Shape optimization and inversion method of a geometry-aware neural optimizer

Abstract

The present disclosure provides a shape optimization and inversion method of a geometry-aware neural optimizer. First, the input geometry to be optimized is modeled as an implicit signed distance function by a geometry representation module, and a denoising mechanism is used to enhance stability during training. Then, forward analysis is performed, the geometry information is injected through a geometry-injected field prediction module, and a gradient path that can be back propagated is constructed. Finally, the optimization step is performed, the iterative update is performed in the latent space through the differentiable optimization / inversion module, the gradient of the updated implicit representation is obtained by back propagating the objective function, and the zero space projection is used to realize the controllable geometry update. Then, iterative update is performed in the latent space, while providing component-level control and boundary consistent projection without remeshing. To solve the problems of existing methods, such as frequent remeshing and high cost forward solving, low iteration efficiency, high dependence on expert experience, and unstable and reliable propagation of the gradient of the objective function to the geometry.

Description

Technical Field

[0001] This disclosure relates to the field of image data processing, and more specifically, to a shape optimization and inversion method for a geometric perception neural optimizer. Background Technology

[0002] Shape geometry is a key control variable in partial differential equation (PDE) control systems, driving two core tasks: (1) Shape optimization: Under the premise of satisfying manufacturing / engineering constraints (such as part freezing, shape deviation constraints, etc.), iteratively update the geometry to minimize / maximize the performance index; (2) Shape inversion: Inversely deduce unknown geometry based on sensing / observation data.

[0003] Existing industrial processes typically employ a closed-loop iterative process of "geometry processing (CAD / mesh) — forward simulation (CFD / FEM) — target evaluation — geometry modification — remesh". This process suffers from the following drawbacks: (i) high cost and slow iteration for forward simulation and remesh; (ii) geometry modifications are often non-differentiable (CAD editing, mesh reconstruction), making gradient transfer difficult end-to-end; and (iii) the need for extensive expert experience to participate in process maintenance.

[0004] In recent years, neural operators / neural PDE solvers (such as Fourier neural operators (FNO), deep operator networks (DeepONet), and unstructured mesh solvers based on Transformer / graph networks) have significantly accelerated forward field prediction. However, most of these works only replace forward solvers, and the geometry is still updated through non-differentiable geometric processing during the optimization process, making it difficult to form an end-to-end differentiable closed loop.

[0005] For "differentiable geometry optimization", existing solutions mainly fall into the following categories: 1) Parametric design variable method: Optimize in a low-dimensional parameter space designed manually (airfoil parameters, spline control points, etc.), updates are stable and interpretable, but the expressive power is limited and it is difficult to cover complex 3D shapes (such as the whole vehicle).

[0006] 2) Latent space optimization methods: Learn encoder-decoder (or self-decoder) representations and perform gradient optimization on high-dimensional latent representations. These methods have a larger design space, but the weak constraints in the latent space make them prone to "drifting away from the data manifold," leading to geometric impracticality / local detail collapse; moreover, many methods only predict scalar objectives (such as drag coefficients) and optimize them directly, lacking field-level interpretability and the ability to constrain local objectives / regions.

[0007] However, the existing technology has the following main drawbacks: 1. Traditional CAD + numerical simulation closed-loop requires frequent remeshing and high-cost forward solving, resulting in low iteration efficiency and high dependence on expert experience.

[0008] 2. Neural substitution models that only accelerate forward analysis are difficult to close loops: the geometric update link is not differentiable, and the gradient of the objective function with respect to geometry cannot be propagated stably and reliably.

[0009] 3. Although low-dimensional parametric optimization is stable, it has limited design space and makes it difficult to achieve fine-grained control and performance improvement for complex 3D geometry.

[0010] 4. High-dimensional latent space optimization is prone to deviating from the shape manifold supported by the training data, resulting in unmanufacturable or local structural damage; and it lacks industrial constraints such as "part-level freezing / local protection".

[0011] 5. Many learning-based optimizations drive updates only on scalar objectives, making it difficult to utilize field-level information for local diagnosis and regional objective definition. Summary of the Invention

[0012] The purpose of this disclosure is to provide a shape optimization and inversion method for a geometry-aware neural optimizer, which aims to solve the problems of existing methods such as frequent regrinding and high-cost forward solving, low iteration efficiency, high dependence on expert experience, and unstable and unreliable propagation of the gradient of the objective function with respect to geometry, so as to enhance the ability to recognize and understand images.

[0013] In general, a shape optimization and inversion method using a geometry-aware neural optimizer is provided. This method is applied to fluid dynamics engineering design scenarios, such as the aerodynamic shape design of vehicles or aircraft. In this scenario, the geometry to be optimized (e.g., the surface of a vehicle body or wing) determines the computational domain of the surrounding fluid flow. Specifically, the optimal geometry refers to the solid geometry that achieves the optimal aerodynamic performance indicators (e.g., minimizing the drag coefficient or maximizing the lift-to-drag ratio) while satisfying engineering constraints (e.g., component freezing). The specific method is as follows: First, the geometric representation module models the geometric shape image of the input 3D model to be optimized as an implicit signed distance function, and a denoising mechanism is used during training to enhance stability; wherein the geometric representation module will model the geometric shape image as an implicit signed distance function. Encoding as implicit representation And through noise reduction training The mapping to geometry is locally smooth, which facilitates stable gradient updates; Then, forward analysis is performed, injecting geometric information through a geometry-injected field prediction module and constructing a gradient path capable of backpropagation; wherein, the geometry-injected field prediction module predicts the physical field on unstructured points / mesh queries. and explicitly establish goals To hidden representation Differentiable gradient pathways; Finally, a geometry optimization step is performed, using a differentiable optimization / inversion module to optimize the latent space. Iterative updates are performed by backpropagating the objective function to obtain the gradient of the updated latent representation and then using null space projection on the gradient to achieve controllable geometric updates; subsequently, in the latent space... It performs iterative updates and provides component-level control and boundary consistency projection of non-repeating meshes to enhance the feature extraction and generation capabilities of 3D geometric image data (such as point clouds or mesh data), outputting the reconstructed 3D model image, realizing the automated generation, optimization and high-precision 3D model reconstruction of geometric configuration images of industrial products such as vehicles and wings.

[0014] The specific implementation method of the geometric representation module function is as follows: First, an implicit signed distance function based on a neural network auto-decoder architecture is used to represent the geometry, modeling the input geometry to be optimized as a continuous scalar field: ;in, For spatial coordinates, A low-dimensional, compact latent space vector (Latent Code) to represent a specific geometry. These are the shared parameters of the neural network decoder; the geometry is defined as the zero isosurface of the function, satisfying: The geometric boundary The geometric configurations corresponding to actual physical objects include: three-dimensional vehicle surfaces (automobile configurations with fastback, notchback, or estateback configurations) and their components (such as rearview mirrors and tires), two-dimensional wing profiles, and obstacle boundaries in the physical wave equation system. During the training phase, the geometry of each training geometric sample is... Associate with a learnable latent representation vector ; By sampling a set of query points in the space surrounding the geometric sample And calculate the corresponding signed distance to the target. To construct training data; to update the shared decoder parameters using joint optimization. Implicit representation of each sample Its optimization objective function includes minimizing the difference between the predicted distance and the target distance. Reconstruct the loss and apply The implicit representation regularization term serves as a Gaussian prior constraint; and during the optimization process, Gaussian perturbations are injected into the implicit representation. ,in This is achieved by enhancing the local smoothness of the latent space-to-geometric mapping through a denoising mechanism.

[0015] The specific implementation method of the geometric injection field prediction module is as follows: First, using a token-based Transformer solver model as the backbone network, the field is predicted on the irregular query point set Q. ; Next, geometric injection is performed, and the specific steps are as follows: Step 1. Convert the implicit representation vector Through a learnable linear projection matrix Feature dimensions mapped to slice tokens ; Step 2. Use slice tokens As a condition, by including the SiLU activation function and the Sigmoid activation function Multilayer perceptron network generates gated vectors The formula is expressed as: ; Step 3. Modulate the mapped hidden representation element-wise using the gated vector to construct the geometric injection increment. And inject it into the slice token using a residual join method: Through the aforementioned fully differentiable gated injection mechanism, a gradient path from the slice space to the geometric latent space is explicitly established in the physics prediction model, enabling the task objective function to... Hidden representation gradient It can transmit data back efficiently.

[0016] The specific implementation method of the differentiable optimization / inversion module is as follows: Step S1: Input the initial geometry Initialize implicit representation And sample the boundary point set on its zero isosurface. ; Step S2: Use the geometry-aware Transformer solver in Predicting Physics Fields And define the task objective based on field-level quantities. ,in, This indicates the number of iterations for optimization / inversion; Indicates the first The geometric implicit representation vector corresponding to the next iteration time; Indicates the first In the next iteration, the set of boundary-consistent query points maintained geometrically at the current level; Step S3: Backpropagation yields... If component freezing is enabled, null projection is performed to obtain... ; Step S4: Update the hidden representation using gradient descent: ,in, This represents the step size of the gradient descent update, i.e., the learning rate; This indicates the safety gradient after component freeze constraint processing; Step S5: For Perform a repetitive mesh projection to restore the geometry to its updated implicit representation. , obtained in the first In the next iteration, the geometrically maintained set of boundary-consistent query points is currently in use. ; Step S6: Repeat S2–S5 until the iteration termination condition is met, and output the optimized geometry. If it is an inversion task, the objective is... To observe the matching error.

[0017] The specific method for boundary-consistent sampling and deduplication-free mesh projection is as follows: One-step projection using SDF gradient: Repeat this process multiple times to quickly pull the point back to the zero isosurface.

[0018] The specific method for component-level control is as follows: sample the constraint point set of the component to be frozen. And construct the constraint Jacobi For unconstrained gradients Calculate the projection matrix ,in Represents the identity matrix. Refers to matrix The Moore-Ponros generalized inverse, and the safety gradient are defined. .

[0019] The technical effects to be achieved by the embodiments of the present invention are as follows: Unifying geometric representation, field-level forward prediction, and geometric update within a single closed loop enables stable implicit representation gradient updates. Simultaneously, it supports component-level constraint control and boundary consistency sampling of the non-repeating mesh, thereby reducing iteration costs and improving optimization stability and engineering usability. Attached Figure Description

[0020] The above and other objects and features of this disclosure will become clearer from the following description taken in conjunction with the accompanying drawings.

[0021] Figure 1 This is a schematic diagram showing a comparison between the shape optimization and inversion method architecture of the geometry-aware neural optimizer according to an embodiment of the present disclosure and the architecture of the classic geometry optimization process method. Figure 2 This is a schematic diagram illustrating the shape optimization and inversion method architecture of a geometry-aware neural optimizer according to an embodiment of the present disclosure; Figure 3This is a schematic diagram of the latent space of a geometric representation module according to an embodiment of the present disclosure; Figure 4 This is a schematic diagram illustrating an experimental setup for an application scenario according to an embodiment of the present disclosure; Figure 5 This is a schematic diagram illustrating forward prediction and shape inversion in a 2D Helmholtz application scenario according to an embodiment of the present disclosure. Detailed Implementation

[0022] The following detailed embodiments are provided to aid the reader in gaining a comprehensive understanding of the methods, apparatus, and / or systems described herein. However, various changes, modifications, and equivalents of the methods, apparatus, and / or systems described herein will become apparent upon understanding this disclosure. For example, the order of operations described herein is merely illustrative and is not limited to those orders set forth herein, but may be changed as will become clear upon understanding this disclosure, except for operations that must occur in a specific order. Furthermore, for clarity and conciseness, descriptions of features known in the art may be omitted.

[0023] The features described herein may be implemented in different forms and should not be construed as limited to the examples described herein. Rather, the examples described herein are provided only to illustrate some of the many feasible ways of implementing the methods, apparatus, and / or systems described herein, which will become clear upon understanding the disclosure of this application.

[0024] As used herein, the term “and / or” includes any one of the associated listed items and any combination of any two or more.

[0025] Although terms such as “first,” “second,” and “third” may be used herein to describe various components, assemblies, regions, layers, or parts, these components, assemblies, regions, layers, or parts should not be limited by these terms. Rather, these terms are used only to distinguish one component, assembly, region, layer, or part from another. Thus, without departing from the teaching of the examples described herein, the first component, first assembly, first region, first layer, or first part referred to as the first component, first assembly, first region, first layer, or first part may also be referred to as the second component, second assembly, second region, second layer, or second part.

[0026] In the specification, when an element (such as a layer, region, or substrate) is described as being "on" another element, "connected to," or "bonded to" another element, the element may be directly "on" another element, directly "connected to," or "bonded to" the other element, or one or more other elements may be present in between. Conversely, when an element is described as being "directly on" another element, "directly connected to," or "directly bonded to" another element, no other elements may be present in between.

[0027] The terminology used herein is for the purpose of describing various examples only and is not intended to limit disclosure. Unless the context clearly indicates otherwise, the singular form is intended to include the plural form as well. The terms “comprising,” “including,” and “having” indicate the presence of the described features, quantities, operations, components, elements, and / or combinations thereof, but do not preclude the presence or addition of one or more other features, quantities, operations, components, elements, and / or combinations thereof.

[0028] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains upon understanding this disclosure. Unless expressly defined herein, terms (such as those defined in a general dictionary) shall be interpreted as having a meaning consistent with their meaning in the context of the relevant field and in this disclosure, and shall not be interpreted in an idealized or overly formalistic manner.

[0029] Furthermore, in the description of the examples, detailed descriptions of well-known related structures or functions will be omitted when it is believed that such detailed descriptions would lead to a vague interpretation of this disclosure.

[0030] Figure 1 This is a schematic diagram illustrating a comparison between a shape optimization and inversion method of a geometry-aware neural optimizer according to an embodiment of the present disclosure and a classical geometry optimization process method, wherein... Figure 1 (a) is the classic geometry optimization process. Figure 1 (b) is the logical flow proposed in this invention.

[0031] To achieve the aforementioned objectives, the present invention employs the following technical framework: Figure 2 As shown.

[0032] This invention proposes a shape optimization and inversion method based on a "geometric perceptual neural optimizer." This method is geared towards shape optimization and inversion based on geometric perception. Determine the computational domain The PDE system aims to achieve a given task objective. Solving the optimal geometry .

[0033] Overall Framework: This invention (GANO) consists of three parts: (1) Geometry Representation Module (StableSDF): Represents geometry Encoding as implicit representation And through noise reduction training to make " →Geometric mapping provides local smoothness, facilitating stable gradient updates; (2) Geometrically Injected Field Prediction Module (GI-Transolver): Predicts physical fields on unstructured points / mesh queries. and explicitly establish goals To hidden representation Differentiable gradient pathways; (3) Differentiable optimization / inversion module: in the latent space It performs iterative updates while providing component-level control (zero-space projection) and boundary-consistent projection of the non-repeating mesh.

[0034] Its specific implementation steps include: a. Geometric Representation: This invention models the geometry to be optimized as an implicit symbolic distance function and employs a denoising mechanism to enhance stability during training.

[0035] b. Forward analysis: Geometric information is injected through a geometry-aware module, and a gradient path that can be backpropagated is constructed.

[0036] c. Optimization: Backpropagate the objective function to obtain the gradient of the updated implicit representation and use null projection on the gradient to achieve controllable geometric updates.

[0037] Furthermore, each module will be explained in detail.

[0038] Geometry Representation Module (StableSDF): (1) Geometry is represented using the implicit signed distance function (SDF): ,satisfy .

[0039] (2) Training phase: For each training geometry Associative learnable latent representations And jointly optimize the shared decoder parameters θ and , minimize Reconstruction losses and additions Implicit means prior.

[0040] (3) Denoising perturbation: Gaussian perturbation is injected into the hidden representation during training. This mechanism forces the decoder to... Effective geometry can be reconstructed within the neighborhood, thereby reducing... This improves the robustness and update stability of the latent space.

[0041] Figure 3 In the diagram, (a) represents linear interpolation between the latent representations of two cars in the dataset. (b) represents sampling latent representations from a Gaussian distribution.

[0042] Geometric Injection Field Prediction Module (GI-Transolver): (1) Using a token-based Transformer solver model as the backbone network, predict the field on the irregular query point set Q. .

[0043] (2) Geometric Injection: Injecting implicit representation Linear mapping to slice dimensions, and based on slices Generate gate vector ,structure And inject it into the token using a residual method: .

[0044] (3) The injection process is completely differentiable, making the objective function differentiable from the objective function. The gradient can be obtained through Effective feedback: .

[0045] Differentiable optimization / inversion module: (1) Boundary consistent sampling and deduplication-free mesh projection: Iteration Maintain the boundary point set at all times .renew Afterwards, the old point set will deviate from the new boundary. To avoid regrid, this invention uses SDF gradient one-step projection: Repeating the process multiple times can quickly pull the point back to the zero isosurface, enabling boundary consistency queries of the non-repeating mesh.

[0046] (2) Component-level control (zero-space projection): Sample constraint point set for the components that need to be frozen And construct the constraint Jacobi For unconstrained gradients Calculate the projection matrix and make safety gradient This operation suppresses the first-order change of the SDF at the constraint point, thereby keeping the geometry of the specified component (such as a vehicle tire / rearview mirror) unchanged.

[0047] (3) Optimization / Inversion Iterative Process: Step S1: Input initial geometry Initialize implicit representation And sample the boundary point set on its zero isosurface. ; Step S2: Use the Geometry-Aware Transformer Solver (GI-Transformer) in Predicting Physics Fields And define the task objective based on field-level quantities. (Can support regionalized objectives); Step S3: Backpropagation yields... If component freezing is enabled, null projection is performed to obtain... ; Step S4: Update the hidden representation using gradient descent: ; Step S5: For Perform a repetitive mesh projection to return it to its original position. ,get ; Step S6: Repeat S2–S5 until the iteration termination condition is met, and output the optimized geometry. If it is an inversion task, the objective is... To observe the matching error.

[0048] Application scenario implementation examples: Example 1: 2D Helmholtz inverse scattering. Given boundary sparse sensor observations, this method is used to invert the shape of obstacles in latent space.

[0049] Example 2: 2D airfoil aerodynamic optimization. Based on the AirFoil_9k dataset, the velocity / pressure field is predicted and lift is maximized under soft drag constraints, achieving a significant lift-to-drag ratio improvement of +55.9% (validated by COMSOL).

[0050] Example 3: 3D vehicle aerodynamic optimization. Based on the DriveAerNet++ dataset, surface pressure is predicted and drag proxy is minimized, achieving a drag reduction of approximately 7% while keeping key standardized components unchanged (validated by OpenFOAM).

[0051] Figure 4 Experimental setups for the above application scenarios are as follows: (a) represents the prediction and inverse problem of scattering field of 2D Helmholtz equation; (b) prediction and optimization of 2D airfoil flow field; and (c) optimization of 3D car surface pressure field.

[0052] Figure 5 Forward prediction and shape inversion for 2D Helmholtz application scenarios, where (a) is a schematic diagram comparing the scattering field prediction results; and (b) is the shape inversion result based on sparse sensor observations.

[0053] To further illustrate the practical application effects and physical significance of the present invention, the following detailed description is provided in conjunction with specific fluid dynamics engineering scenarios (such as automotive aerodynamic design).

[0054] Example: Vehicle aerodynamic shape optimization scenario based on fluid dynamics This embodiment applies the aforementioned geometric perception neural optimization method to the practical engineering problem of automotive aerodynamic shape design. In this scenario, the present invention solves the technical problem of how to improve aerodynamic performance (such as reducing wind resistance) by fine-tuning the vehicle body geometry.

[0055] 1. Geometric shape With computational domain Specific meaning: In this embodiment, the geometry to be optimized Specifically, it refers to the curved surfaces of a car body (such as the roof, side panels, and hood). Since fluids (air) cannot penetrate the car body, the shape of the body surface directly determines the external boundary of the surrounding airflow. Therefore, the computational domain... Specifically, it refers to the airflow field area surrounding the vehicle body. When the vehicle body geometry... When a small deformation occurs, the boundary conditions of the airflow field change accordingly, thereby affecting the pressure and velocity distribution within the flow field.

[0056] 2. Optimal Geometry Specific meaning: In this scenario, "optimal geometry" "It is not an abstract mathematical solution, but rather refers to the reduction of the overall vehicle's drag coefficient while satisfying vehicle engineering and manufacturing constraints (such as unchanged wheelbase and guaranteed interior space)." To achieve the smallest possible vehicle body shape design.

[0057] (1) Specific task objectives Defined as minimizing the aerodynamic drag of a vehicle at high speeds.

[0058] (2) Optimization results: The method of this invention can automatically find the body surface that can smooth airflow separation and reduce tail vortices, thereby achieving "optimal geometry". For example, in the test of the DriveAerNet++ vehicle dataset, the drag coefficient of the body geometry optimized by this method can be reduced by about 6.64%, which directly translates into an increase in the driving range of electric vehicles or a reduction in fuel consumption of fuel vehicles.

[0059] 3. Specific implementation steps: Step S1 (Geometric Encoding): Input the initial design 3D point cloud data of the car into the geometric representation module (StableSDF) and encode it into a low-dimensional implicit representation. .

[0060] Step S2 (Field Prediction): Using the geometrically injected field prediction module (GI-Transolver), the surface pressure distribution of the vehicle body surface under a wind speed of 30 m / s is directly predicted, replacing the traditional CFD simulation that takes several hours.

[0061] Step S3 (Constraint Optimization): Calculate the total drag generated by the predicted pressure field and apply it to the implicit representation. Gradient descent updates are performed. During this process, the null-space projection technique of this invention is used to forcibly set standardized components such as rearview mirrors, tires, and windows as "frozen regions," ensuring that optimization only occurs in the vehicle body skin area and guaranteeing the generated optimal geometry. It meets industrial manufacturing standards.

[0062] While some embodiments of this disclosure have been shown and described, those skilled in the art will understand that modifications may be made to these embodiments without departing from the principles and spirit of this disclosure, which are defined by the claims and their equivalents.

Claims

1. A method for shape optimization and inversion using a geometric perception neural optimizer, characterized in that, The specific method is as follows: First, the geometry of the input vehicle or wing 3D model to be optimized is modeled as an implicit symbolic distance function through the geometric representation module, and a denoising mechanism is used to enhance stability during training; The geometric representation module therein represents the geometric shape Encoding as implicit representation And through noise reduction training The mapping to geometry is locally smooth, which facilitates stable gradient updates; Then, forward analysis is performed, injecting geometric information through a geometry-injected field prediction module and constructing a gradient path capable of backpropagation; wherein, the geometry-injected field prediction module predicts the physical field on unstructured points / mesh queries. and explicitly establish goals To hidden representation Differentiable gradient pathways; Finally, a geometric optimization step is performed, using a differentiable optimization / inversion module to optimize the latent representation in the latent space. Iterative updates are performed by backpropagating the objective function to obtain the gradient of the updated latent representation and then using null space projection on the gradient to achieve controllable geometric updates; subsequently, in the latent space... It performs iterative updates and provides component-level control and boundary consistency projection of the non-repeating mesh to enhance the feature extraction and generation capabilities of 3D geometric image data, output the reconstructed 3D model image, and realize the automated generation, optimization and high-precision 3D model reconstruction of the geometric configuration image of the vehicle or wing. The specific implementation method of the geometric representation module function is as follows: First, the geometry is represented by an implicit signed distance function based on a neural network automatic decoder architecture, which represents the input geometry to be optimized. For a continuous scalar field: , Let be the set of real numbers; where, Spatial coordinates, implicitly represented A low-dimensional compact latent space vector to characterize a specific geometry. Shared parameters for the neural network decoder; the geometry Defined as the zero isosurface of the function, satisfying: ; The specific implementation method of the geometric injection field prediction module is as follows: First, using a token-based Transformer solver model as the backbone network, the field is predicted on the irregular query point set Q. ,in The spatial coordinates representing the specific query point; Next, geometric injection is performed, and the specific steps are as follows: Step 1. Convert the implicit representation vector ,in For the set of real numbers, The dimension of the implicit representation vector is determined by a learnable linear projection matrix. Feature dimensions mapped to slice tokens ; Step 2. Use slice tokens As a condition, Given the set of real numbers, the activation functions include SiLU and Sigmoid. Multilayer perceptron network generates gated vectors The formula is expressed as: , These are the learnable weight matrices of the first linear transformation layer and the second linear transformation layer in the multilayer perceptron network, respectively. Step 3. Modulate the mapped hidden representation element-wise using the gated vector to construct the geometric injection increment. , It is a learnable linear projection matrix; then it is injected into the slice token via residual connection: ; The specific method for component-level control is as follows: sample the constraint point set of the component to be frozen. And construct the constraint Jacobi For unconstrained gradients Calculate the projection matrix ,in Represents the identity matrix. Refers to matrix The Moore-Ponros generalized inverse, and the safety gradient are defined. .

2. The shape optimization and inversion method of a geometric perception neural optimizer as described in claim 1, characterized in that, The geometry The configuration of geometric samples corresponding to actual physical objects includes: three-dimensional vehicle surfaces and their components, two-dimensional wing profiles, and obstacle boundaries in the physical wave equation system; During the training phase, the geometry of each training geometric sample is... Associate with a learnable latent representation vector ; By sampling a set of query points in the space surrounding the geometric sample And calculate the corresponding signed distance to the target. Construct training data; update the shared decoder parameters using a joint optimization approach. Implicit representation of each sample Its optimization objective function includes minimizing the difference between the predicted distance and the target distance. Reconstruct the loss and apply The implicit representation regularization term serves as a Gaussian prior constraint; and during the optimization process, Gaussian perturbations are injected into the implicit representation using a noise injection method. : ,in This is achieved by enhancing the local smoothness of the latent space-to-geometric mapping through a denoising mechanism.

3. The shape optimization and inversion method of a geometric perception neural optimizer as described in claim 2, characterized in that, The specific implementation method of the differentiable optimization / inversion module is as follows: Step S1: Input the initial geometry Initialize implicit representation And sample the boundary point set on its zero isosurface. ; Step S2: Use the geometry-aware Transformer solver in Predicting Physics Fields And define the task objective based on field-level quantities. ,in, This indicates the number of iterations for optimization / inversion; Indicates the first The geometric implicit representation vector corresponding to the next iteration time; Indicates the first In the next iteration, the set of boundary-consistent query points maintained geometrically at the current level; Step S3: Backpropagation yields... If component freezing is enabled, null projection is performed to obtain... ; Step S4: Update the hidden representation using gradient descent: ,in, This indicates the step size for gradient descent updates; Step S5: For Perform a non-repeating mesh projection to obtain the geometry after updating the implicit representation. Thus, in the first In the next iteration, the geometrically maintained set of boundary-consistent query points is currently in use. ; Step S6: Repeat S2–S5 until the iteration termination condition is met, and output the optimized geometry. , For the final The implicit representation of the geometry in the next iteration; if it is an inversion task, the objective is... To observe the matching error.

4. The shape optimization and inversion method of a geometric perception neural optimizer as described in claim 3, characterized in that, The specific method for boundary-consistent sampling and deduplication-free grid projection is as follows: One-step projection using SDF gradient: Repeat this process multiple times to quickly pull the point back to the zero isosurface.

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