] Figure 5 A network structure diagram of a gated recurrent unit (GRU) of the present invention;

[0065] Figure 6 It is a diagram showing the internal structure of the gated cycle unit of the present invention;

[0066] Figure 7 This is a structural diagram of the physical information gated cycle unit of the present invention. DETAILED DESCRIPTION

[0067] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0068] Example 1

[0069] The method for solving the velocity potential field based on physical information gated loop includes the following steps:

[0070] Step S1, normalization of mBL equation.

[0071] Firstly, the velocity potential field of the fluid is spatially divided, and then the mBL equation is normalized according to the regular shape of the velocity potential field. By setting the equation coefficients, initial conditions and boundary conditions of the normalized mBL equation, a velocity potential field with a regular shape is obtained.

[0072] The Benney-Luke equation (BL equation) is a nonlinear partial differential equation proposed by Benney and Luke in 1967 to describe the propagation of water waves on a plane, thereby modeling the propagation of shallow water waves. In the context of three-dimensional ocean internal waves, in order to more accurately describe the characteristics of water wave motion, Yuan Chunxin et al. proposed a modified Benney-Luke equation (mBL equation), as shown below:

[0073] (1);

[0074] In equation (1),

[0075] (1.1);

[0076] (1.2);

[0077] (1.3);

[0078] (1.4);

[0079] In the above four equations, and are the water depth of the upper fluid layer and the water depth of the lower fluid layer, respectively; R is the ratio of the density of the upper fluid layer to the density of the lower fluid layer, is the acceleration due to gravity.

[0080] Without considering the terrain, equation (1) shows that the internal solitary wave has an analytical solution, and the propagation of the solitary wave can be described mathematically. The expressions of the solitary wave solution, the amplitude A(k), and the nonlinear wave velocity v are all existing technical theories and will not be repeated here.

[0081] With the increase of coefficients of the mBL equation and the complexity of initial conditions and boundary conditions, the shape of the velocity potential field of the equation becomes more irregular. In order to deal with this complexity, the present invention normalizes the mBL equation. In order to reduce the complex high-dimensional non-convexity, the velocity potential field is spatially divided and the mBL equation is processed according to its regular shape. At the same time, by appropriately setting the equation coefficients, initial conditions and boundary conditions of the mBL equation, a velocity potential field with a regular shape is obtained, which helps to reduce the complexity of the problem.

[0082] The normalized mBL equation is shown as follows:

[0083] (2);

[0084] in, , , is the coefficient of the equation, calculated by the previous formula, represents the velocity potential value, Velocity potential The first-order partial derivative of Velocity potential The second-order partial derivative of .

[0085] The mBL equation is a two-dimensional equation with a complex structure and non-convex properties. It has a strong time correlation, involves multiple second-order partial derivatives, and the derivation process is complicated. At the same time, since the setting of boundary conditions will affect the characteristics of the equation and the accuracy of the solution, how to determine the appropriate boundary conditions is also a difficult task. Although physical information neural networks have potential in solving partial differential equations, due to the complexity and non-convex properties of the mBL equation and the limitations of the physical information neural network itself, the use of traditional physical information neural networks to solve the mBL equation has high training difficulty and poor training effect. Therefore, the present invention proposes a physical information gated recurrent unit based on time-space domain decomposition to solve the mBL equation.

[0086] In order to solve the mBL equation, the physical information gated recurrent unit of the present invention optimizes the optimization solution of high-dimensional partial differential equations, the capture of the time correlation of partial differential equations, and the balance of data time feature information through three modules: high-dimensional spatiotemporal domain decomposition, backward time slice association, and dual neural network solution. The architecture of each module is as follows: Figures 1 to 3 shown.

[0087] Each step is described in detail below.

[0088] Step S2: high-dimensional spatiotemporal domain decomposition.

[0089] The input overall velocity potential field is first decomposed in the time domain to obtain a velocity potential field with time as a sequence, and then decomposed in the space domain to obtain a high-speed field with time as a sequence and a low-speed field with time as a sequence.

[0090] This step is implemented through the high-dimensional spatiotemporal domain decomposition module, combined with Figure 1 As shown, the high-dimensional spatiotemporal domain decomposition is specifically:

[0091] The time domain decomposition is as follows: the input data is organized into time series data of x*y*t, where x and y represent the spatial position of a spatial point (spatial dimension), and t represents time (time dimension). The data of each time slice is passed to the gated recurrent unit for solution, that is, the velocity potential field processed by each gated recurrent unit contains x*y*1 solutions, thereby realizing the decomposition of the time domain and obtaining a velocity potential field in time sequence.

[0092] As an example, the data set taken is that x contains 512 points in the range of [-1, 1], y contains 1024 points in the range of [-2, 2], and t contains 51 time slices in the range of [0, 7500].

[0093] The data is organized into 512*1024*51 time series data, and the data of each time slice is passed to the gated recurrent unit for solution. That is, the velocity potential field processed by each gated recurrent unit contains 512*1024*1=524288 solutions, thereby achieving time domain decomposition. For the deep neural network solution part, time information is not required, so each time slice only needs 512*1024=524288 two-dimensional data. The velocity potential field of some time slices is as follows Figure 4 As shown, Figure 4 It is only used to show the velocity potential field of different time slices (t=0s, t=1500s, t=3000s, t=4500s, t=6000s, t=7500s as examples in the figure). The three coordinates are x, y coordinates and velocity potential value. The specific values ​​involved have no special meaning and are only used for demonstration. Figure 2 The velocity potential field diagrams in the figure are also for demonstration purposes only.

[0094] The spatial domain decomposition is as follows: for different time slices, the speed threshold of this time slice is obtained by taking the minimum value of the speed potential value of all spatial points in MATLAB; for each time slice, the speed potential field is divided into a high-speed field and a low-speed field according to the set speed threshold, thereby obtaining a high-speed field with time as a sequence and a low-speed field with time as a sequence.

[0095] according to Figure 4 From the six velocity potential field diagrams, it can be seen that for the mBL equation, except for the initial time t=0, which is a plane, the velocity potential fields of other time slices show a regular distribution law: high velocity potential value points distributed in the central area and low velocity potential value points distributed in the surrounding area. Therefore, when dividing, the velocity potential field can be divided into high-speed field and low-speed field according to the set velocity threshold. The high-speed field contains those points whose velocity potential values ​​are greater than the velocity threshold, while the low-speed field contains those points whose velocity potential values ​​are less than the velocity threshold. The choice of this threshold can be adjusted according to the specific situation and application requirements to ensure the accuracy and practicality of the division of high-speed field and low-speed field.

[0096] For different time slices, in MATLAB, the minimum value of the velocity potential value of all spatial points is taken to get the velocity threshold of this time slice. The velocity potential field of different time slices is different, so the velocity threshold is also different. Figure 5 In the figure, the speed threshold of the initial field is 0, the speed threshold of t=1500s is -0.1515, the speed threshold of t=3000s is -0.3040, the speed threshold of t=4500s is -0.4565, the speed threshold of t=6000s is -0.6090, and the speed threshold of t=7500s is -0.7616.

[0097] Step S3: time slice backward correlation calculation.

[0098] The time series data constructed after the processing in step S2 is divided into time steps along the time axis and input into a gated recurrent unit. The gated recurrent unit is used to realize the backward transmission of physical information of different time slices. The input of each gated recurrent unit includes two parts: the input data of the current time slice and the hidden state of the backward transmission of the previous time slice. After calculation by the gated recurrent unit, the output of the number of time slices is obtained, and finally all the outputs are merged into the time series output.

[0099] This step is implemented by the backward time slice association module, combined with Figure 2 As shown, step S3 specifically divides the time series data x*y*t constructed after the processing of step S2 by time steps along the time axis direction to obtain t slices X1, X2, ..., X1 with a size of x*y*1.t , input gated recurrent unit, after calculation, output time slice number t output , ,……, , merged into a time series output, represented as , , ,……, are the velocity potential values ​​corresponding to t time slices respectively.

[0100] This method uses gated recurrent units to achieve backward transmission of physical information in different time slices. The core idea of ​​the gated recurrent unit is to input data and the hidden state of the previous time slice at each time slice and pass them through a recurrent connection. This recurrent connection enables the network to capture the temporal correlation in the sequence data and share parameters when processing inputs of different time slices. The structure of the gated recurrent unit is as follows: Figure 5 shown.

[0101] After the previous steps, a 512*1024*51 time series data is constructed. When the sequence data is passed into the gated recurrent unit network, the sequence data is divided into time slices along the time axis to obtain t (here t = 51) slices of size 512*1024*1, that is, Figure 5 X1, X2, ..., X t . is the initial hidden state. As can be seen from the network structure diagram, the input of each GRU consists of two parts: the input data of this time slice and the hidden state of the previous time slice. After calculating the output speed potential value, the entire network outputs t speed potential values ​​of the time slices, and finally combines these t speed potential values ​​into a sequence output.

[0102] The detailed internal structure of the gated recurrent unit is shown in the figure below: Figure 6 As shown, when the gated recurrent unit processes data, it sets is the input data of the current time slice, is the hidden state of the previous time slice, which contains the physical information of the previous time slice. is the hidden state passed to the next time slice, is a candidate hidden state, It is the reset gate. It is the update gate. is the sigmoid function, and tanh is the tanh function.

[0103] The calculation formulas for the reset gate and update gate are as follows:

[0104] (3);

[0105] (4);

[0106] in Indicates that the hidden state h of the previous time slice is t-1 and the input of the current time slice To connect, W r , b r , W z , b z are learnable weights and biases. The reset gate is responsible for deciding how to fuse the input information of the current time step with the hidden state of the previous time step, while the update gate controls the degree to which the state information of the previous time step is updated in the current state, helping the model decide how much information from the previous time step should be passed to the subsequent time step.

[0107] Candidate hidden states The calculation formula is as follows:

[0108] (5);

[0109] Where ⊙ represents element-by-element multiplication, W and b are learnable weights and bias terms, The smaller the value of The smaller it is, the more information needs to be discarded in the previous time slice; The larger the value of The larger the value, the more information needs to be retained from the previous time slice, and the more the current input information is combined with the previous information; When the value of is close to 0, The value is also close to 0, indicating that the content of the previous time slice needs to be discarded, and only the input of the current time slice is retained, which can be used to discard historical information that is not related to the prediction; When the value of is close to 1, The value is also close to 1, indicating that the hidden state of the previous time slice is retained.

[0110] When the reset gate When the value of is small, it means that more information needs to be discarded in the previous time step. This leads to the weight matrix and The smaller the value of the product of , the smaller the hidden state of the previous time step is, which means that the influence of the current state is smaller. When the value of is large, it means that more information needs to be retained in the previous time step, and the degree of integration of the current input information with the previous information is also large. When the value of is close to 0, the weight matrix and The value of is also close to 0, indicating that the content of the previous time step is completely discarded, and only the input of the current time step is retained, which can be used to eliminate historical information that is irrelevant to the prediction. When the value of is close to 1, the weight matrix and The value of is also close to 1, indicating that the hidden state of the previous time step is completely preserved.

[0111] The formula for updating the hidden state is as follows:

[0112] (6);

[0113] When updating the hidden state, according to the update gate Control the hidden state of the previous time slice and candidate hidden states The reset gate determines which information of the past hidden state should be ignored, and the update gate determines the weight between the past hidden state and the candidate hidden state. Through these gating mechanisms, the gated recurrent unit can selectively retain and forget information, update the hidden state, and pass the physical information of the current time slice backward to the next time slice, realizing the backward association calculation of the time slice.

[0114] Step S4: Solve the dual neural network and calculate the loss.

[0115] Combination Figure 3 As shown, it includes two parts: deep neural network solution and gated recurrent unit solution. First, an additional deep neural network is used to solve the velocity potential field at each time step and calculate the loss. Then, the loss of each time slice when the gated recurrent unit solves the velocity potential field in step S3 is calculated, and the loss of each time slice is summed to obtain the overall loss. Finally, the weighted sum of the losses of the deep neural network and the gated recurrent unit is taken to obtain the total data loss.

[0116] Because it contains the time correlation information transmitted by the hidden state, the velocity potential field solved by the gated recurrent unit has good time correlation, which greatly enhances the physical significance of the solution process, especially the loss part of the equation of physical constraints, which has better interpretability. However, this correlation acts on data loss to the same extent. Although data loss also contains a certain degree of time correlation, when the time step span of the data is large, excessive time correlation will lead to increased data loss in the current time step.

[0117] Therefore, the present invention designs an additional deep neural network to enhance feature extraction and balance the temporal feature information of the data. The deep neural network solution part and the gated recurrent unit solution part solve the velocity potential field respectively, and the results are used to calculate the data loss respectively, and the two are weighted addition. When calculating in parallel, the points (x, y) ∈ HVF are judged to be classified as belonging to the high-speed field or the low-speed field. The points in the high-speed field and the points in the low-speed field are calculated in parallel using two networks respectively. Each network minimizes the loss. When the loss is less than the threshold The training ends when Figure 7 As shown, the physical information gated recurrent unit designed by the present invention for solving the mBL equation based on time-space domain decomposition is demonstrated.

[0118] For deep neural networks, input spatial data ( , ), the velocity potential value can be obtained by solving each time step through the deep neural network , the mean square error can be obtained ; For the gated recurrent unit, the input data X is automatically divided into t (in this case t = 51) X i , X i = (x, y, t), i = 1,2,......,t, after passing through the gated recurrent unit, the output velocity potential value , the mean square error can be obtained ; Solve the mean square error of the current time slice, add up the losses of each time slice, and get the overall loss; weighted sum of the two losses to get the total velocity potential loss , the formula is as follows:

[0119] (7);

[0120] (8);

[0121] (9);

[0122] in, is the velocity potential value solved by the pseudo-spectral method, and N is the number of input spatial points, including the initial points and boundary points.

[0123] The velocity potential obtained by the gated recurrent unit After automatic differentiation, it becomes multiple first-order partial derivatives and second-order partial derivatives. The multiple partial derivatives are substituted into the normalized mBL equation formula (2) in step 1 to become the solution sequence f. Velocity potential value , the first-order partial derivative of the velocity potential with respect to time , Substitute the value of a time slice in the solution sequence f into equations (11) and (12) to solve the mean square error of the current time slice, and add up the loss of each time slice to get the overall loss; where, is the first-order partial derivative of the velocity potential with respect to time obtained by the pseudo-spectral method,

[0124] (10);

[0125] (11);

[0126] (12);

[0127] in, represents the first-order partial derivative of the velocity potential with respect to time, represents the solution sequence, Represents the first-order partial derivative error of the velocity potential value, Represents the error in the equation.

[0128] Step S5: The high-speed field and the low-speed field are calculated in parallel to solve the overall velocity potential field.

[0129] Based on the time-space domain decomposition and parallel computing ideas of the extended physical information neural network, the advantages of parallel computing are used to accelerate the solution process of the mBL equation. For the divided high-speed field and low-speed field, the calculations are completed separately by different servers and then combined into a complete velocity potential field.

[0130] The formula for parallel calculation of different servers is as follows:

[0131] (13);

[0132] (14);

[0133] (15);

[0134] in, represents the sequence of velocity potential values ​​of the overall velocity potential field to be solved, represents the velocity potential value sequence of the high-speed field to be solved, represents the velocity potential value sequence of the low-velocity field to be solved, represents the dual neural network solution of high-speed field, and HFs represents the high-speed field sequence; represents the dual neural network solution of the low-speed field, LFs represents the low-speed field sequence, including the initial field, the initial point and the boundary points in the initial field, Depend on and Taking the union we get, and Have the same structure.

[0135] For the mBL equation, if the model can solve the mBL equation well, then for any point from the initial point and the boundary point, Close to the true value ,That The loss function of the first-order time partial derivative tends to zero It also tends to zero; for the internal space points, because it fits the differential equation very well, tends to 0, When the loss function tends to zero, that is, when the value of the loss function is less than a sufficiently small value ε, it can be considered that for each point in the training set, the value of the neural network tends to the true value. In this way, the problem of solving partial differential equations is transformed into the problem of how to optimize the loss. The loss function is optimized using the back propagation mechanism of the neural network and the L-BFGS optimizer.

[0136] Example 2

[0137] As another embodiment of the present invention, a system for solving velocity potential field based on physical information gated loop is designed to implement the method for solving velocity potential field based on physical information gated loop recorded above, wherein the system includes physical information gated loop units ( Figure 7 In the example, two parallel physical information gated loop units are taken, namely physical information gated loop unit 1 and physical information gated loop unit 2), the physical information gated loop unit includes a high-dimensional space-time domain decomposition module, a backward time slice association module, and a dual neural network solution module. The physical information gated loop unit includes a high-dimensional space-time domain decomposition module, a backward time slice association module, and a dual neural network solution module; the high-dimensional space-time domain decomposition module is used to perform high-dimensional space-time domain decomposition, the backward time slice association module is used to perform time slice backward association calculation, and the dual neural network solution module is used to perform dual neural network solution and calculate loss; for the divided high-speed field and low-speed field, the calculations are completed separately by different servers and then combined into a complete overall velocity potential field. The structure and function implementation of each module can be found in the previous embodiment 1, which will not be repeated here.

[0138] Example 3

[0139] The application of the system for solving the velocity potential field based on the physical information gated loop is used to simulate the flow field. Specifically, by using the method for solving the velocity potential field based on the physical information gated loop as described in the previous embodiment 1, the velocity potential field is solved and a fluid flow field simulation visualization image is output, wherein the visualization method can be implemented using the visualization software of the prior art, which is not the design point of the present invention and will not be repeated here.

[0140] This embodiment introduces a specific use method / application of the present invention, which models the propagation of water waves and accurately describes the characteristics of water wave motion in the context of three-dimensional ocean internal waves. The method of the present invention can better capture the nonlinear behavior and interaction effects of waves and improve the accuracy of the model.

[0141] Visualizing the velocity potential field obtained by the method of the present invention is of great significance, such as (1) Education and research: it can help students and researchers better understand the concept of fluid dynamics. Present research results in academic reports. (2) Engineering design In the fields of ship design, aerospace, automotive engineering, etc., it is used to evaluate the impact of fluid flow on design, optimize structural design, and reduce fluid resistance. (3) Environmental monitoring: observe the diffusion of pollutants in the fluid. (4) Weather forecasting: in atmospheric science, it is used to analyze the movement of airflow and assist in weather forecasting. (5) Medical applications: in biomedical engineering, it is used to analyze the flow characteristics of blood or other fluids.

[0142] Example 4

[0143] The application of the system for solving the velocity potential field based on the physical information gated loop is used to predict the flow rate, and then analyze and predict the fluid behavior. Specifically, by using the method for solving the velocity potential field based on the physical information gated loop as described above, the velocity potential field is solved, and the velocity of the fluid at any point in the flow field can be determined according to the velocity potential field, so it can be used to predict the flow velocity of the fluid under specific conditions, and then predict the fluid behavior.

[0144] When applying, first set the boundary conditions and initial velocity distribution of the flow field according to the actual situation. Through the above-mentioned method of solving the velocity potential field based on physical information gated loop, the following fluid behaviors can be predicted: (1) Streamline distribution: predict the flow path of the fluid in space, that is, the streamline, which helps to understand the overall motion pattern of the fluid. (2) Velocity distribution: determine the velocity magnitude and direction of the fluid at different locations, which is very important for designing pipeline systems and optimizing ship design. (3) Pressure distribution: the pressure distribution of the fluid can be further calculated through the velocity distribution, which is crucial for predicting the load on the structure and the fluid dynamic stability. (4) Eddy and vortex: analyze the eddy and vortex that may be formed in the fluid. These phenomena have an important influence on the mixing, heat dissipation and dynamic performance of the fluid. (5) Wave and wave front evolution: in the marine and lake environments, predict the generation, propagation and breaking of waves, which is crucial for coastal engineering and marine resource management. (6) Flow stability and instability: analyze the stability of fluid flow and predict whether the flow will cause laminar flow to become turbulent. (7) Fluid-structure interaction: predict the impact of fluid flow on structures (such as bridges, buildings, ships, etc.), including loads, vibrations, and noise. (8) Fluid dynamic response: in dynamic systems, predicting the response of fluids to excitations (such as wind, waves, engine vibrations, etc.) is very important for stability analysis of ships and offshore platforms.

[0145] It should be noted that when the velocity potential field obtained by the present invention is used to predict fluid behavior, for different fluid behaviors, the specific implementation methods can refer to the prior art, which is not the design point of the present invention and will not be repeated here. For example, the scheme proposed by the present invention can be used to predict the wave velocity, and then other wave parameters such as wave height, wave period, wave direction, waveform, and wave spectrum can be obtained. The specific calculation method can use the existing technical method, and the wave behavior can be analyzed through the wave parameters.

[0146] In summary, the present invention: First, a high-dimensional spatiotemporal domain decomposition module is designed. This module decomposes the overall velocity potential field in the spatiotemporal domain, and divides the spatial domain into two parts, a high-speed field and a low-speed field, according to the speed threshold, so as to facilitate the parallel solution of the high-speed field and the low-speed field and improve the training efficiency; the overall velocity potential field is constructed as a time series of spatial positions, which distinguishes the spatial position and the time step, and reduces the complexity of solving the overall velocity potential field.

[0147] Second, a backward time slice association module was designed. This module uses a gated recurrent unit to realize the backward transmission of the physical information of the previous time slice in the form of a hidden state. Each time slice can obtain information from the previous time slice, successfully adding time information to the data loss and physical equation loss, and can capture the time correlation of partial differential equations, with better solution effect and interpretability.

[0148] Third, a dual neural network solution module was designed. This module designed an additional deep neural network to enhance feature extraction. At the same time, the deep neural network solution part and the gated recurrent unit solution part solved the velocity potential field respectively, and the results were used to calculate data loss respectively. The weighted addition of the two achieved a balance of the temporal feature information of the data, avoiding the adverse effect of excessive temporal correlation on the data loss of the current time step when the time step span of the data is large.

[0149] Fourth, a physical information gated recurrent unit based on time-space domain decomposition was designed. The network divides high-speed fields and low-speed fields, inputs the velocity potential field sequence data into the gated recurrent unit for solution to obtain time correlation, inputs the time slice spatial position information into the deep neural network for solution, and adds the result to the gated recurrent unit solution result to balance the time feature information in the data loss. The loss of the physical equation can obtain complete time feature information. Finally, the high-speed field and the low-speed field are solved in parallel to improve the solution efficiency.

[0150] The overall loss function of the present invention includes three parts: the total velocity potential value loss solved by the deep neural network and the gated recurrent unit, the loss of the first-order time partial derivative, and the loss of the equation value.

[0151] Fourth, the method of the present invention can be used to predict flow velocity, predict, simulate and analyze fluid flow field, and predict fluid behavior with fast calculation speed and high accuracy.

[0152] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Any changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for solving velocity potential field based on physical information gated loop, characterized in that: The following steps are involved: Step S1, normalization of mBL equation: Firstly, the velocity potential field of the fluid is spatially divided, and then the mBL equation is normalized according to the regular shape of the velocity potential field. By setting the equation coefficients, initial conditions and boundary conditions of the normalized mBL equation, a velocity potential field with a regular shape is obtained. Step S2: high-dimensional spatiotemporal domain decomposition: The input overall velocity potential field is first decomposed in the time domain to obtain a velocity potential field with time as a sequence, and then decomposed in the space domain to obtain a high-speed field with time as a sequence and a low-speed field with time as a sequence; Step S3, time slice backward correlation calculation: The time series data constructed after the processing in step S2 is divided into time steps along the time axis direction, and input into the gated recurrent unit. The gated recurrent unit is used to realize the backward transmission of physical information of different time slices. The input of each gated recurrent unit includes two parts: the input data of the current time slice and the hidden state of the backward transmission of the previous time slice. After the gated recurrent unit is calculated, the output of the number of time slices is obtained, and finally all the outputs are merged into the time series output; Step S4: Solve the dual neural network and calculate the loss: First, an additional deep neural network is used to solve the velocity potential field at each time step and calculate the loss. Then, the loss of each time slice when the gated recurrent unit in step S3 solves the velocity potential field is calculated, and the loss of each time slice is summed to obtain the overall loss. Finally, the weighted sum of the losses of the deep neural network and the gated recurrent unit is taken to obtain the total data loss. Step S5, high-speed field and low-speed field are calculated in parallel to solve the overall velocity potential field: For the divided high-speed field and low-speed field, the calculations are completed separately by different servers and then combined into a complete overall velocity potential field.

2. The method for solving velocity potential field based on physical information gated loop according to claim 1 is characterized in that: The high-dimensional spatiotemporal domain decomposition in step S2 is specifically as follows: the time domain decomposition is as follows: the input data is sorted into time series data of x*y*t, where x and y represent the spatial position of a spatial point, and t represents time. The data of each time slice is respectively passed into the gated recurrent unit for solution, that is, the velocity potential field processed by each gated recurrent unit contains x*y*1 solutions, thereby achieving decomposition in the time domain and obtaining a velocity potential field with time as a sequence; The spatial domain decomposition is as follows: for different time slices, the speed threshold of this time slice is obtained by taking the minimum value of the speed potential value of all spatial points in MATLAB; for each time slice, the speed potential field is divided into a high-speed field and a low-speed field according to the set speed threshold, thereby obtaining a high-speed field with time as a sequence and a low-speed field with time as a sequence.

3. The method for solving velocity potential field based on physical information gated loop according to claim 2 is characterized in that: Step S3 specifically divides the x*y*t time series data constructed after the processing of step S2 by time steps along the time axis to obtain t slices X1, X2, ..., X1, each with a size of x*y*1. t , input gated recurrent unit, after calculation, output time slice number t output , ,……, , merged into a time series output, represented as , , ,……, are the velocity potential values ​​corresponding to t time slices respectively; When the gated recurrent unit processes data, it sets is the input data of the current time slice, is the hidden state of the previous time slice, which contains the physical information of the previous time slice. is the hidden state passed to the next time slice, is a candidate hidden state, is the reset gate, z t is the update gate, σ is the sigmoid function, and tanh is the tanh function; The calculation formulas for the reset gate and update gate are as follows: （3）； （4）； in Indicates that the hidden state h of the previous time slice is t-1 and the input of the current time slice To connect, W r 、b r , W z 、b z are all learnable weights and bias terms; Candidate hidden states The calculation formula is as follows: （5）； ⊙ represents element-by-element multiplication, W and b are learnable weights and bias terms; The formula for updating the hidden state is as follows: （6）； When updating the hidden state, according to the update gate z t Control the hidden state of the previous time slice and candidate hidden states The weight of The reset gate determines which information of the past hidden state is ignored, and the update gate determines the weight between the past hidden state and the candidate hidden state. Through these gating mechanisms, the gated recurrent unit can selectively retain and forget information, update the hidden state, and pass the physical information of the current time slice backward to the next time slice.

4. The method for solving velocity potential field based on physical information gated loop according to claim 3 is characterized in that: Step S4: For the deep neural network, input spatial data ( , ), the velocity potential value can be obtained by solving each time step through the deep neural network , the mean square error can be obtained ;MSE_ξ D For the gated recurrent unit, the input data X is automatically divided into t X i , X i = (x, y, t), i = 1,2,......,t, after passing through the gated recurrent unit, the output velocity potential value , the mean square error can be obtained ; Solve the mean square error of the current time slice, add up the losses of each time slice, and get the overall loss; weighted sum of the two losses to get the total velocity potential loss , the formula is as follows: （7）； （8）； （9）； Among them, α is the weight parameter, is the velocity potential value solved by the pseudo-spectral method, N is the number of input space points, including the initial point and boundary points; The velocity potential obtained by the gated recurrent unit After automatic differentiation, it becomes multiple first-order partial derivatives and second-order partial derivatives. Multiple partial derivatives are substituted into the normalized mBL equation formula in step 1 to become the solution sequence f; velocity potential value , the first-order partial derivative of the velocity potential with respect to time , Substitute the value of a time slice in the solution sequence f into equations (11) and (12) to solve the mean square error of the current time slice, and add up the loss of each time slice to get the overall loss; where, is the first-order partial derivative of the velocity potential with respect to time obtained by the pseudo-spectral method, （10）； （11）； （12）； in, represents the first-order partial derivative of the velocity potential with respect to time, represents the solution sequence, Represents the first-order partial derivative error of the velocity potential value, Represents the error in the equation.

5. The method for solving velocity potential field based on physical information gated loop according to claim 1, characterized in that: In step S5, the formula for parallel calculation of different servers is as follows: （13）； （14）； （15）； in, represents the sequence of velocity potential values ​​of the overall velocity potential field to be solved, represents the velocity potential value sequence of the high-speed field to be solved, represents the velocity potential value sequence of the low-velocity field to be solved, represents the dual neural network solution of high-speed field, and HFs represents the high-speed field sequence; represents the dual neural network solution of the low-speed field, LFs represents the low-speed field sequence, including the initial field, the initial point and the boundary points in the initial field, Depend on and Taking the union we get, and Have the same structure.

6. The method for solving velocity potential field based on physical information gated loop according to claim 1 is characterized in that: The overall loss function consists of three parts: the total velocity potential loss solved by the deep neural network and the gated recurrent unit, the loss of the first-order time partial derivative, and the loss of the equation value.

7. A system for solving velocity potential field based on physical information gated loop, characterized in that: Used to implement the method for solving the velocity potential field based on the physical information gated loop as described in any one of claims 1-6, the system includes a physical information gated loop unit that operates in parallel on different servers, the physical information gated loop unit includes a high-dimensional space-time domain decomposition module, a backward time slice association module, and a dual neural network solution module; the high-dimensional space-time domain decomposition module is used to perform high-dimensional space-time domain decomposition, the backward time slice association module is used to perform time slice backward association calculation, and the dual neural network solution module is used to perform dual neural network solution and calculate loss; for the divided high-speed field and low-speed field, the calculations are completed separately by different servers and then combined into a complete overall velocity potential field.

8. Application of a system for solving velocity potential field based on physical information gated loop, characterized in that: Used to simulate flow fields, specifically, by using the method for solving velocity potential field based on physical information gated loop as described in any one of claims 1 to 6, the velocity potential field is solved and a fluid flow field simulation visualization image is output.

9. Application of a system for solving velocity potential field based on physical information gated loop, characterized in that: Used to predict flow rate, analyze and predict fluid behavior. Specifically, by using the method for solving velocity potential field based on physical information gated loop as described in any one of claims 1 to 6, the velocity potential field is solved, and the velocity of the fluid at any point in the flow field is determined according to the velocity potential field, and the flow rate of the fluid under specific conditions is predicted, thereby predicting the fluid behavior.

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