Moon satellite formation orbit forecasting method based on physical information neural network model

Abstract

The invention relates to a lunar satellite formation orbit forecasting method based on a physical information neural network model, and the method comprises the steps: building a non-spherical perturbation acceleration model for a physical loss function under the inertial coordinates of the lunar center; designing a physical information neural network model: selecting a full-connection deep neural network as a network architecture of the model, and using a composite loss function containing a data loss function and a physical loss function as a loss function of the full-connection deep neural network; training a physical information neural network model; and using the physical information neural network model to predict the orbit state of the satellite formation. The physical information neural network model can output a high-precision orbit state within milliseconds through forward propagation, error accumulation of traditional integration is avoided, calculation complexity is remarkably reduced, and efficient, stable and high-precision online orbit state forecasting can be achieved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of satellite formation, and in particular to a lunar satellite formation orbit prediction method based on a physical information neural network model. BACKGROUND

[0002] In view of the weak signal search in the cosmic dawn and the observation requirement of high-energy astrophysical phenomena, the traditional ground observation method has been difficult to meet the further requirement of scientific exploration due to the blocking of the low-frequency cutoff characteristics of the ionosphere of the earth and the interference of high-intensity artificial electromagnetic noise on the ground. To solve this problem, deploying a lunar satellite formation system with dynamic variable configuration capability in the unique electromagnetic shielding environment of the back of the moon becomes the preferred technical path at present. The system adopts a "breathing" baseline adjustment strategy, and a large-aperture virtual interferometer is constructed by periodically changing the satellite spacing, so as to obtain high-resolution extremely low-frequency astronomical data. Under this task architecture, the frequent change of the formation configuration and the maintenance of the large-scale distribution of the space reference pose a high challenge, and realizing high-precision autonomous orbit determination is not only a prerequisite for guaranteeing the correlation of the interferometric measurement data, but also a key to guaranteeing the long-term stable operation and accurate configuration maintenance of the satellite group in the complex lunar gravity field.

[0003] Unlike the near-earth environment, the lunar gravity field is extremely unevenly distributed, and there is a significant mascons effect, which causes the satellite to be affected by complex non-spherical gravitational perturbation during the lunar flight. Simulation tests show that, under the large-scale dynamic configuration of the "breathing" formation, the traditional low-order dynamic model cannot meet the stringent requirements of the baseline accuracy of the interferometric measurement. Through in-depth dynamic simulation and error analysis, it is found that, in order to offset the accumulated error and achieve good navigation accuracy, the lunar non-spherical perturbation model must be raised to the 25th order (25th 25 times). Only under the premise of fully considering the high-order perturbation environment, can the subtle features of the orbit evolution be effectively captured, and the long-term stability of the formation configuration and the effectiveness of the observation data be ensured.

[0004] However, the introduction of the 25th order non-spherical perturbation model brings huge pressure to the on-board computing resources. Under the traditional dynamic framework, with the increase of the order of the spherical harmonic function, the calculation complexity of the orbit integration increases exponentially. For the on-board computer, real-time solving of such high-dimensional dynamic equations in each filtering period will not only cause great computational overhead, seriously affecting the real-time performance and update frequency of the navigation filtering algorithm, but also in the long-term running process, the traditional numerical integration method is prone to orbit prediction divergence or drift phenomenon due to the accumulation of truncation error and rounding error. This contradiction between calculation load and real-time performance has become the main bottleneck restricting the landing of high-precision lunar formation autonomous navigation technology.

[0005] Therefore, it is urgent to develop a low-complexity, efficient and high-precision lunar satellite formation orbit prediction method. SUMMARY

[0006] To solve at least one of the above problems in the prior art, the application provides a lunar satellite formation orbit prediction method based on a physical information neural network model, comprising the following steps: In the lunar center inertia coordinate, a non-spherical perturbation acceleration model for a physical loss function is established; Designing a physical information neural network model, including: selecting a fully connected deep neural network as the network architecture of the model, using a composite loss function containing a data loss function and a physical loss function as the loss function of the fully connected deep neural network; Training the physical information neural network model; and Using the physical information neural network model to predict the orbit state of the satellite formation.

[0007] Further, training the physical information neural network model comprises: Inputting the simulation data as training data into the fully connected deep neural network to train the physical information neural network model, and using the Adam optimizer and the LBFGS optimizer to optimize the parameters of the fully connected deep neural network in turn until the composite loss function value is lower than the preset threshold during the training process.

[0008] Further, the training data is the orbit state of the satellite formation within a period of time generated by a simulation software, and the orbit state contains three-axis position and three-axis velocity. The input of the fully connected deep neural network is time, and the output is orbit state.

[0009] Further, a plurality of time points are randomly sampled as physical configuration points within the prediction time interval. At the physical configuration point, the predicted acceleration is calculated using the three-axis position predicted by the physical information neural network model, and the physical loss is calculated based on the physical loss function, which is obtained by embedding the non-spherical perturbation acceleration model.

[0010] Further, the non-spherical perturbation acceleration model is: , wherein represents the predicted acceleration predicted by the model, is the lunar gravitational constant, is the distance between the satellite and the lunar center, is the perturbation acceleration caused by the non-spherical gravity of the moon, and the three-axis position .

[0011] Furthermore, establishing a non-spherical perturbation acceleration model for the physical loss function includes: In the lunar-centered inertial coordinate system, based on the three-axis position and three-axis speed Establish the equations of motion for the satellite: , in, It is the lunar gravitational constant. The distance between the satellite and the center of the moon. This is the perturbation acceleration caused by the Moon's non-spherical gravity. , Represents the satellite's velocity vector. Represents the satellite's acceleration vector; Perturbation acceleration caused by the Moon's non-spherical gravity Calculations based on the 25th-order spherical harmonic function expansion include: Lunar gravitational potential function The definition is as follows: , in, R It is the radius of the moon. These represent the lunar latitude and longitude of the satellite in the lunar inertial coordinate system. These are the normalized spherical harmonic coefficients of the lunar gravitational field. for n Step m Second-associative Legendre functions; By calculating the gradient of the potential function, the perturbation acceleration caused by the non-spherical gravity of the moon is obtained: , Using the chain rule, the gradient of the potential function is transformed into a set of... The partial derivative is obtained. : ; D represents the distance between the spacecraft and the center of the moon. These represent the lunar latitude and longitude of the satellite in the lunar inertial coordinate system. , , These represent the unit basis vectors in the radial, latitude, and longitude directions in the spherical coordinate system, respectively. Then Projecting onto the Cartesian coordinate system using the coordinate transformation matrix: ; , , Let x, y, and z represent the components of the gradient of the potential function along the x, y, and z axes in the Cartesian coordinate system. , , These represent the components of the potential function gradient in the radial, dimensional, and longitude directions, respectively, in spherical coordinates. The analytical expressions for each directional component are: , in, Indicates the radius of the moon. This represents the normalized associated Legendre polynomial. and These are the normalized spherical harmonic coefficients; Thus, the non-spherical perturbation acceleration model is obtained: , in This represents the predicted acceleration as predicted by the model. This refers to the perturbation acceleration caused by the Moon's non-spherical gravity.

[0012] Furthermore, the fully connected deep neural network takes time as input and outputs the satellite's three-axis position and three-axis velocity, with the mapping relationship as follows: , in, t For time scalar, The three-axis position of the satellite output by a fully connected deep neural network. and three-axis speed , This includes all parameters to be trained, including weights and biases; A fully connected deep neural network contains 7 hidden layers, each containing 60 neurons. The activation function of a fully connected deep neural network is the hyperbolic tangent function.

[0013] Furthermore, the composite loss function The formula is as follows: , For physical loss weights, For data loss function, For physical loss function; When given Reference orbit points ,in X GT Given the satellite's reference orbital state, the data loss function is: ,in The orbital state is predicted by a fully connected deep neural network, including three-axis position and three-axis velocity; In the selected physical configuration points Above, the predicted velocity and predicted acceleration are calculated using automatic differentiation: , in To predict speed, To predict acceleration; Substitute the predicted acceleration into the non-spherical perturbation acceleration model to calculate the acceleration residual: , in, The gradient vector calculated for the real-time state; The physical loss function is: .

[0014] Furthermore, the order of the non-spherical perturbation acceleration model is at least 25.

[0015] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, performs the steps of a lunar satellite formation orbit prediction method based on a physical information neural network model.

[0016] The present invention also provides a computer system, comprising: A processor, configured to execute machine-executable instructions; and A memory storing machine-executable instructions that, when executed by a processor, perform steps of a lunar satellite formation orbit prediction method based on a physical information neural network model.

[0017] The present invention has at least the following beneficial effects: This invention establishes a non-spherical perturbation acceleration model for the physical loss function, embedding a 25th-order non-spherical perturbation acceleration model as a physical constraint into a fully connected deep neural network. By utilizing the powerful nonlinear fitting capability of the fully connected deep neural network to approximate complex dynamic environments, the trained physical information neural network model can output high-precision orbital states within milliseconds through forward propagation, avoiding the error accumulation of traditional integration, significantly reducing computational complexity, and enabling efficient, stable, and high-precision online orbital state prediction. Attached Figure Description

[0018] Figure 1 The flowchart of a lunar satellite formation orbit prediction method based on a physical information neural network according to an embodiment of the present invention is shown.

[0019] Figure 2 The loss curves during model training and testing according to an embodiment of the present invention are shown.

[0020] Figure 3 The position error curve and velocity error curve predicted by PINNs according to an embodiment of the present invention are shown. Detailed Implementation

[0021] It should be noted that the components in the accompanying drawings may be shown exaggerated for illustrative purposes and may not be to scale.

[0022] In this invention, the various embodiments are merely intended to illustrate the solutions of the invention and should not be construed as limiting.

[0023] In this invention, unless otherwise specified, the quantifiers “a” and “one” do not exclude scenarios involving multiple elements.

[0024] It should also be noted that, in the embodiments of the present invention, only a portion of the parts or components may be shown for clarity and simplicity. However, those skilled in the art will understand that, under the teachings of the present invention, the required parts or components can be added as needed for specific scenarios.

[0025] It should also be noted that within the scope of this invention, the terms "same", "equal", and "equal to" do not mean that the two values ​​are absolutely equal, but allow for a certain reasonable error. In other words, the terms also cover "substantially the same", "substantially equal", and "substantially equal to".

[0026] It should also be noted that in the description of this invention, the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not explicitly or implicitly suggest that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0027] Furthermore, the embodiments of the present invention describe the process steps in a specific order. However, this is only for the convenience of distinguishing each step, and is not a limitation on the order of each step. In different embodiments of the present invention, the order of each step can be adjusted according to the process.

[0028] This invention aims to address the problem that traditional models suffer from high computational load and susceptibility to drift due to the introduction of 25th-order non-spherical perturbations required for high-precision navigation in lunar satellite formations. A trajectory prediction method based on Physics-Informed Neural Networks (PINNs) is proposed. The 25th-order non-spherical perturbation acceleration model is embedded as a physical constraint into the neural network, significantly reducing the computational load while maintaining accuracy, thus meeting the requirements for high-precision autonomous navigation of the formation. In practical applications, only the prediction time needs to be input; the trained PINN model can output high-precision orbital state within milliseconds through forward propagation, avoiding the error accumulation of traditional integration and achieving efficient and stable online prediction.

[0029] Figure 1 The flowchart of a lunar satellite formation orbit prediction method based on a physical information neural network according to an embodiment of the present invention is shown.

[0030] like Figure 1 As shown, a method for predicting the orbits of lunar satellite formations based on a physical information neural network model includes the following steps: Step 1: Establish a non-spherical perturbation acceleration model for the physical loss function in lunar inertial coordinates.

[0031] To accurately describe the satellite's motion in the complex gravitational field of the moon, a non-spherical perturbation acceleration model needs to be established. This model will be embedded as a physical constraint in the subsequent neural network.

[0032] The satellite's orbital state in the lunar inertial coordinate system (J2000) X From three-axis position and three-axis speed Description. The satellite's equation of motion is: , in, It is the lunar gravitational constant. The distance between the satellite and the center of the moon. This is the perturbation acceleration caused by the Moon's non-spherical gravity. Represents the satellite's velocity vector. This represents the satellite's acceleration vector.

[0033] To meet the requirements of high-precision formation navigation, the perturbation acceleration caused by the non-spherical gravity of the moon in this invention... The calculation is based on the expansion of the 25th order spherical harmonic function, and the steps are as follows: Lunar gravitational potential function The definition is as follows: , in,R It is the radius of the moon. These represent the lunar latitude and longitude of the satellite in the lunar inertial coordinate system. These are the normalized spherical harmonic coefficients of the lunar gravitational field. for n Step m Secondary association Legendre function.

[0034] By calculating the gradient of the potential function, the perturbation acceleration caused by the non-spherical gravity of the moon is obtained: , Using the chain rule, the gradient of the potential function is transformed into a set of... The partial derivative is obtained. : ; D represents the distance between the spacecraft and the center of the moon. These represent the lunar latitude and longitude of the satellite in the lunar inertial coordinate system. , , These represent the unit basis vectors in the radial, latitude, and longitude directions in the spherical coordinate system, respectively. Then Projecting onto the Cartesian coordinate system using the coordinate transformation matrix: ; , , Let x, y, and z represent the components of the gradient of the potential function along the x, y, and z axes in the Cartesian coordinate system. , , These represent the components of the potential function gradient in the radial, dimensional, and longitude directions, respectively, in spherical coordinates. The analytical expressions for each directional component are: , in, Indicates the radius of the moon. This represents the normalized associated Legendre polynomial. and These are the normalized spherical harmonic coefficients; Therefore, the non-spherical perturbation acceleration model can be obtained: , in This represents the predicted acceleration as predicted by the model. This represents the perturbation acceleration caused by the Moon's non-spherical gravity. Ideally, the predicted acceleration, when added to the other two terms, should equal zero, as shown in the equation above. However, in reality, there will be errors. It is not zero, which is the acceleration residual mentioned later.

[0035] Given the complexity of the lunar gravitational field, a 25th-order (25×25) spherical harmonic function expansion is explicitly used to accurately calculate the non-spherical perturbation acceleration, thereby capturing the subtle influence of the lunar mass bulge on the formation orbit.

[0036] Step 2: Design a physical information neural network model, including using a fully connected deep neural network as the network architecture of the model, and using a composite loss function that includes a data loss function and a physical loss function as the loss function of the fully connected deep neural network.

[0037] A fully connected deep neural network (DNN) is used as the orbital state predictor. The network input is time, and the output is the satellite's three-axis position and three-axis velocity. The mapping relationship is as follows: , in, t For time scalar, The three-axis position of the satellite output by a fully connected deep neural network. and three-axis speed , For all parameters to be trained (weights and biases), optimize these parameters during model training.

[0038] To approximate the complex 25th-order dynamics model, a fully connected deep neural network employs a deep structure containing multiple hidden layers. In the intermediate layer design of the fully connected deep neural network, there are 7 hidden layers, each containing approximately 60 neurons. This invention uses the hyperbolic tangent function. As an activation function, this is because the subsequent calculation of the physical loss requires taking the second derivative of the network output with respect to time t. The hyperbolic tangent function is infinitely differentiable, which can guarantee the effective propagation of the gradient, thus satisfying the requirements of PINNs for calculating higher-order derivatives and fulfilling the mathematical requirement of embedding the dynamic differential equation into the network loss function.

[0039] To enable the physical information neural network model to not only fit the observed data (three-axis position and velocity) but also follow the physical laws in step one, this invention designs a composite loss function that includes a physical driving component. Composite loss function The data error component (data loss function) And the residual part of the physical equation (physical loss function) composition: , in, This refers to the physical loss weights, which are adjustable hyperparameters that can be adjusted as needed.

[0040] Data loss function Used to constrain the model output to conform to known observation data or boundary conditions, when given High-precision reference orbit points ,in X GT Given the satellite's reference orbital state, the data loss function is: ,in The orbital state is predicted by a fully connected deep neural network, including three-axis position and three-axis velocity.

[0041] Physical loss function By using automatic differentiation techniques, the first and second derivatives of the position output of a fully connected deep neural network are directly calculated over time to obtain the predicted velocity and predicted acceleration.

[0042] In the selected physical configuration points Above, velocity and acceleration are calculated using automatic differentiation: , in To predict speed, To predict acceleration.

[0043] Substitute the predicted acceleration into the non-spherical perturbation acceleration model from step 1 to calculate the acceleration residual: , in, The gradient vector is calculated for the real-time state, which is the perturbation acceleration caused by the non-spherical gravity of the moon; The physical loss function is: .

[0044] The physical loss function forces the fully connected deep neural network to strictly satisfy the 25th-order non-spherical perturbation dynamics constraint in the entire time domain.

[0045] Step 3, training the physical information neural network model, includes: inputting simulation data as training data into a fully connected deep neural network to train the physical information neural network model. During the training process, the Adam optimizer and LBFGS optimizer are used sequentially to optimize the parameters of the fully connected deep neural network until the composite loss function value is lower than a preset threshold.

[0046] The training data consists of the orbital states of a satellite formation over a period of time, generated using simulation software. The orbital states include three-axis position and three-axis velocity.

[0047] Using the High Precision Orbit Propagator (HPOP) in STK (Systems Tool Kit) software, with the force model set to a 25×25 order lunar gravity field, flight orbit data of the satellite formation over a period of time were generated and used as the standard reference value in the loss function. X GT .

[0048] To calculate the physical loss, a large number of time points are randomly sampled within the predicted time interval as physical placement points. t k These points do not require corresponding true label values ​​(standard reference values); they are only used to calculate physical residuals, thereby achieving unsupervised physical constraint learning. At the physical configuration points, the predicted acceleration is calculated using the model's predicted triaxial positions, and the physical loss is calculated based on the physical loss function, which is embedded from a 25th-order non-spherical perturbation acceleration model. Specifically, after calculating the predicted acceleration, the acceleration residuals are calculated based on the 25th-order non-spherical perturbation acceleration model, and the physical loss is calculated based on the acceleration residuals.

[0049] First, the training data is divided into a training set and a validation set, and then input into a fully connected deep neural network. During the training process, the training set is repeatedly used to train and adjust the parameters, and the validation set is used for validation.

[0050] A hybrid optimization algorithm is used for model training. First, the Adam optimizer is used for a fast global search to optimize the parameters of the fully connected deep neural network, causing the loss function to decrease rapidly. Once the loss stabilizes—that is, when the loss on the training set (physical equation residuals and data residuals) no longer decreases significantly, and the loss on the validation set remains stable—the algorithm switches to the LBFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno) optimizer for second-order high-precision fine-tuning until the loss function value is below a preset threshold. This yields the optimal parameters for the fully connected deep neural network, completing model training. After training, the PINNs model can be used for online orbit prediction.

[0051] In one embodiment, the loss curve can be used to intuitively determine whether the loss is no longer decreasing significantly.

[0052] Step 4: Use the physical information neural network model to predict the orbital state of the satellite formation.

[0053] For any time Only one forward propagation is needed to output the orbital state: .

[0054] When predicting the three-axis position and three-axis velocity of a satellite at any new moment, only this time needs to be used as input. The network calculates layer by layer (forward propagation) to directly obtain the output result. The whole process is done in one step without any iteration or step-by-step advancement.

[0055] This process eliminates the need for stepwise integration from the initial state, achieving real-time prediction with O(1) complexity. It transforms the solution of high-dimensional nonlinear differential equations into lightweight algebraic operations, avoiding the trajectory drift problem caused by the accumulation of truncation and rounding errors in traditional numerical integration. Furthermore, the computational complexity is independent of the prediction duration, enabling millisecond-level real-time response.

[0056] Compared to existing navigation filtering algorithms, which suffer from high computational complexity, poor real-time performance, and susceptibility to drift over long periods of operation, the orbit prediction method based on a physical information neural network model embeds a 25th-order non-spherical perturbation acceleration model as a physical constraint into a fully connected deep neural network. By leveraging the powerful nonlinear fitting capability of the fully connected deep neural network to approximate complex dynamic environments, the trained physical information neural network model can significantly reduce computational complexity while maintaining prediction accuracy comparable to traditional high-order dynamic models, thus achieving efficient and stable online orbit state prediction.

[0057] In summary, the method of this invention effectively solves the problem of high-precision, high-real-time orbit prediction faced by "breathing" lunar formations in long-term stable operation in complex gravitational fields, and provides key navigation support for future deployment of ultra-low frequency space interferometry arrays on the far side of the moon.

[0058] Figure 2 The loss curves during model training and testing according to an embodiment of the present invention are shown. Figure 3 The position error curve and velocity error curve predicted by PINNs according to an embodiment of the present invention are shown.

[0059] To verify the effectiveness of the orbit prediction method of this invention, a simulation experiment was conducted using a single lunar orbiting satellite. The satellite was set to operate in a near-circular lunar orbit at an altitude of approximately 300 km to simulate the orbital environment of a typical observation mission. The dynamic model was truncated to order 25 to accurately characterize the non-spherical gravitational perturbations caused by the lunar mass anomaly. A high-precision reference orbit was generated by STK / HPOP under the same force model, with a time span of 7 days, serving as supervisory data (training data) for neural network training.

[0060] During training, a two-stage optimization strategy was employed, combining 5,000 real orbital data points (training data) with 20,000 randomly sampled physical configuration points within the prediction interval: first, pre-training was performed using the Adam optimizer, followed by further training using the LBFGS optimizer. The loss calculated during training and testing, under the condition that both input and output are normalized, is as follows: Figure 2 As shown, the initial training loss was high, then decreased rapidly and stabilized; the test loss was close to the training loss, indicating that the model had good generalization ability and no overfitting occurred.

[0061] 12-hour orbital forecast results are as follows Figure 3 As shown in the figure. Simulation results show that the position error is 435.2m (3σ) and the velocity error is less than 0.33m / s (3σ), which meets the basic requirements for orbital accuracy for lunar formation navigation.

[0062] The orbit prediction method based on physical information neural networks (PINNs) of this invention does not require stepwise integration from the initial state, effectively avoiding the orbit drift problem caused by the accumulation of truncation and rounding errors in traditional numerical integration. While ensuring high accuracy, it significantly improves computational efficiency and long-term prediction stability, and can fully support the real-time and autonomous orbit determination requirements of high-precision lunar orbit missions.

[0063] While some embodiments of the present invention have been described in this application, those skilled in the art will understand that these embodiments are merely illustrative. Numerous variations, alternatives, and improvements will arise in those skilled in the art under the teachings of this invention without departing from its scope. The appended claims are intended to define the scope of the invention and thereby cover methods and structures within the scope of the claims themselves and their equivalents.

Claims

1. A method for predicting the orbits of lunar satellite formations based on a physical information neural network model, characterized in that, Includes the following steps: In lunar inertial coordinates, a non-spherical perturbation acceleration model is established for the physical loss function; Design a physical information neural network model, including: selecting a fully connected deep neural network as the network architecture of the model, and using a composite loss function that includes a data loss function and a physical loss function as the loss function of the fully connected deep neural network; Training a physical information neural network model; and Predicting the orbital state of satellite formations using a physical information neural network model.

2. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 1, characterized in that, Training a physical information neural network model includes: Simulation data is used as training data to input into a fully connected deep neural network to train a physical information neural network model. During the training process, the Adam optimizer and LBFGS optimizer are used sequentially to optimize the parameters of the fully connected deep neural network until the composite loss function value is lower than a preset threshold.

3. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 2, characterized in that, The training data is the orbital state of a satellite formation over a period of time, generated using simulation software. The orbital state includes three-axis position and three-axis velocity. The input of a fully connected deep neural network is time, and the output is the orbital state.

4. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 2, characterized in that, Multiple time points are randomly sampled within the predicted time interval as physical configuration points; At the physical configuration point, the predicted acceleration is calculated using the three-axis position predicted by the physical information neural network model, and the physical loss is calculated based on the physical loss function, which is obtained by embedding a non-spherical perturbation acceleration model.

5. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 1, characterized in that, Non-spherical perturbation acceleration model: ， in This represents the predicted acceleration as predicted by the model. It is the lunar gravitational constant. The distance between the satellite and the center of the moon. Perturbation acceleration caused by the non-spherical gravity of the Moon, three-axis position .

6. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 1, characterized in that, Establishing a non-spherical perturbation acceleration model for the physical loss function includes: In the lunar-centered inertial coordinate system, based on the three-axis position and three-axis speed Establish the equations of motion for the satellite: ， in, It is the lunar gravitational constant. The distance between the satellite and the center of the moon. This is the perturbation acceleration caused by the Moon's non-spherical gravity. , Represents the satellite's velocity vector. Represents the satellite's acceleration vector; Perturbation acceleration caused by the Moon's non-spherical gravity Calculations based on the 25th-order spherical harmonic function expansion include: Lunar gravitational potential function The definition is as follows: ， in, R It is the radius of the moon. These represent the lunar latitude and longitude of the satellite in the lunar inertial coordinate system. These are the normalized spherical harmonic coefficients of the lunar gravitational field. for n Step m Second-associative Legendre functions; By calculating the gradient of the potential function, the perturbation acceleration caused by the non-spherical gravity of the moon is obtained: ， Using the chain rule, the gradient of the potential function is transformed into a set of... The partial derivative is obtained. : ； D represents the distance between the spacecraft and the center of the moon. These represent the lunar latitude and longitude of the satellite in the lunar inertial coordinate system. , , These represent the unit basis vectors in the radial, latitude, and longitude directions in the spherical coordinate system, respectively. Then Projecting onto the Cartesian coordinate system using the coordinate transformation matrix: ； , , Let x, y, and z represent the components of the gradient of the potential function along the x, y, and z axes in the Cartesian coordinate system. , , These represent the components of the potential function gradient in the radial, dimensional, and longitude directions, respectively, in spherical coordinates. The analytical expressions for each directional component are: ， in, Indicates the radius of the moon. This represents the normalized associated Legendre polynomial. and These are the normalized spherical harmonic coefficients; Thus, the non-spherical perturbation acceleration model is obtained: ， in This represents the predicted acceleration as predicted by the model. This refers to the perturbation acceleration caused by the Moon's non-spherical gravity.

7. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 1, characterized in that, The fully connected deep neural network takes time as input and outputs the satellite's three-axis position and three-axis velocity, with the following mapping relationship: ， in, t For time scalar, The three-axis position of the satellite output by a fully connected deep neural network. and three-axis speed , This includes all parameters to be trained, including weights and biases; A fully connected deep neural network contains 7 hidden layers, each containing 60 neurons. The activation function of a fully connected deep neural network is the hyperbolic tangent function.

8. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 5, characterized in that, Composite loss function The formula is as follows: ， For physical loss weights, For data loss function, For physical loss function; When given Reference orbit points ,in X GT Given the satellite's reference orbital state, the data loss function is: ,in The orbital state is predicted by a fully connected deep neural network, including three-axis position and three-axis velocity; In the selected physical configuration points Above, the predicted velocity and predicted acceleration are calculated using automatic differentiation: ， in To predict speed, To predict acceleration; Substitute the predicted acceleration into the non-spherical perturbation acceleration model to calculate the acceleration residual: ， in, The gradient vector calculated for the real-time state; The physical loss function is: 。 9. The lunar satellite formation orbit prediction method based on a physical information neural network model according to claim 1, characterized in that, The order of the non-spherical perturbation acceleration model is at least 25.

10. A computer-readable storage medium having a computer program stored thereon, the computer program performing the steps of the method according to any one of claims 1-9 when executed by a processor.

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