Neural network processing method and system
Patent Information
- Application Number
- CN202280099223.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-05
- Publication Date
- 2025-04-08
Smart Images
Figure CN119790403A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of data processing, and in particular to a neural network processing method and system. Background Art
[0002] Neural network technology is applied in many fields to solve technical problems, for example, solving partial differential equations (PDEs) that characterize fields such as physics, engineering, and finance. Physics informed neural networks (PINNs) have been proposed for their excellent performance in solving high-dimensional PDEs. By specifying a loss function, the neural network is constrained to satisfy the physical principles and conditions specified by the PDE. In addition, the efficiency of solving PDEs depends largely on these conditions, which becomes a limiting factor and hinders the widespread application of PINNs. Summary of the invention
[0003] The embodiments of the present application provide a neural network processing method and system, which can improve the efficiency of solving differential equations.
[0004] In a first aspect, a neural network processing system is provided, the system comprising: a parameter generator for obtaining extended parameters according to a problem statement parameter of a model, and obtaining a first set of input parameters by applying the extended parameters to the collocation points of the model; and a neural network for running the first set of input parameters to obtain a solution of a differential equation corresponding to the model.
[0005] Optionally, the differential equation is a partial differential equation, which can be used to describe a model, such as but not limited to, a vehicle, a bridge, a fluid, or any other object to be evaluated for various characteristics.
[0006] Optionally, the collocation points are sampled inside the model domain and include spatial coordinates and / or time coordinates.
[0007] Question statement parameters can be used to express the conditions of the model, which is crucial for solving differential equations. In the absence of conditions, differential equations can have infinite solutions. In other words, the process of solving differential equations can be understood as the process of training points to find the result (for example, the output of a neural network) that satisfies the equation and the conditions. Question statement parameters can also be called task parameters or task setting parameters.
[0008] According to the neural network processing system provided in the first aspect, the input of the neural network is not only the collocation points, but also a set of input parameters obtained by applying the extended parameters to the collocation points, and the dimension of this set of input parameters is higher than the dimension of the collocation points. The extended parameters are related to the problem statement parameters of the model. When the neural network starts running, the extended parameters with model characteristics are used to obtain this set of input parameters, thereby improving the efficiency of solving differential equations.
[0009] It should be noted that collocations usually do not include model features. If collocations are used alone as input to a neural network, more calculations may be required to satisfy the equations and conditions.
[0010] In some implementations, the parameter generator is used to decompose the question statement parameters related to the model using basis functions to obtain the extended parameters.
[0011] It should be noted that the extended parameters are obtained by decomposing the problem statement parameters, which include the problem-specific features of the model, and thus can improve the efficiency of solving differential equations.
[0012] In some implementations, the parameter generator is used to select one or more functions from the decomposed question statement parameters as the expansion parameters.
[0013] Optionally, the parameter generator is used to select one or more functions according to the contribution.
[0014] It should be noted that the accuracy of the solution depends largely on the way the model is expressed. In most cases, in order to achieve acceptable accuracy, the model needs to be manually customized according to the specific situation, which makes the physical information neural network less scalable. In the present invention, the selected one or more functions are used as part of the neural network input, which can reduce the need for manual customization, so the above system can achieve acceptable accuracy in different situations.
[0015] For example, the selected N functions are functions with the largest factorization coefficients among the functions selected from the decomposed question statement parameters, where N is greater than or equal to 1. In some implementations, the parameter generator is used to construct one or more coefficient vectors from the decomposed question statement parameters as the extended parameters.
[0016] It is understood that the coefficient vector can be in the form of an amplitude multiplied by a basis function. In addition, the coefficient vector is obtained by decomposing the problem statement parameters. Therefore, the coefficient vector can show how accurately the function approximates the original function.
[0017] It should be noted that when the model problem statement changes, the neural network usually needs to be retrained, and the retraining process may take a lot of time. In the present invention, the coefficient vector constructed as part of the neural network input can avoid the retraining process or reduce the time of the retraining process.
[0018] In some implementations, the problem statement parameters include at least one non-zero parameter of the following parameters associated with the model: boundary conditions, initial conditions, sources, or geometry.
[0019] It should be noted that boundary conditions, initial conditions, sources or geometric shapes can be used to approximate the solution of the model, thereby improving the efficiency of solving differential equations.
[0020] It should be noted that the basis functions that can be used to reveal the problem statement parameters and decomposition methods are not limited. For example, the basis functions are trigonometric functions, polynomial functions, or Bessel functions, but are not limited to this. For example, trigonometric function decomposition can be performed by Fourier transform, and polynomial function decomposition can be performed by approximating the problem statement parameters with a polynomial of a given degree. Therefore, the dimension of the neural network input can be expanded, and the efficiency of solving differential equations can be improved.
[0021] In some implementations, after the neural network runs the first set of input parameters, the parameter generator is used to: adjust the extended parameters, and obtain a second set of input parameters by applying the adjusted extended parameters to the matching points; the neural network is used to: run the second set of input parameters to obtain the solution of the differential equation corresponding to the model.
[0022] For example, the parameter generator can fine-tune expansion parameters, e.g., functions or coefficient vectors, that are applied to the collocation points, thereby changing the parameters that expand the dimensionality of the neural network.
[0023] It should be noted that the parameter generator can adjust the extended parameters multiple times, that is, the neural network can run the adjusted set of input parameters multiple times during the training process. There is no limit to the number of times the parameter generator can adjust the extended parameters.
[0024] It should be noted that the above system can adjust the expansion parameters during operation, which can improve the accuracy and efficiency of solving differential equations.
[0025] In the following, the second aspect provides a neural network processing method corresponding to the neural network processing system in the first aspect. The contents not described in detail can refer to the system embodiment in the first aspect above, and will not be described in detail here.
[0026] In a second aspect, a neural network processing method is provided, comprising: obtaining an extended parameter according to a problem statement parameter of a model; obtaining a first set of input parameters by applying the extended parameter to a collocation point of the model; and running the first set of input parameters to obtain a solution of a differential equation corresponding to the model.
[0027] The above method can be executed by the neural network processing system provided in the first aspect.
[0028] It should be understood that the input of the neural network includes not only the spatial coordinates but also the extended parameters. In addition, the extended parameters are related to the problem statement parameters of the model. When the neural network starts running, the extended parameters with the model characteristics are used as the input of the neural network, thereby improving the efficiency of solving differential equations.
[0029] According to the neural network processing system provided in the first aspect, the input of the neural network is not only the collocation points, but also a set of input parameters obtained by applying the extended parameters to the collocation points, and the dimension of this set of input parameters is higher than the dimension of the collocation points. The extended parameters are related to the problem statement parameters of the model. When the neural network starts running, the extended parameters with model characteristics are used to obtain this set of input parameters, thereby improving the efficiency of solving differential equations.
[0030] In some implementations, obtaining the extended parameters includes: decomposing the question statement parameters using basis functions to obtain the extended parameters.
[0031] In some implementations, obtaining the extended parameters includes: selecting one or more functions from the decomposed question statement parameters as the extended parameters.
[0032] In some implementations, the obtaining of the extended parameters includes: constructing one or more coefficient vectors from the decomposed question statement parameters as the extended parameters.
[0033] In some implementations, the problem statement parameters include at least one non-zero parameter of the following parameters associated with the model: boundary conditions, initial conditions, sources, or geometry.
[0034] In some implementations, the method further includes: adjusting the extended parameters after running the first set of input parameters; obtaining a second set of input parameters by applying the adjusted extended parameters to the matching points; and running the second set of input parameters to obtain the solution of the differential equation corresponding to the model.
[0035] The relevant explanations and beneficial effects of the neural network processing method provided in the second aspect can be referred to the description in the first aspect accordingly, and will not be repeated here.
[0036] In the following, the third aspect provides a neural network processing device corresponding to the neural network processing system in the first aspect. The contents not described in detail can refer to the system embodiment in the first aspect above, and will not be described in detail here.
[0037] In a third aspect, a neural network processing device is provided. The device includes: a decomposition unit, which is used to decompose question statement parameters related to a model using basis functions; a selection unit, which is used to select one or more functions from the decomposed question statement parameters as extension parameters; and a generation unit, which is used to obtain a first set of input parameters by applying the extension parameters to the matching points of the model.
[0038] In the following, the fourth aspect provides a neural network processing device corresponding to the neural network processing system in the first aspect. The contents not described in detail can refer to the system embodiment in the first aspect above, and will not be described in detail here.
[0039] In a fourth aspect, a neural network processing device is provided. The device includes: a decomposition unit, used to decompose question statement parameters related to a model using basis functions; a selection unit, used to select one or more coefficient vectors from the decomposed question statement parameters as extension parameters; and a generation unit, used to obtain a first set of input parameters by applying the extension parameters to the collocation points of the model.
[0040] In a fifth aspect, an embodiment of the present application provides an electronic device. The electronic device has the function of implementing the method in the second aspect. The function can be implemented by hardware, or by hardware executing corresponding software. The hardware of the software includes one or more modules corresponding to the function.
[0041] In a sixth aspect, an embodiment of the present application provides a computer-readable storage medium including instructions. When the instructions are executed on a computer, the computer is caused to execute the method in the second aspect or any possible implementation of the second aspect.
[0042] In a seventh aspect, an electronic device is provided. The electronic device includes a processor and a memory. The processor is connected to the memory. The memory is used to store instructions, and the processor is used to execute the instructions. When the processor executes the instructions stored in the memory, the processor executes the method in the second aspect or any possible implementation of the second aspect.
[0043] In an eighth aspect, a chip system is provided. The chip system includes a memory and a processor, wherein the memory is used to store a computer program, and the processor is used to call the computer program from the memory and run the computer program, so that a server provided with the chip executes the method in the second aspect or any possible implementation of the second aspect.
[0044] In a ninth aspect, an embodiment of the present application provides a computer program product. When the computer program product is run on an electronic device, the electronic device executes the method in the second aspect or any possible implementation of the second aspect.
[0045] Based on the above description, the neural network processing method, device and system provided in the embodiments of the present invention can improve the efficiency of solving differential equations. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] One or more embodiments are exemplarily described by corresponding drawings, and these exemplary descriptions and drawings do not constitute limitations on the embodiments. Elements with the same reference numerals in the drawings are described as similar elements, and the scale of the drawings is not limited. In the drawings:
[0047] Figure 1 is a schematic block diagram of a neural network processing system provided in an embodiment of the present invention;
[0048] Figure 2 is a schematic block diagram of an execution process of a parameter generator provided in an embodiment of the present invention;
[0049] Figure 3 is a schematic block diagram of a parameter generator provided in an embodiment of the present invention;
[0050] Figure 4 is a schematic block diagram of a parameter generator provided in an embodiment of the present invention executed in a first manner;
[0051] Figure 5 is a schematic block diagram of a parameter generator provided in an embodiment of the present invention executed in a second manner;
[0052] Figure 6 is a schematic flow chart of a neural network processing method provided in an embodiment of the present invention;
[0053] Figure 7 is a schematic flow chart of a neural network processing method implemented in a first manner provided in an embodiment of the present invention;
[0054] Figure 8 It is a schematic flow chart of a neural network processing method implemented in the second manner provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0055] In order to understand the features and technical contents of the embodiments of the present invention in more detail, the implementation of the embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, which are only used for reference and illustration and are not used to limit the embodiments of the present invention. In the following technical description, for ease of explanation, many details will be described to provide a thorough understanding of the disclosed embodiments. However, one or more embodiments may be implemented without these details. In other cases, in order to simplify the drawings, well-known structures and devices may be simplified for display.
[0056] 1. Differential Equations
[0057] Many technical problems can be modeled and analyzed using differential equations. An exemplary differential equation is a partial differential equation (PDE). PDEs can be used to describe or model various objects, such as, but not limited to, vehicles, bridges, fluids, or any other object that is evaluated for various characteristics. PDEs are differential equations that include multivariable functions and their partial derivatives.
[0058] For example, the function u(x1,x2,…,x d ) and boundary conditions (BC) are described as the following functions:
[0059]
[0060] in, is the boundary of the domain Ω. It should be noted that the initial condition (IC) can be considered as a special type of boundary condition.
[0061] It is understandable that the question statement may also include a source, a geometric shape, etc. This embodiment of the present invention does not specifically limit this.
[0062] 2. Physics informed neural network (PINN)
[0063] PINN can be applied to different types of PDEs. PINN uses automatic differentiation to embed PDEs into the loss of a neutral network (NN). A neural network with parameter θ can be constructed. to perform automatic differentiation. It can be viewed as a substitute for the solution u(x), which receives input x and outputs a vector with the same dimensions as u. Here, θ = {W l ,b l}, 1≤l≤L is a neural network The main task of PINN is to find a neural network that satisfies both PDE equations and conditions (including boundary conditions, initial conditions, sources, geometric shapes, etc.). Construct two training sets T for differential operators and conditions. f and T b , which results in two terms in the loss function. The differential operator is trained to be close to zero in the collocation points (points in the domain), and the neural network's approximation of the function should be close to the condition, where the loss function can be described as:
[0064]
[0065] By specifying the loss function, the neural network It is restricted to satisfy the physical principles and conditions specified by PDE. Then, the appropriate θ can be searched by minimizing the loss function L.
[0066] The efficiency of PINN depends largely on the construction of the NN-PDE system. The formulation of the problem (regarding IC, BC, source, geometry, etc.) has a great impact on the accuracy of the solution. In addition, the training process also has a great impact on the efficiency.
[0067] Therefore, the present application discloses a neural network processing method and system, which can improve the efficiency of solving differential equations.
[0068] Figure 1 The PINN system 100 for solving differential equations is shown by way of example. Figure 1 As shown, system 100 includes parameter generator 110 and NN 120 .
[0069] The parameter generator 110 is used to obtain extended parameters according to the question statement parameters of the model, and apply the extended parameters to the matching points of the model to obtain a first set of input parameters.
[0070] The NN 120 is used to execute the first set of input parameters to obtain a solution to the differential equation corresponding to the model.
[0071] In general, the PINN system 100 uses a physical information method to solve differential equations with the help of neural networks. By adding extension parameters related to the problem statement parameters of the task to be solved, the dimensionality of the NN input can be automatically expanded. Therefore, the efficiency of solving differential equations can be improved.
[0072] refer to Figure 1Optionally, the differential equation is a partial differential equation that can be used to describe a model, such as, but not limited to, a vehicle, a bridge, a fluid, or any other object to be evaluated for various characteristics. The model can be of various types and can be analyzed using one or more PDEs. The partial differential equation corresponding to the model can be expressed as a technical problem about the model. For example, the method of the present invention can be used to evaluate various characteristics of a physical problem, such as, but not limited to, motion, displacement, change, or any change in sound, heat, electrostatics, fluid flow, elasticity, quantum mechanics, heat transfer, and other dynamic characteristics of the model.
[0073] Problem statement parameters (such as, but not limited to, boundary conditions, initial conditions, sources, or geometry) can be used to explain various features of the model. For example, when analyzing a rigid body, the position of the rigid body is described by six variables, and the dynamic behavior of the rigid body occurs in a finite-dimensional configuration space. When modeling a fluid, the configuration of the fluid occurs in an infinite-dimensional configuration space.
[0074] The parameter generator 110 may generate matching points through space coordinates and time coordinates, and obtain extended parameters according to question statement parameters.
[0075] It should be understood that the input of the neural network is not only the collocation points, but also a set of input parameters obtained by applying the extended parameters to the collocation points, and the dimension of this set of parameters is higher than the dimension of the collocation points. The extended parameters are related to the problem statement parameters of the model. When the neural network starts running, the extended parameters with the model characteristics are used to obtain this set of input parameters, thereby improving the efficiency of solving differential equations.
[0076] Optionally, after NN 120 runs the first set of input parameters, parameter generator 110 is used to adjust the expansion parameters, and apply the adjusted expansion parameters to the matching points to obtain a second set of input parameters; NN 120 is used to run the second set of input parameters to obtain a solution to the differential equation corresponding to the model.
[0077] Optionally, after one or more NN processing iterations, NN 120 may generate a set of output parameters that may be used during the solution process to update the inputs of NN 120. For example, the parameter generator may fine-tune expansion parameters, e.g., functions or coefficient vectors, that are applied to the collocations, thereby changing the parameters that expand the dimensionality of the neural network.
[0078] It should be noted that the parameter generator can adjust the extended parameters multiple times, that is, the neural network can run the adjusted set of input parameters multiple times during the training process. There is no limit to the number of times the parameter generator can adjust the extended parameters.
[0079] It should be noted that the above system can adjust the expansion parameters during operation, which can improve the accuracy and efficiency of solving differential equations.
[0080] For example, the parameter generator 110 may modify the first set of input parameters into a new second set of input parameters according to the accuracy of the output parameters. For another example, the parameter generator 110 may add new parameters to the first set of input parameters according to the accuracy of the output parameters to generate a new set of input parameters. Therefore, the system 100 may fine-tune the extended parameters during operation, which can improve the accuracy and efficiency of solving differential equations.
[0081] In the following, the manner in which the parameter generator 110 generates the first set of input parameters is further disclosed.
[0082] Figure 2 is a schematic block diagram of a parameter generator 110 provided in an embodiment of the present invention.
[0083] The parameter generator 110 may expand the dimension of the NN 120 input by generating a first set of input parameters that are not only collocation points but also a set of input parameters obtained by applying the expansion parameters to the collocation points.
[0084] Generally, the spatial coordinates (x, t) may be randomly sampled in the spatial domain according to a uniform distribution, which is not specifically limited in the embodiment of the present invention.
[0085] There are two main ways to obtain the extended parameters, depending on what these parameters represent. The first way can be to obtain the extended parameters based on the basis functions themselves applied to the collocation points; the second way can be to obtain the extended parameters based on the coefficients decomposed into the basis functions. By solving the problem of automatic neural network model construction in the first way, acceptable accuracy can be achieved under different problem settings. In addition, by solving the problem of automatically selecting coefficients to parameterize the problem, generalization ability can be improved. Both methods can be performed by the parameter generator 110. For example, Figure 3 It is a reference Figure 1 and Figure 2 A block diagram of one example of a parameter generator 110 is shown and described.
[0086] like Figure 3 As shown, some examples of the parameter generator 110 include a decomposition unit 111 , a selection unit 112 , and a generation unit 113 .
[0087] When the parameter generator 110 is applied in the first manner, the decomposition unit 111 can be used to decompose the problem statement parameters using basis functions, wherein the problem statement parameters include at least one non-zero parameter of the following parameters: boundary conditions, initial conditions, sources or geometric shapes. The problem statement parameters may also include any other problem parameters that describe specific features of the model. It should be noted that the problem statement parameters can be used to approximate the solution of the problem, thereby improving the efficiency of solving differential equations.
[0088] It should be noted that the basis functions that can be used to reveal the problem statement parameters and decomposition methods are not limited. For example, the basis functions can be trigonometric functions, polynomial functions, or Bessel functions. Optionally, the trigonometric function decomposition can be performed by Fourier transform, and the polynomial function decomposition can be performed by approximating the problem setting parameters with a polynomial of a given degree. It should be noted that trigonometric functions, polynomial functions, and Bessel functions can all be used to reveal the problem statement parameters, thereby expanding the dimension of the neural network input and improving the efficiency of solving differential equations.
[0089] The selection unit 112 may be configured to select one or more functions from the decomposed question statement parameters as expansion parameters.
[0090] Optionally, the selection unit 112 is configured to select one or more functions according to the contribution degree.
[0091] For example, the selection unit 112 selects the approximate values (f1(x, t), f2(x, t), ..., f N The contribution of each function to (x, t) is selected from N functions, where N is a positive integer.
[0092] For example, the selected N functions are functions with the largest factorization coefficients among the functions selected from the decomposed question statement parameters.
[0093] Alternatively, in a first experiment, N may be equal to 1 or 2; or, the number of functions may be selected so as to provide an approximation of the problem statement with a desired accuracy, for example, to achieve 95% accuracy of the BC approximation, 10 basis functions are sufficient, so if the accuracy target is 95%, N is equal to 10. Thus, the efficiency of solving differential equations can be improved.
[0094] Optionally, after each training, the accuracy of the output is checked. If the accuracy is less than a preset value (eg, 90%), other M functions are selected according to the factorization coefficients. M is a positive integer, for example, M is equal to 1 or 2.
[0095] For example, in the first experiment, the selection unit 112 selects N functions, and after approximation, the selection unit 112 selects the function with the largest factorization coefficient, and checks the accuracy starting from one function. If the accuracy is less than 90%, another function is added and the accuracy is checked again, and so on.
[0096] The generation unit 113 may be used to expand the dimensionality of the NN input using one or more functions selected to be applied to the collocation points.
[0097] For example, the first set of input parameters includes x', t', g1(x', t'), g2(x', t') ... g N (x', t'), where the point (x', t') is the coordinate, g1(x', t'), g2(x', t')...g N (x',t') are the selected N functions.
[0098] It should be noted that the accuracy of the solution depends largely on the way the model is expressed. In most cases, in order to achieve higher accuracy, the model needs to be manually customized according to the specific situation, which makes the physical information neural network less scalable. In the present invention, the selected one or more functions are used as part of the neural network input, which can reduce the need for manual customization, so the above system can achieve acceptable accuracy in different situations.
[0099] When the parameter generator 110 is applied in the second manner, the decomposition unit 111 may be used to decompose the question sentence parameters using basis functions.
[0100] The decomposition process is similar to that of the first method and will not be described here.
[0101] The selection unit 112 may be configured to construct one or more coefficient vectors as expansion parameters from the decomposed question statement parameters.
[0102] It can be understood that the coefficient vector can be in the form of amplitudes obtained by decomposition using basis functions. In addition, the coefficient vector is obtained by decomposing the problem statement parameters. Therefore, the coefficient vector can show how accurately the function approximates the original function. For example, if the solution is to be generalized by different problem statement parameters, several coefficient vectors can be obtained, which are in the form of [(x,a1),(x,a2),…,(x,a n )], where x = x1, x2, ... x n , represents the collocation point, a n =a n1 、a n2 ……a nm , represents a coefficient vector, but is not limited to this.
[0103] For example, the selection unit 112 can construct a set of coefficient vectors corresponding to the basis functions for different question statements (for parameterizing the model) (e.g., (P1, P2, ... P N )), and construct collocations (x1, t1; x2, t2; ...; x N ,t N ).
[0104] The generation unit 113 is used to expand the NN input using one or more coefficient vectors.
[0105] It should be noted that when the question statement changes, the neural network usually needs to be retrained, and the retraining process may take a lot of time. In the present invention, the coefficient vector constructed as part of the neural network input can avoid the retraining process or reduce the time of the retraining process.
[0106] In addition, it should be noted that basis functions (such as but not limited to trigonometric functions and Chebyshev polynomial functions) can be used to decompose question statement parameters.
[0107] For example, the Fourier transform allows one to take essentially arbitrary (complex-valued) functions, in this case corresponding to the problem statement parameters of the model (e.g., initial conditions, boundary conditions, sources, geometry), and decompose functions that depend on space or time into functions that depend on spatial or temporal frequencies. This helps to approximate the problem statement using a family of trigonometric functions that vary in frequency and amplitude. The corresponding interpolating polynomials minimize the Runge phenomenon and provide the best consistent approximation of polynomials on continuous functions.
[0108] In one example of the first method applied to the decomposition unit 111, Figure 4 An example of the parameter generator 110 applied in the first way is shown.
[0109] For example, the famous Korteweg-De Vries equation derived from hydroacoustics is used to verify the neural network processing system provided in the embodiment of the present invention. The Korteweg-De Vries equation related to hydroacoustics can be expressed as:
[0110]
[0111] Among them, the function u is the surface elevation, which can be used to represent the elliptical cosine wave on the water surface, the water depth is h, and g represents the value of the earth's gravity.
[0112] The problem statement parameters (initial conditions, boundary conditions and sources) can be expressed as:
[0113]
[0114] source:0
[0115] Among them, cn represents the Jacobi elliptic function, u0 represents the trough level, Δ represents the width parameter, m represents the ellipse parameter, c represents the phase velocity, and H represents the wave height.
[0116] The problem statement parameters are decomposed by Fourier transform into: sin(2πf x1 x), cos(2πf x1 x)……sin(2πf t1 t), sin(2πf t1 t), etc. Therefore, the input of the NN includes the expanded parameters decomposed by Fourier transform.
[0117] The calculations show that the first method can improve the accuracy by up to 35 times compared to the method without using the extended parameters as NN input. In addition, the first method improves the accuracy without increasing the calculation time.
[0118] In one example of the second method applied to the decomposition unit 111, Figure 5 An example of the parameter generator 110 applied in the second way is shown.
[0119] For another example, the famous Korteweg-De Vries equation with soliton solution is used to verify the neural network processing system provided in the embodiment of the present invention. The Korteweg-De Vries equation with soliton solution can be expressed as:
[0120]
[0121] Among them, the problem statement parameters (initial conditions, boundary conditions and sources) can be expressed as:
[0122]
[0123] source:0
[0124] Among them, a and b represent independent parameters that affect the boundary appearance and initial conditions, on this basis the problem is parameterized.
[0125] A set of question statement parameters (with different a and b) can be decomposed into a0, a1x, a2x2...a through polynomial approximation. N x N . Coefficient vector a0, a1, a2...a N is the expansion parameter. Therefore, an input to NN is [x, t, a 01 ,a 11 ,…,aN1 ], and the other input is [x,t,a 0m ,a 1m ,…,a Nm ]. x, t can be the same in all inputs. NN is trained on the entire large dataset.
[0126] Calculations have proven that this innovation increases training speed and achieves the desired accuracy (up to 100 times improvement), which is higher than the original method (the present application provides up to 3 times accuracy improvement in RMSE and up to 2.7 times accuracy improvement in relative error).
[0127] The device embodiment is described above, and the method embodiment will be described below. It should be understood that the description of the method embodiment corresponds to the description of the device embodiment. Therefore, the content not described in detail can refer to the above device embodiment, and for the sake of brevity, it will not be repeated here.
[0128] Figure 6 The process flow chart of the neural network processing method provided by the embodiment of the present invention is shown. The method is applied to the neural network processing system 100, and the method is applied to the neural network processing system 100 provided in the above embodiment, the system 100 includes a parameter generator and a NN, and the method includes the following steps:
[0129] S610: Acquire extended parameters according to the question statement parameters of the model;
[0130] S620: Obtain a first set of input parameters by applying the extended parameters to the collocation points of the model;
[0131] S630: Execute the first set of input parameters to obtain a solution to the differential equation corresponding to the model.
[0132] Optionally, the differential equation is a partial differential equation, which can be used to describe a model, such as but not limited to, a vehicle, a bridge, a fluid, or any other object to be evaluated for various characteristics.
[0133] Optionally, obtaining the extended parameters includes: using a basis function to decompose the question statement parameters to obtain the extended parameters.
[0134] Optionally, obtaining the extended parameters includes: selecting one or more functions from the decomposed question statement parameters as extended parameters.
[0135] Optionally, obtaining the extended parameters includes: constructing one or more coefficient vectors as extended parameters from the decomposed question statement parameters.
[0136] Optionally, the problem statement parameters include at least one non-zero parameter of the following parameters associated with the model: boundary conditions, initial conditions, sources, or geometry.
[0137] Optionally, the method further includes: adjusting the extended parameters after running the first set of input parameters; obtaining the second set of input parameters by applying the adjusted extended parameters to the matching points; and running the second set of input parameters to obtain a solution to the differential equation corresponding to the model.
[0138] It should be understood that the input of the neural network is not only the collocation points, but also a set of input parameters obtained by applying the extended parameters to the collocation points, and the dimension of this set of parameters is higher than the dimension of the collocation points. The extended parameters are related to the problem statement parameters of the model. When the neural network starts running, the extended parameters with the model characteristics are used to obtain this set of input parameters, thereby improving the efficiency of solving differential equations.
[0139] exist Figure 6 In the illustrated embodiment, the parameter generator is the same as the parameter generator 110 in the system 100 in the above embodiment, and the NN is the same as the NN 120 in the system 100 in the above embodiment. The relevant contents are referred to the above description and will not be repeated here.
[0140] Figure 7 The process flow chart of the neural network processing method provided by the embodiment of the present invention is shown. The method is applied to the neural network processing system 100, and the method is applied to the neural network processing system 100 provided in the above embodiment, the system 100 includes a parameter generator and a NN, and the method includes the following steps:
[0141] S710: The parameter generator obtains question statement parameters related to the model.
[0142] S720: The parameter generator uses basis functions to decompose the question statement parameters.
[0143] S730: The parameter generator selects one or more functions as extended parameters.
[0144] S740: The parameter generator obtains the matching points of the model.
[0145] S750: Obtain a first set of input parameters by applying the extended parameters to the collocation points of the model.
[0146] S760: The NN runs the first set of input parameters to obtain a solution to the differential equation corresponding to the model.
[0147] Optional S770: The NN determines whether additional fine-tuning is required based on the solution obtained in S760. For example, if the accuracy of the solution meets the preset conditions, additional fine-tuning is not required. If the accuracy of the solution does not meet the preset conditions, additional fine-tuning is required. In addition, if additional fine-tuning is required, the above process returns to S720, that is, the preliminary solution is passed to the parameter generator.
[0148] For example, if the NN determines that additional fine-tuning is required, the parameter generator may regenerate input parameters that are a second set of input parameters obtained by the parameter generator applying adjusted extended parameters to the matching points, and the second set of input parameters is run by the NN to obtain a solution to the differential equation corresponding to the model.
[0149] It should be noted that S720 to S770 can be performed multiple times. The parameter generator can adjust the extended parameters multiple times, that is, the neural network can run the adjusted set of input parameters multiple times during the training process. The number of times the parameter generator adjusts the extended parameters is not limited.
[0150] It should be noted that the accuracy of the solution depends largely on the way the model is expressed. In most cases, in order to achieve acceptable accuracy, the model needs to be manually customized according to the specific situation, which makes the physical information neural network less scalable. In the present invention, the selected one or more functions are used as part of the neural network input, which can reduce the need for manual customization, so the above system can achieve acceptable accuracy in different situations.
[0151] exist Figure 7 In the illustrated embodiment, the parameter generator is the same as the parameter generator 110 in the system 100 in the above embodiment, and the NN is the same as the NN 120 in the system 100 in the above embodiment. The relevant contents are referred to the above description and will not be repeated here.
[0152] Figure 8 The process flow chart of the neural network processing method provided by the embodiment of the present invention is shown. The method is applied to the neural network processing system 100, and the method is applied to the neural network processing system 100 provided in the above embodiment, the system 100 includes a parameter generator and a NN, and the method includes the following steps:
[0153] S810: Send question statement parameters related to the model to a parameter generator.
[0154] S820: The parameter generator decomposes the question statement using basis functions.
[0155] S830: The parameter generator constructs one or more coefficient vectors as extended parameters.
[0156] S840: The parameter generator obtains the matching points of the model.
[0157] S850: Obtain a first set of input parameters by applying the extended parameters to the collocation points of the model.
[0158] S860: The NN runs the first set of input parameters to obtain a solution to the differential equation corresponding to the model.
[0159] Optional S870: The NN determines whether additional fine-tuning is required based on the solution obtained in S860. If additional fine-tuning is required, the above process returns to S820, that is, the preliminary solution is passed to the parameter generator.
[0160] Similarly, S820 to S870 may be performed multiple times, which will not be described in detail here.
[0161] exist Figure 8 In the illustrated embodiment, the parameter generator is the same as the parameter generator 110 in the system 100 in the above embodiment, and the NN is the same as the NN 120 in the system 100 in the above embodiment. The relevant contents are referred to the above description and will not be repeated here.
[0162] The terms used in this application are only used to describe the embodiments and are not used to limit the claims. The singular forms "one / a kind (a)" and "the" used in the description of the embodiments and claims also include plural forms, unless the context clearly indicates otherwise. Similarly, the term "and / or" used in this application represents and includes any or all possible combinations of one or more associated list items. In addition, the term "including" and its variants used in this application indicate the presence of the features, integers, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their combinations.
[0163] The various aspects, embodiments, implementations or features of the described embodiments may be used alone or in any combination. The various aspects of the described embodiments may be implemented by software, hardware, or a combination of software and hardware. The described embodiments may also be embodied by a computer-readable medium storing computer-readable code, the computer-readable code comprising instructions executable by at least one computing device. The computer-readable medium may be associated with any data storage device that can store data readable by a computer system. Examples of computer-readable media may include read-only memory, random access memory, CDROM, HDD, DVD, magnetic tape, and optical data storage devices. The computer-readable medium may also be distributed in a network-coupled computer system so that the computer-readable code is stored and executed in a distributed manner.
[0164] The above technical description can be made with reference to the accompanying drawings, which form part of the present application and illustrate the implementation mode according to the described embodiments by description. Although these embodiments are described in sufficient detail to enable those skilled in the art to implement these embodiments, these embodiments are not restrictive; therefore, other embodiments can be used and can be changed without departing from the scope of the described embodiments. For example, the order of the operations described in the flowchart is not restrictive, so the order of two or more operations shown in the flowchart and described according to the flowchart can be changed according to several embodiments. For example, in several embodiments, one or more operations shown in the flowchart and described according to the flowchart are optional or can be deleted. In addition, certain steps or functions can be added to the disclosed embodiments, or the order of two or more steps can be exchanged. All these changes are deemed to be included in the disclosed embodiments and claims.
[0165] In addition, the terms used in the above technical description are used to provide a thorough understanding of the described embodiments. However, too much detail is not required to implement the described embodiments. Therefore, the description of the above embodiments is for the purpose of illustration and description. The embodiments proposed in the above description and the examples disclosed according to these embodiments are provided separately to increase the context and facilitate the understanding of the described embodiments. The above description is not intended to be exhaustive, nor is it intended to limit the described embodiments to the precise form of the invention. According to the above guidance, several modifications, selections and changes can be made. In some cases, in order to avoid unnecessary impact on the described embodiments, well-known process steps are not described in detail.
Claims
1. A neural network processing system, characterized in that: include: a parameter generator for obtaining extended parameters according to the problem statement parameters of the model, and obtaining a first set of input parameters by applying the extended parameters to the collocation points of the model; A neural network is configured to execute the first set of input parameters to obtain a solution to a differential equation corresponding to the model.
2. The system according to claim 1, characterized in that The parameter generator is specifically used for: The question statement parameters are decomposed using basis functions to obtain the extended parameters.
3. The system according to claim 2, characterized in that The parameter generator is specifically used for: One or more functions are selected from the decomposed question statement parameters as the expansion parameters.
4. The system according to claim 2, characterized in that The parameter generator is specifically used for: One or more coefficient vectors are constructed from the decomposed question statement parameters as the expansion parameters.
5. The system according to any one of claims 2 to 4, characterized in that The problem statement parameters include at least one non-zero parameter of the following parameters associated with the model: boundary conditions, initial conditions, sources, or geometry.
6. The system according to any one of claims 1 to 5, characterized in that After the neural network is run with the first set of input parameters, the parameter generator is used to: adjusting the extended parameters, and obtaining a second set of input parameters by applying the adjusted extended parameters to the matching points; The neural network is used to: The second set of input parameters is run to obtain the solution to the differential equation corresponding to the model.
7. A neural network processing method, characterized in that: include: Get the extended parameters according to the question statement parameters of the model; Obtaining a first set of input parameters by applying the extended parameters to the collocation points of the model; The first set of input parameters is run to obtain a solution to a differential equation corresponding to the model.
8. The method according to claim 7, characterized in that The obtaining of extended parameters includes: The question statement parameters are decomposed using basis functions to obtain the extended parameters.
9. The method according to claim 8, characterized in that The obtaining of extended parameters includes: One or more functions are selected from the decomposed question statement parameters as the expansion parameters.
10. The method according to claim 8, characterized in that The obtaining of extended parameters includes: One or more coefficient vectors are constructed from the decomposed question statement parameters as the expansion parameters.
11. The method according to any one of claims 8 to 10, characterized in that The problem statement parameters include at least one non-zero parameter of the following parameters associated with the model: boundary conditions, initial conditions, sources, or geometry.
12. The method according to any one of claims 8 to 11, characterized in that Also includes: After running the first set of input parameters, adjusting the extended parameters; Obtaining a second set of input parameters by applying the adjusted extended parameters to the matching points; The second set of input parameters is run to obtain the solution to the differential equation corresponding to the model.
13. A computer-readable storage medium having instructions, characterized in that: When the instructions are executed on a computer, the computer is caused to perform the method according to any one of claims 7 to 12.
14. An electronic device, characterized in that: It comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor is used to call the computer program from the memory and run the computer program, so that a computer provided with a chip executes the method according to any one of claims 7 to 12.
15. A computer program product, characterized in that When the computer program product is run on a computer, the computer is caused to execute the method according to any one of claims 7 to 12.