Method and device for improving prediction precision

Abstract

The invention discloses a method and a device for improving prediction precision. The method comprises the following steps: processing obtained point cloud coordinate data of three-dimensional structure information of a to-be-predicted material; constructing a prediction model, wherein the prediction model comprises a lifting module, a plurality of implicit layer modules and a projection module; wherein the lifting module maps low-dimensional point cloud features to a high-dimensional feature space through a multi-layer perceptron (MLP); the implicit layer module maps original point cloud features to low-dimensional implicit points through mapping scores, Fourier transform and inverse transform are executed in an implicit space, and a result is reflected to an original space through inverse mapping; the projection module maps the high-dimensional features of the original spatial data to a target physical quantity space through MLP; using a prediction model to predict the processed point cloud coordinate data, and outputting a stress distribution result; and optimizing the prediction model according to the error between the prediction result and the real stress distribution so as to improve the prediction precision of the model. According to the method, the prediction precision of the model can be improved.

Description

[0001] This application claims priority to the Chinese patent application filed with the State Intellectual Property Office of China on March 24, 2025, with application number 202510350280.7 and application name “A method and device for improving prediction accuracy”, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The present invention relates to the field of model calculation technology, and in particular to a method and device for improving prediction accuracy. Background Art

[0003] In fields such as elasticity, plasticity, fluid mechanics, and aerodynamics, it is often necessary to predict or solve the corresponding physical properties of complex systems based on input features. Fourier neural operators can reduce computational costs by learning the relationship between input and output, replacing traditional numerical simulations or experimental measurements. The Fourier Neural Operator (FNO) demonstrates unique advantages in predictive computing through its frequency-domain operation mechanism. Combining the Fourier transform with a deep learning framework enables efficient modeling of the global dependencies of complex systems. By performing parameterized learning in Fourier space, FNO effectively overcomes the curse of dimensionality that traditional methods face when dealing with long-range spatiotemporal interactions. This feature gives it significant advantages in physical systems with strong nonlocal effects, such as turbulence simulation and atmospheric dynamics. Furthermore, the Fourier Neural Operator is naturally adaptable to the resolution of the input data, enabling it to operate effectively at varying spatial resolutions. The computational efficiency of the Fourier Neural Operator is primarily due to its efficient implementation of the Fast Fourier Transform (FFT) algorithm, which exhibits excellent computational performance on regular uniform grids. However, when processing unstructured grid data, existing methods usually need to interpolate the data onto a uniform grid for calculation. This interpolation process inevitably introduces numerical errors, thereby affecting the overall accuracy of the model. Summary of the Invention

[0004] In order to solve the problems existing in the prior art, the embodiments of the present application provide a method, apparatus, computing device, computer storage medium and product including a computer program for improving prediction accuracy, which can improve the accuracy of the model during prediction.

[0005] In the first aspect, an embodiment of the present application provides a method for improving prediction accuracy, comprising: processing the point cloud coordinate data of the acquired three-dimensional structural information of the material to be predicted; constructing a prediction model, the prediction model comprising a lifting module, multiple implicit layer modules and a projection module; wherein the lifting module maps the low-dimensional point cloud features to the high-dimensional feature space through a multi-layer perceptron MLP; the implicit layer module maps the original point cloud features to low-dimensional implicit points through mapping scores, performs Fourier transform and inverse transform in the implicit space, and maps the results back to the original space through inverse mapping; the projection module maps the high-dimensional features of the original space data to the target physical quantity space through MLP; uses the prediction model to predict the processed point cloud coordinate data and outputs the stress distribution result; optimizes the prediction model according to the error between the prediction result and the true stress distribution to improve the model prediction accuracy.

[0006] In some possible implementations, the construction of the prediction model also includes using a multi-subspace learning mechanism to enhance the generalization ability of the model, and the number of subspaces is 8; each subspace independently learns the implicit mapping relationship, and finally splices the outputs of each subspace.

[0007] In some possible implementations, the calculation of the mapping score includes: generating an initial correlation score between the original point and the implicit point through a learnable transformation; and for each implicit point, normalizing the contribution weight of the original point through a Softmax function.

[0008] In some possible implementations, the Fourier transform and inverse transform of the implicit layer include: performing a fast Fourier transform on the implicit points, truncating high-frequency modes and retaining low-frequency components; applying a learnable linear transformation matrix in the frequency domain; and converting the result back to the implicit space through an inverse fast Fourier transform (IFFT).

[0009] In some possible implementations, the inverse mapping reuses the mapping scores of the forward mapping to inversely map the weighted sum of implicit point features to the original point cloud space.

[0010] In some possible implementations, when constructing the implicit points, the implicit points in the tth layer among the multiple implicit layers are expressed as:

[0011]

[0012] Where, IP t Characterize the representation of the hidden point of the t-th hidden layer, y i represents the i-th implicit point, N represents the total number of grid points, w i,j Characterizes the mapping score between the i-th grid point and the j-th implicit point, W V The weight matrix representing the acquired value vector, v t Characterize the distribution function of the t-th layer grid point, xi Represents the i-th grid point.

[0013] In some possible implementations, the processing of the acquired point cloud coordinate data of the three-dimensional structural information of the material to be predicted includes: preprocessing the point cloud coordinate data, including data cleaning, denoising and normalization operations; and converting the preprocessed point cloud coordinate data into a format suitable for prediction model input.

[0014] In some possible implementations, the method is applied to estimating the internal stress of an incompressible material with an arbitrary central void, wherein the input of the prediction model is the point cloud coordinates of the material structure, and the output is the stress of the material.

[0015] In the second aspect, an embodiment of the present application provides a device for improving prediction accuracy, including: an acquisition module for acquiring point cloud coordinates of three-dimensional structural information of a material to be predicted; a processing module for processing the acquired point cloud coordinate data of the three-dimensional structural information of the material to be predicted; the processing module is also used to construct a prediction model, and the prediction model includes a lifting module, multiple implicit layer modules and a projection module; wherein the lifting module maps low-dimensional point cloud features to high-dimensional feature space through a multi-layer perceptron MLP; the implicit layer module maps the original point cloud features to low-dimensional implicit points through mapping scores, performs Fourier transform and inverse transform in the implicit space, and maps the results back to the original space through inverse mapping; the projection module maps the high-dimensional features of the original space data to the target physical quantity space through MLP; the processing module is also used to use the prediction model to predict the processed point cloud coordinate data and output the stress distribution result; the processing module is also used to optimize the prediction model according to the error between the prediction result and the true stress distribution to improve the model prediction accuracy.

[0016] In a third aspect, an embodiment of the present application provides a computer-readable storage medium comprising computer-readable instructions. When a computer reads and executes the computer-readable instructions, the computer executes the method as described in any one of the first aspects.

[0017] In a fourth aspect, an embodiment of the present application provides a computing device comprising a processor and a memory, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, the method as described in any one of the first aspects is executed.

[0018] In a fifth aspect, an embodiment of the present application provides a product comprising a computer program, which, when the computer program product runs on a processor, enables the processor to execute the method as described in any one of the first aspects. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0020] Figure 1 This is a flow chart of a method for improving prediction accuracy provided by an embodiment of the present application;

[0021] Figure 2 This is a schematic diagram of stress prediction of an elastic material provided in an embodiment of the present application;

[0022] Figure 3 This is a schematic diagram of the structure of a prediction model provided in an embodiment of the present application;

[0023] Figure 4 Schematic diagram of a process of performing Fourier transform at an implicit point provided by an embodiment of the present application;

[0024] Figure 5 Schematic diagram of the predicted results of the model provided in the embodiments of the present application on various data sets and the differences with the real data;

[0025] Figure 6 This is a structural diagram of a device for improving prediction accuracy provided in an embodiment of the present application. DETAILED DESCRIPTION

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0027] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

[0028] The terms "first" and "second" in this specification and claims are used to distinguish different objects rather than to describe a specific order of objects. For example, "first response message" and "second response message" are used to distinguish different response messages rather than to describe a specific order of response messages.

[0029] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0030] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more, for example, multiple processing units means two or more processing units, etc.; multiple elements means two or more elements, etc.

[0031] To facilitate understanding of the embodiments of the present application, further explanation will be given below with reference to specific embodiments in conjunction with the accompanying drawings. The embodiments do not constitute a limitation on the embodiments of the present invention.

[0032] First, the technical terms involved in the embodiments of this application are introduced:

[0033] 1. Spatial domain refers to the distribution of physical quantities (such as velocity, pressure, and stress) in space. In scientific computing and engineering simulation, the spatial domain is usually represented as a geometric region (such as a two-dimensional plane or a three-dimensional volume), where each point has the value of one or more physical quantities.

[0034] Next, the technical solutions provided in the embodiments of the present application are introduced.

[0035] Traditional numerical simulation methods typically face two major challenges when dealing with complex physical systems (such as turbulence, porous media flow, and material mechanics). One is the curse of dimensionality, and the other is the limitation of non-uniform grids. For the curse of dimensionality, high-resolution grids will lead to an exponential increase in computational complexity. For the limitation of non-uniform grids, the Fourier transform relies on a uniform grid, and unstructured grids require interpolation processing, which introduces numerical errors and reduces prediction accuracy. The Fourier Neural Operator (FNO) partially solves these problems through global convolution in the frequency domain, but is still limited by the dependence on uniform grids and the insufficient expression ability of a single feature space.

[0036] In view of this, an embodiment of the present application provides a method for improving prediction accuracy. Through a prediction model constructed by implicit point construction, multi-subspace learning and a bidirectional mapping mechanism, the model extracts information from grid points (such as physical coordinates, normal vectors, signed distance functions, etc.) and establishes a mapping relationship from these features to physical quantities (such as velocity, pressure, temperature, etc.) to improve the accuracy and generalization ability of FNO on non-uniform grids.

[0037] For example, Figure 1A flow chart of a method for improving prediction accuracy provided by an embodiment of the present application is shown as follows: Figure 1 As shown, the prediction accuracy improvement method may include the following steps:

[0038] S11: Processing the acquired point cloud coordinate data of the three-dimensional structural information of the material to be predicted.

[0039] In this embodiment, the three-dimensional structural information of an incompressible material with an arbitrary central void is obtained, and the material structure is converted into high-precision point cloud coordinate data through technologies such as laser scanning, CT scanning or CAD modeling to ensure that the data can accurately reflect the geometric shape and internal void characteristics of the material. The collected point cloud coordinate data is preprocessed, including data cleaning, denoising and normalization operations, to improve the quality and consistency of the data and make it more suitable for the input requirements of the model. The input of the model is a function a(x) defined in the spatial domain, such as initial conditions, boundary conditions, etc. In actual calculations, the input function a(x) will be discretized into values on the grid points, for example a={a(x1),a(x2),a(x3),…,a(x N )}, where N is the number of discrete points. Since the purpose of the embodiment of the present application is to predict the data of the material, there will be a corresponding output result after the input of the model. The goal of this method is to learn a mapping G:a(x)→u(x), that is, a mapping from the input function a(x) to the output function u(x). The model output u(x) is another function defined in the spatial domain, which represents the result after the input function is mapped by a certain operator. The output function will also be discretized into values on the grid points, for example u={u(x1),u(x2),u(x3),…,u(x N )}. The output represents the solution related to the partial differential equation, such as pressure field, velocity field, etc. The set of discrete points of input and output are the same.

[0040] For example, see Figure 2 , Figure 2 A schematic diagram of stress prediction of an elastic material is shown. Figure 2 As shown in the figure, the Elasticity dataset is used as an example of data input. This dataset is used to estimate the stress of elastic materials under given structures. The model aims to estimate the internal stress of incompressible materials with arbitrary central voids. The proxy model input is the material structure, that is, the coordinates of the point cloud, and the output is stress. The material structure is discretized into a 972-point cloud. The features of each sample are represented as a 972×2 matrix, indicating the two-dimensional position coordinates of each discrete point. The target data dimension is a vector of length 972, representing the stress value at each point.

[0041] It is worth noting that the examples in this application use the Elasticity dataset as an example. This dataset provides high-resolution fundamental data for studying the mechanical properties of elastic materials and can effectively evaluate the performance of proxy models in elastic mechanics. The Elasticity dataset can be equivalently replaced by other datasets, such as the Plasticity dataset, the Airfoil dataset, the Pipe dataset, the Navier-Stokes dataset, and the Darcy dataset.

[0042] The Plasticity dataset aims to predict the future deformation of plastic materials when impacted by an arbitrarily shaped mold. For each sample, the data features have a dimension of 101×31, representing the discretized mesh shape of the mold. The target data has a dimension of 20×101×31×4, recording the deformation of each grid point in four directions for the next 20 time steps. This dataset provides high-resolution time series data for studying plastic material deformation prediction and serves as an important benchmark for evaluating surrogate models in time-dependent scenarios.

[0043] The Airfoil dataset is used to estimate the Mach number distribution based on airfoil shape. The model input data is a 221×51-dimensional discretized airfoil mesh; the output data is the Mach number distribution for each grid point. All airfoil samples are generated by deforming the NACA-0012 case provided by relevant organizations. This dataset provides important benchmark data for studying aerodynamic characteristics and optimizing airfoil design.

[0044] The Pipe dataset is designed to estimate horizontal fluid velocity based on pipe structures. This dataset contains multiple pipe-shaped samples, each discretized into a 129×129 structured grid. Each sample feature has a shape of 129×129×2 and contains the location information for each discretized grid point. The output is the velocity value for each grid point, with dimensions of 129×129×1.

[0045] The Navier-Stokes data set is used to simulate the flow of an incompressible viscous fluid on a unit annulus. The density of the fluid is kept constant and the viscosity is set to 10. -5 m 2 / s. In this dataset, the fluid field is discretized into a regular 64×64 grid. The task for each example is to predict the fluid state changes in the next 10 time steps based on observations from the past 10 time steps. This task has a time-series nature, requiring the model to not only capture the local dynamics of the fluid but also effectively predict its evolution.

[0046] The Darcy dataset simulates fluid flow in porous media. The process is first discretized into a regular 421×421 grid to capture the detailed characteristics of the porous media. To reduce computational complexity and accommodate the needs of the primary experiment, the data is then downsampled to a resolution of 85×85 for processing. The input of the dataset is structural information about the porous media, and the output is the fluid pressure at each grid point.

[0047] S12: Build a prediction model.

[0048] In this embodiment, after processing the acquired data, a prediction model can be constructed, and the processed data can be processed by the prediction model. Figure 3 FIG. 1 shows a schematic diagram of a prediction model provided in an embodiment of the present application. Figure 3 As shown, the prediction model may include a lifting module P, an implicit layer L consisting of T implicit modules, and a projection module Q.

[0049] Among them, the lifting module is used to increase the dimension of features, that is, to map low-dimensional input to a high-dimensional feature space. Specifically, the input function a(x) is first mapped from a low-dimensional space to a higher-dimensional feature space through a lifting module, with the goal of extracting the features of the input function. Specifically, the input function a(x) is mapped from a low-dimensional space to a higher-dimensional feature space at each discrete point x i The value a(x i ) is mapped to a high-dimensional vector v(x i The boosting module is a point-by-point multilayer perceptron (MLP). The calculation formula of the MLP with two fully connected layers is as follows:

[0050] v(x i )=W2·σ(W1·a(x i )+b1)+b2

[0051] In the formula, v(x i ) represents the feature vector processed by the lifting module, a(x i ) represents the input function at position x i , W1 and W2 represent the weight matrices of the two fully connected layers, b1 and b2 represent the bias vectors of the two fully connected layers, and σ represents the nonlinear activation function between the two linear layers.

[0052] The projection module is used to map high-dimensional features back to the physical quantity space (such as velocity, stress, etc.), and process them point by point using MLP. The output dimension is consistent with the target physical quantity (such as 1D velocity). Specifically, the final MLP of the model is used to map the results in the high-dimensional feature space back to the target output space. This process is called "projection", and its purpose is to convert the learned high-dimensional features into the final output function u(x). During projection, the high-dimensional feature vector is at each discrete point x i The value u(x i ). This mapping is performed element-wise.

[0053] The implicit layer exists between the lifting module and the projection module and consists of T identical modules, including T layers of Fourier transform modules on implicit points. Implicit points are low-dimensional feature representations constructed in the implicit layer and are used to replace the original high-dimensional grid points for calculations. The implicit layer maps the original grid point features to the implicit points. Each module contains two submodules: a feedforward neural network module and a Fourier neural operator on implicit points (IPFNO) module, expressed as:

[0054] v t' =v t +IPFNO(Norm(v t ))

[0055] v t+1 =v t' +FFN(Norm(v t' ))

[0056] Where, v t' Characterizes the function of the t-th layer grid point after being processed by the IPFNO submodule, v t Characterize the distribution function of the t-th layer grid point, v t+1 Characterizes the distribution function of the grid points in the t+1th layer.

[0057] Each submodule uses pre-normalization and residual connections. "FFN" is a feed-forward neural network with two fully connected layers. The following describes the IPFNO submodules.

[0058] The implicit layer is the core improvement module of the IPFNO framework provided in the embodiment of the present application, which aims to solve the problem of dependence of the traditional Fourier neural operator (FNO) on the uniform grid. Its core functions include: dimensionality reduction, feature extraction, and bidirectional mapping. Among them, dimensionality reduction refers to mapping the original high-resolution non-uniform grid to low-dimensional implicit points to reduce computational complexity. Feature extraction refers to dynamically selecting important features through mapping scores and retaining global dependencies. Bidirectional mapping refers to the realization of lossless information conversion between implicit space and original space.

[0059] The mapping score is a key parameter of the implicit layer, which is used to quantify the strength of the association between the original grid points and the implicit points. For the representation of the t-th layer, IPFNO uses the mapping function Mapping(v t ; θ), construct the mapping relationship from the original feature space to the implicit point feature space. The mapping function Mapping can be linear or nonlinear, and the parameter θ is a learnable parameter. The input feature dimension of Mapping is the same as v(x), and the output dimension is the same as the number of implicit points. The number of implicit points is a hyperparameter. The relationship between the grid points in the input space and the implicit space points is independent of each other. The mapping mechanism Mapping has nothing to do with the resolution of the original input space, that is, the number of sampling points of the input function, but is only related to the feature representation of the grid points at the tth layer. And different grid points, their relationship with the implicit points is independent of each other. Assuming that x1 and x2 are two sampling points in the input function space, their relationship with the implicit point can be expressed as: Mapping(v t ;θ)(x1)∈R d ×M and Mapping(v t ;θ)(x2)∈R d×M , where d represents the dimension of the input function, M represents the number of implicit points, and R represents the set of real numbers. The mapping score is only related to its own feature representation x and parameter θ.

[0060] The mapping score is normalized by the softmax function and expressed as:

[0061]

[0062] w i is a vector of length M, then the mapping score between the i-th grid point and the j-th implicit point can be expressed as w i,j , and there are

[0063] When constructing implicit points, IPFNO uses a learnable linear transformation to map the information of the grid cells. The representation obtained by mapping contains the actual information of the input features, also called the value vector. The value vector is learned through linear transformation. The formula of linear transformation is: V v t (x)∈R 1×d , where W V Characterize the weight matrix of the acquired value vector, and W V ∈R d ×d The i-th implicit point of the t-th layer can be expressed as: Where, IP t Characterize the representation of the hidden point of the t-th hidden layer, y i represents the i-th implicit point, N represents the total number of grid points, w i,j Characterizes the mapping score between the i-th grid point and the j-th implicit point, W V Representation of the weight matrix representation of the acquired value vector, v t Characterize the distribution function of the t-th layer grid point, x i Representing the i-th grid point, the i-th implicit point of the t-th layer is the weighted sum of all the grid points of the t-th layer. Therefore, the formula can also be written in the form of an integral: IP t (y i )=∫ D w i,j W V v t (x)dx, where D represents the spatial domain and dx represents the integration of x.

[0064] Given an input function v defined on the spatial domain D t (x), where x∈D represents the spatial coordinates. In the tth layer, the function is mapped to the implicit spatial domain Ω, which is represented by IP t (y)∈R 1×d It is worth noting that IP t (y) and the input function v t (x) have the same feature dimension d, which ensures the consistency of the feature space. In particular, regardless of the original input function v t (x) is defined in the two-dimensional space D∈R 2 Or three-dimensional space D∈R 3, after being transformed in this layer, they will be mapped to a unified implicit representation space Ω. Performing 1D-FNO on the implicit point can extract the low-frequency information on the implicit point. An important feature of this mapping is that it achieves resolution reduction: let the number of original grid points be N, and the number of implicit points be M, often M<<N. This dimensionality reduction feature not only significantly reduces the computational complexity, but also retains the key spatial feature information, providing an effective low-dimensional embedding space for subsequent feature extraction and representation learning. The main function of the implicit point construction is to transform a set of non-uniform grid data on the spatial domain D into a A set of ordered signals mapped to the domain Ω Since the Fast Fourier Transform can only be applied to uniform grids, it cannot be directly used for physical fields with irregular geometric shapes. By constructing implicit points, the non-uniform grid points are transformed into a set of points in the domain Ω, which allows the Fourier transform of the implicit points to be performed.

[0065] When performing Fourier transform on an implicit point, a simple parameterized Fourier neural operator can be used to extract the low-frequency modal information on the implicit point. The calculation formula of the Fourier layer is:

[0066]

[0067] Where, represents the kernel integral operator, φ represents the learnable linear transformation in the frequency domain, Characterize the inverse fast Fourier transform, Characterize the Fast Fourier Transform, R φ A linear transformation whose characterization parameter is φ.

[0068] This process uses fast Fourier transform to transform the input function IP t (y) Convert to the frequency domain and implement efficient global convolution operations in the frequency domain. By truncating high-frequency modes and retaining only low-frequency components, efficient representation and calculation of high-dimensional functions can be achieved.

[0069] The Fourier transform converts spatial domain signals to the frequency domain, which can efficiently capture global dependencies (such as low-frequency modes representing smooth changes and high-frequency modes representing detailed fluctuations). In the frequency domain, the computational complexity of convolution operations (such as global convolution) is significantly reduced. After the frequency domain operation is completed, the result needs to be converted back to the spatial domain (i.e., the inverse mapping of the implicit point) for further processing or output. The core goal of the Fourier transform of the implicit point and its inverse mapping is to achieve lossless information conversion, that is, to efficiently and accurately transfer physical quantity information between the implicit space and the original space.

[0070] In the formula, Mapping(v t; θ) constructs the mapping relationship between implicit points and grid points in the original spatial domain, and reuses this mapping relationship when inversely mapping implicit points back to the original grid points. The process of executing Fourier neural operators in the implicit space and inversely mapping information back to the original spatial domain can be simply described as:

[0071]

[0072] The representation is mapped back from domain Ω to the original spatial domain D. When the two domains are converted to each other, a unified mapping fraction w is reused, that is, the information in the implicit space is mapped to the original information. Ensuring the uniformity of the mapping relationship can avoid additional errors. Operations such as Fourier transform performed on the original domain D are now transformed to another spatial domain, and the two domains can be converted to each other through mapping fractions and integral operations. In order to achieve bidirectional conversion of representations between the implicit spatial domain Ω and the original spatial domain D, the embodiment of the present application adopts a unified mapping mechanism. By reusing the same mapping fraction w, the signal in domain D can be converted to domain Ω, and the formula is: IP t (y i )=∫ D w i,j v t (x i ), the signal in domain Ω can also be converted to domain D, the formula is: t' (x i )=∫ Ω w i,j IP t' (y j ), thereby recovering the information in the original space. The consistency of this bidirectional mapping simplifies the model design and significantly reduces the additional errors introduced by inconsistent mappings. From a mathematical point of view, the mapping score w defines the transformation relationship between the points in the two domains. The integral operation realizes a continuous mapping from the implicit space to the original space. This bidirectional mapping has a consistency guarantee. By reusing the same mapping score, it avoids the information loss or error accumulation caused by the use of different mapping functions. The mapping score can be shared between the two domains, reducing the number of model parameters while improving computational efficiency. Operations in the original space domain D can be converted to the implicit space domain Ω through the mapping score w, thereby reducing the computational complexity while maintaining computational accuracy. The unified mapping score w and integral operation realize the bidirectional conversion between the implicit space domain Ω and the original space domain D.

[0073] In some possible embodiments, a multi-subspace learning mechanism is used when constructing the model.

[0074] In this embodiment, multi-subspace learning can exploit data features from different perspectives, improving the model's expressiveness and generalization capabilities. Among attention mechanisms, the multi-head attention mechanism is a typical application of multi-subspace learning. It effectively captures the diverse features and relationships of the data by mapping the input data into multiple independent subspaces (i.e., "heads"), calculating attention weights within each subspace, and ultimately integrating the calculation results from each subspace. When constructing implicit points, implicit points are constructed from multiple subspaces, and subsequent calculations and operations are performed independently and in parallel within each subspace. Each subspace has an independent mapping score. In each subspace, IPFNO performs independent operations to capture the local relationships between data features in each subspace. Finally, the results from multiple subspaces are spliced together to obtain the final output. Multi-subspace learning enables the model to learn data features from multiple perspectives (subspaces), thereby enhancing the model's expressiveness. Each subspace focuses on learning different aspects of the data, thereby avoiding feature loss or bias that may be caused by a single subspace. This multi-subspace learning approach aligns with the goal of multi-subspace learning, namely, to more comprehensively represent high-dimensional data through multiple low-dimensional subspaces.

[0075] For example, Figure 4 Figure 2 shows a schematic diagram of the process of Fourier transform at an implicit point. Figure 4 As shown, the yellow part at the bottom represents the input. The features of the input grid cells are first processed by the mapping mechanism Mapping(v t ;θ) gets the mapping score between the grid unit and the implicit point (the red point in the figure), and the linear transformation W T The product of the mapping score and the value vector constructs the representation IP of the implicit point t (y j ). The Fourier neural operator is applied to the representation of the implicit point and transforms it in the frequency domain. The representation of the implicit point after the frequency domain operation is IP' t (y j ) is de-mapped back to the features of the grid cells by reusing the mapping scores. The purple block in the figure represents a subspace, and the above calculations are performed independently and in parallel in different subspaces.

[0076] In some possible embodiments, the number of subspaces is 8.

[0077] S13: Use the prediction model to predict the processed point cloud coordinate data, output the stress distribution result, and optimize the prediction model based on the error between the prediction result and the actual stress distribution.

[0078] In this embodiment, the preprocessed point cloud coordinate data is used as input, and the real stress distribution data is used as the output label to train the IPFNO model. During the training process, an optimization algorithm (such as Adam, etc.) is used to adjust the weight parameters of the model to minimize the error between the predicted stress and the real stress until the model converges, thereby obtaining a trained IPFNO model with good generalization ability. During training, the batch size (such as 32) can be set according to the video memory capacity. The number of training rounds can be selected as 500, and an early stopping mechanism is used to prevent overfitting. The processed point cloud coordinate data is predicted using the prediction model, and the stress distribution result is output; the prediction model is optimized based on the error between the prediction result and the real stress distribution.

[0079] S14: Verify and apply the model.

[0080] In this embodiment, the point cloud coordinate data of the new material sample for which internal stress estimation is required is processed in accordance with the format and preprocessing method required by the model, and is input into the trained IPFNO model as input data. The model maps the input point cloud coordinates to a high-dimensional feature space through the lifting module P. After feature extraction and frequency domain operations by T implicit layer modules, the features are mapped back to the original space through the projection module Q, and finally the stress distribution prediction value corresponding to the input point cloud coordinates is output. The predicted stress distribution results are analyzed and interpreted, and the mechanical properties and structural safety of the material are evaluated based on information such as the stress concentration area and the maximum stress value. The prediction results are applied to the actual engineering design and manufacturing process to provide a basis for the optimized design, performance improvement and fault prevention of materials, such as guiding the shape optimization of mechanical parts, the seismic design of building structures, and the weight reduction design of aerospace structures. Figure 5 The figure shows the predicted results of the model provided in the embodiment of the application on various data sets and the difference between the predicted results and the real data. Figure 5 As shown, by the method provided in the embodiments of the present application, predictions are performed on the Elasticity dataset, Plasticity dataset, Airfoil dataset, Pipe dataset, Navier-Stokes dataset, and Darcy dataset, respectively. The true values are basically consistent with the predicted values, the error rate is small, and the prediction accuracy is high.

[0081] Next, we will introduce the specific implementation steps of this model using pipe flow as an example. Pipes of various shapes are first discretized to obtain grid points that can represent the pipe shape. Assume that there are N grid points in this problem. The model input is the coordinates of these grid points, which are (N, 2). The desired output is the velocity value at each point, so the model output is (N, 1). The input passes through the lifting module P, T submodules, and the projection module Q to obtain the final output. After calculating the error between the model's output value and the true value, the model weights are updated, and the network is trained. After 500 rounds of training, the final model is obtained. The trained model can be used for subsequent stress analysis.

[0082] The above is an introduction to the method for improving prediction accuracy provided by the embodiment of the present application. By constructing a prediction model, the material to be predicted is predicted, wherein the prediction model includes an improvement module, multiple implicit layer modules and a projection module. The high-dimensional original grid point features are compressed to low-dimensional implicit points through mapping scores, which significantly reduces the computational complexity. The Fourier transform is performed on the implicit points to truncate high-frequency modes and retain low-frequency global information. By reusing the mapping scores, the implicit point features are losslessly mapped back to the original space to avoid interpolation errors. Multiple independent subspaces are set to learn different implicit mapping relationships respectively and enhance the model's expression capabilities. This solution is applicable to fields such as elasticity and fluid mechanics, supports direct processing of non-uniform grids, and significantly improves prediction accuracy and computational efficiency.

[0083] It is understandable that the size of the sequence number of each step in the above-mentioned embodiments does not mean the order of execution, and the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application. In addition, in some possible implementations, the steps in the above-mentioned embodiments can be selectively executed according to actual conditions, and can be partially executed or fully executed, which is not limited here. All or part of any features of any embodiment of the present application can be freely and arbitrarily combined without contradiction. The combined technical solution is also within the scope of the present application.

[0084] Based on the method in the above embodiment, the embodiment of the present application also provides a device for improving prediction accuracy. For example, Figure 6 A device for improving prediction accuracy is shown, which is deployed on a computing device. The device 600 includes: an acquisition module 601 and a processing module 602.

[0085] The acquisition module 601 is used to obtain the point cloud coordinates of the three-dimensional structural information of the material to be predicted.

[0086] A processing module 602 is used to process the acquired point cloud coordinate data of the three-dimensional structural information of the material to be predicted;

[0087] The processing module 602 is also used to construct a prediction model, which includes a lifting module, multiple implicit layer modules and a projection module; wherein the lifting module maps low-dimensional point cloud features to high-dimensional feature space through a multi-layer perceptron MLP; the implicit layer module maps the original point cloud features to low-dimensional implicit points through mapping scores, performs Fourier transform and inverse transform in the implicit space, and maps the results back to the original space through inverse mapping; the projection module maps the high-dimensional features of the original space data to the target physical quantity space through MLP.

[0088] The processing module 602 is further configured to use the prediction model to predict the processed point cloud coordinate data and output a stress distribution result.

[0089] The processing module 602 is further configured to optimize the prediction model according to the error between the prediction result and the actual stress distribution, so as to improve the prediction accuracy of the model.

[0090] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0091] Based on the methods in the above embodiments, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the methods in the above embodiments.

[0092] Based on the methods in the above embodiments, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the methods in the above embodiments.

[0093] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0094] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0095] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid state drive (SSD)).

[0096] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

Claims

1. A method for improving prediction accuracy, characterized in that: The method comprises: Processing the acquired point cloud coordinate data of the three-dimensional structural information of the material to be predicted; Construct a prediction model, the prediction model including a lifting module, multiple implicit layer modules and a projection module; wherein the lifting module maps low-dimensional point cloud features to a high-dimensional feature space through a multi-layer perceptron (MLP); the implicit layer module maps original point cloud features to low-dimensional implicit points through mapping scores, performs Fourier transform and inverse transform in the implicit space, and maps the results back to the original space through inverse mapping; the projection module maps the high-dimensional features of the original spatial data to the target physical quantity space through the MLP; Use the prediction model to predict the processed point cloud coordinate data and output stress distribution results; According to the error between the predicted result and the actual stress distribution, the prediction model is optimized to improve the prediction accuracy of the model.

2. The method according to claim 1, characterized in that The construction of the prediction model also includes adopting a multi-subspace learning mechanism to enhance the generalization ability of the model, and the number of the subspaces is 8; Each subspace learns the implicit mapping relationship independently, and finally concatenates the outputs of each subspace.

3. The method according to claim 1, characterized in that The calculation of the mapping score includes: Generate the initial correlation scores between the original points and the implicit points through a learnable transformation; For each implicit point, the contribution weight of the original point is normalized by the Softmax function.

4. The method according to claim 1, wherein The Fourier transform and inverse transform of the implicit layer include: Perform fast Fourier transform on the implicit points to truncate high-frequency modes and retain low-frequency components; Apply a learnable linear transformation matrix in the frequency domain; The result is converted back to implicit space via an inverse fast Fourier transform (IFFT).

5. The method according to claim 1, wherein The inverse mapping reuses the mapping scores of the forward mapping and inversely maps the weighted sum of implicit point features to the original point cloud space.

6. The method according to claim 1, characterized in that When constructing the implicit points, the implicit points in the tth layer of multiple implicit layers are expressed as: Where, IP t Characterize the representation of the hidden point of the t-th hidden layer, y i represents the i-th implicit point, N represents the total number of grid points, w i,j Characterizes the mapping score between the i-th grid point and the j-th implicit point, W V The weight matrix representing the acquired value vector, v t Characterize the distribution function of the t-th layer grid point, x i Represents the i-th grid point.

7. The method according to claim 1, characterized in that The processing of the acquired point cloud coordinate data of the three-dimensional structural information of the material to be predicted includes: Preprocess the point cloud coordinate data, including data cleaning, denoising and normalization operations; Convert the preprocessed point cloud coordinate data into a format suitable for prediction model input.

8. The method according to claim 1, characterized in that The method is applied to estimate the internal stress of incompressible materials with arbitrary central voids, where the input of the prediction model is the point cloud coordinates of the material structure and the output is the stress of the material.

9. A device for improving prediction accuracy, characterized in that: The device comprises: An acquisition module is used to obtain the point cloud coordinates of the three-dimensional structural information of the material to be predicted; A processing module, used to process the acquired point cloud coordinate data of the three-dimensional structural information of the material to be predicted; The processing module is further used to construct a prediction model, which includes a lifting module, multiple implicit layer modules and a projection module; wherein the lifting module maps low-dimensional point cloud features to high-dimensional feature space through a multi-layer perceptron (MLP); the implicit layer module maps original point cloud features to low-dimensional implicit points through mapping scores, performs Fourier transform and inverse transform in the implicit space, and maps the results back to the original space through inverse mapping; the projection module maps high-dimensional features of original spatial data to target physical quantity space through MLP; The processing module is further configured to use the prediction model to predict the processed point cloud coordinate data and output a stress distribution result; The processing module is further configured to optimize the prediction model according to the error between the prediction result and the actual stress distribution, so as to improve the prediction accuracy of the model.

10. A computer-readable storage medium comprising computer-readable instructions, which, when a computer reads and executes the computer-readable instructions, causes the computer to execute the method according to any one of claims 1 to 8.

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