Path planning method, equipment, medium and product

Abstract

The invention discloses a path planning method and device, a medium and a product, and belongs to the technical field of data processing. According to the path planning method, an ordinary differential equation set configured with training data is converted into a training sequence set capable of being trained by an initial calculation model, and the training sequence set can express ordinary differential equation characteristics from multiple dimensions such as a structural level, topological characteristics, dynamic behaviors and functional attributes; the initial calculation model is trained through the training sequence set to obtain the first calculation model, so that the trained first calculation model can meet the physical law or system characteristics of an ordinary differential equation, guarantee is provided for the precision of data output by the first calculation model, the calculation complexity and memory overhead are remarkably reduced, and the calculation efficiency is improved. And millisecond-level real-time solution is realized.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to path planning methods, devices, media and products. Background Art

[0002] With the continuous development of science and technology, path planning technology has been widely used in the fields of controlling robotic arms, autonomous driving, robot navigation, logistics and distribution. The core of path planning lies in how to solve ordinary differential equations (ODE) efficiently and accurately to obtain the optimal path from the starting point to the end point. Traditional path planning methods mainly rely on numerical calculation methods to solve ordinary differential equations, such as the Euler method and the Runge-Kutta method, but these methods often face the trade-off between computational efficiency and accuracy when dealing with complex systems. In the existing technology, solving ordinary differential equations is the key link in path planning.

[0003] However, existing technologies still have the following problems in dealing with ordinary differential equations (ODEs) solving and path planning: First, traditional ODE solving methods are difficult to optimize in terms of efficiency and accuracy, especially when dealing with high-dimensional, rigid and parameterized ODEs, which have high computational complexity, large memory overhead and poor numerical stability; Second, existing methods lack an in-depth understanding and utilization of the characteristics of ordinary differential equations, especially the identification of conserved quantities and the handling of constraints; Third, existing models lack targeted training strategies when dealing with different types of ordinary differential equations, making it difficult to simultaneously take into account the solution requirements of rigid and non-rigid equations. Summary of the Invention

[0004] In response to the problems that existing ODE solving methods are difficult to coordinately optimize in terms of efficiency and accuracy and have high computational complexity, we now provide a path planning method, equipment, medium and product that are designed to efficiently process various ordinary differential equations, improve path planning accuracy and efficiency, and reduce computational complexity.

[0005] To achieve the above objectives, some embodiments of the present application provide the following aspects:

[0006] In a first aspect, some embodiments of the present application provide a path planning method, including:

[0007] Determining a training sequence set based on a set of ordinary differential equations configured with training data;

[0008] Training the initial computing model based on the training sequence set to determine a first computing model;

[0009] The target data is input into the first calculation model to determine the target path.

[0010] Optionally, determining a training sequence set based on a set of ordinary differential equations configured with training data includes:

[0011] Parsing a set of ordinary differential equations configured with training data to determine a set of abstract syntax trees;

[0012] The abstract syntax tree set is processed by a symbolic differential encoder to determine the training sequence set.

[0013] Optionally, parsing the set of ordinary differential equations configured with training data to determine the set of abstract syntax trees includes:

[0014] Parsing the ordinary differential equations in the ordinary differential equation set configured with training data one by one by a syntax parser to obtain the abstract syntax tree set including a plurality of abstract syntax trees;

[0015] Each of the ordinary differential equations corresponds to an abstract syntax tree.

[0016] Optionally, the processing the abstract syntax tree set by a symbolic differential encoder to determine the training sequence set includes:

[0017] When parsing a set of ordinary differential equations configured with training data, the symbolic differential encoder identifies conserved quantities of each of the ordinary differential equations;

[0018] Determining the constraint terms corresponding to the ordinary differential equations according to the conservation quantities of the ordinary differential equations by using the Lagrange multiplier method;

[0019] Adding the conserved quantity as a symbolic variable to the abstract syntax tree corresponding to the ordinary differential equation to form a training sequence corresponding to the ordinary differential equation;

[0020] The training sequence set consists of a plurality of training sequences.

[0021] Optionally, the training the initial computing model based on the training sequence set to determine the first computing model includes:

[0022] Based on the type of ordinary differential equation corresponding to each training sequence in the training sequence set, selecting a corresponding training strategy to train the current computing model to be trained, and determining a second computing model;

[0023] Perform mixed precision training on the second computing model to obtain the first computing model.

[0024] Optionally, the selecting a corresponding training strategy to train the current computing model to be trained based on the ordinary differential equation type corresponding to each training sequence in the training sequence set to determine the second computing model includes:

[0025] Training an initial computing model based on the training sequence in the training sequence set:

[0026] When the type of the ordinary differential equation corresponding to the training sequence is a non-rigid equation, the first strategy is used to train the current computational model to be trained, a third computational model is determined, and the third computational model is used as the current computational model to be trained;

[0027] When the type of the ordinary differential equation corresponding to the training sequence is a stiff equation, the second strategy is used to train the current computational model to be trained, a third computational model is determined, and the third computational model is used as the current computational model to be trained;

[0028] The second calculation model is obtained until the training of all the training sequences in the training sequence set is completed.

[0029] Optionally, performing mixed precision training on the second computing model to obtain the first computing model includes:

[0030] The weights of the second computing model are partitioned by sensitivity, the loss function is scaled, and the second computing model is trained using random sampling to obtain the first computing model.

[0031] In a second aspect, some embodiments of the present application further provide an electronic device comprising: one or more processors; and a memory storing computer program instructions, wherein the computer program instructions, when executed, cause the processor to perform the steps of the method described above.

[0032] In a third aspect, some embodiments of the present application further provide a computer-readable medium having computer program instructions stored thereon, wherein the computer program instructions can be executed by a processor to implement the method described above.

[0033] In a fourth aspect, some embodiments of the present application further provide a computer program product, comprising a computer program / instruction, which implements the steps of the above-described method when executed by a processor.

[0034] Compared with the related art, in the solution provided in the embodiment of the present application, the path planning method converts a set of ordinary differential equations configured with training data into a training sequence set that can be used for training the initial computing model. The training sequence set can express the characteristics of ordinary differential equations from multiple dimensions such as structural level, topological characteristics, dynamic behavior, and functional properties; the initial computing model is trained using the training sequence set to obtain a first computing model, so that the trained first computing model can meet the physical laws or system characteristics of the ordinary differential equations, provide a guarantee for the accuracy of the output data of the first computing model, significantly reduce the computational complexity and memory overhead, and achieve millisecond-level real-time solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] One or more embodiments are exemplarily illustrated by pictures in the corresponding drawings. These exemplifications do not constitute limitations on the embodiments. Elements with the same reference numerals in the drawings are represented as similar elements. Unless otherwise stated, the figures in the drawings do not constitute proportional limitations.

[0036] Figure 1 A method flow chart of an embodiment of the path planning method described in this application;

[0037] Figure 2 This is a flow chart of an exemplary method for obtaining a training sequence set in this application;

[0038] Figure 3 This is a flow chart of another exemplary method for obtaining a training sequence set in the present application;

[0039] Figure 4 A flow chart of a method for obtaining a first calculation model according to an embodiment of the present application;

[0040] Figure 5 This is an exemplary structural diagram of the electronic device of this application. DETAILED DESCRIPTION

[0041] The advantages of the present application are further described below with reference to the accompanying drawings and specific embodiments.

[0042] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, identical numerals in different figures represent identical or similar elements, unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all possible embodiments consistent with the present disclosure. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present disclosure, as detailed in the appended claims.

[0043] The terms used in this disclosure are for the purpose of describing specific embodiments only and are not intended to limit the disclosure. As used in this disclosure and the appended claims, the singular forms "a," "an," "the," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0044] It should be understood that although the terms first, second, third, etc. may be used in this disclosure to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from each other. For example, without departing from the scope of this disclosure, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining."

[0045] In the description of this application, it should be understood that the numerical labels before the steps do not indicate the order in which the steps are executed. They are only used to facilitate the description of this application and to distinguish each step. Therefore, they cannot be understood as limitations on this application.

[0046] The path planning method of the embodiment of the present application can be applied to the fields of robot control (such as: robotic arm control), autonomous driving, robot navigation, logistics distribution, etc. The path planning method of the present application converts a set of ordinary differential equations configured with training data into a set of training sequences that can be used for training the initial computing model. The training sequence set can express the characteristics of ordinary differential equations from multiple dimensions such as structural level, topological characteristics, dynamic behavior, and functional attributes; the initial computing model is trained using the training sequence set to obtain a first computing model, so that the trained first computing model can meet the physical laws or system characteristics of the ordinary differential equations, provide a guarantee for the accuracy of the output data of the first computing model, significantly reduce the computational complexity and memory overhead, and achieve millisecond-level real-time solution.

[0047] Example 1

[0048] This application proposes a path planning method to solve the defects of ODE solution methods in terms of efficiency and accuracy, which are difficult to optimize in a coordinated manner and have high computational complexity. Figure 1 , which is a flow chart of a path planning method according to a preferred embodiment of the present application. As can be seen from the figure, the path planning method provided in this embodiment mainly includes the following steps:

[0049] S1. Determine a training sequence set based on a set of ordinary differential equations configured with training data;

[0050] S2. Based on the training sequence set, the initial computing model is trained to determine the first computing model;

[0051] S3. Input the target data into the first calculation model to determine the target path.

[0052] The target data can be information required for path planning, such as the starting point, end point, and obstacle locations. The first computational model uses the input target data, combined with the properties of ordinary differential equations and conservation constraints learned during training, to generate a target path that satisfies physical constraints. The target path is a series of consecutive points or states representing the optimal or suboptimal path from the starting point to the end point.

[0053] This path planning method, based on the properties of ordinary differential equations and conservation constraints, can generate paths that conform to physical laws, improving the accuracy and reliability of path planning. This method is particularly suitable for path planning scenarios that require consideration of physical constraints, such as robot motion planning and autonomous vehicle path planning.

[0054] In this embodiment, the path planning method converts a set of ordinary differential equations configured with training data into a training sequence set that can be used for training the initial computing model. The training sequence set can express the characteristics of the ordinary differential equations from multiple dimensions such as structural level, topological characteristics, dynamic behavior, and functional attributes; the initial computing model is trained using the training sequence set to obtain a first computing model, so that the trained first computing model can meet the physical laws or system characteristics of the ordinary differential equations, provide a guarantee for the accuracy of the output data of the first computing model, significantly reduce the computational complexity and memory overhead, and achieve millisecond-level real-time solution.

[0055] In this embodiment, the path planning method first determines a training sequence set based on a set of ordinary differential equations configured with training data. The set of ordinary differential equations contains multiple ordinary differential equations, and these equations are configured with corresponding training data. The training data can be the position information of various physical systems, such as the starting position coordinates and the end position coordinates. By inputting the position information into the ordinary differential equation, the ordinary differential equation configured with training data can be obtained. The traditional method is to input the position information into the ordinary differential equation, and obtain the moving path by the ordinary differential equation operation. The present application converts the ordinary differential equation configured with training data into a training sequence for the initial calculation model training and learning, thereby obtaining a first calculation model that can reflect the characteristics of the ordinary differential equation. The target path can be obtained by inputting the position information into the first calculation model, which reduces the computational complexity and memory overhead and achieves millisecond-level real-time solution.

[0056] Further, see Figure 2 Step S1 shown may include the following steps:

[0057] S11. Parse the set of ordinary differential equations configured with training data to determine a set of abstract syntax trees;

[0058] Specifically, step S11 may include: parsing the ordinary differential equations in the ordinary differential equation set configured with training data one by one through a syntax parser to obtain the abstract syntax tree set including multiple abstract syntax trees; wherein each of the ordinary differential equations corresponds to one abstract syntax tree.

[0059] In this embodiment, the parser converts the mathematical expression of an ordinary differential equation into a tree structure, where the nodes of the tree represent operators or variables, and the edges of the tree represent operational relationships. For example, for the equation dx / dt=ax+b, the root node of the abstract syntax tree is "=", the left subtree is "dx / dt", and the right subtree is "+". The left subtree of "+" is "a×x", and the right subtree is "b".

[0060] S12. Process the abstract syntax tree set through a symbolic differential encoder to determine the training sequence set.

[0061] Specifically, see Figure 3 The illustrated S12 may include:

[0062] S121. When parsing a set of ordinary differential equations configured with training data, the symbolic differential encoder identifies conserved quantities (such as total energy, momentum, etc., which are potential conserved quantities) of each of the ordinary differential equations;

[0063] In this embodiment, the symbolic differential encoder automatically identifies conserved quantities in a system by analyzing the structure and properties of ordinary differential equations. For example, for a Hamiltonian system, the symbolic differential encoder can identify that the system's total energy is conserved; for a Newtonian system, it can identify conservation of momentum or conservation of angular momentum.

[0064] S122. Determine the constraint terms corresponding to the ordinary differential equations according to the conservation quantities of the ordinary differential equations by the Lagrange multiplier method;

[0065] The Lagrange multiplier method is a mathematical technique for constrained optimization problems. It incorporates constraints into the objective function by introducing Lagrange multipliers. In this embodiment, conserved quantities are used as constraints, and the constraint terms are constructed using the Lagrange multiplier method to ensure that conserved quantities are maintained during the path planning process.

[0066] S123. Adding the conserved quantity as a symbolic variable to the abstract syntax tree corresponding to the ordinary differential equation to form a training sequence corresponding to the ordinary differential equation;

[0067] The training sequence set consists of multiple training sequences.

[0068] In this embodiment, by adding conserved quantities as symbolic variables to the abstract syntax tree, the computational model can learn the conservation properties of the system, thereby maintaining these physical constraints in subsequent path planning.

[0069] Further, see Figure 4 Step S2 shown may include the following steps:

[0070] S21. Based on the type of ordinary differential equation corresponding to each training sequence in the training sequence set, select a corresponding training strategy to train the current computing model to be trained, and determine a second computing model;

[0071] In this embodiment, the computational model currently being trained can be an initial computational model or an intermediate model during the training process. During the first training, the computational model currently being trained is the initial computational model; during subsequent training, the computational model currently being trained is the intermediate model. The initial computational model can be a pre-designed neural network structure, such as a recurrent neural network, a long short-term memory network, or a graph neural network.

[0072] Specifically, step S21 may include:

[0073] Training an initial computing model based on the training sequence in the training sequence set:

[0074] When the type of the ordinary differential equation corresponding to the training sequence is a non-rigid equation, the first strategy is used to train the current computational model to be trained, a third computational model is determined, and the third computational model is used as the current computational model to be trained;

[0075] In this embodiment, the third calculation model is the intermediate model.

[0076] When the type of the ordinary differential equation corresponding to the training sequence is a stiff equation, the second strategy is used to train the current computational model to be trained, a third computational model is determined, and the third computational model is used as the current computational model to be trained;

[0077] The second calculation model is obtained until the training of all the training sequences in the training sequence set is completed.

[0078] Non-stiff equations and stiff equations have different characteristics in numerical solution. Non-stiff equations can usually be solved using explicit methods, while stiff equations require implicit methods to ensure numerical stability. Therefore, for non-stiff equations, the first strategy can adopt a larger learning rate and an explicit optimization algorithm, such as the Adam (Adaptive Moment Estimation) optimizer; the training goal is to build basic dynamic pattern cognition to prevent the model from falling into complex numerical instability too early; taking the Van der Pol oscillator (a classic nonlinear dynamic system) as an example, its nonlinear damping characteristics can train the model to capture basic dynamic behaviors such as periodic solutions and limit cycles; the first strategy can adopt time domain segmentation: decomposing long-term integrals into short segments, forcing the model to learn local dynamics rather than relying on historical memory; using weighted mean square error, giving higher weights to the oscillation peak area, enhancing phase synchronization capabilities.

[0079] For stiff equations, the second strategy can use a smaller learning rate and an implicit optimization algorithm, such as the L-BFGS optimizer, to ensure the stability of the training process. The gradual introduction of stiff terms and high-dimensional couplings gradually expands the model's modeling capabilities for complex systems (multi-scale, strong nonlinearity) for the training of stiff equations. Specifically, it includes: stiff term injection: gradually increasing the value (from 1 to 1000) in the Van der Pol equation to introduce a stiff behavior of separation of fast and slow variables; high-dimensional coupling expansion: simulating multi-body interactions by adding coupling terms or constructing a chain ODE system; progressive gradient clipping: 1) dynamic threshold: adaptively adjust the clipping amplitude according to the statistics of the gradient distribution (such as quantiles) to avoid gradient explosion caused by stiff terms; 2) hierarchical constraints: impose stricter gradient restrictions on the network parameters corresponding to the stiff terms to protect model stability.

[0080] In this embodiment, during the training of the initial computational model based on the training sequences in the training sequence set, a learned multi-scale dynamics model may be used to improve the robustness of the model after sparsification and quantization, and avoid the loss of key features.

[0081] S22. Perform mixed precision training on the second computing model to obtain the first computing model.

[0082] Furthermore, step S22 may include: performing sensitivity partitioning on the weights of the second computing model, scaling the loss function, and training the second computing model using random sampling to obtain the first computing model.

[0083] Mixed-precision training is a technique that improves training efficiency and model performance. Sensitivity partitioning involves classifying weights into high-sensitivity and low-sensitivity categories based on their impact on the model output. High-sensitivity weights are stored and calculated using high-precision data (such as float32 (single-precision floating point numbers)), while low-sensitivity weights are stored and calculated using low-precision data (such as float16 (half-precision floating point numbers) or int8 (8-bit integers)), thereby reducing memory usage and computational complexity. Loss function scaling is used to prevent vanishing or exploding gradients in low-precision calculations. By multiplying the loss function by an appropriate scaling factor, the gradient value remains within an appropriate range. Random sampling involves randomly selecting a portion of the training data for model updates during training, rather than using all training data. This can speed up training and enhance the model's generalization capabilities. Random sampling uses multi-scale time windows: randomly extracting time segments of different lengths (such as short-term transients and long-term steady states) to force the model to generalize across time scales; non-uniform sampling: increasing the sampling density for rapidly changing stages (such as the transient response of rigid systems) and enhancing local detail modeling.

[0084] Example 2

[0085] Embodiment 2 of the present application relates to a path planning method. The set of ordinary differential equations of this embodiment may include various types of ordinary differential equations, such as linear equations, nonlinear equations, rigid equations, and nonrigid equations. These equations describe the dynamic behavior of different physical systems, such as spring-mass systems, swing systems, circuit systems, etc. Each ordinary differential equation is configured with corresponding training data, which can be obtained through experimental measurements or by numerically solving the equations. Embodiment 2 is roughly the same as Embodiment 1, with the main differences being:

[0086] In step S11, the set of ordinary differential equations configured with training data is parsed to determine a set of abstract syntax trees. This process converts mathematical expressions into a structured representation that can be processed by a computer. An abstract syntax tree is a tree-like data structure used to represent the grammatical structure of a program or expression. In this embodiment, an abstract syntax tree is used to represent the structure of ordinary differential equations, facilitating subsequent symbolic processing and computation.

[0087] The parser first converts the mathematical expression of ordinary differential equations into tokens, and then builds an abstract syntax tree according to the grammar rules. 2 x / dt2+ω2x=0 (simple harmonic oscillator equation), the syntax parser will convert it into an abstract syntax tree, where the root node is "=", and the left subtree represents "d 2 x / dt2+ω2x", the right subtree represents "0". The root node of the left subtree is "+", and its left subtree represents "d 2x / dt2", the right subtree represents "ω2x".

[0088] In step S12, the set of abstract syntax trees is processed using a symbolic differential encoder to determine a set of training sequences. A symbolic differential encoder is a tool that symbolically differentiates mathematical expressions. It can calculate the derivatives of expressions and represent them in symbolic form. In this embodiment, the symbolic differential encoder is used to analyze the structure of ordinary differential equations, identify conserved quantities, and generate training sequences.

[0089] The symbolic differential encoder first traverses the abstract syntax tree, identifying the variables, constants, and operators in the equation. It then applies symbolic differentiation rules to compute the derivatives of the expression and analyze the structural properties of the equation. This analysis allows the symbolic differential encoder to identify conserved quantities in the equation, such as energy, momentum, and angular momentum.

[0090] For example, for a Hamiltonian system, the symbolic differential encoder can identify the total energy H as conserved by analyzing the Hamiltonian and the canonical equations. For a Lagrangian system, the symbolic differential encoder can identify the conserved quantities of the system by analyzing the Lagrangian and the Euler-Lagrange equations.

[0091] In this way, the symbolic differential encoder converts the abstract syntax tree of the ordinary differential equation into a training sequence containing information about conserved quantities. The training sequence not only contains the structural information of the original ordinary differential equation but also includes the conserved quantities as additional symbolic variables. These training sequences constitute the training sequence set for subsequent model training.

[0092] Example 3

[0093] The third embodiment of the present application relates to a path planning method. The third embodiment is substantially the same as the first embodiment, with the main difference being:

[0094] In step S11, the set of ordinary differential equations configured with training data is parsed, and the process of determining the set of abstract syntax trees includes: parsing the ordinary differential equations in the set of ordinary differential equations configured with training data one by one through a syntax parser to obtain an abstract syntax tree set including multiple abstract syntax trees; each ordinary differential equation corresponds to an abstract syntax tree.

[0095] A parser is a tool that converts mathematical expressions or program code into a structured representation. In this embodiment, the parser is used to convert ordinary differential equations into an abstract syntax tree (AST). The parser first decomposes the mathematical expression of the ordinary differential equation into tokens, such as variables, constants, and operators. Then, according to predefined grammatical rules, these tokens are organized into a tree structure, namely an AST.

[0096] The parser processes ordinary differential equations as follows:

[0097] First, the parser reads the mathematical expression of an ordinary differential equation, such as dx / dt=f(x,t).

[0098] Then, the syntax parser breaks down the expression into lexical units, such as "dx / dt", "=", "f", "(", "x", "", "t", ")", etc.

[0099] Next, the parser constructs an abstract syntax tree based on the grammar rules. In this example, the root node of the abstract syntax tree is "=", the left subtree represents "dx / dt", and the right subtree represents "f(x,t)".

[0100] Finally, the parser returns the constructed abstract syntax tree.

[0101] For each ODE, the parser generates a corresponding abstract syntax tree (AST). These ASTs form an AST collection. The structure of the AST reflects the mathematical structure of the ODE, facilitating subsequent symbolic processing and computation.

[0102] For example, for the Lorentz system of ordinary differential equations:

[0103] dx / dt=σ(yx)

[0104] dy / dt=x(ρ-z)-y

[0105] dz / dt=xy-βz

[0106] The parser generates an abstract syntax tree for each equation. The root node of the first equation's abstract syntax tree is "=", its left subtree represents "dx / dt", and its right subtree represents "σ(yx)". The root node of the second equation's abstract syntax tree is "=", its left subtree represents "dy / dt", and its right subtree represents "x(ρ-z)-y". The root node of the third equation's abstract syntax tree is "=", its left subtree represents "dz / dt", and its right subtree represents "xy-βz".

[0107] In step S12, the symbolic differential encoder processes the set of abstract syntax trees to determine a set of training sequences. The symbolic differential encoder analyzes the structure of the abstract syntax tree, identifies the conserved quantities of the ordinary differential equation, and generates a training sequence containing the conserved quantity information.

[0108] Example 4

[0109] The fourth embodiment of the present application relates to a path planning method. The fourth embodiment is substantially the same as the first embodiment, with the main difference being:

[0110] In step S12, the abstract syntax tree set is processed by a symbolic differential encoder to determine a training sequence set, which includes: when parsing a set of ordinary differential equations configured with training data, the symbolic differential encoder identifies the conserved quantities (such as total energy, momentum, etc., which are potential conserved quantities) of each ordinary differential equation; the constraint terms corresponding to the ordinary differential equations are determined based on the conserved quantities of each ordinary differential equation through the Lagrange multiplier method; the conserved quantities are added as symbolic variables to the abstract syntax tree corresponding to the ordinary differential equation to form a training sequence corresponding to the ordinary differential equation; the training sequence set consists of multiple training sequences.

[0111] The symbolic differential encoder is a tool that can perform symbolic differentiation and analysis on mathematical expressions. In this embodiment, the symbolic differential encoder is used to identify conserved quantities of ordinary differential equations and generate a training sequence containing the conserved quantity information.

[0112] The process of the symbolic differential encoder to identify the conserved quantities of ordinary differential equations is as follows:

[0113] First, the symbolic differential coder analyzes the structure of the ordinary differential equation and identifies the variables, constants, and operators in the equation.

[0114] The symbolic differentiation encoder then applies symbolic differentiation rules to compute the derivatives of each term in the equation.

[0115] Next, the symbolic differential encoder analyzes the equations for symmetries and invariances, identifying potential conserved quantities.

[0116] Finally, the symbolic differential encoder verifies whether the identified conserved quantities satisfy the conservation law, i.e., remain unchanged during the system evolution.

[0117] For example, for Hamiltonian systems, the symbolic differential encoder can identify that total energy H is conserved by analyzing the Hamiltonian and canonical equations. For systems with rotational symmetry, the symbolic differential encoder can identify that angular momentum is conserved. For systems with translational symmetry, the symbolic differential encoder can identify that linear momentum is conserved.

[0118] The Lagrange multiplier method is used to determine the constraints corresponding to the ordinary differential equations based on the conserved quantities of each ordinary differential equation. The Lagrange multiplier method is a mathematical method for solving constrained optimization problems. In this embodiment, the Lagrange multiplier method is used to incorporate conserved quantities as constraints into the path planning problem.

[0119] The application process of the Lagrange multiplier method is as follows:

[0120] First, the path planning problem is formulated as an optimization problem, where the goal is to minimize a cost function (such as path length, energy consumption, etc.).

[0121] Then, the conserved quantity is expressed as a constraint, which requires that the conserved quantity remains unchanged during the path planning process.

[0122] Next, the Lagrange multiplier is introduced to construct the Lagrange function L = f(x) + λg(x), where f(x) is the original objective function, g(x) is the constraint condition, and λ is the Lagrange multiplier.

[0123] Finally, the stationary point of the Lagrangian function is solved to obtain the optimal solution that satisfies the constraints.

[0124] In this way, the Lagrange multiplier method transforms the conservation constraints into constraints in the optimization problem, ensuring that the generated paths satisfy the conservation laws of the physical system.

[0125] The conserved quantity is added as a symbolic variable to the abstract syntax tree corresponding to the ordinary differential equation, forming a training sequence corresponding to the ordinary differential equation. This step integrates the conserved quantity information into the abstract syntax tree, allowing the subsequent computational model to learn the conserved quantity constraints.

[0126] Specifically, for each ordinary differential equation (ODE) corresponding abstract syntax tree (AST), the identified conserved quantities are added as new symbolic variable nodes. These conserved quantity nodes, along with the original variable and operator nodes, form an extended AST. This extended AST incorporates not only the structural information of the original ODE but also the conserved quantity information, enabling a more comprehensive representation of the properties of the physical system.

[0127] For example, for a system with energy conservation, the abstract syntax tree corresponding to its ordinary differential equation will add a symbolic variable node representing energy. This node is connected to the original tree structure, representing the relationship between the energy conservation constraint and the system dynamics.

[0128] The training sequence set consists of multiple training sequences, each corresponding to an ordinary differential equation and its conservation information. These training sequences will be used for subsequent model training, enabling the computational model to learn the dynamic characteristics and conservation constraints of the physical system.

[0129] Example 5

[0130] The fifth embodiment of the present application relates to a path planning method. The fifth embodiment is substantially the same as the first embodiment, with the main difference being:

[0131] Step S2 trains the initial calculation model based on the training sequence set. The process of determining the first calculation model includes:

[0132] S21. Based on the ordinary differential equation type corresponding to each training sequence in the training sequence set, select a corresponding training strategy to train the current computing model to be trained, and determine the second computing model; perform mixed precision training on the second computing model to obtain the first computing model.

[0133] S22. The initial computational model is a neural network model capable of learning and predicting the behavior of dynamic systems. In this embodiment, the initial computational model can be various types of neural networks, such as feedforward neural networks, recurrent neural networks, and graph neural networks. The structure and parameters of the initial computational model are designed based on the specific application scenario and data characteristics.

[0134] Based on the type of ordinary differential equation corresponding to each training sequence in the training sequence set, a corresponding training strategy is selected to train the current computational model to be trained, thereby determining a second computational model. Ordinary differential equations can be divided into different types, such as linear equations, nonlinear equations, stiff equations, and nonstiff equations. Different types of ordinary differential equations have different mathematical properties and therefore require different training strategies.

[0135] Specifically, the initial computational model is trained based on the training sequence in the training sequence set: when the type of ordinary differential equation corresponding to the training sequence is a non-rigid equation, the first strategy is adopted to train the computational model to be trained, and the third computational model is determined, and the third computational model is used as the computational model to be trained; when the type of ordinary differential equation corresponding to the training sequence is a rigid equation, the second strategy is adopted to train the computational model to be trained, and the third computational model is determined, and the third computational model is used as the computational model to be trained; until the training of all training sequences in the training sequence set is completed, and the second computational model is obtained.

[0136] Nonstiff equations are those that can remain stable during numerical solution without requiring extremely small step sizes. For nonstiff equations, the first strategy is to use explicit optimization algorithms, such as gradient descent and the Adam optimizer. These algorithms are computationally efficient and suitable for nonstiff problems. Furthermore, a larger learning rate and fewer iterations can be used to speed up training.

[0137] Stiff equations require very small step sizes to maintain stability during numerical solution. For stiff equations, the second strategy employs implicit optimization algorithms, such as the L-BFGS optimizer and the conjugate gradient method. While computationally complex, these algorithms can handle the numerical instabilities of stiff problems. Furthermore, a small learning rate and a high number of iterations are required to ensure training stability.

[0138] In this way, for each training sequence in the training sequence set, an appropriate training strategy is selected based on the type of ordinary differential equation it corresponds to, and the parameters of the computational model are gradually updated. After each training session, the updated model is used as the current model to be trained, and the next training sequence is processed. This continues until all training sequences are trained, resulting in a second computational model.

[0139] The second computational model is trained with mixed precision to obtain the first computational model. Mixed precision training is a technique that improves training efficiency and model performance by combining numerical representations of different precisions, such as float32 (single precision) and float16 (half precision).

[0140] The weights of the second computational model are partitioned by sensitivity, the loss function is scaled, and the second computational model is trained using random sampling to obtain the first computational model. Sensitivity partitioning involves categorizing weights into high-sensitivity and low-sensitivity groups based on their impact on the model output. High-sensitivity weights are stored and calculated using high-precision data (e.g., float32); low-sensitivity weights are stored and calculated using low-precision data (e.g., float16).

[0141] Weight sensitivity can be assessed by calculating the gradient magnitude of the weights and the impact of weight changes on the loss function. Typically, certain layers in a network (such as the input and output layers) require higher accuracy, while intermediate layers require less accuracy. By partitioning the sensitivity, we can reduce memory usage and computational complexity while maintaining model performance.

[0142] Loss function scaling is used to prevent vanishing or exploding gradients in low-precision computations. In half-precision (float16) computations, the limited range of values can easily lead to gradients being too small to be represented (vanishing gradients) or too large to overflow (exploding gradients). By multiplying the loss function by an appropriate scaling factor, the gradients can be kept within the range representable in half-precision, ensuring training stability.

[0143] Random sampling involves randomly selecting a portion of the training data during training to update the model, rather than using the entire training data. This approach can speed up training, reduce memory usage, and enhance the model's generalization capabilities. Random sampling can employ various strategies, such as simple random sampling, stratified random sampling, and importance sampling. Choosing the appropriate sampling strategy depends on the specific application scenario.

[0144] Mixed-precision training improves training efficiency and reduces memory usage and computational complexity while maintaining model performance. This is particularly important for large-scale models and datasets, significantly shortening training time and reducing hardware requirements.

[0145] Example 6

[0146] Embodiment 6 of the present application relates to a path planning method. Embodiment 6 is substantially the same as Embodiment 1, with the main difference being that: Step S21 trains an initial computational model based on a training sequence in a training sequence set: when the ordinary differential equation type corresponding to the training sequence is a non-rigid equation, a first strategy is used to train the computational model currently to be trained, a third computational model is determined, and the third computational model is used as the computational model currently to be trained; when the ordinary differential equation type corresponding to the training sequence is a rigid equation, a second strategy is used to train the computational model currently to be trained, a third computational model is determined, and the third computational model is used as the computational model currently to be trained; until the training of all training sequences in the training sequence set is completed, and a second computational model is obtained.

[0147] The initial computational model is the starting point of the path planning method. It is an untrained neural network model. The structure and parameters of the initial computational model are designed based on the specific application scenario and data characteristics. In this embodiment, the initial computational model can be various types of neural networks, such as feedforward neural networks, recurrent neural networks, and graph neural networks.

[0148] Each training sequence in the training sequence set corresponds to an ordinary differential equation and its conservation properties. These ordinary differential equations can be divided into different types, such as nonstiff and stiff. Nonstiff and stiff equations have different characteristics in numerical solution and therefore require different training strategies.

[0149] For non-stiff equations, the first strategy is used for training. The first strategy may include the following features:

[0150] Use explicit optimization algorithms such as gradient descent, Adam optimizer, etc.

[0151] Use a larger learning rate, such as 0.01 or 0.001.

[0152] Use a smaller number of iterations, such as 100 or 200 iterations.

[0153] Use batch gradient descent or mini-batch gradient descent, and the batch size can be larger, such as 64 or 128.

[0154] Use a simple regularization method such as L2 regularization.

[0155] For stiff equations, the second strategy is used for training. The second strategy may include the following features:

[0156] Use implicit optimization algorithms such as L-BFGS optimizer, conjugate gradient method, etc.

[0157] Use a smaller learning rate, such as 0.0001 or 0.00001.

[0158] Use a higher number of iterations, such as 500 or 1000 iterations.

[0159] Use mini-batch gradient descent or stochastic gradient descent with a small batch size such as 16 or 32.

[0160] Use stronger regularization methods, such as L1 regularization, Dropout, etc.

[0161] The training process involves processing each training sequence in the training sequence set one by one. For each training sequence, an appropriate training strategy is selected based on the type of ordinary differential equation it corresponds to. The current computational model to be trained is trained to obtain an updated model (the third computational model). The third computational model is then used as the current computational model to be trained, and processing continues with the next training sequence.

[0162] Specifically, the training process can be described as follows:

[0163] Initialize the calculation model to obtain an initial calculation model.

[0164] For each training sequence in the training sequence set:

[0165] Determine the type of ordinary differential equation (non-stiff or stiff) corresponding to the training sequence.

[0166] If it is a non-rigid equation, the first strategy is used to train the current computational model to be trained to obtain a third computational model.

[0167] If it is a rigid equation, the second strategy is used to train the current computational model to be trained to obtain a third computational model.

[0168] The third computing model is used as the computing model currently to be trained.

[0169] After completing the training of all training sequences, a second calculation model is obtained.

[0170] In this way, the computational model gradually learns from the information in the training sequence, mastering the dynamic characteristics and conservation constraints of different types of ordinary differential equations. The resulting second computational model is capable of handling various types of ordinary differential equations and generating paths that conform to physical laws.

[0171] Step S22 performs mixed precision training on the second computational model to obtain the first computational model. Mixed precision training is a technique that improves training efficiency and model performance by combining numerical representations of different precisions, such as float32 (single precision) and float16 (half precision).

[0172] Example 7

[0173] The seventh embodiment of the present application relates to a path planning method. The seventh embodiment is substantially the same as the first embodiment, with the main difference being:

[0174] Step S22 performs mixed precision training on the second computing model to obtain the first computing model, including: sensitivity partitioning the weights of the second computing model, scaling the loss function, and training the second computing model using random sampling to obtain the first computing model.

[0175] The second computational model is obtained by training the initial computational model. It has learned the information in the training sequence and grasped the dynamic characteristics and conservation constraints of different types of ordinary differential equations. To further improve the model's performance and training efficiency, the second computational model is trained with mixed precision to obtain the first computational model.

[0176] Mixed-precision training is a training technique that combines numerical representations of different precisions. Traditional deep learning training typically uses single-precision floating-point numbers (float32). In mixed-precision training, calculations are performed using both single-precision floating-point numbers and half-precision floating-point numbers (float16). Half-precision floating-point numbers occupy only half the memory of single-precision floating-point numbers and are faster, but offer lower accuracy. By properly combining the two precisions, training efficiency can be improved while maintaining model performance.

[0177] Sensitivity partitioning of the second computational model's weights is the first step in mixed-precision training. Weight sensitivity refers to the degree to which a weight affects the model's output. Highly sensitive weights have a significant impact on the model's output and require high-precision (float32) storage and computation. Low-sensitivity weights have a minimal impact on the model's output and can be stored and computed using low-precision (float16) storage and computation.

[0178] The evaluation of weight sensitivity can be performed by the following methods:

[0179] Calculate the gradient magnitude of the weights: Weights with large gradient magnitudes usually have a greater impact on the model output and should be calculated with high precision.

[0180] Calculate the impact of weight changes on the loss function: make small perturbations to each weight and observe the change in the loss function. Use high precision for weights with large changes.

[0181] According to the position of the network layer: Generally, the input layer and output layer of the network have higher requirements on accuracy, while the intermediate layers have relatively lower requirements on accuracy.

[0182] Through sensitivity analysis, the weights of the second computational model are divided into high-sensitivity and low-sensitivity categories. High-sensitivity weights are stored and calculated using float32; low-sensitivity weights are stored and calculated using float16. This reduces memory usage and computational complexity while maintaining model performance.

[0183] Scaling the loss function is the second step in mixed-precision training. Half-precision (float16) computations have a limited range of values, which can easily lead to gradients being too small to be represented (vanishing gradients) or too large to overflow (exploding gradients). By multiplying the loss function by an appropriate scaling factor, the gradient values can be kept within the range representable by half-precision, thus ensuring training stability.

[0184] There are two methods for scaling the loss function: static scaling and dynamic scaling. Static scaling uses a fixed scaling factor throughout the training process; dynamic scaling dynamically adjusts the scaling factor based on the magnitude of the gradient. In this embodiment, dynamic scaling can be used to automatically adjust the scaling factor based on the magnitude of the gradient in each iteration to ensure that the gradient value remains within an appropriate range.

[0185] The third step in mixed-precision training is to train the second computational model using random sampling. Random sampling involves randomly selecting a portion of the training data during training for model updates, rather than using the entire training data. This approach can speed up training, reduce memory usage, and enhance the model's generalization capabilities.

[0186] Random sampling can employ various strategies, such as simple random sampling, stratified random sampling, and importance sampling. In this embodiment, importance sampling can be employed to assign sampling probabilities based on the impact of training data on model performance. Training data with a greater impact on model performance is assigned a higher sampling probability, while training data with a smaller impact is assigned a lower sampling probability. This allows the model to focus more on important training data, improving training efficiency and model performance.

[0187] By partitioning the weights of the second computational model based on sensitivity, scaling the loss function, and training it using random sampling, we can obtain a first computational model with improved performance and higher training efficiency. The first computational model not only retains the physical knowledge learned by the second computational model, but also has better computational efficiency and generalization capabilities.

[0188] The target data is input into the first computational model to determine the target path. The target data contains the information necessary for path planning, such as the starting point, end point, and environmental constraints. Based on this information and combined with the physics knowledge learned during training, the first computational model generates a path from the starting point to the end point. This path not only meets the starting and end point requirements but also complies with the dynamic characteristics of the physical system and conservation constraints.

[0189] When deploying the first computational model on hardware in real-world applications, sparse attention and hierarchical quantization compression can be implemented based on the target hardware's characteristics to achieve end-to-end low-latency inference. Target hardware is analyzed to determine INT8 / FP16 computing bottlenecks and acceleration unit support. Advanced mixed-precision training is pre-adapted to FP16 compute units, reducing deployment and tuning costs. Hierarchical quantization compression: Sensitive parameters remain in FP16; non-sensitive parameters (such as the ambient noise module) are compressed to INT8, and the quantization threshold is dynamically calibrated. Progressive gradient clipping has screened out sensitive parameters, and the post-quantization rigid system stability error is less than 1%. The end-to-end inference engine optimization combines the computation graph for symbolic differential encoding with sparsification and quantization operators into a single kernel. Memory pre-allocation: Pre-allocates graphics memory based on a discretization strategy to eliminate redundant copies. Basic support for mixed-precision training: Advanced mixed-precision (FP32 / FP16) training makes the model weight distribution more adaptable to quantization compression, reducing the risk of accuracy loss. Computational collaboration with adaptive discretization: Spatiotemporal discretization dynamically identifies key computational areas (such as transient stages), guiding the sparse attention mechanism to retain core connections and prune redundant nodes.

[0190] Generalization guaranteed by progressive training: Multi-scale dynamics models learned in the elementary to intermediate stages improve the robustness of the model after sparsification and quantization, avoiding the loss of key features.

[0191] This application uses a symbolic differential encoder to parse ordinary differential equations into abstract syntax trees, and generates a calculation sequence through topological sorting, characterizing the AST from multiple dimensions such as structural level, topological characteristics, dynamic behavior, and functional attributes. At the same time, the Lagrange multiplier method is used to integrate conservation laws into the loss function, which significantly reduces the computational complexity and memory overhead, and achieves millisecond-level real-time solution, meeting the rapid response requirements of scenarios such as autonomous driving and robot control. The sparse attention mask reduces the computational complexity by more than 50%.

[0192] A phased training strategy, including pre-training of low-dimensional non-rigid equations, the gradual introduction of rigid terms and high-dimensional coupling, and fine-tuning with mixed precision and random time sampling, is employed. Combined with dynamic gradient clipping threshold adjustment and a random time sampler, this adaptive spatiotemporal discretization intelligently adjusts the discretization strategy based on the dynamic characteristics of the solution curve, ensuring numerical stability. Physical constraints are injected to ensure the model conforms to physical laws, significantly reducing the long-term simulation errors caused by discretization in traditional numerical methods. In scenarios such as rocket engine combustion simulations, gradient clipping improves training stability by 40%, and adaptive sampling reduces transient pressure peak prediction errors by 25%.

[0193] Through hardware-aware model compression, including sparse attention masks, hierarchical quantization, and end-to-end inference engine optimization, it effectively addresses complex problems such as rigid equations and multi-scale physical field coupling. Even with small amounts of data, the model can be guided by physical priors to generate predictions that conform to dynamics. The stability error of the rigid system after quantization is less than 1%. Sparse attention and hierarchical quantization compression are implemented based on the characteristics of the target hardware to achieve end-to-end low-latency inference. Mixed-precision training makes the model weight distribution more adaptable to quantization compression, reducing the risk of accuracy loss, providing an efficient and lightweight solution engine for industrial simulation, scientific computing, and real-time decision-making systems.

[0194] It should be noted that the first embodiment, the second embodiment, the third embodiment, the fourth embodiment, the fifth embodiment, the sixth embodiment, and the seventh embodiment are all a type of path planning method.

[0195] The steps of the various methods above are divided only for the purpose of clear description. During implementation, they can be combined into one step or some steps can be split and decomposed into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this patent. Adding insignificant modifications or introducing insignificant designs to the algorithm or process without changing the core design of the algorithm and process are all within the scope of protection of this patent.

[0196] In addition, some embodiments of the present application further provide an electronic device. The electronic device may be various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, etc. The electronic device may also be various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, wearable devices, and other similar computing devices.

[0197] The electronic device includes: one or more processors; and a memory storing computer program instructions, wherein the computer program instructions, when executed, enable the processor to perform the steps of the method provided in any one or more of the above embodiments. Figure 5 An exemplary structural diagram of the electronic device is disclosed. Figure 5As shown, the electronic device includes: one or more processors 1101, a memory 1102, and interfaces for connecting various components, including high-speed interfaces and low-speed interfaces. The various components are connected to each other using different buses and can be installed on a common motherboard or installed in other ways as needed. The processor can process instructions executed in the electronic device, including instructions stored in or on the memory to display graphical information of a GUI on an external input / output device (such as a display device coupled to the interface). In some other embodiments, if necessary, multiple processors and / or multiple buses can be used together with multiple memories and multiple memories. Similarly, multiple electronic devices can be connected, and each device provides some necessary operations (for example, as a server array, a group of blade servers, or a multi-processor system). Among them, the components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present application described and / or required herein.

[0198] The electronic device may further include: an input device 1103 and an output device 1104. The processor 1101, the memory 1102, the input device 1103 and the output device 1104 may be connected via a bus or other means. Figure 5 The bus connection is taken as an example.

[0199] The input device 1103 can receive input digital or character information and generate key signal input related to user settings and function control of the electronic device, such as input devices such as a touch screen, a keypad, a mouse, a trackpad, a touch pad, an indicator stick, one or more mouse buttons, a trackball, and a joystick. The output device 1104 can include a display device, an auxiliary lighting device (e.g., an LED), and a tactile feedback device (e.g., a vibration motor). The display device can include, but is not limited to, a liquid crystal display (LCD), a light emitting diode (LED) display, and a plasma display. In some embodiments, the display device can be a touch screen.

[0200] To provide interaction with a user, the electronic device may be a computer. The computer may include: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or trackball), through which the user can provide input to the computer. Other types of devices may also be used to provide interaction with the user; for example, the feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form (including acoustic input, voice input, or tactile input).

[0201] In the embodiments of the present application, a computer program / instruction is stored on a computer-readable medium. When executed by a processor, the computer program / instruction implements the steps of the method provided in any one or more of the above embodiments. The computer-readable medium may be included in the electronic device described in the above embodiments, or it may exist independently and not be incorporated into the device. The computer-readable medium carries one or more computer-readable instructions.

[0202] The memory 1102 can be used as a non-transitory computer-readable storage medium to store non-transitory software programs, non-transitory computer executable programs, and modules. The processor 1101 executes the non-transitory software programs, instructions, and modules stored in the memory 1102 to execute various functional applications and data processing of the server, thereby implementing the program instructions / modules corresponding to the method provided in any one or more of the above embodiments of the present application.

[0203] The memory 1102 may include a program storage area and a data storage area, wherein the program storage area may store an operating system and applications required for at least one function; the data storage area may store data created based on the use of the electronic device, etc. In addition, the memory 1102 may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory 1102 may optionally include a memory remotely located relative to the processor 1101, and these remote memories may be connected to the electronic device via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0204] It should be noted that the computer-readable medium described in this application may be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. The computer-readable medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared or semiconductor system, device or component, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this application, a computer-readable medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device or device.

[0205] Computer-readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology for information storage. The information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc-read only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape disk storage or other magnetic storage devices or any other non-transmission medium that can be used to store information that can be accessed by a computing device.

[0206] Computer program code for performing the operations of the present application can be written in one or more programming languages, or a combination thereof, including object-oriented programming languages such as Java, Smalltalk, C++, and conventional procedural programming languages such as "C" or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on the remote computer or server. In cases involving a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0207] In the above-described embodiment, can realize wholly or in part by software, hardware, firmware or its arbitrary combination.For example, can adopt application-specific integrated circuit (ASIC), general computer or any other similar hardware device to realize.In certain embodiments, the software program of the present application can be carried out to realize above steps or function by processor.Similarly, the software program of the present application (comprising relevant data structure) can be stored in computer-readable recording medium, for example, RAM memory, magnetic or optical drive or floppy disk and similar device.In addition, some steps or functions of the present application can adopt hardware to realize, for example, as the circuit that cooperates with processor to perform each step or function.

[0208] The computer program product provided by the embodiment of the present application includes one or more computer programs / instructions, and when the computer program / instructions are executed by the processor, all or part of the process or function described in the embodiment of the present application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instruction can be stored in a computer-readable storage medium, or transmitted from a computer-readable storage medium to another computer-readable storage medium. For example, the computer instruction can be transmitted from a website site, a computer, a server or a data center by wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or a data center that includes one or more available media integrations. The available medium can be a magnetic medium, (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid-state hard disk (SSD)).

[0209] The flowcharts or block diagrams in the accompanying drawings illustrate the possible architectures, functions and operations of the devices, methods and computer program products according to various embodiments of the present application. In this regard, each box in the flowchart or block diagram can represent a module, program segment or part of code, and the module, program segment or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, as well as the combination of boxes in the block diagram and / or flowchart, can be implemented with a dedicated hardware-specific system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0210] The scope of this application is defined by the appended claims rather than the foregoing description and is therefore intended to encompass within this application all changes that come within the meaning and range of equivalents of the claims. Any reference signs in the claims should not be construed as limiting the claims to which they relate. In addition, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units or devices stated in a device claim may also be implemented by one unit or device through software or hardware. Words such as "first" and "second" are only used to distinguish the description and do not indicate any particular order, nor should they be understood as indicating or implying relative importance.

[0211] The above description is merely a specific embodiment of the present application, but the scope of protection of this application is not limited thereto. Any modifications or substitutions that can be easily proposed by a person skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims, and the above embodiments should be regarded as exemplary and non-limiting.

Claims

1. A path planning method, characterized in that: include: Determining a training sequence set based on a set of ordinary differential equations configured with training data; Training the initial computing model based on the training sequence set to determine a first computing model; The target data is input into the first calculation model to determine the target path.

2. The path planning method according to claim 1, characterized in that: The step of determining a training sequence set based on a set of ordinary differential equations configured with training data comprises: Parsing a set of ordinary differential equations configured with training data to determine a set of abstract syntax trees; The abstract syntax tree set is processed by a symbolic differential encoder to determine the training sequence set.

3. The path planning method according to claim 2, characterized in that: The step of parsing a set of ordinary differential equations configured with training data to determine a set of abstract syntax trees includes: Parsing the ordinary differential equations in the ordinary differential equation set configured with training data one by one by a syntax parser to obtain the abstract syntax tree set including a plurality of abstract syntax trees; Each of the ordinary differential equations corresponds to an abstract syntax tree.

4. The path planning method according to claim 3, characterized in that: The processing of the abstract syntax tree set by a symbolic differential encoder to determine the training sequence set includes: When parsing a set of ordinary differential equations configured with training data, the symbolic differential encoder identifies conserved quantities of each of the ordinary differential equations; Determining the constraint terms corresponding to the ordinary differential equations according to the conservation quantities of the ordinary differential equations by using the Lagrange multiplier method; Adding the conserved quantity as a symbolic variable to the abstract syntax tree corresponding to the ordinary differential equation to form a training sequence corresponding to the ordinary differential equation; The training sequence set consists of a plurality of training sequences.

5. The path planning method according to claim 1, wherein: The training of the initial computing model based on the training sequence set to determine the first computing model includes: Based on the type of ordinary differential equation corresponding to each training sequence in the training sequence set, selecting a corresponding training strategy to train the current computing model to be trained, and determining a second computing model; Perform mixed precision training on the second computing model to obtain the first computing model.

6. The path planning method according to claim 3, characterized in that: The selecting a corresponding training strategy to train the current computation model to be trained based on the ordinary differential equation type corresponding to each training sequence in the training sequence set to determine the second computation model includes: Training an initial computing model based on the training sequence in the training sequence set: When the type of the ordinary differential equation corresponding to the training sequence is a non-rigid equation, the first strategy is used to train the current computational model to be trained, a third computational model is determined, and the third computational model is used as the current computational model to be trained; When the type of the ordinary differential equation corresponding to the training sequence is a stiff equation, the second strategy is used to train the current computational model to be trained, a third computational model is determined, and the third computational model is used as the current computational model to be trained; The second calculation model is obtained until the training of all the training sequences in the training sequence set is completed.

7. The path planning method according to claim 5, characterized in that: The performing mixed precision training on the second computing model to obtain the first computing model includes: The weights of the second computing model are partitioned by sensitivity, the loss function is scaled, and the second computing model is trained using random sampling to obtain the first computing model.

8. An electronic device, characterized in that: The electronic device comprises: one or more processors; and A memory storing computer program instructions, which, when executed, cause the processor to perform the steps of the method according to any one of claims 1 to 7.

9. A computer-readable medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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