Physical-guided neural network based prediction method for grinding wheel removal function

Abstract

The present application relates to a kind of physical guiding neural network based on small grinding head removal function prediction method, comprising: constructing physical guiding neural network, including physical guiding model, feature encoding unit, feature fusion unit, feature decoding unit;Space distribution parameter is input into the normalization geometric kernel of physical guiding neural network inside generation small grinding head removal function physical guiding model;Space distribution feature tensor and process feature tensor are obtained by the encoding processing of feature encoding unit;Multi-scale deep fusion is carried out to two kinds of feature tensors, and fusion feature tensor is obtained;The fusion feature tensor is decoded using feature decoding unit, and the predicted small grinding head removal function is obtained;After constructing loss function, the actual process parameter is input into the small grinding head removal function prediction model trained, and the corresponding small grinding head removal function is output;The advantage is that the restoration degree of removal function edge area and asymmetric feature is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of optical manufacturing technology, and in particular to a method for predicting the removal function of a small grinding head based on a physically guided neural network. Background Technology

[0002] Small-head grinding technology is a key technology in the optical processing of large-aperture optical components, playing an irreplaceable role in both grinding and polishing stages. In computer-controlled optical surface forming technology, the accuracy of the removal function is fundamental to achieving determinism in optical processing. However, traditional methods, based on the Preston equation and the motion law of the grinding head, establish a linear model, simplifying the coupling effect of complex process parameters to a single parameter K. This fails to accurately describe the nonlinear removal process in actual processing, resulting in insufficient prediction accuracy and poor versatility, thus limiting the determinism of small-head grinding. This invention utilizes the nonlinear fitting capability of neural networks to establish a precise mapping relationship between complex process parameters and the removal function during the removal process, significantly improving the prediction accuracy of the removal function and thereby enhancing the determinism of small-head grinding.

[0003] Existing neural network-based methods for predicting the removal characteristics of optical components primarily focus on the removal rate, rarely offering direct predictions of the three-dimensional removal function. Predicting only the removal rate is insufficient to meet the practical processing requirements of large-aperture optical components. In the field of optical processing, methods for predicting the three-dimensional removal function in magnetorheological polishing exist. These methods establish a mapping relationship between the magnetorheological ribbon and the removal function using a neural network, reducing the dimensionality of the three-dimensional removal function to multiple sets of two-dimensional data to lower the learning difficulty of the neural network, thus achieving magnetorheological removal function prediction under small sample conditions. However, due to the dimensionality reduction process, some fine three-dimensional features and spatial distribution information of the removal function inevitably suffer some loss during the conversion, making it difficult to fully preserve the spatial distribution characteristics of the removal function. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for predicting the removal function of a small grinding head based on a physically guided neural network, comprising the following steps: S1: Obtain the actual removal function under different original process parameters. The original process parameters and the actual removal function correspond one-to-one. Standardize the original process parameters to obtain standardized process parameters. Clean the actual removal functions to obtain standardized removal function samples. The standardized process parameters and the standardized removal function samples constitute a standardized process database. S2: Construct a physical guidance neural network, including a physical guidance model, a feature encoding unit, a feature fusion unit, and a feature decoding unit; input spatial distribution parameters into the physical guidance model, output a normalized geometric kernel, and apply spatial scale constraints and morphological constraints limited by polishing kinematics to the physical guidance neural network; S3: Use the feature encoding unit to extract the features of the normalized geometric kernel and the standardized process parameters respectively, and after encoding processing, obtain the spatial distribution feature tensor and the process feature tensor; S4: Use the feature fusion unit to perform multi-scale deep fusion on the spatial distribution feature tensor and process feature tensor extracted in step S3 to obtain the fused feature tensor; S5: Use the feature decoding unit to decode the fused feature tensor obtained in step S4 to obtain the predicted small grinding head removal function; S6: Construct a loss function, conduct iterative training of the physical-guided neural network, and after determining that the iteration has converged, obtain the trained small grinding head removal function prediction model. S7: Input the actual process parameters into the small grinding head removal function prediction model and output the corresponding small grinding head removal function.

[0005] Preferably, the standardized process parameters in step S1 include: mirror material, asphalt type, groove shape, rotation speed, normal pressure, abrasive type, abrasive particle size, and abrasive concentration; the spatial distribution parameters in step S2 include: grinding disc diameter and eccentricity distance.

[0006] Preferably, in step S2, the normalized geometric kernel output by the physics-guided model is represented as follows: ; Where r represents the grinding disc radius of the small grinding head, and e represents the eccentricity distance; G raw The two-dimensional spatial distribution representing the ideal removal function.

[0007] Preferably, in step S2: The feature coding unit includes a spatial feature coding branch and a process feature coding branch; The feature fusion unit is used to fuse the features output by the spatial feature coding branch and the process feature coding branch; The feature decoding unit is used to output the predicted small grinding head removal function.

[0008] Preferably, in step S3, the normalized geometric kernel output by the physical guidance model is extracted using the spatial feature encoding branch, and after encoding, a spatial distribution feature tensor is obtained; the process parameters are extracted using the process feature encoding branch, and after encoding, a process feature tensor is obtained.

[0009] Preferably, the spatial feature encoding in step S3 is processed using a spatial channel self-attention gating mechanism to obtain a channel attention weight vector, which is then combined with residual connections and shallow convolutional transformations to output a spatial distribution feature tensor.

[0010] Preferably, the process feature encoding in step S3 adopts a two-level progressive gating attention mechanism. First, the importance weights of process parameters are generated through parameter-level gating attention, and then the feature weights are generated through feature-level gating attention, finally obtaining the process feature tensor.

[0011] Preferably, in step S4, during feature fusion, the normalized geometric kernel output by the physics-guided model is also skipped, and the expression for feature fusion is as follows: ; in, Tensor representing spatial distribution characteristics; Represents the set of real numbers; Representative process parameter characteristics; Jump connections representing the normalized geometric kernel; , representing the dimension-aligned projection matrix; The number of channels in the tensor representing the spatial distribution characteristics. Represents the dimension of process feature encoding; the total number of input channels is C out Represents the number of output channels; k represents the kernel size; Broadcast This represents broadcast operations.

[0012] Preferably, step S5 uses a smoothing branch to smooth the predicted small grinding head removal function to ensure that the prediction result meets the continuity requirement of the removal distribution. The smoothing branch is represented as follows: ; in, Represents smoothing; This represents the original predicted small grinding head removal function. This represents a smooth prediction function for small grinding head removal. The expression for the function to predict the removal of small grinding heads is as follows: ; in, , representing the mixing coefficient; This represents a monotonically nonnegative activation function.

[0013] Preferably, the loss function in step S6 includes a data fitting term and a physical constraint term, wherein the physical constraint term includes a volume removal rate constraint term and a peak removal rate constraint term, and the loss function expression is as follows: ; in, Representative data fitting term; This represents the volume removal rate constraint. The weighting coefficients representing the volume removal rate constraint term; This represents the peak removal rate constraint. The weighting coefficient represents the peak removal rate constraint term.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: 1. This invention does not require any dimensionality reduction or dimensionality increase processing on the 3D removal function, and directly predicts the complete 3D spatial distribution, completely avoiding the inevitable loss of 3D fine features and spatial distribution information during dimensionality reduction, and in particular significantly improving the restoration degree of the edge region and asymmetric features of the removal function; 2. The physical-guided residual learning paradigm is adopted to replace the pure data-driven fitting learning, which enables the model to learn corrections based on existing physical laws. This not only significantly reduces the risk of overfitting and enhances the generalization ability, but also gives the model stronger physical interpretability. 3. Prior physical knowledge provides the "basic framework" for removing functions in the model. The neural network only needs to learn the residual part between the traditional model and the actual result. Under the same prediction accuracy requirements, the required experimental sample size can be reduced by more than 50%, which greatly reduces the experimental cost and R&D cycle. It is especially suitable for small grinding head processing scenarios with many process parameters and high experimental costs. Attached Figure Description

[0015] Figure 1 This is a flowchart of a small grinding head removal function prediction method based on a physically guided neural network according to an embodiment of the present invention.

[0016] Figure 2 This is a neural network structure diagram of the small grinding head removal function prediction method based on a physical guided neural network provided in an embodiment of the present invention. Detailed Implementation

[0017] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0019] This invention provides a method for predicting the removal function of a small grinding head based on a physically guided neural network. It uses the traditional physical model of the small grinding head removal function as the physical guide for neural network learning, transforming the learning mode from pure data fitting modeling to a learning mode based on the physical model and targeting the residual between the traditional model and the actual removal function. This effectively preserves the spatial characteristics of the small grinding head removal function, significantly reducing the learning difficulty of the neural network while fully retaining its three-dimensional spatial distribution characteristics. This achieves the technical effect of accurately predicting the three-dimensional removal function of a small grinding head using only a small number of samples. Figure 1 As shown, the specific steps include: S1. Obtain the actual removal functions under different combinations of original process parameters to form an initial process database, with one-to-one correspondence between the original process parameters and the actual removal functions; standardize the original process parameters to obtain standardized process parameters, and clean the actual removal functions to obtain standardized removal function samples. The standardized process parameters and standardized removal function samples constitute a standardized process database. The method for standardizing and coding the original process parameters is as follows: The original process parameters include discrete process parameters and continuous process parameters. Discrete process parameters include: mirror material, asphalt type, groove shape, abrasive type, etc.; continuous process parameters include: normal pressure, rotational speed, abrasive particle size, abrasive concentration, etc. Discrete process parameters are encoded using a one-hot encoding method; For continuous process parameters, a minimum-maximum normalization mapping is applied to the [0,1] interval. The normalization calculation expression is as follows: ; in, Represents normalized continuous process parameters; The original values ​​of the parameters representing continuous process; This represents the minimum value of the continuous process parameter in the initial process database; This represents the maximum value of the continuous process parameter in the initial process database; The processed standardized process parameters correspond one-to-one with the standardized removal function samples to form a standardized process database. The standardized process database is divided into a training set and a validation set according to a preset ratio. The ratio of the training set to the validation set ranges from 7:3 to 9:1, with an optimal ratio of 8:2. The rules for data cleaning of the actual removal function are as follows: Samples that do not meet the physical non-negativity constraint and exceed the equipment range or exhibit obvious measurement anomalies are removed from the measured actual removal function; within a single sample, outlier sampling points on the spatial grid are removed using a three-standard-deviation criterion, and the results are completed using the neighborhood mean; the mean of repeated measurements under the same original process parameter combination is taken; the dimensions and coordinate references of each sample are unified, and the actual removal function is resampled to a unified grid resolution of size H×W, where H and W range from 64 to 256, with a preferred value of 128, ultimately yielding a standardized removal function sample; In some implementations, the actual removal function under different combinations of original process parameters is obtained through orthogonal experiments; In some implementations, more comprehensive original process parameters can be obtained with fewer experiments by using experimental design methods such as uniform design, response surface design, and Latin hypercube design. In some implementations, logarithmic transformation and standardization to a specific interval can be used to standardize and encode the original process parameters, making the processed data more suitable for neural network learning.

[0020] S2. Construct a physically guided neural network, including a physically guided model, feature encoding unit, feature fusion unit, and feature decoding unit; input spatial distribution parameters into the physically guided model as a physical prior module, and apply spatial scale constraints and morphological constraints defined by polishing kinematics to the physically guided neural network; such as Figure 2 The diagram shown is a neural network structure diagram of a small grinding head removal function prediction method based on a physical guided neural network. The construction of the physics-guided model includes the following steps: The material removal rate during the polishing process can be expressed using the Preston equation as: ; in, Represents the Preston coefficient; P Represents normal pressure; V Represents the relative velocity of the processing points. z This represents the depth of material removal at the processing point; t Represents processing time; Polishing employs a planar rotational motion mode, with the grinding disc rotating around its own center and simultaneously revolving around the processing point. The relative velocity at the processing point is determined by this revolving motion. Based on the proportion of time the grinding disc covers the processing point, a one-dimensional radial distribution of the ideal removal function is derived, as expressed below: ; in, Represents the radial distance from any point on the optical surface to the machining point; The radius of the grinding disc represents the size of the grinding head; Represents the eccentric distance; Represents rotational speed, measured in rpm; Represents the removal rate per unit time, in units of ; Among them, the Preston coefficient Normal pressure With rotational speed The effect only influences the amplitude of the ideal removal function in a product form, without affecting its spatial distribution; the spatial distribution of the ideal removal function is entirely determined by the millstone radius. With eccentricity Therefore, the grinding wheel radius and eccentricity distance are the spatial distribution parameters input to the physical guidance model; By removing the magnitude term from the ideal removal function expression, we obtain the kinematic geometric kernel determined only by the spatial distribution parameters, as follows: ; By using rotational symmetry mapping, the one-dimensional radial distribution of the ideal removal function is transformed into a two-dimensional spatial distribution, as shown below: ; in, Represents two-dimensional spatial coordinates. Represents the distribution center; due to spatial distribution parameters and Two-dimensional spatial distribution with different values The amplitude scales differ. To eliminate the interference of these differences on the input of the physics-guided neural network, the two-dimensional spatial distribution is subjected to min-max normalization to obtain the normalized geometric kernel, which is the output of the physics-guided model. The normalized geometric kernel is represented as follows: ; The physical guidance model is embedded in the physical guidance neural network in the form of analytical formulas. Without any learnable parameters, it is directly generated as a fixed prior during the forward propagation stage of the network, and the normalized geometric kernel is output to the feature encoding unit. This applies the spatial scale and morphological constraints of polishing kinematics to the physical guidance neural network. The feature coding unit contains parallel spatial feature coding branches and process feature coding branches; The feature fusion unit is used to fuse the output features of the two branches; The feature decoding unit is used to output the prediction result of the small grinding head removal function.

[0021] S3. Using feature encoding units, extract the features of the normalized geometric kernel and process parameters respectively, and after encoding processing, obtain the spatial distribution feature tensor and the process feature tensor; specifically, using the spatial feature encoding branch, extract the normalized geometric kernel output by the physical guidance model, and after encoding processing, obtain the spatial distribution feature tensor; using the process feature encoding branch, extract the process parameters, and after encoding processing, obtain the process feature tensor; this includes the following sub-steps: S31. Spatial Feature Coding: A spatial channel self-attention gating mechanism is used to enhance the intermediate layer features of the encoder. Let the intermediate layer feature tensor of the encoder be... C represents the intermediate layer feature tensor The total number of channels; H and W represent the spatial height and spatial width of the intermediate layer feature tensor, respectively; Represents the set of real numbers; for intermediate layer feature tensors Global average pooling and global max pooling are performed on the C channels respectively to obtain the global average feature vector Z. avg and the global maximum eigenvector Z max , means as follows: ; ; Where i=1,2,…,H represents the position index in the spatial height direction; j=1,2,…,W represents the position index in the spatial width direction; Represents a C-dimensional real vector space; The global average eigenvector Z avg and the global maximum eigenvector Z max The inputs are sequentially processed into the same set of compressed-excitation networks, each generating a set of branch channel attention weights. The two sets of branch channel attention weights are then added element-wise and fused to obtain the final complete channel attention weight vector s, as shown in the following expression: ; in, ; , representing the projection matrix; , represents the excitation matrix, and a represents the channel compression ratio; Represents the Sigmoid activation function; , representing the modified linear unit; Using the channel attention weight vector s to apply the intermediate layer feature tensor Channel-by-channel weighting yields the attention-weighted features, expressed as follows: ; Where c represents the channel index, c=1,2,…,C; This represents the attention-weighted feature value at the (i,j)th spatial location in the c-th channel; Let represent the feature value at the (i,j)th spatial location in the c-th channel; The weight coefficient of the c-th channel in the channel attention weight vector s; By combining the output features of the spatial attention module constructed from residual connections, the spatial distribution feature tensor obtained after spatial feature encoding is obtained, which is represented as: ; in, Tensor representing spatial distribution characteristics; This represents a shallow convolutional transformation, where the feature dimensions remain unchanged before and after the transformation. S32. Process Feature Coding: A two-level progressive gating attention mechanism is adopted. The first level filters important process parameter variables at the process parameter level, and then the second level filters effective features at the coding feature level to achieve progressive refinement of parameter information. The specific steps are as follows: (1) Parameter-level gated attention mechanism: Self-gating is applied to the input process parameters, as shown in the following expression: ; ; in, d represents the importance weight of standardized process parameters; p The dimension representing the standardized process parameter vector p; This represents the filtered process parameters that retain the key components after weighted screening. , representing the first-level projection matrix; , representing the second-level projection matrix; d h represents the hidden layer dimension; p represents the input standardized process parameter vector; This indicates element-wise multiplication; the parameter-level gating attention mechanism enables the physical-guided neural network to automatically distinguish the relative contribution of each process parameter under the current process conditions; (2) Feature-level gating attention mechanism: The filtered process parameters obtained through the parameter-level gating attention mechanism are... The high-dimensional feature space is mapped through multi-layer nonlinear encoding, as shown in the following expression: ; in, This represents the high-dimensional process features obtained by mapping the process parameters after screening. , representing the encoding projection matrix; Representative process parameter feature encoding dimension; Represents the activation function; High-dimensional process characteristics Implement gating selection, the expression is as follows: ; ; in, represents the process feature tensor after two-stage screening; g represents the gating weight of the process parameter features. , , representing the gated projection matrix; Representative process parameter feature encoding dimension; Represents the intermediate dimension of gating; Represents the hyperbolic tangent activation function; The two branches complete feature extraction in parallel, respectively preserving the spatial information of physical morphology and the nonlinear coupling information of process parameters. No 3D data dimensionality reduction processing is performed throughout the process, and the refined spatial features of the 3D removal function are fully preserved. S4. Multi-scale deep fusion is performed on the spatial distribution feature tensor and process feature tensor extracted in step S3 using the feature fusion unit to obtain the fused feature tensor; the fused feature tensor integrates global and local features, physical rules and process coupling information. During the fusion, in addition to the spatial distribution feature tensor and the process feature tensor, a normalized geometric kernel is also connected in a skip connection. The fusion process is set at the input of the decoder, and the input sources of the decoder are divided into three parts: spatial distribution feature tensor. Process feature tensor and the jump connection of the normalized geometric kernel ; in, The number of channels representing the spatial distribution characteristics tensor; Representative process parameter feature encoding dimension; Because spatial features are prone to losing low-frequency spatial details after deep encoding, skip connections using physical priors can fully preserve kinematic structure information. However, directly concatenating the three data sources through simple channels can lead to problems such as process parameter features being overwhelmed by spatial distribution features and physical priors being suppressed by deep semantic features. Therefore, a strategy of dimension alignment followed by interactive fusion is adopted in the fusion stage: the process feature tensor is first aligned to channel dimensions via linear projection, then expanded to a spatial resolution consistent with the spatial distribution features through broadcasting operations. The three types of features with dimension matching are then concatenated along the channel dimensions. Subsequently, fusion convolution is used to complete the interactive fusion of local features. The expression for feature fusion is as follows: ; in, Represents the dimension alignment projection matrix; d e Represents the dimension of process feature encoding; C sThe number of channels representing the spatial distribution feature tensor; the total number of input channels is C out Represents the number of output channels; Represents the kernel size; Broadcast ( ) represents broadcast operation, which expands the process feature vector to a spatial resolution consistent with the spatial distribution feature tensor.

[0022] S5: Use the feature decoding unit to decode the fused feature tensor obtained in step S4 to obtain the predicted three-dimensional removal function of the small grinding head; The mapping relationship of the physical-guided neural network is defined as follows: ; in, Represents the set of real numbers; d p The dimension representing the standardized process parameter vector p; This represents the removal function's prediction of the image's spatial resolution; This represents all trainable parameters of a physically guided neural network. The original predicted small grinding head removal function is expressed as: ; Where p represents a standardized process parameter vector; The normalized geometric kernel representing the output of the physics-guided model; The fused features are decoded by a convolutional decoder. To enhance the spatial smoothness and physical plausibility of the prediction results, a smoothing branch is used to smooth the prediction results, ensuring that the prediction results meet the requirement of distributive continuity. The smoothing branch is represented as follows: ; in, This represents a smooth prediction function for small grinding head removal. Represents smoothing; The original predicted small grinding head removal function and the smoothed predicted small grinding head removal function are weighted and mixed to obtain the predicted small grinding head removal function, as shown in the following expression: ; in, , representing the mixing coefficient, can be adjusted according to the predicted morphological effect; this scheme uses a fixed value. ; This represents a monotonically nonnegative activation function, ensuring that the predicted removal result satisfies the physical nonnegativity constraint. The decoding process does not add any intermediate processing steps such as dimensionality reduction, dimensionality increase, or interpolation compensation, and directly outputs the complete three-dimensional spatial distribution result, completely avoiding the loss of fine spatial features.

[0023] S6: Construct a loss function and conduct iterative training based on the physical guided neural network. When the loss on the validation set no longer decreases for several consecutive rounds, or when the training reaches the preset maximum number of iterations, the physical guided neural network is determined to have converged, and the trained small grinding head removal function prediction model is obtained. The loss function includes a data fitting term and a physical constraint term. The physical constraint term includes a volume removal rate constraint term and a peak removal rate constraint term, and the expression is as follows: ; Among them, the data fitting term For pixel-by-pixel Loss is represented as follows: ; in, Z represents the predicted small grinding head removal function; Z represents the true value of the standardized removal function sample. The volumetric removal rate (VRR) constraint is expressed as follows: ; The Peak Removal Rate (PRR) constraint is expressed as follows: ; in, This represents the area that has been effectively removed. Represents the set of real numbers; Represents two-dimensional real Euclidean space; The weighting coefficients representing the volume removal rate constraint term; The weighting coefficients represent the peak removal rate constraint term; the weighting coefficients are set according to the order of magnitude of each loss to ensure that they have similar gradient contributions in the early stages of training. Iterative training uses an adaptive gradient optimization algorithm to update network weight parameters, preferably using the Adam or AdamW optimizer, with an initial learning rate ranging from 10. -5 ~10 -3 The preferred value is 10. -4 The batch size ranges from 4 to 32, and the maximum number of iterations ranges from 500 to 2000. The convergence criterion is as follows: training is terminated early when the value of the validation set loss function fails to improve for 20 to 50 consecutive iterations, or training is terminated when the preset maximum number of iterations is reached. The network parameters corresponding to the minimum validation set loss are selected as the small grinding head removal function prediction model after training.

[0024] S7. Input the actual process parameters from the actual processing scenario into the trained small grinding head removal function prediction model, and output the corresponding small grinding head removal function.

[0025] The entire prediction process requires no manual intervention or intermediate processing steps. The predicted removal function for small grinding heads combines physical rationality with process fitting accuracy, exhibiting high fidelity in edge regions and asymmetric features. It can be directly integrated into a computer-controlled optical surface shaping (CCOS) system for practical processing scenarios such as polishing path planning and residence time calculation, achieving high-precision polishing removal prediction under small sample conditions. In addition to being applicable to small grinding head polishing scenarios, it can also be applied to removal function prediction scenarios for various optical precision processing technologies, including but not limited to: airbag polishing removal function prediction, stress disk polishing removal function prediction, magnetorheological polishing removal function prediction, jet polishing removal function prediction, ion beam shaping removal function prediction, and plasma polishing removal function prediction.

[0026] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0027] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for predicting the removal function of a small grinding head based on a physically guided neural network, characterized in that, Includes the following steps: S1: Obtain the actual removal function under different original process parameters. The original process parameters and the actual removal function correspond one-to-one. Standardize the original process parameters to obtain standardized process parameters. Clean the actual removal functions to obtain standardized removal function samples. The standardized process parameters and the standardized removal function samples constitute a standardized process database. S2: Construct a physical guidance neural network, including a physical guidance model, a feature encoding unit, a feature fusion unit, and a feature decoding unit; input spatial distribution parameters into the physical guidance model, output a normalized geometric kernel, and apply spatial scale constraints and morphological constraints limited by polishing kinematics to the physical guidance neural network; S3: Use the feature encoding unit to extract the features of the normalized geometric kernel and the standardized process parameters respectively, and after encoding processing, obtain the spatial distribution feature tensor and the process feature tensor; S4: Use the feature fusion unit to perform multi-scale deep fusion on the spatial distribution feature tensor and process feature tensor extracted in step S3 to obtain the fused feature tensor; S5: Use the feature decoding unit to decode the fused feature tensor obtained in step S4 to obtain the predicted small grinding head removal function; S6: Construct a loss function, conduct iterative training of the physical-guided neural network, and after determining that the iteration has converged, obtain the trained small grinding head removal function prediction model. S7: Input the actual process parameters into the small grinding head removal function prediction model and output the corresponding small grinding head removal function.

2. The method for predicting the small grinding head removal function based on a physically guided neural network according to claim 1, characterized in that, The standardized process parameters in step S1 include: mirror material, asphalt type, groove shape, rotation speed, normal pressure, abrasive type, abrasive particle size, and abrasive concentration; the spatial distribution parameters in step S2 include: grinding disc diameter and eccentricity distance.

3. The method for predicting the removal function of a small grinding head based on a physically guided neural network according to claim 1, characterized in that, In step S2, the normalized geometric kernel output by the physics-guided model is represented as follows: ； in, r The radius of the grinding disc represents the small grinding head. e G represents the eccentric distance; raw The two-dimensional spatial distribution representing the ideal removal function.

4. The method for predicting the small grinding head removal function based on a physically guided neural network according to claim 1, characterized in that, In step S2: the feature coding unit includes a spatial feature coding branch and a process feature coding branch; The feature fusion unit is used to fuse the features output by the spatial feature coding branch and the process feature coding branch; The feature decoding unit is used to output the predicted small grinding head removal function.

5. The method for predicting the small grinding head removal function based on a physically guided neural network according to claim 4, characterized in that, In step S3, the normalized geometric kernel output by the physical guidance model is extracted using the spatial feature encoding branch, and after encoding, a spatial distribution feature tensor is obtained; the process parameters are extracted using the process feature encoding branch, and after encoding, a process feature tensor is obtained.

6. The method for predicting the removal function of a small grinding head based on a physically guided neural network according to claim 5, characterized in that, The spatial feature encoding in step S3 is processed using a spatial channel self-attention gating mechanism to obtain the channel attention weight vector. Then, combined with residual connections and shallow convolutional transformation, the spatial distribution feature tensor is output.

7. The method for predicting the removal function of a small grinding head based on a physically guided neural network according to claim 5, characterized in that, The process feature encoding in step S3 adopts a two-level progressive gating attention mechanism. First, the importance weights of process parameters are generated through parameter-level gating attention, and then the feature weights are generated through feature-level gating attention, finally obtaining the process feature tensor.

8. The method for predicting the removal function of a small grinding head based on a physically guided neural network according to claim 1, characterized in that, Step S4 also involves skip connections to the normalized geometric kernel during feature fusion. The expression for feature fusion is as follows: ； in, Tensor representing spatial distribution characteristics; Represents the set of real numbers; Representative process parameter characteristics; Jump connections representing the normalized geometric kernel; , representing the dimension-aligned projection matrix; The number of channels in the tensor representing the spatial distribution characteristics. Represents the dimension of process feature encoding; the total number of input channels is C out Represents the number of output channels; k represents the kernel size; Broadcast This represents broadcast operations.

9. The method for predicting the removal function of a small grinding head based on a physically guided neural network according to claim 1, characterized in that, Step S5 uses a smoothing branch to smooth the predicted small grinding head removal function, ensuring that the prediction result meets the continuity requirement of the removal distribution. The smoothing branch is represented as follows: ； in, Represents smoothing; This represents the original predicted small grinding head removal function; This represents a function for smoothly predicting the removal of small grinding heads; The expression for the function predicting the removal of the small grinding head is as follows: ； in, , representing the mixing coefficient; This represents a monotonically nonnegative activation function.

10. The method for predicting the removal function of a small grinding head based on a physically guided neural network according to claim 1, characterized in that, The loss function in step S6 includes a data fitting term and a physical constraint term. The physical constraint term includes a volume removal rate constraint term and a peak removal rate constraint term. The expression for the loss function is as follows: ； in, Representative data fitting term; This represents the volume removal rate constraint. The weighting coefficients representing the volume removal rate constraint term; This represents the peak removal rate constraint. The weighting coefficient represents the peak removal rate constraint term.

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