Physical information neural network training method and device, equipment and medium
By using Voronoi graphs in physical information neural networks to optimize the distribution of residual points, the training convergence problem caused by uneven distribution of residual points in the prior art is solved, and higher training accuracy and stability are achieved.
Patent Information
- Application Number
- CN202411567759.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-05
- Publication Date
- 2025-02-18
AI Technical Summary
The residual point generation method in the existing physical information neural network only considers the location of the points and does not consider the division of the space occupied by the points, resulting in too many distributions in narrow spaces or too few distributions in broad spaces, affecting training convergence.
The Voronoi graph is used to optimize the position of residual points, generate the centroid Voronoi graph or constrained Voronoi graph, and use it for the training process of physical information neural networks. By optimizing the discrete point distribution of the Voronoi graph, it conforms to the density distribution of the residuals of the physical information neural network.
It significantly improves the accuracy of physical information neural network training and shows high stability under different initialization conditions.
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Figure CN119476387A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of neural network training, and in particular to a physical information neural network training method, device, equipment and medium. Background Art
[0002] Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving partial differential equations (PDEs). By incorporating the residuals of the PDEs into the loss function of the neural network using automatic differentiation, PINNs can seamlessly combine real-world measurement data with the physical constraints given by the differential equations. Compared to traditional numerical PDE solvers (such as the finite difference method and the finite element method), PINNs are meshless and therefore highly flexible, and are well suited for solving high-dimensional problems. So far, PINNs have been shown to be useful in a variety of physical scenarios.
[0003] Despite the success of PNNs, they still face challenges in accuracy, computational efficiency, and training robustness, especially for problems with complex geometries and multi-scale phenomena. Therefore, a series of extensions to the basic PNNs have been proposed. These improvements can be summarized as follows: time-marching causality, where related work points out that existing PNN forms cannot respect the spatiotemporal causal structure inherent in the evolution of physical systems; loss recalibration, where researchers adjust the weights of each residual point to address hard-to-fit regions; innovative optimizers and novel loss functions, where the objective function is improved to make the loss function smoother; and domain decomposition, where these works decompose the solution domain of complex problems into smaller units and address smooth transitions at the boundaries, thereby reducing the difficulty of training PNNs. Optimizing the distribution of residual points in the solution space is also an important improvement. Existing techniques treat residual points as limited resources, hoping to reasonably allocate residual points based on residual values, focusing on hard-to-fit regions while not ignoring other areas that may cause training degradation.
[0004] The existing technology is mainly divided into two residual point generation methods: uniform sampling and adaptive sampling, where adaptive sampling can be achieved in two ways: repeated addition of points and repeated sampling. Equidistant grid sampling and random sampling are the two most commonly used uniform sampling methods. In addition, Latin hypercube sampling, Sobol sampling, Halton sampling and Hammersley sampling are also gradually applied to the training process of physical information neural networks, and are usually better than the first two methods. The remaining adaptive sampling methods include the residual-based adaptive refinement (RAR) method, which is improved by repeatedly adding new residual points. Similarly, there is an improved version of the residual-based adaptive distribution (RAD) method and the (residual-based adaptive refinement with distribution, RAR-D) method, etc. The main difference between these studies lies in the form of the probability density function.
[0005] The above residual point generation methods only consider the position of the points, without considering the division of the space occupied by the points. Too many residual points distributed in a small space or too few in a wide space are not conducive to the training convergence of PINN. In this case, although those adaptive sampling methods can adaptively adjust the point distribution according to the residual, they cannot balance the high and low residual areas well, resulting in unstable results. Summary of the invention
[0006] In view of this, an embodiment of the present application provides a residual point generation method for improving the accuracy of a physical information neural network, so as to achieve the purpose of improving the accuracy of a physical information neural network.
[0007] The embodiment of the present application provides the following technical solution: a physical information neural network training method, comprising: Acquire initial residual points in the calculation region, use the initial residual points as discrete points of the Voronoi diagram, and generate an initial Voronoi diagram according to the calculation region and the initial residual points, so as to divide the calculation region into a plurality of Voronoi units, and each of the Voronoi units corresponds to one initial residual point; Optimizing the initial Voronoi diagram at discrete points to generate a centroid Voronoi diagram or a constrained Voronoi diagram; The discrete points in each Voronoi unit in the centroid Voronoi diagram or the constrained Voronoi diagram are used in the training process of the physical information neural network.
[0008] According to an embodiment of the present application, performing discrete point optimization on the initial Voronoi diagram to generate a centroid Voronoi diagram includes: The distance from each point in the initial Voronoi diagram to the nearest discrete point to the point is expressed as a first formula; A weight is set for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; the product of the first formula and the weight of the corresponding point is expressed as a second formula; According to the second formula, a weighted sum of the shortest distances from each point in the initial Voronoi diagram to a discrete point in the Voronoi diagram is expressed as a third formula; The third formula is minimized so that the discrete point distribution of the obtained centroid Voronoi diagram conforms to the density distribution of the physical information neural network residual.
[0009] According to an embodiment of the present application, the third formula is expressed as:
[0010] in, is the weighted sum of the shortest distances from each point in the initial Voronoi diagram to the discrete points in the Voronoi diagram, is the number of Voronoi cells in the initial Voronoi diagram, For point The weight of , is the physical information neural network residual, is the distance from each point in the initial Voronoi diagram to the nearest discrete point, and X represents a discrete point in the Voronoi diagram.
[0011] According to an embodiment of the present application, minimizing the third formula includes: minimizing the third formula using an L-BFGS algorithm.
[0012] According to an embodiment of the present application, performing discrete point optimization on the initial Voronoi diagram to generate a constrained Voronoi diagram includes: Setting a weight for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; Applying constraints related to the weight to each Voronoi unit in the initial Voronoi diagram respectively, so that the weight accumulation of the points in each Voronoi unit is equal; The sum of the weight accumulation amounts in each Voronoi cell in the initial Voronoi diagram is expressed as a fourth formula; The fourth formula is minimized so that the obtained discrete point distribution of the constrained Voronoi diagram conforms to the density distribution of the physical information neural network residual.
[0013] According to an embodiment of the present application, the fourth formula is expressed as:
[0014] in, is the sum of the weight accumulation of each Voronoi unit in the initial Voronoi diagram, X represents the discrete point of the Voronoi diagram, is the number of Voronoi cells in the initial Voronoi diagram, For point The weight of is the physical information neural network residual, and c is the weight accumulation of each point in the Voronoi cell.
[0015] According to an embodiment of the present application, minimizing the fourth formula includes: minimizing the fourth formula using an L-BFGS algorithm.
[0016] The present application also provides a physical information neural network training device, comprising: A Voronoi diagram generation module, used for obtaining initial residual points in a calculation area, taking the initial residual points as discrete points of a Voronoi diagram, and generating an initial Voronoi diagram according to the calculation area and the discrete points, so as to divide the calculation area into a plurality of Voronoi units, and each of the Voronoi units corresponds to one initial residual point; An optimization module, used for performing discrete point optimization on the initial Voronoi diagram to generate a centroid Voronoi diagram or a constrained Voronoi diagram; A neural network training module is used to use the residual points in each Voronoi unit in the centroid Voronoi diagram or the constrained Voronoi diagram for the training process of the physical information neural network.
[0017] The present application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned physical information neural network training method when executing the computer program.
[0018] The present application also provides a computer-readable storage medium, which stores a computer program for executing the above-mentioned physical information neural network training method.
[0019] Since the residual point generation method in the physical information neural network in the prior art only considers the position of the point, but does not consider the division of the space occupied by the point, and the residual points are too many in a small space or too few in a wide space, which is not conducive to the training convergence of PINN. Therefore, compared with the prior art, the beneficial effects that can be achieved by at least one of the above technical solutions adopted in the embodiments of this specification include at least: the embodiment of the present invention proposes a new residual point generation method for the training of the physical information neural network, and optimizes the position of the residual point by using the Voronoi diagram. The stations (discrete points) corresponding to the obtained Voronoi diagram are used as the residual points for the subsequent neural network optimization, which can significantly improve the accuracy of the physical information neural network training and is relatively stable when facing different initialization conditions. BRIEF DESCRIPTION OF THE DRAWINGS
[0020] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0021] Figure 1 This is a flow chart of a physical information neural network training method according to an embodiment of the present invention; Figure 2 A schematic diagram of an adaptive residual point generation algorithm in an embodiment of the present invention; Figure 3 (a) and (b) are schematic diagrams of uniform residual point generation algorithms in embodiments of the present invention; FIG4(a), FIG4(b), FIG4(c), and FIG4(d) are schematic diagrams of residual point distribution of the adaptive sampling method RCVT of an embodiment of the present invention under the Navier-Stokes (NS) equation; FIG5(a), FIG5(b), FIG5(c), and FIG5(d) are schematic diagrams of distribution of RVT residual points of the adaptive sampling method of an embodiment of the present invention under the Navier-Stokes (NS) equation; Figure 6 It is a structural diagram of a physical information neural network training device according to an embodiment of the present invention; Figure 7 It is a schematic diagram of the structure of the computer device of the present invention. DETAILED DESCRIPTION
[0022] The embodiments of the present application are described in detail below with reference to the accompanying drawings.
[0023] The following describes the implementation methods of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present application.
[0024] like Figure 1 As shown, an embodiment of the present invention provides a physical information neural network training method, comprising: S101. Acquire an initial residual point in the calculation region, use the initial residual point as a discrete point of the Voronoi diagram, and generate an initial Voronoi diagram according to the calculation region and the initial residual point, so as to divide the calculation region into a plurality of Voronoi units, and each Voronoi unit corresponds to one initial residual point; S102. Optimize the initial Voronoi diagram for discrete points to generate a centroid Voronoi diagram or a constrained Voronoi diagram; S103. Using the discrete points in each Voronoi unit in the centroid Voronoi diagram or the constrained Voronoi diagram for the training process of the physical information neural network.
[0025] In view of the problems and shortcomings in the prior art, the embodiment of the present invention proposes a residual point generation method for improving the accuracy of a physical information neural network to train a physical information neural network. The method generates residual points based on the Voronoi diagram partitioning result. The Voronoi diagram is a method of dividing a domain into each region close to a given set of points in the domain (called discrete points or sites). For each site (discrete point), there is a corresponding region, called a Voronoi unit, which consists of all points that are closer to the site than to any other point. Directly applying the above-mentioned Voronoi diagram partitioning method will result in uneven heights of the units in the region. Therefore, the present invention proposes an improved partitioning method for the centroid Voronoi diagram. Common methods for generating centroid Voronoi diagrams are the Lloyd method and the Newton optimization method. Another intuitive method to improve the spatial partitioning result is to adjust the position of the point so that the specific values related to the size of the Voronoi region occupied by the point are as equal as possible to enhance the uniformity of each region, which is a constrained Voronoi diagram. The new sampling methods proposed in the embodiments of the present invention are based on the above-mentioned two improved Voronoi diagram segmentations. The embodiment of the invention uses all the sites in the Voronoi cells as the residual points used in PINN.
[0026] In one implementation of an embodiment of the present invention, the initial Voronoi diagram is optimized for discrete points to generate a centroid Voronoi diagram, including: expressing the distance from each point in the initial Voronoi diagram to the discrete point closest to the point as a first formula; setting a weight for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; expressing the product of the first formula and the weight of the corresponding point as a second formula; according to the second formula, expressing the weighted sum of the shortest distances from each point in the initial Voronoi diagram to the discrete points of the Voronoi diagram as a third formula; and minimizing the third formula so that the discrete point distribution of the obtained centroid Voronoi diagram conforms to the density distribution of the residual of the physical information neural network.
[0027] In this embodiment, the third formula is expressed as:
[0028] in, is the weighted sum of the shortest distances from each point in the initial Voronoi diagram to the discrete points in the Voronoi diagram, is the number of Voronoi cells in the initial Voronoi diagram, For point The weight of is the physical information neural network residual, is the distance from each point in the initial Voronoi diagram to the nearest discrete point, and X represents a discrete point in the Voronoi diagram.
[0029] Wherein, the L-BFGS algorithm is used to minimize the third formula.
[0030] In another implementation of the embodiment of the present invention, the initial Voronoi diagram is optimized for discrete points to generate a constrained Voronoi diagram, including: setting weights for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; applying constraints related to the weights to each Voronoi unit in the initial Voronoi diagram, so that the accumulated weights of the points in each Voronoi unit are equal; expressing the sum of the accumulated weights of each Voronoi unit in the initial Voronoi diagram as a fourth formula; and minimizing the fourth formula so that the obtained discrete point distribution of the constrained Voronoi diagram conforms to the density distribution of the residual of the physical information neural network.
[0031] In this embodiment, the fourth formula is expressed as:
[0032] in, is the sum of the weight accumulation of each Voronoi unit in the initial Voronoi diagram, X represents the discrete point of the Voronoi diagram, is the number of Voronoi cells in the initial Voronoi diagram, For point The weight of is the physical information neural network residual, and c is the weight accumulation of each point in the Voronoi unit. The L-BFGS algorithm is used to minimize the fourth formula.
[0033] Next, a specific embodiment is used to describe step S102 in the method in detail.
[0034] This step uses the following two steps: Step (1): Point optimization generation method based on Voronoi diagram.
[0035] Step (2): Residual point distribution method based on the above point generation algorithm.
[0036] Next, we will explain each step in this process in detail: The step (1) mainly comprises the following steps: Step (1-1): Point optimization generation method based on Voronoi diagram - objective function.
[0037] Assume that in the defined space domain There is a set of points , called a site (i.e. the discrete point mentioned above). The unit of the Voronoi diagram Satisfies the following properties:
[0038] Assuming Voronoi cells There is a point inside ,from arrive The distance to the nearest station is: Similarly, All points in The sum of the shortest distances can also be expressed as ,in is the number of cells in the Voronoi space, if each point There is a weight ,but All points in The weighted sum of the shortest distances can also be expressed as the following energy function (the third formula above):
[0039] By optimizing the site position to minimize , the resulting Voronoi diagram is called the Centroid Voronoi Diagram (CVT).
[0040] In another optimization method, constraints are imposed on the Voronoi cells , to ensure that the function in each unit The Voronoi diagram obtained by equal accumulation is called the constrained Voronoi diagram. It is expressed as the minimization of the following energy function (the fourth formula above):
[0041] Step (1-2): Point optimization generation method based on Voronoi diagram - optimization algorithm.
[0042] This embodiment uses the quasi-Newton method to minimize equations (2) and (3). The gradient of equation (2) is ,in The density can be regarded as of The mass center of mass. The gradient of equation (3) is ,in is with The number of adjacent Voronoi cells, is the Voronoi cell and This embodiment applies the L-BFGS method to minimize the two energy functions.
[0043] The step (2) mainly includes the following steps: Step (2-1): Adaptive residual point generation based on the above point generation algorithm.
[0044] Using the above node generation algorithm, the distribution of residual points can be obtained. If the weight is set in the energy function ,and and If the optimization is based on equation (2), the point generation algorithm based on residuals is called RCVT sampling. If the optimization is based on equation (3), the point generation algorithm based on residuals is called residual constrained Voronoi tessellation (RVT) sampling. Figure 2 For any point in the PDE solution domain , first calculate the PDE residual , then calculate , as shown below: in It is normalized , this embodiment performs a gamma transform on it, aiming to adjust the contrast of the residual amplitudes between different regions.
[0045] Step (2-2): Generate uniform residual points based on the above point generation algorithm.
[0046] Next, we will explain two methods for generating uniform residual points. , then the point after minimizing the energy function As uniform residual sampling points. In addition, if the optimization is based on equation (2), this uniform point generation algorithm is called CVT sampling. If the optimization is based on equation (3), it means that all Voronoi cells are expected to have the same area, so this generation process is called area-constrained Voronoi tessellation (AVT) sampling, such as Figure 3 shown.
[0047] The embodiment of the present invention includes two types of uniform sampling methods, two types of uniform resampling methods and two types of adaptive sampling methods. The two types of adaptive sampling methods can significantly improve the accuracy of PINN training and are relatively stable when facing different initialization conditions, as shown in Figures 4 and 5.
[0048] like Figure 6 As shown, the present application also provides a physical information neural network training device 200, comprising: A Voronoi diagram generation module 201 is used to obtain initial residual points in the calculation area, use the initial residual points as discrete points of the Voronoi diagram, and generate an initial Voronoi diagram according to the calculation area and the discrete points, so as to divide the calculation area into a plurality of Voronoi units, and each of the Voronoi units corresponds to one initial residual point; An optimization module 202 is used to perform discrete point optimization on the initial Voronoi diagram to generate a centroid Voronoi diagram or a constrained Voronoi diagram; The neural network training module 203 is used to use the residual points in each Voronoi cell in the centroid Voronoi diagram or the constrained Voronoi diagram for the training process of the physical information neural network.
[0049] In specific implementation, the optimization module 202 performs discrete point optimization on the initial Voronoi diagram to generate a centroid Voronoi diagram, including: expressing the distance from each point in the initial Voronoi diagram to the nearest discrete point to the point as a first formula; setting a weight for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; expressing the product of the first formula and the weight of the corresponding point as a second formula; according to the second formula, expressing the weighted sum of the shortest distances from each point in the initial Voronoi diagram to the discrete points of the Voronoi diagram as a third formula; and minimizing the third formula so that the discrete point distribution of the obtained centroid Voronoi diagram conforms to the density distribution of the residual of the physical information neural network.
[0050] In specific implementation, the optimization module 202 performs discrete point optimization on the initial Voronoi diagram to generate a constrained Voronoi diagram, including: setting weights for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; applying constraints related to the weights to each Voronoi unit in the initial Voronoi diagram, so that the accumulated weights of the points in each Voronoi unit are equal; expressing the sum of the accumulated weights of each Voronoi unit in the initial Voronoi diagram as a fourth formula; and minimizing the fourth formula so that the obtained discrete point distribution of the constrained Voronoi diagram conforms to the density distribution of the residual of the physical information neural network.
[0051] In one embodiment, a computer device is provided, such as Figure 7 As shown, it includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the above-mentioned physical information neural network training method is implemented.
[0052] Specifically, the computer device may be a computer terminal, a server or a similar computing device.
[0053] In this embodiment, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program for executing the above-mentioned physical information neural network training method.
[0054] Specifically, computer-readable storage media include permanent and non-permanent, removable and non-removable media that can be used to store information by any method or technology. Information can be computer-readable instructions, data structures, program modules or other data. Examples of computer-readable storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, tape disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable storage media does not include temporary computer-readable media (transitory media), such as modulated data signals and carrier waves.
[0055] Obviously, those skilled in the art should understand that the modules or steps of the above-mentioned embodiments of the present invention can be implemented by a general computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, and in some cases, the steps shown or described can be executed in a different order from that here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. In this way, the embodiments of the present invention are not limited to any specific combination of hardware and software.
[0056] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.
Claims
1. A physical information neural network training method, characterized in that: include: Acquire initial residual points in the calculation region, use the initial residual points as discrete points of the Voronoi diagram, and generate an initial Voronoi diagram according to the calculation region and the initial residual points, so as to divide the calculation region into a plurality of Voronoi units, and each of the Voronoi units corresponds to one initial residual point; Optimizing the initial Voronoi diagram at discrete points to generate a centroid Voronoi diagram or a constrained Voronoi diagram; The discrete points in each Voronoi unit in the centroid Voronoi diagram or the constrained Voronoi diagram are used in the training process of the physical information neural network.
2. The physical information neural network training method according to claim 1, characterized in that: The initial Voronoi diagram is optimized for discrete points to generate a centroid Voronoi diagram, including: The distance from each point in the initial Voronoi diagram to the nearest discrete point to the point is expressed as a first formula; A weight is set for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; the product of the first formula and the weight of the corresponding point is expressed as a second formula; According to the second formula, a weighted sum of the shortest distances from each point in the initial Voronoi diagram to a discrete point in the Voronoi diagram is expressed as a third formula; The third formula is minimized so that the discrete point distribution of the obtained centroid Voronoi diagram conforms to the density distribution of the physical information neural network residual.
3. The physical information neural network training method according to claim 2, characterized in that: The third formula is expressed as: in, is the weighted sum of the shortest distances from each point in the initial Voronoi diagram to the discrete points in the Voronoi diagram, is the number of Voronoi cells in the initial Voronoi diagram, For point The weight of , is the physical information neural network residual, is the distance from each point in the initial Voronoi diagram to the nearest discrete point, and X represents a discrete point in the Voronoi diagram.
4. The physical information neural network training method according to claim 2, characterized in that: Minimizing the third formula includes: minimizing the third formula using an L-BFGS algorithm.
5. The physical information neural network training method according to claim 1, characterized in that: Optimizing the initial Voronoi diagram at discrete points to generate a constrained Voronoi diagram, including: Setting a weight for each point in the initial Voronoi diagram, wherein the weight is a function that is positively correlated with the residual network of the physical information neural network; Applying constraints related to the weight to each Voronoi unit in the initial Voronoi diagram respectively, so that the weight accumulation of the points in each Voronoi unit is equal; The sum of the weight accumulation amounts in each Voronoi cell in the initial Voronoi diagram is expressed as a fourth formula; The fourth formula is minimized so that the obtained discrete point distribution of the constrained Voronoi diagram conforms to the density distribution of the physical information neural network residual.
6. The physical information neural network training method according to claim 5, characterized in that: The fourth formula is expressed as: in, is the sum of the weight accumulation of each Voronoi unit in the initial Voronoi diagram, X represents the discrete point of the Voronoi diagram, is the number of Voronoi cells in the initial Voronoi diagram, For point The weight of is the physical information neural network residual, and c is the weight accumulation of each point in the Voronoi cell.
7. The physical information neural network training method according to claim 5, characterized in that: Minimizing the fourth formula includes: minimizing the fourth formula using an L-BFGS algorithm.
8. A physical information neural network training device, characterized in that: include: A Voronoi diagram generation module, used for obtaining initial residual points in a calculation area, taking the initial residual points as discrete points of a Voronoi diagram, and generating an initial Voronoi diagram according to the calculation area and the discrete points, so as to divide the calculation area into a plurality of Voronoi units, and each of the Voronoi units corresponds to one initial residual point; An optimization module, used for performing discrete point optimization on the initial Voronoi diagram to generate a centroid Voronoi diagram or a constrained Voronoi diagram; A neural network training module is used to use the residual points in each Voronoi unit in the centroid Voronoi diagram or the constrained Voronoi diagram for the training process of the physical information neural network.
9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the physical information neural network training method described in any one of claims 1 to 7 is implemented.
10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program for executing the physical information neural network training method according to any one of claims 1 to 7.