Four-side gridding-oriented multi-target distance field calculation method based on physical information neural time field

Abstract

The invention discloses a four-side gridding-oriented multi-target distance field calculation method based on a physical information neural time field, and the method comprises the steps: constructing a deep neural network model which comprises an input encoder, a symmetric feature fusion module and a time field predictor; for the query point, calculating a corresponding real speed value, and training a deep neural network model, so that a prediction speed calculated from the predicted factorization time field value is converged to a real speed within an error range; based on the trained deep neural network model, for each query point, predicting a factorization time field value, calculating time required for propagation from the query point to all target points, calculating distances from the query point to all the target points by combining a bidirectional search method, and taking the minimum value as a distance value of the query point, and finally, a complete multi-target distance field is formed. The method can directly control the propagation velocity of some areas in the training stage, and further adjusts the distance gradient and density.

Description

Technical Field

[0001] The present invention relates to the fields of computer graphics, computational geometry and deep learning technology, and in particular to a multi-target distance field calculation method based on physical information neural time field for quadrilateral meshing. Background Art

[0002] Three-dimensional path planning technology is a key technology in many fields, including computer graphics, robotic navigation, virtual reality, and medical modeling. In particular, finding the optimal path from a starting point to a destination in a three-dimensional mesh structure has important application value in tasks such as virtual character movement, simulation animation, scene interaction, and three-dimensional modeling. Traditional methods often rely on graph-theoretic path search (such as the Dijkstra algorithm and the A* algorithm) or numerical solutions (such as the Fast Marching Method (FMM)), which discretize the mesh into a graph structure and then calculate the shortest path. Although these methods are effective in low-dimensional scenarios, they have high computational complexity and difficulty in real-time response when applied to high-resolution meshes or high-dimensional configuration spaces. They also lack good continuity and differentiability, limiting their further application in gradient-derivative path optimization, robotic control, or neural network integration.

[0003] Another common approach uses distance fields to generate isosurfaces, which are then used to reconstruct a 3D mesh. For example, the marching cubes algorithm or neural implicit modeling techniques based on signed distance functions (SDFs) can be used for object reconstruction and surface extraction. However, once the mesh is generated, these methods cannot control the distance distribution and sampling density, making them difficult to adjust flexibly.

[0004] In recent years, neural networks have made significant progress in implicit function modeling, particularly by combining signed distance function learning techniques with Eikonal equation solvers. This has enabled neural network modeling of arrival time fields in continuous space. However, existing methods often focus on modeling from a single source point to a target point, lacking efficient mechanisms for processing arbitrary query points to multiple target points and the ability to flexibly adjust density. Summary of the Invention

[0005] The purpose of the present invention is to propose a neural time field calculation method for estimating the shortest arrival time distance from a point to a set of target points in a three-dimensional grid scene.

[0006] The technical solution to achieve the purpose of the present invention is: a multi-target distance field calculation method based on physical information neural time field for four-sided meshing, the specific steps are as follows:

[0007] Step 1, temporal field modeling: Construct a deep neural network model, including an input encoder, a symmetric feature fusion module, and a temporal field predictor. The input encoder is used to embed the spatial coordinates of the query point and the target point into high-dimensional feature representations and output the position encoding features of the query point and the target point. The symmetric feature fusion module is used to combine the output query point p and the target point p. i The position encoding feature is obtained by the time field predictor, which maps the symmetric feature into a factorized time field value.

[0008] Step 2, training process: for the query point p, calculate the corresponding true speed value, train the deep neural network model, and make the predicted speed calculated from the predicted factorized time field value converge to the true speed within the error range;

[0009] Step 3, reasoning process: Based on the trained deep neural network model, for each query point, predict the factorized time field value, calculate the time required for propagation from the query point to the target point, combine the two-way search method, calculate the distance between the query point and the target point, and take the minimum value as the distance value of the query point, finally forming a complete multi-target distance field.

[0010] Further, step 1, time field modeling: build a deep neural network model, which inputs the query point p and the target point p i The geometric coding outputs the factorized time field value τ(p,p i ), where the deep neural network model uses a multi-branch neural network structure, including:

[0011] The input encoder consists of a fully connected layer and a sub-network with a residual structure, which combines the query point p with the target point p i The spatial coordinates of are embedded into high-dimensional feature representation, and the query point p and the target point p are output. i The position encoding features f(p) and f(p i ); In the input encoder, the spatial coordinates pass through two fully connected layers, four sub-networks with residual structures, and one fully connected layer, and the position encoding features of the output points are output. The ELU activation function is used in the first two fully connected layers and the four sub-networks with residual structures;

[0012] Symmetric feature fusion module, which uses nonlinear symmetric fusion structure to combine f(p) and f(p i ), and obtain the symmetric feature Φ(p,p i ) as the input of the time field predictor, where the function of the nonlinear symmetric fusion structure is as follows:

[0013] Φ(p,p i )=Concat(min(f(p),f(pi )),max(f(p),f(p i )))

[0014] The time field predictor adopts a multi-layer fully connected network. It first extracts fusion features by a fully connected layer (FC) and ELU activation function (ELU). Then, it models the deep nonlinear relationship between input pairs through six groups of sub-modules with residual structures (ResNet) and ELU activation function. Then, it passes through a fully connected layer (FC) and ELU activation function, and a fully connected layer and Sigmoid activation function, and finally outputs the factorized time field value τ(p,pi)∈(0,1].

[0015] Further, step 2, training process: for the query point p, calculate the corresponding true speed value S * (p), the predicted speed S(p) is calculated using the factorized time field value τ(p,pi), and the deep neural network model is trained to make the predicted speed S(p) converge to the true speed S within the error range. * (p), the specific method is:

[0016] The true velocity value of the definition point is the clip function transformation of its closest distance to the obstacle, expressed as:

[0017]

[0018] in is the obstacle point set, Calculate the shortest distance between the current point and the obstacle, d min ,d max are the minimum and maximum distance thresholds, s const is a user-defined velocity constant, and the clip function limits the distance function to the interval [d min ,d max ]Inside;

[0019] Using the Eikonal equation expansion term, the predicted speed S(p) is calculated from the predicted τ(p,pi), which is different from the actual speed S * (p) is compared and the loss function is constructed as:

[0020]

[0021] In the process of training the deep neural network model, by minimizing the loss function, the predicted speed S(p) converges to the actual speed S within the error range. * (p).

[0022] Furthermore, in the process of training the deep neural network model, an optimization strategy based on gradient descent is adopted, a gradually decaying learning rate scheduling strategy is adopted, and AdamW is selected as the optimizer.

[0023] Further, step 3, reasoning process: Based on the trained deep neural network model, for any query point p, predict the factorized time field value τ(p,pi), and calculate the distance from the query point p to the target point p i The time required for propagation T(p,p i ), combined with the bidirectional search method, calculate the query point p and the target point p i The distance d(p,p i ), take the minimum value as the distance value of the query point, and finally form a complete multi-target distance field. The specific method is:

[0024] Using the trained deep neural network model, all target points p i ∈S extracts the position coding feature, caches it into the embedding vector list, extracts the position coding feature f(p) for any query point p, and performs symmetrical feature fusion with the position coding features of all target points to obtain the symmetrical feature Φ(p,p i ), the symmetric feature Φ(p,p i ) is mapped to the factorized time field value τ(p,pi), and the distance from the query point p to all target points p is calculated. i The time required for propagation T(p,p i );

[0025] For each target point p i , using a bidirectional search method to calculate the query point p and the target point p i the distance between them;

[0026]

[0027] Where α∈R is the step size hyperparameter, p j and Starting from p and starting from p i Starting from the point of the j-th step of the search, when p j+1 and When the distance between them is less than the preset accuracy, the search is considered complete:

[0028]

[0029] Where ε>0 is the preset accuracy hyperparameter;

[0030] Calculate the query point p to all target points p i After the distance, filter out the shortest distance:

[0031]

[0032] The shortest distance is used as the final multi-target distance field. On the plane area with the contour boundary as the target point set, the distance field is used as a guide to calculate the contour lines and gradient directions to form a quadrilateral mesh for finite element simulation.

[0033] Further, calculate the query point p to all target points p i When the distance is greater than , vectorized forward inference is performed on the GPU through tensor broadcast, so that all d(p,p i ).

[0034] Furthermore, when the number of target points n is greater than a threshold, a KD-tree is used to establish a spatial index for the target point set S. For each query point p, the query(p,k) operation is used to return the k closest target points in Euclidean space; the reasoning operation is only performed on these k candidate points to obtain the approximate optimal time distance.

[0035] A multi-target distance field calculation system based on physical information neural time field for four-sided gridding is characterized by implementing the multi-target distance field calculation method based on physical information neural time field for four-sided gridding to realize the multi-target distance field calculation based on physical information neural time field for four-sided gridding, and is divided into three modules, which respectively execute steps 1 to 3.

[0036] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for calculating a multi-target distance field based on a physical information neural time field for four-sided meshing is implemented to achieve multi-target distance field calculation based on a physical information neural time field for four-sided meshing.

[0037] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the method for calculating a multi-target distance field based on a physical information neural time field for four-sided meshing is implemented to realize a multi-target distance field calculation based on a physical information neural time field for four-sided meshing.

[0038] Compared with the existing technology, the significant advantage of the present invention is that by learning a time field function in a continuous space and combining it with the velocity field control mechanism, the propagation speed of certain areas (such as near barrier holes or near the target) can be directly controlled during the training phase, thereby adjusting the distance gradient and density. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flowchart of algorithm reasoning according to an embodiment of the present invention.

[0040] Figure 2 Flowchart of algorithm training according to an embodiment of the present invention.

[0041] Figure 3 Schematic diagram of the network structure of an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0043] This paper presents a multi-target distance field calculation method based on a physical information neural time field for quadrilateral meshing. Based on a neural network-trained time field model, it efficiently estimates the shortest arrival time distance from any point to a set of multiple target points in a three-dimensional grid environment. The main design points are as follows:

[0044] 1) Learn the time field function in continuous space by training a neural network that follows the Eikonal equation constraints. Given an arbitrary query point p and a target set S = p1, p2, p3, ... p n , the method of the present invention can efficiently estimate:

[0045]

[0046] where d(p,p i ) is generated by the neural network from p to p i The shortest distance estimate satisfies the speed constraint (such as the speed in the obstacle area is zero).

[0047] 2) Solve the nonlinear first-order PDE (Eikonal equation), which can directly model the transition from the query point p to the target point p i The shortest arrival time field is obtained by using a bidirectional search strategy that starts from the query point and the target at the same time and moves along the time field gradient to obtain the shortest distance d(p,p i ).

[0048] 3) Provide a batch computing and acceleration structure for quickly selecting the nearest target in a practical grid environment.

[0049] like Figure 1 As shown in the figure, the multi-target distance field calculation method based on physical information neural time field for four-sided meshing is as follows:

[0050] Step 1, time field modeling:

[0051] Build a deep neural network model whose input is the query point p and the target point p i The geometric encoding is mapped to the factorized time field value τ(p,pi ), τ(p,p i ) is the ratio of arrival time to Euclidean distance, specifically:

[0052]

[0053] Formula (2) is the Eikonal equation, where T(p,p i ) represents the distance from the starting point p to the target point p i The time required for propagation.

[0054] The deep neural network model uses a multi-branch neural network structure and consists of three modules:

[0055] 1. Input Encoders

[0056] The input encoder is used to compare the query point p with the target point p i The spatial coordinates of are embedded into high-dimensional feature representation, and the query point p and the target point p are output. i The position encoding feature vector f(p) and f(p i ).

[0057] A fully connected network of Multilayer Perceptron (MLP) and Residual Networks (ResNet) can be used, which has strong nonlinear expression capabilities. Specifically:

[0058] The input encoder consists of two layers of fully connected layers (FC) and ELU activation function, which are repeated twice to preliminarily extract nonlinear features. It is then connected to a four-layer sub-network with a residual structure (ResNet+ELU activation) to enhance the expressiveness of the model and alleviate the gradient vanishing problem in deep training. Finally, the position encoding feature f(q) of the output point is output through a fully connected layer.

[0059] 2. Symmetrical feature fusion module

[0060] In order to satisfy T(p,p i )=T(p i ,p) symmetry requirements, a nonlinear symmetric fusion structure is used to combine f(p) and f(p i ), and obtain the symmetric feature Φ(p,p i ) as the input to the time field predictor.

[0061] The operation function is as follows:

[0062] Φ(p,p i )=Concat(min(f(p),f(p i )),max(f(p),f(pi ))) (3)

[0063] 3. Time field generator

[0064] In the temporal field predictor, the symmetric feature Φ(p,p i )After passing through a multi-layer fully connected network, the output factorized time field value τ(p,pi)∈(0,1] is obtained.

[0065] First, a fully connected layer FC and ELU activation function are used to extract fusion features. Next, six sub-modules with residual structures (ResNet+ELU activation function) are used to further model the deep nonlinear relationship between input pairs. Finally, two fully connected layers are used to output factorized temporal field values, where the first layer uses the ELU activation function and the second layer uses the Sigmoid activation function.

[0066] In summary, the ELU activation function is used in the time field predictor to enhance the nonlinear expression ability of the network and alleviate the gradient vanishing problem. In addition, in order to ensure that the predicted time factor τ(p,p i ) falls within the reasonable physical range of (0,1]. A sigmoid activation function is introduced to constrain the output value to the interval (0,1). This design ensures the differentiability and convergence of the time field function and facilitates subsequent model calculations (such as velocity inversion).

[0067] Step 2, training process:

[0068] Randomly sample the configuration point pair (p,p i ), used to train the network. Calculate the true speed value S for each point * (p) and S * (p i ), defined as the clip function transformation of the shortest distance to the obstacle, ensuring that the speed in the obstacle area is close to 0.

[0069] The Clip function is as follows:

[0070]

[0071] in is the obstacle point set, Calculate the shortest distance between the current point and the obstacle. min ,d max are the minimum and maximum distance thresholds respectively. s const is a user-defined velocity constant. The clip function constrains the distance function to the interval [d min ,d max ]Inside.

[0072] Using the Eikonal equation extension, the predicted speed S(p i );

[0073] The Eikonal equation expansion is:

[0074]

[0075] in is the factorized time field value τ(p,p i ) in p i The partial derivative at can be obtained through back propagation of deep neural networks.

[0076] Let p = p i , p i Substituting =p into formula (4) yields the equation for solving S(p).

[0077]

[0078] Compare the predicted speed with the actual speed and construct the loss function as follows:

[0079]

[0080] Predicted speed S(p) and actual speed S * (p) are obtained by formulas (4) and (5) respectively. In the process of deep neural network training, the parameters in the network are continuously updated by minimizing the loss function defined by (6), so that the predicted speed S(p) output by the network converges to the actual speed S within the error range. * (p).

[0081] Furthermore, a gradient descent-based optimization strategy is employed during training, with all gradients automatically computed via automatic differentiation to ensure efficient and accurate gradient propagation. AdamW is used as the optimizer to enhance convergence stability, and a gradually decaying learning rate scheduling strategy is employed to further optimize the convergence speed and generalization performance of the training process.

[0082] Step 3, reasoning process:

[0083] Based on the trained deep neural network model, all target points p i ∈S performs a batch encoding (i.e. f(p i )), cached as an embedding vector list, for any query point p, encoded as f(p), symmetrical feature fusion is performed with all target point position encoding features, and all τ(p,p i ), and calculate all T(p,p i )=||pp i|| / τ(p,p i ).

[0084] For each target point p i , calculate the query point p and the target point p i The distance d(p,p i );

[0085] During the calculation process, the following two-way search method is used:

[0086]

[0087] Where α∈R is the step size hyperparameter, p j and Starting from p and starting from p i Starting from the point of the j-th step of the search, when p j+1 and When the distance between them is less than the preset accuracy, the search is considered complete:

[0088]

[0089] Where ε>0 is the preset accuracy hyperparameter.

[0090] Since the velocity model controls the magnitude of the gradient, the gradient will become larger when the velocity is low (especially near obstacles). To mitigate such unsafe operations, the gradient is multiplied by S(p), so that as well as Since the velocity model takes a smaller value when approaching an obstacle, S 2 The (p) term dynamically reduces the gradient step size. Furthermore, the symmetry of the proposed model enables us to perform gradient descent in both directions, from the starting point to the target point, and from the target point to the starting point. Therefore, the final path solution updates the starting and target configurations in both directions via iterative gradient descent.

[0091] final,

[0092] Calculate the distance from point p to all points p in the set i After calculating the distance, you can filter out the shortest distance:

[0093]

[0094] The distance field on the plane area is calculated based on the contour boundary as the target point set. The distance field is used as a guide to calculate the contour lines and gradient directions to form a quadrilateral mesh, which can be used for finite element simulation, etc.

[0095] Furthermore, vectorized forward inference is performed on the GPU through tensor broadcasting, so that all d(p,p i), which relies on the GPU batch processing capabilities of deep learning frameworks such as PyTorch or TensorFlow.

[0096] Furthermore, in order to reduce the amount of calculation, when the number of target points n is large, KD-tree is first used to establish a spatial index for the target point set S. The specific steps are: Build it as a KD-tree (using libraries such as sklearn, flann, or faiss); for each query point p, use the query(p,k) operation to return the k closest target points in Euclidean space; perform inference operations only on these k candidate points to obtain an approximate optimal time distance.

[0097] In summary, by learning a time field function in a continuous space and combining it with a velocity field control mechanism, the present invention can directly control the propagation speed in certain areas (such as near obstruction holes or near the target) during the training phase, thereby adjusting the distance gradient and density.

[0098] The present invention also proposes a multi-target distance field calculation system based on physical information neural time field for four-sided gridding, which is characterized by implementing the multi-target distance field calculation method based on physical information neural time field for four-sided gridding to realize the multi-target distance field calculation based on physical information neural time field for four-sided gridding, and is divided into three modules, which respectively execute steps 1 to 3.

[0099] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for calculating a multi-target distance field based on a physical information neural time field for four-sided meshing is implemented to achieve multi-target distance field calculation based on a physical information neural time field for four-sided meshing.

[0100] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the method for calculating a multi-target distance field based on a physical information neural time field for four-sided meshing is implemented to realize a multi-target distance field calculation based on a physical information neural time field for four-sided meshing.

[0101] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0102] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A multi-target distance field calculation method based on physical information neural time field for four-sided meshing, characterized by: The specific steps are as follows: Step 1, temporal field modeling: Construct a deep neural network model, including an input encoder, a symmetric feature fusion module, and a temporal field predictor. The input encoder is used to embed the spatial coordinates of the query point and the target point into high-dimensional feature representations and output the position encoding features of the query point and the target point. The symmetric feature fusion module is used to combine the output query point p and the target point p. i Position encoding features are used to obtain symmetric features; The temporal field predictor maps symmetric features into factorized temporal field values; Step 2, training process: for the query point p, calculate the corresponding true speed value, train the deep neural network model, and make the predicted speed calculated from the predicted factorized time field value converge to the true speed as much as possible within the error range; Step 3, inference process: Based on the trained deep neural network model, for each query point, predict the factorized time field value, calculate the time required for propagation from the query point to all target points, and combine the two-way search method to calculate the distance between the query point and all target points. Take the minimum value as the distance value of the query point, and finally form a complete multi-target distance field.

2. The method for calculating multi-target distance fields based on physical information neural time fields for quadrilateral meshing according to claim 1 is characterized in that: Step 1, time field modeling: Build a deep neural network model with input query point p and target point p i The geometric coding outputs the factorized time field value τ(p,p i ), where the deep neural network model uses a multi-branch neural network structure, including: The input encoder consists of a fully connected layer and a sub-network with a residual structure. The spatial coordinates pass through two fully connected layers, four sub-networks with a residual structure, and one fully connected layer, outputting the position encoding features of the point. The ELU activation function is used in the first two fully connected layers and the four sub-networks with a residual structure. The symmetric feature fusion module adopts a nonlinear symmetric fusion structure, and the function is as follows: Φ(p,p i )=Concat(min(f(p),f(p i )),max(f(p),f(p i ))) The time field predictor adopts a multi-layer fully connected network. It first extracts fusion features by a fully connected layer and the ELU activation function, then models the deep nonlinear relationship between input pairs through six groups of sub-modules with residual structures and the ELU activation function, and then passes through a fully connected layer and the ELU activation function, and then a fully connected layer and the Sigmoid activation function, and finally outputs the factorized time field value τ(p,pi)∈(0,1].

3. The method for calculating multi-target distance fields based on physical information neural time fields for quadrilateral meshing according to claim 1 is characterized in that: Step 2, training process: For the query point p, calculate the corresponding true speed value S * (p), the predicted speed S(p) is calculated using the factorized time field value τ(p,pi), and the deep neural network model is trained to make the predicted speed S(p) converge to the true speed S within the error range. * (p), the specific method is: The true velocity value of the definition point is the clip function transformation of its closest distance to the obstacle, expressed as: in is the obstacle point set, Calculate the shortest distance between the current point and the obstacle, d min ,d max are the minimum and maximum distance thresholds, s const is a user-defined velocity constant, and the clip function limits the distance function to the interval [d min ,d max ]Inside; Using the Eikonal equation expansion term, the predicted speed S(p) is calculated from the predicted τ(p,pi), which is different from the actual speed S * (p) is compared and the loss function is constructed as: In the process of training the deep neural network model, by minimizing the loss function, the predicted speed S(p) converges to the actual speed S within the error range. * (p).

4. The method for calculating multi-target distance fields based on physical information neural time fields for quadrilateral meshing according to claim 1 is characterized in that: In the process of training the deep neural network model, an optimization strategy based on gradient descent and a gradually decaying learning rate scheduling strategy are adopted, and the optimizer is AdamW.

5. The method for calculating multi-target distance fields based on physical information neural time fields for quadrilateral meshing according to claim 1 is characterized in that: Step 3, reasoning process: Based on the trained deep neural network model, for each query point p, predict the factorized time field value τ(p,pi), and calculate the distance from the query point p to the target point p i The time required for propagation T(p,p i ), combined with the bidirectional search method, calculate the query point p and the target point p i The distance d(p,p i ), take the minimum value as the distance value of the query point, and finally form a complete multi-target distance field. The specific method is: Using the trained deep neural network model, all target points p i ∈S extracts the position coding feature, caches it into the embedding vector list, extracts the position coding feature f(p) for any query point p, and performs symmetrical feature fusion with the position coding features of all target points to obtain the symmetrical feature Φ(p,p i ), the symmetric feature Φ(p,p i ) is mapped to the factorized time field value τ(p,pi), and the distance from the query point p to all target points p is calculated. i The time required for propagation T(p,p i ); For each target point p i , using a bidirectional search method to calculate the query point p and the target point p i the distance between them; Where α∈R is the step size hyperparameter, p j and Starting from p and starting from p i Starting from the point of the j-th step of the search, when p j+1 and When the distance between them is less than the preset accuracy, the search is considered complete: Where ε>0 is the preset accuracy hyperparameter; Calculate the query point p to all target points p i After the distance, filter out the shortest distance: The shortest distance is used as the final multi-target distance field. On the plane area with the contour boundary as the target point set, the distance field is used as a guide to calculate the contour lines and gradient directions to form a quadrilateral mesh for finite element simulation.

6. The method for calculating multi-target distance fields based on physical information neural time fields for quadrilateral meshing according to claim 5 is characterized in that: Calculate the distance from query point p to all target points p i When the distance is greater than , vectorized forward inference is performed on the GPU through tensor broadcast, so that all d(p,p i ).

7. The method for calculating multi-target distance fields based on physical information neural time fields for quadrilateral meshing according to claim 6 is characterized in that: When the number of target points n is greater than a threshold, a KD-tree is used to establish a spatial index for the target point set S. For each query point p, the query(p,k) operation is used to return the k closest target points in Euclidean space. The reasoning operation is performed only on these k candidate points to obtain the approximate optimal time distance.

8. A multi-target distance field calculation system based on physical information neural time field for four-sided gridding, characterized by: Implement the multi-target distance field calculation method based on physical information neural time field for four-sided gridding as described in any one of claims 1-7 to realize the multi-target distance field calculation based on physical information neural time field for four-sided gridding, and divide it into three modules to execute steps 1 to 3 respectively.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the method for calculating a multi-target distance field based on a physical information neural time field for four-sided meshing according to any one of claims 1 to 7 is implemented to realize a multi-target distance field calculation based on a physical information neural time field for four-sided meshing.

10. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the method for calculating a multi-target distance field based on a physical information neural time field for four-sided meshing according to any one of claims 1 to 7 is implemented to realize a multi-target distance field calculation based on a physical information neural time field for four-sided meshing.

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