Method for reconstructing deformation field in hybrid additive-subtractive manufacturing based on physical information neural network
By constructing a Physical Information Neural Network (PINN) to reconstruct the deformation field in additive and subtractive manufacturing, the problem of insufficient physical law constraints in traditional methods is solved, and the accurate reconstruction of the stepped deformation field in the additive and subtractive manufacturing process is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-02-26
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies are insufficient to effectively characterize the stepped deformation field caused by the complex thermo-mechanical coupling effect during additive and subtractive manufacturing processes. Traditional methods lack physical constraints and have insufficient reconstruction accuracy.
A Physical Information Neural Network (PINN) is constructed, which takes the vertices of the CAD model as input and outputs the position of the deformed vertex and its neighborhood rotation angle. The non-rigid deformation amount, measurement data fidelity and boundary conditions are integrated through a loss function to train and reconstruct the piecewise deformation field of material addition and subtraction. The complete deformation field is generated by mask extraction and union operation.
It achieves accurate reconstruction of the stepped deformation field during the additive and subtractive manufacturing process, overcomes the insufficient physical constraints of traditional methods, and improves reconstruction accuracy and physical interpretability.
Smart Images
Figure CN122154303A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of computer-aided manufacturing, specifically relating to a method for reconstructing the deformation field in additive and subtractive manufacturing based on physical information neural networks. Background Technology
[0002] Hybrid manufacturing technology, which combines the design freedom of additive manufacturing with the high precision of subtractive manufacturing, has become an effective strategy for manufacturing complex cavity metal parts. However, the repeated melting-solidification cycles during metal additive manufacturing, coupled with the mechanical effects of subsequent cutting, lead to complex thermo-mechanical coupling effects within the workpiece. This effect is further amplified in the additive-subtractive alternating process: the thermal contraction of the newly deposited layer causes secondary deformation of adjacent machined surfaces, while the heat input from subsequent deposits may trigger further displacement of the machined areas. This dynamic cumulative effect ultimately forms a geometric deformation with a stepped characteristic, and characterizing this stepped deformation is crucial for controlling additive-subtractive induced deformation.
[0003] The thermo-mechanical deformation field generated during additive manufacturing can be obtained through finite element simulation. However, this method suffers from high computational cost, and its accuracy is affected by the mesh size and physical assumptions. While data-driven methods such as spline interpolation and kriging interpolation can reconstruct the deformation field using sparse measurement points, they lack physical constraints and are prone to producing displacement solutions that do not conform to physical laws, such as high-frequency displacement field fluctuations.
[0004] Furthermore, existing methods for reconstructing deformation fields based on sparse measurement points mainly consider the inherent smoothness of deformation. However, the deformation fields of additive and subtractive materials are characterized by smoothness within segments and discontinuous abrupt changes between segments, making them difficult to effectively represent using traditional continuous deformation models. Therefore, there is an urgent need to develop efficient deformation field reconstruction methods that integrate physical information for the unique segmented deformation fields of additive and subtractive materials. Summary of the Invention
[0005] To address the aforementioned issues, this invention discloses a method for reconstructing the deformation field in hybrid additive and subtractive manufacturing based on a physical information neural network. This method constructs a physical information neural network that integrates the input CAD model and sparsely sampled measurement data. The original CAD mesh model vertices are used as input, and the deformed vertex positions and their neighborhood rotation angles are used as outputs. The loss function integrates three important aspects of deformation: non-rigid deformation, in-machine measurement data fidelity, and boundary conditions. By minimizing the loss function, the deformation field of each additive and subtractive segment can be effectively characterized. Finally, the deformation fields of each segment are synthesized into a stepped overall additive and subtractive segment deformation field.
[0006] To achieve the above objectives, the technical solution of the present invention is as follows:
[0007] A method for reconstructing the deformation field in additive-subtractive hybrid manufacturing based on physical information neural networks includes the following steps:
[0008] Step 1: Construct a Physical Information Neural Network (PINN) with the original CAD model vertex coordinates as input, and output the vertex positions and local rotation Euler angles after the model is deformed; the network contains fully connected layers and branch structures, wherein the first branch outputs the deformed coordinates, the second branch outputs the local rotation Euler angles, and the original coordinates and deformed coordinates are associated through residual connections;
[0009] Step 2: Construct the loss function representing deformation energy in PINN obtained in Step 1, calculate the energy loss corresponding to the non-rigid deformation of the local region formed by each vertex and its adjacent vertices in the original CAD model, and minimize the difference between the side length output by PINN and the side length after applying a pure rigid rotation.
[0010] Step 3: Construct the loss function representing the fidelity of the measurement point in PINN obtained in Step 1. This is achieved by minimizing the difference between the signed distance from the center point of the probe ball to the deformed surface and the radius of the ball. The signed distance calculation includes three cases: patch projection, edge projection, and vertex projection of the curved triangular mesh.
[0011] Step 4: Construct the loss function representing the boundary conditions in PINN obtained in Step 1, restrict the movement of vertices connected to the substrate, and minimize the deviation between their deformed positions and their initial design positions;
[0012] Step 5: Collect the on-machine measurement point cloud corresponding to the surface of different material addition and subtraction segments. The coordinates of the point cloud represent the position of the probe ball center. This data is used as the PINN data. Combined with the loss functions of Steps 2 to 4, the physical information neural network is trained through the backpropagation algorithm.
[0013] Step 6: Train the PINN for each added or subtracted material segment according to the methods in Steps 1 to 5 and reconstruct the deformation field; extract the deformation results of each segment through a mask, and finally synthesize the complete stepped deformation field through a union operation.
[0014] The specific implementation process of step 1 is as follows:
[0015] The constructed physical information neural network takes the coordinates (x, y, z) of the vertices of the theoretical triangular mesh as input and passes them through several fully connected layers as hidden layers for nonlinear feature extraction. Then, it splits into two branches. The first branch outputs the deformed vertex coordinates (x', y', z') after passing through several fully connected hidden layers, and the second branch outputs the Euler angles (α, β, γ) representing the local neighborhood rotation state of the input vertex after passing through several fully connected hidden layers. The network adopts a residual connection mechanism, where the original vertex coordinates are directly added to the deformed coordinates output by the first branch, ensuring that the initial output of the network approximates the vertex position of the original model, while accelerating training convergence.
[0016] The specific implementation process of step 2 is as follows:
[0017] Considering the physical law that the deformation field must conform to smoothness, a loss function representing the energy of non-rigid deformation is constructed in PINN to quantify the difference in the local neighborhood before and after deformation. This ensures that the new position after deformation is achieved through rigid rotation rather than non-rigid stretching or shearing, thereby minimizing non-rigid deformation. Specifically, for each vertex i in the original triangular mesh, its position is... Extract the set of adjacent vertices within its one-ring neighborhood. The coordinates of the adjacent vertices are The new position of vertex i after deformation is denoted as Its neighborhood vertex position is Calculate the actual length of each side and apply the rigid transformation. The difference in length is used to represent the energy of non-rigid deformation at vertex i, i.e. It is related to the output of the first branch of the neural network, where Indicates the weighting coefficient. This represents the local neighborhood rotation matrix at position i, which is related to the output of the second branch of the neural network; therefore It is the function that outputs the vertex coordinates and Euler angles in step 1, while the overall non-rigid deformation energy of the entire mesh is... .
[0018] The specific implementation process of step 3 is as follows:
[0019] PINN measurement point fidelity requires that the center point of the probe's measuring ball maintain a tangential constraint with the reconstructed deformed part surface, i.e., the center point of the probe's measuring ball... To the reconstructed and deformed part surface The directed distance is the radius r of the measuring sphere, which is achieved by minimizing the fidelity loss function of the measuring point. ,in It is the number of measurement points. and They are arrive The nearest point and its surface normal; calculate the distance from the center point of the sphere to the triangular mesh. When calculating directed distances, it is necessary to distinguish between three cases of contact points: in-plane, on an edge, and on a vertex; among these, when the contact point between the measuring sphere and the face is located inside the triangular face, Take the normal vector of the facet; when the contact point is located on the edge, It is obtained by interpolating the normal vectors at the two vertices of the edge; when the contact point is located at a vertex. Take the normal vector at that vertex directly.
[0020] The specific implementation process of step 4 is as follows:
[0021] The boundary conditions for deformation field reconstruction in PINN restrict the vertices connected to the substrate. The displacement, the loss function of the boundary conditions is minimized by the fixed end vertex of the substrate. Position after deformation Compared with the initial design location The sum of squared distances between them is achieved by minimizing... .
[0022] The specific implementation process of step 5 is as follows:
[0023] For each segment of the part to be processed, after the addition or subtraction of materials is completed, a multi-axis in-machine measurement operation is performed on that segment. Measurement G-code is run, and N sets of coordinate point cloud data for the center points of the measured spheres are obtained for N segments. For each set of point cloud data, the output (x', y', z', α, β, γ) of PINN in step 1 is used to construct the non-rigid deformation energy loss function, measurement point fidelity loss function, and boundary condition loss function in steps 2-4, respectively. The overall loss function is expressed as the weighted sum of these three loss functions. During the training phase, Kaiming uniform initialization is used to make the initial output of the network with residual connections approximate the original mesh. All loss functions of the neural network are differentiable with respect to the output, and the output of the neural network is differentiable with respect to the network weights and bias parameters. Network training is achieved through backpropagation. After training, the new positions of all vertices of the mesh are calculated through forward propagation to form the deformation field. (i=1,2,…N).
[0024] The specific implementation process of step 6 is as follows:
[0025] The PINN is trained and the deformation field is reconstructed for each additive / subtractive material segment according to steps 1-5; the mask for the i-th manufacturing segment is defined. For the part surface corresponding to this segment, N deformation fields obtained in step 5 are obtained through masking operations. Extract the deformation fields of each of the N addition / subtraction segments from (i=1,2,…N). Interference data from adjacent segments is masked; the deformation field results extracted from each segment by the mask are fused, and then the result is obtained through union operation. Generate a complete stepped deformation field It accurately characterizes the discontinuous deformation features caused by repeated heating and cutting, while suppressing physical distortion caused by global smoothing operations.
[0026] The beneficial effects of this invention are as follows:
[0027] The PINN-based deformation field reconstruction method proposed in this invention fully utilizes the information of the theoretical CAD model and incorporates physical deformation constraints. Compared with traditional data-driven interpolation methods, it can obtain a more physically interpretable deformation field. By using segmented independent training, mask extraction, and union operation, it overcomes the limitation of traditional methods in being unable to characterize discontinuous deformation fields and achieves accurate reconstruction of the stepped deformation field of metal parts with added or subtracted materials. Attached Figure Description
[0028] Figure 1 This is a flowchart illustrating the overall process of the deformation field reconstruction method for additive and subtractive manufacturing based on a physical information neural network, implemented according to the present invention.
[0029] Figure 2 This is a diagram of the overall architecture of the Physical Information Neural Network (PINN) implemented according to the present invention.
[0030] Figure 3 This is a schematic diagram of the non-rigid deformation energy achieved according to the present invention, where (a) and (b) represent the vertices before and after deformation, respectively. The neighborhood of.
[0031] Figure 4 The diagram illustrates the fidelity of measurement point data achieved according to the present invention, where (a) represents the contact between the probe head and the curved surface, and (b) to (d) represent the contact points between the measuring ball and the deformed curved surface located inside the surface, on the edge, and on the vertex, respectively.
[0032] Figure 5 This is a schematic diagram of the boundary conditions implemented according to the present invention, wherein V bnd This represents the set of vertices connected to the substrate.
[0033] Figure 6 This is a schematic diagram illustrating how the deformation field of each segment is reconstructed separately according to the present invention, and how the deformation of each segment is extracted by a mask and a complete stepped deformation field is synthesized. Detailed Implementation
[0034] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.
[0035] The overall flowchart of this invention is shown below. Figure 1 This invention is based on Figure 2 Taking the conical cavity part on the left as an example, it is divided into four segments as shown in the diagram. Figure 2 The workpiece was manufactured using an alternating sequence of material addition and subtraction, as shown in the diagram (A1-S1-A2-S2-A3-S3-A4-S4). Without interference between the probe and the workpiece during the material addition and subtraction process, four sets of point cloud data were obtained by using machine measurement to contact the inner surface of each segment after milling, with the probe in contact with the surface.
[0036] In step 1, a Physical Information Neural Network (PINN) is constructed, such as... Figure 2 As shown, a triangular mesh model is used to represent the theoretical CAD model. The vertex coordinates (x, y, z) of the triangular mesh are used as input to a multilayer perceptron, which is then fed into two fully connected layers as hidden layers, each with 256 neurons, for nonlinear feature extraction. The network then splits into two branches. The first branch, after passing through two fully connected hidden layers, outputs the deformed vertex coordinates (x', y', z'). The second branch, after passing through two fully connected hidden layers, outputs the Euler angles (α, β, γ) representing the local neighborhood rotation state of the input vertex. Each layer in both branches has 256 neurons. The network employs a residual connection mechanism, where the original vertex coordinates (x, y, z) are directly added to the deformed coordinates (x', y', z') output from the first branch, ensuring that the initial output of the network approximates the vertex positions of the original model and accelerating training convergence. The GELU function is used as the activation function for the neural network.
[0037] In step 2, considering the physical law that the deformation field must conform to smoothness, a loss function representing the energy of non-rigid deformation is constructed in PINN to quantify the difference in the local neighborhood rotation matrix before and after deformation, ensuring that the new position after deformation is achieved as rigidly as possible through rotation rather than non-rigid stretching or shearing. Figure 3 As shown, for each vertex i in the original triangular mesh, its position is... Extract the set of adjacent vertices within its one-ring neighborhood. The coordinates of the adjacent vertices are For this neighborhood, each edge originating from i... Using a common rotation matrix Rotate to new edge Wherein, the new position of vertex i after deformation is denoted as Its neighborhood vertex position is The Euler angle of the local neighborhood rotation of the i-th vertex is ( Then the rotation matrix of the i-th vertex. Represented as
[0038] ;
[0039] Calculate the actual length of each side and apply the rigid transformation The difference in length is used to represent the energy of non-rigid deformation at vertex i, i.e. ,in Represents the weighting coefficient, through Calculations show that and Let $i$ represent the two opposite corners corresponding to edge $ij$. Next, the non-rigid deformation energy at the $i$-th vertex obtained above is extended to the set of all vertices $V$ of the triangular mesh and summed to obtain the overall non-rigid deformation energy of the entire mesh. .
[0040] In step 3, the PINN measurement point fidelity requirement dictates that the center point of the probe's measuring ball maintains a tangential constraint with the reconstructed deformed part surface. For the k-th in-machine measurement point, the center point of the probe's measuring ball... To the reconstructed and deformed part surface The directed distance is ,in and They are arrive The nearest point and its surface normal, such as Figure 4 As shown in (a). The measuring ball and the surface of the deformed part. Tangent means Where r is the radius of the measuring sphere. Therefore, to achieve the goal of keeping the measuring sphere tangent to the reconstructed deformed part surface at all locations, it is necessary to minimize the fidelity loss function of the measuring points. ,in This is the total number of measurement points. For example... Figure 4 As shown in (b) to (d), calculate the distance from the center point of the measuring sphere to the triangular mesh. When dealing with directed distances, it is necessary to distinguish between three cases of contact points and their corresponding normal vectors. The differences are: in-plane (b), on edge (c), and on vertex (d). Given the pre-calculated normals of the model's triangular mesh surface and vertex normals, when the contact point between the sphere and the facet is located inside the triangular facet, Take the normal vector of the facet; when the contact point is located on the edge, The normal vectors at the two vertices of this edge and the point The coordinates of the centroid are obtained through linear interpolation; when the contact point is located at the vertex... Take the normal vector at that vertex directly.
[0041] In step 4, since the metal additive manufacturing process begins on a substrate, the fixed and clamped substrate restricts the overall deformation of the part. However, this does not mean that the points attached to the substrate... Completely fixed, despite the high rigidity of the substrate, due to thermodynamic reasons, Small displacements may also occur. Therefore, a boundary condition loss function was added for points connected to the substrate. Apply soft constraints to minimize the total displacement. The loss function of the boundary conditions is obtained by minimizing the displacement at the fixed end vertex of the substrate. Position after deformation Compared with the initial design location The sum of squared distances between them is achieved by minimizing... .
[0042] In step 5, for each segment of the part to be processed, after the addition or subtraction of materials is completed, a multi-axis in-machine measurement operation is performed on that segment. Measurement G-code is run, and N sets of coordinate point cloud data for the center points of the measured spheres are obtained for the N addition and subtraction segments. For each set of point cloud data, the output (x', y', z', α, β, γ) of PINN in step 1 is used to construct the non-rigid deformation energy loss function in steps 2-4. Measurement point fidelity loss function and boundary condition loss function The overall loss function is expressed as a weighted sum of the three loss functions.
[0043] ;
[0044] in They represent , and Weights, for example , , Therefore, the overall loss function is the value of the deformed mesh vertex position. It is a function of the Euler angles α, β, γ of the rotation in its neighborhood. During the training phase, the learning rate is set to 10. -4 Kaiming uniform initialization is used to make the initial output of the network with residual connections approximate the original mesh. All loss functions of the neural network are differentiable with respect to the output (x', y', z', α, β, γ), and the output of the neural network is also differentiable with respect to the network weights and bias parameters. Therefore, the training process of PINN can be efficiently implemented using the backpropagation algorithm. After training, a single forward propagation operation can calculate the new positions of all vertices of the mesh, forming the deformation field. (i=1,2,…N).
[0045] In step 6, the PINN is trained and the deformation field is reconstructed for each additive / subtractive material segment according to the methods in steps 1-5. The mask for the i-th manufacturing segment is defined. For the part surface corresponding to this segment, the four deformation fields obtained in step 5 are calculated using masking operations. The deformation fields of the four addition and subtraction material segments are extracted respectively. Interference data from adjacent segments is masked. The deformation field results extracted from each segment by the mask are fused together using a union operation. Generate a complete stepped deformation field It accurately characterizes the discontinuous deformation features caused by repeated heating and cutting, while suppressing physical distortion caused by global smoothing operations.
[0046] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.
Claims
1. A method for reconstructing the deformation field in additive-subtractive hybrid manufacturing based on physical information neural networks, characterized in that, Includes the following steps: Step 1: Construct a Physical Information Neural Network (PINN) with the original CAD model vertex coordinates as input, and output the vertex positions and local rotation Euler angles after the model is deformed. The network includes a fully connected layer and a branch structure, where the first branch outputs the deformed coordinates, the second branch outputs the local rotation Euler angles, and the original coordinates and deformed coordinates are associated through residual connections. Step 2: Construct the loss function representing deformation energy in PINN obtained in Step 1, calculate the energy loss corresponding to the non-rigid deformation of the local region formed by each vertex and its adjacent vertices in the original CAD model, and minimize the difference between the side length output by PINN and the side length after applying a pure rigid rotation. Step 3: Construct the loss function representing the fidelity of the measurement point in PINN obtained in Step 1. This is achieved by minimizing the difference between the signed distance from the center point of the probe ball to the deformed surface and the radius of the ball. The signed distance calculation includes three cases: patch projection, edge projection, and vertex projection of the curved triangular mesh. Step 4: Construct the loss function representing the boundary conditions in PINN obtained in Step 1, restrict the movement of vertices connected to the substrate, and minimize the deviation between their deformed positions and their initial design positions; Step 5: Collect the on-machine measurement point cloud corresponding to the surface of different material addition and subtraction segments. The coordinates of the point cloud represent the position of the probe ball center. This data is used as the PINN data. Combined with the loss functions of Steps 2 to 4, the physical information neural network is trained through the backpropagation algorithm. Step 6: Train the PINN for each added or subtracted material segment according to the methods in Steps 1 to 5 and reconstruct the deformation field; extract the deformation results of each segment through a mask, and finally synthesize the complete stepped deformation field through a union operation.
2. The method for reconstructing the deformation field in additive and subtractive manufacturing based on a physical information neural network according to claim 1, characterized in that, The specific implementation process of step 1 is as follows: The constructed physical information neural network takes the coordinates (x, y, z) of the vertices of the theoretical triangular mesh as input and passes them through several fully connected layers as hidden layers for nonlinear feature extraction. Then, it splits into two branches. The first branch outputs the deformed vertex coordinates (x', y', z') after passing through several fully connected hidden layers, and the second branch outputs the Euler angles (α, β, γ) representing the local neighborhood rotation state of the input vertex after passing through several fully connected hidden layers. The network adopts a residual connection mechanism, where the original vertex coordinates are directly added to the deformed coordinates output by the first branch, ensuring that the initial output of the network approximates the vertex position of the original model, while accelerating training convergence.
3. The method for reconstructing the deformation field in additive and subtractive manufacturing based on a physical information neural network according to claim 1, characterized in that, The specific implementation process of step 2 is as follows: Considering the physical law that the deformation field must conform to smoothness, a loss function representing the energy of non-rigid deformation is constructed in PINN to quantify the difference in the local neighborhood before and after deformation, ensuring that the new position after deformation is achieved through rigid rotation rather than non-rigid stretching or shearing as much as possible; thus minimizing non-rigid deformation; specifically, for each vertex i in the original triangular mesh, its position is... Extract the set of adjacent vertices within its one-ring neighborhood. The coordinates of the adjacent vertices are ; The new position of vertex i after deformation is denoted as Its neighborhood vertex position is Calculate the actual length of each side and apply the rigid transformation. The difference in length is used to represent the energy of non-rigid deformation at vertex i, i.e. It is related to the output of the first branch of the neural network, where Indicates the weighting coefficient. This represents the local neighborhood rotation matrix at position i, which is related to the output of the second branch of the neural network; therefore It is the function that outputs the vertex coordinates and Euler angles in step 1, while the overall non-rigid deformation energy of the entire mesh is... .
4. The method for reconstructing the deformation field in additive and subtractive manufacturing based on a physical information neural network according to claim 1, characterized in that, The specific implementation process of step 3 is as follows: PINN measurement point fidelity requires that the center point of the probe's measuring ball maintain a tangential constraint with the reconstructed deformed part surface, i.e., the center point of the probe's measuring ball... To the reconstructed and deformed part surface The directed distance is the radius r of the measuring sphere, which is achieved by minimizing the fidelity loss function of the measuring point. ,in It is the number of measurement points. and They are arrive The nearest point and its surface normal; calculate the distance from the center point of the sphere to the triangular mesh. When calculating directed distances, it is necessary to distinguish between three cases of contact points: in-plane, on an edge, and on a vertex; among these, when the contact point between the measuring sphere and the face is located inside the triangular face, Take the normal vector of the facet; when the contact point is located on the edge, It is obtained by interpolating the normal vectors at the two vertices of the edge; when the contact point is located at a vertex. Take the normal vector at that vertex directly.
5. The method for reconstructing the deformation field in additive and subtractive manufacturing based on a physical information neural network according to claim 1, characterized in that, The specific implementation process of step 4 is as follows: The boundary conditions for deformation field reconstruction in PINN restrict the vertices connected to the substrate. The displacement, the loss function of the boundary conditions is minimized by the fixed end vertex of the substrate. Position after deformation Compared with the initial design location The sum of squared distances between them is achieved by minimizing... .
6. The method for reconstructing the deformation field in additive and subtractive manufacturing based on a physical information neural network according to claim 1, characterized in that, The specific implementation process of step 5 is as follows: For each segment of the part to be processed, after the addition or subtraction of materials is completed, a multi-axis in-machine measurement operation is carried out for that segment. The measurement G-code is run, and N sets of coordinate point cloud data of the center point of the measurement sphere are obtained for N addition and subtraction segments. For each set of point cloud data, the output (x', y', z', α, β, γ) of PINN in step 1 is used to construct the non-rigid deformation energy loss function, measurement point fidelity loss function and boundary condition loss function in steps 2 to 4, respectively. The overall loss function is expressed as the weighted sum of these three loss functions. During the training phase, Kaiming uniform initialization is used to make the initial output of the network with residual connections approximate the original mesh. All loss functions of the neural network are differentiable with respect to the output, and the output of the neural network is differentiable with respect to the network weights and bias parameters. Network training is achieved through backpropagation. After training, the new positions of all vertices of the mesh are calculated through forward propagation to form the deformation field. , where i = 1, 2, ..., N.
7. The method for reconstructing the deformation field in additive and subtractive manufacturing based on a physical information neural network according to claim 1, characterized in that, The specific implementation process of step 6 is as follows: The PINN is trained and the deformation field is reconstructed for each additive / subtractive material segment according to steps 1-5; the mask for the i-th manufacturing segment is defined. For the part surface corresponding to this segment, N deformation fields obtained in step 5 are obtained through masking operations. Extract the deformation fields of each of the N addition and subtraction material segments respectively. Where i=1,2,…N; interference data from adjacent segments are masked; the deformation field results of each segment extracted by the mask are fused by union operation. Generate a complete stepped deformation field It accurately characterizes the discontinuous deformation features caused by repeated heating and cutting, while suppressing physical distortion caused by global smoothing operations.