CN-122020753-A - Model feature space-based three-dimensional geometric spectrum analysis method and system

CN122020753ACN 122020753 ACN122020753 ACN 122020753ACN-122020753-A

Abstract

The invention discloses a three-dimensional geometric spectrum analysis method and a system based on a model feature space, wherein the method comprises the steps of inputting coordinates in an effective definition domain of a three-dimensional geometric shape and shape codes corresponding to the three-dimensional geometric shape into a trained neural network, and outputting a group of feature function values and a gradient vector of the coordinates, wherein the feature function values and the coordinates can represent the whole shape space; training the neural network, including calculating energy values of each characteristic function output by the neural network according to a step vector of coordinates for randomly sampled shape codes, performing ascending order sequencing to obtain a characteristic function sequence, performing orthogonal projection on the characteristic function sequence to obtain a target characteristic function, constructing a corresponding loss function based on a preset partial differential equation type, substituting the target characteristic function into the corresponding loss function, and updating parameters of the neural network by minimizing the loss function to obtain the trained neural network. The invention can realize continuous shape space spectrum analysis of characteristic value crossing problem without depending on grids.

Inventors

LI XIAOLI
DING RUNDONG
DU ZHENLONG
CHEN DONG

Assignees

南京工业大学

Dates

Publication Date: 20260512
Application Date: 20260126

Claims (10)

1. The three-dimensional geometric spectrum analysis method based on the model feature space is characterized by comprising the following steps of: inputting coordinates in the effective definition domain of the three-dimensional geometric shape and shape codes corresponding to the three-dimensional geometric shape into a trained neural network, and outputting a group of feature function values capable of representing the whole shape space and a gradient vector of the coordinates; Training the neural network, comprising the steps of calculating the energy value of each characteristic function output by the neural network according to a step vector of coordinates for randomly sampling shape codes, and carrying out ascending sort according to the energy values to obtain a characteristic function sequence of the current shape codes, wherein the energy values are used for representing the frequency or deformation potential energy of the characteristic function; Orthographically projecting the characteristic function sequence to obtain a target characteristic function; And constructing a corresponding loss function based on a preset partial differential equation type, substituting the target characteristic function into the corresponding loss function, and updating parameters of the neural network by minimizing the loss function to obtain the trained neural network.
2. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 1, wherein: Orthographically projecting the sequence of feature functions to obtain an objective feature function includes: and determining the kth characteristic function of the characteristic function sequence as an orthogonal projection base, projecting the kth characteristic function into an orthogonal complement space of a subspace formed by the kth characteristic function and the kth characteristic function, and calculating projection components of the characteristic function on the projection base to obtain an orthogonalized target characteristic function.
3. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 2, wherein: orthographically projecting the sequence of feature functions to obtain an objective feature function further includes: Taking the target characteristic function of the first k-1 characteristic functions after projection as a constant without gradient; Respectively solving inner products of the k-1 constants and the corresponding objective characteristic function, multiplying the inner products by the corresponding constants, and summing the k-1 products; subtracting the kth characteristic function from the sum to obtain an objective characteristic function of the kth characteristic function.
4. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 1, wherein: The preset partial differential equation type comprises a Laplacian operator and a linear elastic operator, and the calculation of the energy of each characteristic function output by the neural network according to a gradient vector of coordinates comprises the following steps: taking the Rayleigh quotient value of the characteristic function value output by the neural network as an energy value; When the preset partial differential equation type is Laplacian, multiplying the feature function value by a step vector of corresponding coordinates to obtain the square sum of Euclidean norms of the vectors, then obtaining a ratio with the square sum of the feature function value, and taking the ratio as a Rayleigh Li Shang value of the feature function value; When the preset partial differential equation type is a linear elastic algorithm, the elastic potential energy density is obtained through calculation based on the linear strain tensor of the characteristic function and the Rayleigh constant of the material, and the ratio of the elastic potential energy density to the square sum of the characteristic function values is used as the Rayleigh quotient value of the characteristic function values.
5. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 4, wherein: When the preset partial differential equation type is Laplacian, constructing a loss function of the Laplacian according to the following formula: Wherein, the A loss function representing a laplacian spectral analysis, Parameters representing a neural network; Representing mathematical expectation operators, directed to shape space Shape coding for middle-wear sampling from a particular distribution The desired value is calculated and the desired value, Representing the total number of objective feature functions to be solved, Representing shape encoding from a current sample The determined valid domain is defined by the user, In order to differentiate the volume elements, Represents the output of the neural network and is orthogonalized The function of the characteristics of the individual targets, Representation relative to space coordinates Is a step-wise degree operator of (1), Representing the square of the euclidean norm of the vector.
6. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 4, wherein: When the preset partial differential equation type is a linear elastic operator, constructing a loss function of the linear elastic operator according to the following formula: Wherein, the Representing a loss function of the linear elastic operator spectral analysis, Represent the first The linear strain tensor corresponding to the characteristic function is defined as , Representing displacement gradient tensors Is a transpose of (2); Representing the sum of the squares of all the elements of the matrix, Representing the square of the trace of the matrix, In order to achieve a shear modulus, the polymer is, As a constant of the properties of the material, Representing mathematical expectation operators, directed to shape space Shape coding for middle-wear sampling from a particular distribution The desired value is calculated and the desired value, In order to differentiate the volume elements, Representing shape encoding from a current sample The determined valid definition field.
7. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 1, wherein: the method further comprises the steps of: the method comprises the steps of configuring a multi-layer perceptron mechanism in a neural network, arranging a position coding layer at the input end of the neural network, mapping space coordinates into continuous space representation feature vectors, inputting the feature vectors into the multi-layer perceptron mechanism, and configuring the output end of the neural network A first channel is initialized to a constant value with output independent of input, and the rest The channels are configured to output feature function values to be learned.
8. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 1, wherein: the method further comprises the steps of: The boundaries of the three-dimensional geometry are defined as zero isosurface of the scalar function, and the signs of the scalar function values are used to distinguish between the interior and exterior of the geometry to determine the effective domain of the three-dimensional geometry.
9. The model feature space-based three-dimensional geometric spectrum analysis method according to claim 1, wherein: Updating parameters of the neural network by minimizing the loss function includes: The parameters of the updated neural network are updated by using a gradient descent or Adam optimizer through a back propagation algorithm until the loss function converges to a minimum or a preset number of iterations is reached.
10. A model feature space-based three-dimensional geometric spectrum analysis system for implementing the model feature space-based three-dimensional geometric spectrum analysis method according to any one of claims 1 to 9, wherein the system comprises: The spectrum analysis module is used for inputting coordinates in the effective definition domain of the three-dimensional geometric shape and shape codes corresponding to the three-dimensional geometric shape into the trained neural network and outputting a group of feature function values capable of representing the whole shape space and a gradient vector of the coordinates; The training module is used for training the neural network, and the training module comprises: The energy value calculation module is used for calculating the energy value of each characteristic function output by the neural network according to a step vector of coordinates for the shape coding of random sampling, and carrying out ascending sort according to the energy values to obtain a characteristic function sequence of the current shape coding, wherein the energy value is used for representing the frequency or deformation potential energy of the characteristic function; the orthogonal projection module is used for carrying out orthogonal projection on the characteristic function sequence to obtain an objective characteristic function; And the updating module is used for constructing a corresponding loss function based on a preset partial differential equation type, substituting the target characteristic function into the corresponding loss function, and updating the parameters of the neural network by minimizing the loss function to obtain the trained neural network.

Description

Model feature space-based three-dimensional geometric spectrum analysis method and system Technical Field The invention belongs to the technical fields of computer graphics, computational physics simulation and deep learning intersection. In particular to a three-dimensional geometric spectrum analysis method and system based on model feature space. Background In the fields of modern industrial manufacturing, computer animation, virtual reality and scientific computing, physical simulation phenomena including mechanical and acoustic behaviour are very important. Partial differential equations are mathematical tools for describing the physical phenomena, and feature analysis is performed on the differential operators, so that feature values and feature functions of the differential operators are solved, and the partial differential equations are a common method for analyzing the inherent properties of a physical system. The characteristic function not only reveals the resonance mode and natural vibration frequency of the objective object, but also can encode geometric information, and can be used for shape description, relation calculation, physical simulation and the like. Currently, the industry typically performs modeling analysis in a continuously changing shape space when designing products. However, existing spectral analysis techniques present significant technical bottlenecks in dealing with such continuous shape spaces. The traditional spectrum analysis method mainly relies on discretized grids, and follows the flows of grid generation, matrix construction and feature decomposition. For each new sample in the shape space, a high-quality grid is required to be regenerated and a huge sparse matrix is required to be constructed, the main process is high in calculation cost, and the change of grid topological connectivity can cause jump of operator matrix dimensions, so that characteristic values and characteristic functions are not tiny with respect to shape coding, and an automatic shape optimization path based on gradients is blocked. In recent years, although implicit neural representation techniques have been introduced to solve the problem of solving partial differential equations without meshes, the challenge of eigenvalue crossover is faced when expanding to continuous shape space. According to perturbation theory, when the geometric domain is continuously deformed, energy curves of different physical modes may intersect. The existing neural spectrum method generally adopts a fixed ordering strategy, namely, the specific output channel of the forced neural network is always fitted with the firstSmall eigenvalues, i.e. the eigenvalues being ordered from small to largeThe eigenvalues of the bits. In the vicinity of the feature value intersection point, the forced fixed ordering can cause severe modal jump of the output function, so that the loss function generates non-conductive kinks about shape coding, which not only damages the smoothness of optimization, causes the neural network to be difficult to converge, but also can generate feature fields which are discontinuous in shape space and even are wrong physically, and cannot be used for subsequent micro-design and real-time simulation tasks. Therefore, there is a need for a continuous shape spatial spectrum analysis method that can be free of grid dependence and that can effectively address the problem of eigenvalue crossover. Disclosure of Invention The invention aims to solve the defects in the prior art, and provides a three-dimensional geometric spectrum analysis method and system based on a model feature space, which aims to solve the technical problems that features can be solved only by independently carrying out grid discretization on each shape in the prior art, the calculation cost is high and cannot be reduced, and the mode confusion and optimized divergence are caused by feature value intersection in the continuous shape change process. The invention solves the optimization problem caused by modal intersection by uniformly solving the eigenvalue and the eigenvalue in the shape space of continuous parameterization by using the implicit neural field, and realizes the method of real-time dimension reduction physical simulation and micro reverse design. The invention adopts the following technical scheme. The first aspect of the invention provides a three-dimensional geometric spectrum analysis method based on a model feature space, which comprises the following steps: inputting coordinates in the effective definition domain of the three-dimensional geometric shape and shape codes corresponding to the three-dimensional geometric shape into a trained neural network, and outputting a group of feature function values capable of representing the whole shape space and a gradient vector of the coordinates; Training the neural network, comprising the steps of calculating the energy value of each characteristic function output by the neural net