Compressible gas-water medium Riemann solution unsupervised neural network modeling method

Abstract

The invention relates to an unsupervised neural network modeling method for a compressible gas-water medium Riemannian solution, belongs to the technical field of fluid mechanics simulation, and keeps the output of a Riemannian problem interface pressure solution as a positive value through a nonlinear conversion function. Through construction of a physical constraint function, label data is completely got rid of in a Riemannian solution prediction mode, and the method has the advantages that compared with a standard supervised learning neural network modeling method, a Riemannian problem does not need to be solved in advance to generate label data, and output of a neural network conforms to a Riemannian solution relationship through construction of the constraint function; compared with a traditional calculation method based on theoretical derivation, complex mathematical derivation is not needed, construction of an iterative algorithm is avoided, and the difficulty in solving complex problems is reduced; and in combination with the strong prediction capability of the neural network and the accuracy of the physical principle, a new thought and a new technical means are provided for simulation of the multi-medium flow interface problem in the high-speed flow field.

Description

Technical Field

[0001] The invention relates to an unsupervised neural network modeling method for compressible gas-water medium Riemann solution integrating physical constraints, and belongs to the technical field of fluid mechanics simulation. Background Art

[0002] Multi-media fluid dynamics is a discipline that studies the flow laws generated by the interaction of two or more different media. It essentially has a material interface with arbitrary topological structure. It has a large number of application needs in aerospace, weapon physics, biomedicine and other fields. It usually has the characteristics of large deformation, strong nonlinearity, and strong coupling of multiple physical processes. The calculation and modeling methods of the two-medium Riemann problem based on the Euler equation provide a theoretical framework for revealing the inherent laws and evolutionary characteristics of complex flows and the coupling effects of different media. Due to the influence of the differences in physical parameters and the complexity of interface discontinuity mechanisms, traditional methods based on theoretical derivation generally require an iterative process and also need to ensure that the iterative algorithm converges. The calculation may be cumbersome and may face problems such as low computational efficiency. If the inherent mechanism under complex physical characteristics is considered, the establishment of the interface coupling model may be difficult or even difficult to solve.

[0003] Machine learning methods embedded with domain knowledge show great potential for solving the above problems. The essence of machine learning is different from the traditional thinking mode. It requires the construction of a sufficiently complex trainable system so that the system can learn the features by itself. However, in recent years, most of the methods for predicting Riemann solutions using neural networks are limited to solving single-medium flows, and basically use supervised learning methods that use the exact solution of the Riemann problem as label data, which is not conducive to the widespread application of machine learning methods represented by neural networks in predicting Riemann solutions.

[0004] In short, the calculation of the two-medium Riemann problem can reveal the coupling effect of different fluids, which is very critical in the numerical simulation of compressible multi-medium fluid dynamics. If the traditional method based on theoretical derivation is used, it may face problems such as low computational efficiency and even difficulty in solving. The current machine learning methods cannot be widely used. It is urgent to construct an unsupervised neural network modeling method suitable for the Riemann solution of compressible gas-water media to solve the above difficulties. Summary of the invention

[0005] The technical problem solved by the present invention is: to provide an unsupervised neural network modeling method for the Riemann solution of a compressible gas-water medium integrating physical constraints, to add a nonlinear conversion function before the output layer of the neural network, to keep the output of the Riemann problem, that is, the interface pressure solution, as a positive value, and to construct a physical constraint function after the output layer of the neural network, so that the output of the neural network conforms to the Riemann solution relationship. The present invention does not need to solve the Riemann problem in advance to generate label data, does not need complex mathematical derivation, and also avoids constructing an iterative algorithm, which significantly reduces the difficulty of solving complex problems; combined with the powerful predictive ability of neural networks and the accuracy of physical principles, it provides new ideas and technical means for the simulation of multi-media flow interface problems in high-speed flow fields.

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

[0007] A compressible gas-water medium Riemann solution unsupervised neural network modeling method, comprising:

[0008] Construct the neural network input layer and use the initial conditions of the Riemann problem as the input features of the neural network;

[0009] Constructing a neural network hidden layer after the neural network input layer, wherein the number of neural network hidden layers H and the number of neurons M in each hidden layer are used as adjustable parameters;

[0010] Constructing a neural network conversion layer after the neural network hidden layer, wherein the nonlinear conversion function in the neural network conversion layer is represented by ζ;

[0011] A neural network output layer is constructed after the neural network conversion layer as the interface pressure solution of the Riemann problem. The neural network output layer refers to a layer based on the basic framework of the neural network Π θ The output of (x), where the subscript θ represents the neural network parameters;

[0012] The specific volume ν on the left and right sides of the Riemann problem interface is calculated based on the output layer of the neural network IQ (Π θ (x)), where the subscript I represents the flow field interface;

[0013] Based on the specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)), calculate the function f on the left and right sides of the Riemann problem interface Q (Π θ (x));

[0014] Based on the functions f on the left and right sides of the Riemann problem interface Q (Π θ (x)), calculate the physical constraint function ψ(Π θ (x));

[0015] Construct a loss function, which is a physical constraint function ψ(Π θ (x)) is the mean squared error loss function.

[0016] In the above-mentioned unsupervised neural network modeling method for the Riemann solution of compressible gas-water medium, the initial condition of the Riemann problem is expressed as x=[p L ,p R ,ρ L ,ρ R ,Δu] T , where Δu=u R -u L represents the velocity difference on both sides of the flow field interface, p represents the fluid pressure, ρ represents the fluid density, the subscript L represents the left flow field, R represents the right flow field, and T represents transposition.

[0017] In the above-mentioned unsupervised neural network modeling method for compressible gas-water medium Riemann solution, in the network architecture of the hidden layer of the neural network, σ is the activation function in the hidden layer of the neural network, η j is the linear function of the jth hidden layer, denoted as η j (t) = b j +W j t, Wj is the weight matrix corresponding to the jth hidden layer, b j is the bias vector corresponding to the jth hidden layer, and t is the output result of the previous layer of the neural network.

[0018] In the above-mentioned unsupervised neural network modeling method of the Riemann solution of compressible gas-water medium, the activation function σ in the hidden layer of the neural network is a hyperbolic tangent activation function, which is expressed as:

[0019]

[0020] Among them, e t is the base of the natural logarithm e raised to the power of t, e -t It is the base of the natural logarithm, e, raised to the power of -t.

[0021] In the above-mentioned unsupervised neural network modeling method for the Riemann solution of compressible gas-water medium, for different initial conditions x of the Riemann problem, based on the obtained basic framework of the neural network Π θ (x) Output the interface pressure solution p of the Riemann problem I , that is, p I =Π θ (x); The interface solution of the Riemann problem includes the interface pressure solution, the interface velocity solution and the interface density solution, wherein the interface velocity solution and the interface density solution are obtained according to the interface pressure solution predicted by the neural network.

[0022] In the above-mentioned unsupervised neural network modeling method for compressible gas-water medium Riemann solution, the calculation formula of the interface velocity solution is:

[0023]

[0024] The calculation formula of the interface density solution is:

[0025]

[0026] Wherein, p represents fluid pressure, u represents fluid velocity, subscript L represents left flow field, subscript R represents right flow field, for gas medium, Γ represents gas specific heat ratio γ, B=0, for water medium, Γ and B represent specific values.

[0027] In the above-mentioned unsupervised neural network modeling method of the Riemann solution of compressible gas-water medium, the nonlinear conversion function ζ in the neural network conversion layer is a Softplus function, which is expressed as: where e t It is the base of the natural logarithm, e, raised to the power of t.

[0028] In the above-mentioned unsupervised neural network modeling method for compressible gas-water medium Riemann solution, the basic framework of the neural network Π θ (x) is expressed as:

[0029]

[0030] Among them, x is the input of the neural network, η is the linear function of the hidden layer, σ is the activation function in the hidden layer of the neural network, and ζ is the nonlinear conversion function of the neural network.

[0031] In the above-mentioned unsupervised neural network modeling method for the Riemann solution of compressible gas-water medium, the specific volumes ν on the left and right sides of the Riemann problem interface are IQ (Π θ (x)) is expressed as:

[0032]

[0033] Where ε is the Heaviside step function, expressed as:

[0034]

[0035] Where, subscript I represents the flow field interface, subscript L represents the left flow field, subscript R represents the right flow field, and ν Q The specific volume representing the initial condition of the Riemann problem is defined as ν Q =1 / ρ Q , p represents the fluid pressure, ρ represents the fluid density, for gas medium, Γ represents the gas specific heat ratio γ, B=0, for water medium, Γ and B represent specific values.

[0036] In the above-mentioned unsupervised neural network modeling method for compressible gas-water medium Riemann solution, for air, γ = 1.4; for water medium, Γ = 4.4, B = 6 × 10 8 Pa.

[0037] In the above-mentioned unsupervised neural network modeling method for the Riemann solution of compressible gas-water medium, the functions f on the left and right sides of the Riemann problem interface are Q (Π θ (x)) is expressed as:

[0038]

[0039] Among them, δ is a small amount, take δ = 1.0 × 10 -6 .

[0040] In the above-mentioned Riemann solution unsupervised neural network modeling method for compressible gas-water medium, the physical constraint function ψ(Π θ (x)) is expressed as:

[0041] ψ(Π θ (x)) = f L (Π θ (x))+f R (Π θ (x))+Δu

[0042] Where Δu=u R -u L It represents the velocity difference on both sides of the flow field interface. The subscript L represents the left flow field, and R represents the right flow field.

[0043] In the above-mentioned Riemann solution unsupervised neural network modeling method for compressible gas-water medium, the loss function is expressed as:

[0044]

[0045] Where N represents the number of samples.

[0046] The above-mentioned unsupervised neural network modeling method of the Riemann solution of compressible gas-water medium also includes: training the constructed loss function to obtain a machine learning model of the gas-water medium coupling effect, embedding the machine learning model into a compressible gas-water medium fluid dynamics simulation program, and dealing with the fluid interface evolution problem caused by the gas-water medium coupling effect.

[0047] A compressible gas-water medium Riemann solution unsupervised neural network, comprising:

[0048] The neural network input layer uses the initial conditions of the Riemann problem as the input features of the neural network;

[0049] A neural network hidden layer is arranged after the neural network input layer, and the number of neural network hidden layers H and the number of neurons M in each hidden layer are used as adjustable parameters;

[0050] A neural network conversion layer, which is arranged after the neural network hidden layer, wherein the nonlinear conversion function is represented by ζ;

[0051] The neural network output layer is set after the neural network conversion layer, as the interface pressure solution of the Riemann problem, which refers to the basic framework of the neural network Π θ The output value of (x), where the subscript θ represents the neural network parameters;

[0052] Constraint functions, including physical constraint functions ψ(Π θ (x)) and loss function, where the physical constraint function ψ(Π θ (x)) includes: calculating the specific volume ν on the left and right sides of the Riemann problem interface based on the output layer of the neural network IQ (Π θ (x)), where the subscript I represents the flow field interface; based on the specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)), calculate the function f on the left and right sides of the Riemann problem interface Q (Π θ (x)); based on the function f on the left and right sides of the Riemann problem interface Q (Π θ (x)) to calculate the physical constraint function ψ(Π θ (x)); the loss function is the physical constraint function ψ(Π θ (x)) is the mean squared error loss function.

[0053] Compared with the prior art, the present invention has at least the following beneficial effects:

[0054] (1) The unsupervised neural network modeling method for the Riemann solution of compressible gas-water medium provided by the embodiment of the present invention maintains the output of the interface pressure solution of the Riemann problem as a positive value through a nonlinear conversion function. By constructing a physical constraint function, the label data is completely eliminated in the way of predicting the Riemann solution. The advantages are: compared with the standard supervised learning neural network modeling method, there is no need to solve the Riemann problem in advance to generate label data, and the output of the neural network is made to conform to the Riemann solution relationship by constructing a constraint function; compared with the traditional calculation method based on theoretical derivation, there is no need for complex mathematical derivation, and it also avoids constructing an iterative algorithm, reducing the difficulty of solving complex problems; combining the powerful predictive ability of neural networks and the accuracy of physical principles, it provides new ideas and technical means for the simulation of multi-media flow interface problems in high-speed flow fields.

[0055] (2) The unsupervised neural network modeling method for the Riemann solution of compressible gas-water medium proposed in the embodiment of the present invention completely gets rid of label data in the way of predicting the Riemann solution. Compared with the standard supervised learning neural network modeling method, it is not necessary to solve the Riemann problem in advance and generate label data. Only by constructing the constraint function, the output of the neural network can be made to conform to the Riemann solution relationship.

[0056] (3) The unsupervised neural network modeling method for the Riemann solution of compressible gas-water medium proposed in the embodiment of the present invention does not require a complex mathematical derivation process in the way of predicting the Riemann solution. It only needs to establish the relationship between shock waves and rarefaction waves. Compared with the traditional calculation method based on theoretical derivation, it reduces the difficulty of solving complex problems and avoids constructing iterative algorithms. The calculation is simpler and more universal.

[0057] (4) The unsupervised neural network modeling method of the Riemann solution of compressible gas-water medium proposed in the embodiment of the present invention is a new type of fluid mechanics simulation method with potential. It combines the powerful predictive ability of neural networks with the accuracy of physical principles, and provides new ideas and technical means for the simulation of multi-media flow interface problems in high-speed flow fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The initial value Riemann problem of the one-dimensional two-medium inviscid flow Euler equation and its wave system structure in the embodiment of the present invention;

[0059] Figure 2 It is an unsupervised neural network architecture of the Riemann solution of the compressible gas-water medium in the embodiment of the present invention;

[0060] Figure 3 This is a method for using the Riemann solution for predicting compressible gas-water media based on a neural network model in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0062] The present invention provides an unsupervised neural network modeling method for compressible gas-water medium Riemann solution integrating physical constraints, which is divided into three parts: constructing a basic framework of a neural network, constructing a physical constraint function of a neural network, and constructing a loss function:

[0063] Part 1: Constructing the basic framework of a neural network

[0064] 1) Construct the neural network input layer. The initial condition of the Riemann problem x = [p L ,p R ,ρ L ,ρ R ,Δu] T As the input feature of the neural network. Where Δu=u R-u L represents the velocity difference on both sides of the flow field interface, p represents the fluid pressure, ρ represents the fluid density, the subscript L represents the left flow field, and R represents the right flow field.

[0065] 2) Construct the hidden layer of the neural network. The hidden layer of the neural network is established after the input layer, where the number of hidden layers H of the neural network, the number of neurons M in each hidden layer and other hyperparameters are used as adjustable parameters. In this network architecture, ηj is the linear function of the jth hidden layer, expressed as η j (t) = b j +W j t.W j is the weight matrix corresponding to the jth hidden layer, b j is the bias vector corresponding to the jth hidden layer, and t is the output result of the previous layer of the neural network. σ is the activation function in the hidden layer. Preferably, σ is taken as the hyperbolic tangent activation function, which is expressed as e t is the base of the natural logarithm e raised to the power of t, e -t It is the base of the natural logarithm, e, raised to the power of -t.

[0066] 3) Construct a neural network conversion layer. In order to keep the output of the neural network positive, a neural network conversion layer is established after the hidden layer, and the Softplus function ζ is used as a nonlinear conversion function, expressed as

[0067]

[0068] 4) Construct the neural network output layer. The neural network output layer is established after the conversion layer as the interface pressure solution of the Riemann problem, expressed as Π θ (x). Combine the above steps 1) to 3), represents the basic framework of the neural network (including input layer, hidden layer, conversion layer, and output layer), the subscript θ represents the neural network parameters; x is the input of the neural network, η j is the linear function of the jth hidden layer, σ is the activation function in the hidden layer of the neural network, and ζ is the nonlinear conversion function of the neural network.

[0069] 2. Constructing Neural Network Physical Constraint Function

[0070] 5) Calculate the interface specific volume. Based on the output data of the neural network, the interface pressure Π θ (x), calculate the specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)):

[0071]

[0072] ε is the Heaviside step function, expressed as

[0073]

[0074] The subscript I represents the flow field interface. For gas medium, Γ represents the gas specific heat ratio γ, B = 0, for example, for air, γ = 1.4; for water medium, Γ represents a specific value, for example, Γ = 4.4, B = 6 × 10 8 Pa.

[0075] 6) Calculate the function f Q Based on the specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)), calculate the function f on the left and right sides of the Riemann problem interface Q (Π θ (x)):

[0076]

[0077] Wherein, δ is a small amount, and in the embodiment of the present invention, δ=1.0×10 -6 .

[0078] 7) Calculate the physical constraint function. Based on the functions f on the left and right sides of the Riemann problem interface Q (Π θ (x)), calculate the physical constraint function ψ(Π θ (x)):

[0079] ψ(Π θ (x)) = f L (Π θ (x))+f R (Π θ (x))+Δu

[0080] 3. Constructing loss function

[0081] 8) Construct the loss function. The loss function is defined as the physical constraint function ψ(Π θ (x))’s mean square error loss function:

[0082]

[0083] Where N represents the number of samples.

[0084] The constructed loss function is trained to obtain a machine learning model of gas-water medium coupling, and the machine learning model is embedded in a compressible gas-water medium fluid dynamics simulation program to deal with the fluid interface evolution problem caused by the gas-water medium coupling.

[0085] According to the physical constraint neural network model, through data training, the hyperparameters in the neural network are optimized, including the number of hidden layers H of the neural network, the number of neurons M in each hidden layer, etc., until the physical constraint function ψ(Π θ The training results of (x)) meet the requirements.

[0086] In terms of the use of the neural network model, for different Riemann problem initial conditions x, the neural network model Π obtained at this time θ (x) can output the interface pressure solution p of the Riemann problem I , that is, p I =Π θ (x). Other Riemann problem interface solutions, namely the interface velocity solution and the interface density solution, are obtained based on the interface pressure solution predicted by the neural network. Specifically, the calculation formula of the interface velocity solution is:

[0087]

[0088] The calculation formula of the interface density solution is:

[0089]

[0090] Wherein, the subscript L represents the left flow field, the subscript R represents the right flow field, p represents the fluid pressure, u represents the fluid velocity, for gas medium, Γ represents the gas specific heat ratio γ, B=0, and for water medium, Γ and B represent specific values.

[0091] Example

[0092] Problems such as gas-liquid mixing in the combustion chamber of a scramjet engine, underwater explosions, and underwater gas jets all involve the interaction of two compressible fluids. To correctly simulate the evolution of the two-medium flow field, it is necessary to establish an interface condition model for different media and use the interface condition model to calculate the two-medium flow field, thereby obtaining a simulation of the interface evolution and instability process. When defining the interface conditions of the compressible two-medium flow field, it is necessary to solve the initial value Riemann problem of the one-dimensional two-medium inviscid flow Euler equation along the interface normal:

[0093]

[0094] Where U = [ρ, ρu, E] T ,F=[ρu,ρu 2 +p,(E+p)u] T They represent the conserved variables and flux in the normal direction of the interface. ρ is the fluid density, u is the fluid velocity, p is the fluid pressure, and E = ρe + ρu 2 / 2 is the total energy of the fluid, and e is the internal energy per unit mass of the fluid. L =[ρ L ,ρ L u L,E L ] T and U R =[ρ R ,ρ R u R ,E R ] T is the position x of the flow field interface I The two fluid constant states are separated. The subscript L represents the left flow field, R represents the right flow field, and I represents the flow field interface. Figure 1 .

[0095] The closure of the above equations requires the addition of a state equation. The present invention focuses on the rigid gas state equation

[0096] p=(Γ-1)ρe-ΓB

[0097] The compressible gas-water medium flow problem described in this paper. When the parameters Γ and B of this equation represent different values, they correspond to different media. For gas medium, Γ in the above formula represents the gas specific heat ratio γ, B = 0, for example, for air, γ = 1.4; for water medium, Γ in the above formula represents a specific value, for example, Γ = 4.4, B = 6×10 8 Pa.

[0098] This embodiment integrates the unsupervised neural network modeling method of the compressible gas-water medium Riemann solution of physical constraints, such as Figure 2 As shown, the interface pressure, density and velocity solutions of the gas-water medium Riemann problem are predicted. It is divided into three parts: constructing the basic framework of the neural network, constructing the physical constraint function of the neural network, and constructing the loss function. The specific implementation process is:

[0099] 1. Constructing the basic framework of neural network

[0100] 1) Construct the neural network input layer. The initial condition of the Riemann problem x = [p L ,p R ,ρ L ,ρ R ,Δu] T As the input feature of the neural network. Here, Δu = u R -u L Represents the velocity difference on both sides of the flow field interface.

[0101] 2) Construct the hidden layer of the neural network. The hidden layer of the neural network is established after the input layer, where the number of hidden layers H of the neural network, the number of neurons M in each hidden layer and other hyperparameters are used as adjustable parameters. In this network architecture, ηj is the linear function of the jth hidden layer, expressed as η j (t) = b j +W j t.W jis the weight matrix corresponding to the jth hidden layer, B j is the bias vector corresponding to the jth hidden layer. σ is the activation function in the hidden layer. Preferably, σ is taken as the hyperbolic tangent activation function, expressed as

[0102]

[0103] 3) Construct the neural network conversion layer. A neural network conversion layer is established after the hidden layer, and the Softplus function ζ is used as the nonlinear conversion function. It is expressed as

[0104] 4) Construct the neural network output layer. The neural network output layer is established after the conversion layer as the interface pressure solution of the Riemann problem, expressed as Π θ (x). Combine the above steps 1) to 3), Represents the basic framework of the neural network. The subscript θ represents the neural network parameters.

[0105] 2. Constructing Neural Network Physical Constraint Function

[0106] 5) Calculate the interface specific volume. Based on the output data of the neural network, the interface pressure Π θ (x), calculate the specific volume on the left and right sides of the Riemann problem interface

[0107]

[0108] ε is the Heaviside step function, expressed as

[0109]

[0110] 6) Calculate the function f Q Based on the specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)), calculate the function f on the left and right sides of the Riemann problem interface Q (Π θ (x)):

[0111]

[0112] Here, δ is a small quantity and can be taken as δ = 1.0 × 10 -6 .

[0113] 7) Calculate the physical constraint function. Based on the functions f on the left and right sides of the Riemann problem interface Q (Π θ (x)), calculate the physical constraint function ψ(Π θ (x)

[0114] ψ(Π θ (x)) = fL (Π θ (x))+f R (Π θ (x))+Δu

[0115] 3. Constructing loss function

[0116] 8) Construct the loss function. The loss function is defined as the physical constraint function ψ(Π θ (x))’s mean square error loss function:

[0117]

[0118] Here, N represents the number of samples.

[0119] The embodiment of the present invention provides a method for training an unsupervised neural network model of a compressible gas-water medium Riemann solution integrating physical constraints:

[0120] According to the physical constraint neural network model, through data training, the hyperparameters in the neural network are optimized, including the number of hidden layers H of the neural network, the number of neurons M in each hidden layer, etc., until the physical constraint function ψ(Π θ The training results of (x)) meet the requirements.

[0121] An embodiment of the present invention provides a method for using an unsupervised neural network model of a compressible gas-water medium Riemann solution integrating physical constraints:

[0122] In terms of the use of the neural network model, for different Riemann problem initial conditions x, the neural network model Π obtained at this time θ (x) can output the interface pressure solution p of the Riemann problem I , that is, p I =Π θ (x). Other Riemann problem interface solutions, namely the interface velocity solution and the interface density solution, are obtained based on the interface pressure solution predicted by the neural network, such as Figure 3 Specifically, the calculation formula of the interface velocity solution is:

[0123]

[0124] The calculation formula of the interface density solution is:

[0125]

[0126] The above description is only the best specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0127] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A compressible gas-water medium Riemann solution unsupervised neural network modeling method, characterized in that: include: Construct the neural network input layer and use the initial conditions of the Riemann problem as the input features of the neural network; Constructing a neural network hidden layer after the neural network input layer, wherein the number of neural network hidden layers H and the number of neurons M in each hidden layer are used as adjustable parameters; Constructing a neural network conversion layer after the neural network hidden layer, wherein the nonlinear conversion function in the neural network conversion layer is represented by ζ; A neural network output layer is constructed after the neural network conversion layer as the interface pressure solution of the Riemann problem. The neural network output layer refers to a layer based on the basic framework of the neural network Π θ The output of (x), where the subscript θ represents the neural network parameters; The specific volume ν on the left and right sides of the Riemann problem interface is calculated based on the output layer of the neural network IQ (Π θ (x)), where the subscript I represents the flow field interface; Based on the specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)), calculate the function f on the left and right sides of the Riemann problem interface Q (Π θ (x)); Based on the functions f on the left and right sides of the Riemann problem interface Q (Π θ (x)), calculate the physical constraint function ψ(Π θ (x)); Construct a loss function, which is a physical constraint function ψ(Π θ (x)) is the mean squared error loss function.

2. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 1 is characterized in that: The initial condition of the Riemann problem is expressed as x=[p L ,p R ,ρ L ,ρ R ,Δu] T , where Δu=u R -u L represents the velocity difference on both sides of the flow field interface, p represents the fluid pressure, ρ represents the fluid density, the subscript L represents the left flow field, R represents the right flow field, and T represents transposition.

3. The unsupervised neural network modeling method for compressible gas-water medium Riemann solution according to claim 1 is characterized in that: In the network architecture of the neural network hidden layer, σ is the activation function in the neural network hidden layer, ηj is the linear function of the jth hidden layer, expressed as η j (t) = b j +W j t,W j is the weight matrix corresponding to the jth hidden layer, b j is the bias vector corresponding to the jth hidden layer, and t is the output result of the previous layer of the neural network.

4. The unsupervised neural network modeling method for compressible gas-water medium Riemann solution according to claim 3 is characterized in that: The activation function σ in the hidden layer of the neural network is a hyperbolic tangent activation function, expressed as: Among them, e t is the base of the natural logarithm e raised to the power of t, e -t It is the base of the natural logarithm, e, raised to the power of -t.

5. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 1 is characterized in that: For different Riemann problem initial conditions x, based on the obtained neural network basic framework Π θ (x) Output the interface pressure solution p of the Riemann problem I , that is, p I =Π θ (x); The interface solution of the Riemann problem includes the interface pressure solution, the interface velocity solution and the interface density solution, wherein the interface velocity solution and the interface density solution are obtained according to the interface pressure solution predicted by the neural network.

6. The unsupervised neural network modeling method for compressible gas-water medium Riemann solution according to claim 5, characterized in that: The calculation formula of the interface velocity solution is: The calculation formula of the interface density solution is: Wherein, p represents fluid pressure, u represents fluid velocity, subscript L represents left flow field, subscript R represents right flow field, for gas medium, Γ represents gas specific heat ratio γ, B=0, for water medium, Γ and B represent specific values.

7. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 1 is characterized in that: The nonlinear conversion function ζ in the neural network conversion layer is a Softplus function, which is expressed as: where e t It is the base of the natural logarithm, e, raised to the power of t.

8. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 1, characterized in that: The basic framework of the neural network θ (x) is expressed as: Among them, x is the input of the neural network, η is the linear function of the hidden layer, σ is the activation function in the hidden layer of the neural network, and ζ is the nonlinear conversion function of the neural network.

9. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 1, characterized in that: The specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)) is expressed as: Where ε is the Heaviside step function, expressed as: Where, subscript I represents the flow field interface, subscript L represents the left flow field, subscript R represents the right flow field, and ν Q The specific volume representing the initial condition of the Riemann problem is defined as ν Q =1 / ρ Q , p represents the fluid pressure, ρ represents the fluid density, for gas medium, Γ represents the gas specific heat ratio γ, B=0, for water medium, Γ and B represent specific values.

10. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 6 or 9, characterized in that: For air, γ = 1.4; for water medium, Γ = 4.4, B = 6 × 10 8 Pa.

11. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 9 or 10, characterized in that: The functions f on the left and right sides of the Riemann problem interface Q (Π θ (x)) is expressed as: Among them, δ is a small amount, take δ = 1.0 × 10 -6 .

12. The unsupervised neural network modeling method for compressible gas-water medium Riemann solution according to claim 1, characterized in that: The physical constraint function ψ(Π θ (x)) is expressed as: ψ(Π θ (x))=f L (P θ (x))+f R (P θ (x))+Δu Where Δu=u R -u L It represents the velocity difference on both sides of the flow field interface. The subscript L represents the left flow field, and R represents the right flow field.

13. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 1, characterized in that: The loss function is expressed as: Where N represents the number of samples.

14. The unsupervised neural network modeling method of compressible gas-water medium Riemann solution according to claim 1, characterized in that: Also includes: The constructed loss function is trained to obtain a machine learning model of gas-water medium coupling, and the machine learning model is embedded in a compressible gas-water medium fluid dynamics simulation program to deal with the fluid interface evolution problem caused by the gas-water medium coupling.

15. A compressible gas-water medium Riemann solution unsupervised neural network, characterized in that: include: The neural network input layer uses the initial conditions of the Riemann problem as the input features of the neural network; A neural network hidden layer is arranged after the neural network input layer, and the number of neural network hidden layers H and the number of neurons M in each hidden layer are used as adjustable parameters; A neural network conversion layer, which is arranged after the neural network hidden layer, wherein the nonlinear conversion function is represented by ζ; The neural network output layer is set after the neural network conversion layer, as the interface pressure solution of the Riemann problem, which refers to the basic framework of the neural network Π θ The output value of (x), where the subscript θ represents the neural network parameters; Constraint functions, including physical constraint functions ψ(Π θ (x)) and loss function, where the physical constraint function ψ(Π θ (x)) includes: calculating the specific volume ν on the left and right sides of the Riemann problem interface based on the output layer of the neural network IQ (Π θ (x)), where the subscript I represents the flow field interface; based on the specific volume ν on the left and right sides of the Riemann problem interface IQ (Π θ (x)), calculate the function f on the left and right sides of the Riemann problem interface Q (Π θ (x)); based on the function f on the left and right sides of the Riemann problem interface Q (Π θ (x)) to calculate the physical constraint function ψ(Π θ (x)); the loss function is the physical constraint function ψ(Π θ (x)) is the mean squared error loss function.

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