Method for inverting asteroid gravity field and internal structure based on machine learning

Abstract

The invention provides a method for inverting a gravitational field and an internal structure of an asteroid based on machine learning, which is characterized in that when a planet deep neural gravitational field network model based on machine learning is trained, the internal density distribution of the asteroid is speculated according to external observation information, and the process is also called gravity inversion. According to the invention, gravity inversion is carried out by using the planetary deep neural gravity field model based on deep learning, and prior density constraints in various forms can be carried out through a loss function mode, so that the search space of gravity inversion optimization is reduced, and the stability and accuracy of gravity inversion are improved. The planetary deep neural gravity field model can integrate multi-source gravity observation data processing, and can simultaneously encode a gravity field model, an internal structure model and a three-dimensional shape model of an asteroid. According to the method, the scientific value and practical significance of planet exploration are improved, and beneficial theoretical support and practical guidance are provided for deep space exploration.

Description

Technical Field

[0001] The present invention relates to the field of deep space exploration technology, and in particular to a method for inverting the gravity field and internal structure of an asteroid based on machine learning. Background Art

[0002] There are still many challenges in the study of the gravity field and internal structure of asteroids. The most effective and reliable way to measure the gravity field of an asteroid is to conduct on-site detection by launching a spacecraft. Since the United States launched the first asteroid probe in December 1978, humans have successfully launched and completed more than 20 asteroid probes with corresponding detection mission targets, and less than 30 asteroids have been detected. For the vast majority of asteroids, ground-based optical observations are limited. It can be said that humans know very little about asteroids. In addition, asteroids have weak gravity and are affected by the sun and other celestial bodies. There are a series of complex dynamic mechanisms, which leads to their diverse dynamic environments, greatly increasing the difficulty of planning and implementing asteroid exploration missions.

[0003] At present, the gravity observation data of asteroid probes are mainly ground-based two-way Doppler velocity measurement signals, and there is little practice in the fusion processing of multi-source observation data (such as lidar, images, etc.) of other payloads on the probe. How to process the multi-source data of the probe to invert the internal distribution characteristics of the asteroid is also a hot spot and difficulty in related research. When modeling the asteroid gravity field, due to the irregular shape of the asteroid, the use of spherical harmonic series expansion may not converge. When using gravity data to invert the internal structure, there is also non-uniqueness of the inversion results. Therefore, it is not possible to uniquely determine the internal structure of the asteroid using only the gravity field model. Summary of the invention

[0004] The present invention provides a method for inverting the gravity field and internal structure of an asteroid based on machine learning, so as to solve the defects existing in the prior art.

[0005] In a first aspect, the present invention provides a method for inverting the gravity field and internal structure of an asteroid based on machine learning, comprising: Acquire a measured gravity field dataset and a terrain dataset of a sample planet, and preprocess the measured gravity field dataset and the terrain dataset to obtain a training set and a test set; Constructing a planetary deep neural gravity field model, wherein the planetary deep neural gravity field model includes a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics, and the planetary internal structure characteristics; Using the training set to train the planetary deep neural gravity field model to obtain an initially trained planetary deep neural gravity field model; Inverting the test set using the initially trained planetary deep neural gravity field model to obtain a trained planetary deep neural gravity field model; The measured gravity field data and topographic data of the planet to be measured are input into the trained planetary deep neural gravity field model, and the inversion results of the planetary gravity field and internal structure are output.

[0006] According to a method for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention, the measured gravity field dataset and the terrain dataset are preprocessed to obtain a training set and a test set, including: Formatting the measured gravity field dataset and the terrain dataset into PyTorch tensors and performing dimensionless processing; The processed data is divided into the training set and the test set according to a preset division ratio.

[0007] According to a method for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention, a planetary deep neural gravity field model is constructed, including: A deep neural network is used to obtain a relationship function between gravitational acceleration and position, wherein the relationship function has solutions outside the planet, on the surface of the planet, and inside the planet and is differentiable for any order; Determine the external gravity field characteristics of the planet, the surface shape characteristics of the planet, and the internal structure characteristics of the planet by using the automatic differentiation characteristics of the deep neural network; The loss function is constructed which is jointly constrained by the external gravity field characteristics of the planet, the surface shape characteristics of the planet and the internal structure characteristics of the planet.

[0008] According to a method for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention, the loss function includes: Determine that the planetary deep neural gravity field model is a fully connected network based on a sinusoidal activation function, and the loss function for:

[0009]

[0010]

[0011]

[0012]

[0013] in, 、 、 、 is the weight of each constraint, is the external observation constraint, is the loss function constrained by the physical law, is the range density constraint loss function, is the spherical harmonic coefficient constraint loss function, is the expression of the fully connected network, is the number of spherical harmonic coefficients, , are the minimum and maximum values ​​of the internal density constraints, respectively. is the constrained interior density of the asteroid, is the straight-line distance from the asteroid surface to the observation point, is the measured spherical harmonic coefficient vector, Predict the spherical harmonic coefficient vector for the network.

[0014] According to a method for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention, the planetary deep neural gravity field model is trained using the training set to obtain an initially trained planetary deep neural gravity field model, including: Without considering the spherical harmonic coefficient constraint, the internal density is constrained to the average density, and a pre-trained model representing the gravity field of a homogeneous asteroid is obtained; Spherical harmonic coefficient constraints and normal density change constraints are added to the pre-trained model, and the internal density range constraints are adjusted to ~ ; When the loss function When the minimum is reached, the training ends and the initially trained planetary deep neural gravity field model is obtained.

[0015] In a second aspect, the present invention also provides a system for inverting the gravity field and internal structure of an asteroid based on machine learning, comprising: An acquisition module is used to acquire a measured gravity field dataset and a terrain dataset of a sample planet, and preprocess the measured gravity field dataset and the terrain dataset to obtain a training set and a test set; A construction module for constructing a planetary deep neural gravity field model, wherein the planetary deep neural gravity field model includes a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics, and the planetary internal structure characteristics; A training module, used to train the planetary deep neural gravity field model using the training set to obtain an initially trained planetary deep neural gravity field model; An inversion module, used to invert the test set using the initially trained planetary deep neural gravity field model to obtain a trained planetary deep neural gravity field model; The output module is used to input the measured gravity field data and terrain data of the planet to be measured into the trained planetary deep neural gravity field model, and output the inversion results of the planetary gravity field and internal structure.

[0016] In a third aspect, the present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements any of the methods described above for inverting the gravity field and internal structure of an asteroid based on machine learning.

[0017] In a fourth aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a method for inverting the gravity field and internal structure of an asteroid based on machine learning as described in any one of the above.

[0018] The method for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention uses a planetary deep neural gravity field model based on deep learning for gravity inversion. Compared with traditional methods, it can perform various forms of prior density constraints by means of loss functions, thereby reducing the search space for gravity inversion optimization and improving the stability and accuracy of gravity inversion. The planetary deep neural gravity field model can integrate multi-source gravity observation data processing, and can simultaneously encode the gravity field model, internal structure model and three-dimensional shape model of the asteroid. The present invention will improve the scientific value and practical significance of planetary exploration, and provide useful theoretical support and practical guidance for deep space exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0020] Figure 1 It is a flow chart of the method for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention; Figure 2 It is a flow chart of asteroid deep neural gravity field model training provided by the present invention; Figure 3 This is a flow chart of the gravity field solution of the Bennu asteroid provided by the present invention; Figure 4It is a schematic diagram of the structure of the system for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention; Figure 5 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] In view of the shortcomings of the prior art, the present invention provides a method for inverting the gravity field and internal structure of an asteroid based on machine learning, which can perform various forms of prior density constraints through loss functions, thereby reducing the search space of gravity inversion optimization and improving the stability and accuracy of gravity inversion.

[0023] Figure 1 is a flow chart of a method for inverting asteroid gravity field and internal structure based on machine learning provided by an embodiment of the present invention, such as Figure 1 As shown, including: Step 100: obtaining a measured gravity field dataset and a terrain dataset of a sample planet, and preprocessing the measured gravity field dataset and the terrain dataset to obtain a training set and a test set; Step 200: constructing a planetary deep neural gravity field model, wherein the planetary deep neural gravity field model includes a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics, and the planetary internal structure characteristics; Step 300: using the training set to train the planetary deep neural gravity field model to obtain an initially trained planetary deep neural gravity field model; Step 400: Invert the test set using the initially trained planetary deep neural gravity field model to obtain a trained planetary deep neural gravity field model; Step 500: Input the measured gravity field data and terrain data of the planet to be measured into the trained planetary deep neural gravity field model, and output the inversion results of the planetary gravity field and internal structure.

[0024] Specifically, an embodiment of the present invention first prepares the measured gravity field data and terrain data set of the planet for training and testing, and constructs a planetary deep neural gravity field model. The planetary deep neural gravity field model uses a deep neural network to express the gravity field acceleration as a function of position. There are solutions outside the asteroid, on the surface of the asteroid, and inside the asteroid, and they are differentiable for any order. The planetary deep neural gravity field network is trained using the training set data. During the network training process, the automatic differentiation characteristics of the neural network are used to construct a loss function through external gravity observations, asteroid shape models, physical equations, prior internal density assumptions and other information to jointly constrain the planetary deep neural gravity field neural network. Finally, the trained network model is used to invert the planetary gravity field on the test set data.

[0025] It is understandable that when training a planetary deep neural gravity field network model based on machine learning, the internal density distribution of the asteroid is actually inferred based on external observation information. This process is also called gravity inversion. Using a planetary deep neural gravity field model based on deep learning for gravity inversion, various forms of prior density constraints can be performed by means of loss functions, thereby reducing the search space for gravity inversion optimization and improving the stability and accuracy of gravity inversion. The planetary deep neural gravity field model can integrate multi-source gravity observation data processing, and can simultaneously encode the gravity field model, internal structure model and three-dimensional shape model of the asteroid. The present invention will improve the scientific value and practical significance of planetary exploration, and provide useful theoretical support and practical guidance for deep space exploration.

[0026] Based on the above embodiment, step 100 includes preparing measured gravity field data and terrain data sets of the planet for training and testing.

[0027] The measured gravity field data and terrain data of the planet are formatted into PyTorch tensors so that they can be used for training. And dimensionless processing is performed, which can eliminate the units of the original physical quantities, simplifying the problem and making it easier to compare and analyze.

[0028] Step 200 includes constructing a deep neural gravity field model of the planet.

[0029] The planetary deep neural gravity field model uses a deep neural network to express the gravity field acceleration as a function of position. Solutions exist outside the asteroid, on the surface of the asteroid, and inside the asteroid, and are differentiable for any order. During the network training process, the automatic differentiation characteristics of the neural network are used to construct a loss function through external gravity observations, asteroid shape models, physical equations, prior internal density assumptions, and other information to jointly constrain the planetary deep neural gravity field model neural network. The training process is as follows: Figure 2 shown.

[0030] Step 300 includes training a planetary deep neural gravity field network using the training set data.

[0031] Firstly, a homogeneous spherical asteroid was considered to evaluate the model performance. Secondly, an irregularly shaped double-layer heterogeneous asteroid was constructed to further analyze the model's ability to deduce the internal structure. Finally, the measured gravity data of the asteroid were processed.

[0032] In order to select the truncation order of the coefficients, the signal-to-noise ratio of the measured spherical harmonic gravity field coefficients must first be analyzed. That is, the ratio of the measured gravity coefficients to the coefficient uncertainty is calculated. In addition, the terrain model is expanded into spherical harmonic coefficients according to the homogeneous density hypothesis and subtracted from the measured coefficients. The signal-to-noise ratio of the coefficients carrying heterogeneous information can be obtained by comparing the measured coefficient uncertainty. Finally, the difference between the spherical harmonic coefficients of the homogeneous terrain model and the measured gravity field is analyzed, and considering the computational cost, the 4th-order measured gravity field is finally selected to train the planetary deep neural gravity field model and invert the internal structure of the asteroid. In addition, the constraint of spherical harmonic coefficients being 0 is also considered in the training of the planetary deep neural gravity field model, and their respective uncertainties are set to the corresponding spherical harmonic coefficient values ​​after the homogeneous shape model is expanded.

[0033] (1) (2) (3) (4) (5) Where: 、 、 、 is the weight of each constraint item. During training, the importance of each constraint item can be adjusted by adjusting the weight. is the external observation constraint, Constrained by the laws of physics, is the loss function of range density constraint, is the spherical harmonic coefficient constraint, is the expression of the fully connected network, is the number of spherical harmonic coefficients, , are the minimum and maximum values ​​of the internal density constraints, is the constrained interior density of the asteroid, is the straight-line distance from the asteroid surface to the observation point, is the measured spherical harmonic coefficient vector, Predict the spherical harmonic coefficient vector for the network. The loss function terms are in the outer space of the asteroid 、 Interior Space and global space U Sampling is calculated.

[0034] For the planetary deep neural gravity field model of the asteroid, the global physical law constraint of equation (2), the density range constraint of equation (3), the spherical harmonic coefficient constraint of equation (4), and the normal density change constraint of equation (5) are considered for model training. The training adopts a coarse-to-fine approach. First, the spherical harmonic coefficient constraint is not considered, and the internal density is constrained to the average density, so that a pre-trained model representing the gravity field of the homogeneous asteroid can be obtained. Then, the spherical harmonic coefficient constraint and the normal density change constraint are added to the pre-trained model, and the internal density range constraint is adjusted to ~ , allowing it to produce heterogeneous internal density distribution, and after training is completed, the final planetary deep neural gravity field model can be obtained.

[0035] It should be noted that there is no gravity observation information in the interior of the asteroid, so it is impossible to directly constrain the observed value of the acceleration output by the network. However, the expression of the corresponding acceleration field can be obtained based on the fact that the gravitational potential of the asteroid satisfies the Poisson equation inside, and it can be concluded that the divergence of the acceleration field inside the asteroid is directly related to the internal density, so some prior assumptions can be made for the internal density inferred by the network. According to the expression of the gravitational potential in the polyhedron model and the orthogonal relationship of the spherical harmonic coefficients, the predicted value of the gravity field coefficient can be obtained by volume integration of the density value output by the network. Finally, by comparing the difference between the spherical harmonic coefficients predicted by the network and the measured coefficients, and considering the covariance matrix of the measured coefficients, the loss function of the spherical harmonic coefficient constraint is obtained. In addition to the measured spherical harmonic coefficients, the value of the constraint and its uncertainty can be set according to the prior knowledge of the asteroid and the physical meaning of each coefficient, and other forms of constraints can be set according to the different characteristics of the target to better train the network.

[0036] During the training process of the planetary deep neural gravity field network, the appropriate spherical harmonic coefficient cutoff order is selected to generate the gravity field model. The training is conducted in a coarse-to-fine manner. When the overall loss function L reaches the minimum, the training ends and the final planetary deep neural gravity field network model is obtained.

[0037] Finally, the trained network model is used to invert the planetary gravity field on the test set data.

[0038] by Figure 3The solution of the gravity field of the Bennu asteroid shown in the figure is used as an example to illustrate. First, the dynamic modeling is performed. The prior parameters are input to obtain the motion equation and the variational equation. The numerical integration is obtained from the motion equation and the variational equation, and then converted into a state vector, a state transfer matrix and a sensitivity matrix. Further metrology modeling is performed, and then the measured observations are input to obtain the observation residuals and the observation partial derivatives. Then the error equation is established, and the least squares method is used to solve the parameter correction value. If the value meets the convergence condition, the least squares method is used to obtain the corrected parameters and the parameter covariance. Otherwise, the iterative solution is performed again, and the dynamic modeling is performed again.

[0039] The system for inverting the gravity field and internal structure of an asteroid based on machine learning provided by the present invention is described below. The system for inverting the gravity field and internal structure of an asteroid based on machine learning described below and the method for inverting the gravity field and internal structure of an asteroid based on machine learning described above can be referenced to each other.

[0040] Figure 4 is a schematic diagram of the structure of a system for inverting the gravity field and internal structure of an asteroid based on machine learning provided by an embodiment of the present invention, such as Figure 4 As shown, it includes: an acquisition module 41, a construction module 42, a training module 43, an inversion module 44 and an output module 45, wherein: The acquisition module 41 is used to acquire the measured gravity field data set and terrain data set of the sample planet, and pre-process the measured gravity field data set and the terrain data set to obtain a training set and a test set; the construction module 42 is used to construct a planetary deep neural gravity field model, and the planetary deep neural gravity field model includes a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics and the planetary internal structure characteristics; the training module 43 is used to train the planetary deep neural gravity field model using the training set to obtain an initially trained planetary deep neural gravity field model; the inversion module 44 is used to invert the test set using the initially trained planetary deep neural gravity field model to obtain a trained planetary deep neural gravity field model; the output module 45 is used to input the measured gravity field data and terrain data of the planet to be measured into the trained planetary deep neural gravity field model, and output the inversion results of the planetary gravity field and internal structure.

[0041] Figure 5 An example of a physical structure diagram of an electronic device is shown in FIG. Figure 5As shown, the electronic device may include: a processor (processor) 510, a communication interface (Communications Interface) 520, a memory (memory) 530 and a communication bus 540, wherein the processor 510, the communication interface 520, and the memory 530 communicate with each other through the communication bus 540. The processor 510 can call the logic instructions in the memory 530 to execute a method for inverting the gravity field and internal structure of an asteroid based on machine learning, the method comprising: obtaining a measured gravity field dataset and a terrain dataset of a sample planet, preprocessing the measured gravity field dataset and the terrain dataset to obtain a training set and a test set; constructing a planetary deep neural gravity field model, the planetary deep neural gravity field model comprising a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics and the planetary internal structure characteristics; using the training set to train the planetary deep neural gravity field model to obtain an initially trained planetary deep neural gravity field model; using the initially trained planetary deep neural gravity field model to invert the test set to obtain a trained planetary deep neural gravity field model; inputting the measured gravity field data and terrain data of the planet to be measured into the trained planetary deep neural gravity field model, and outputting the inversion results of the planetary gravity field and internal structure.

[0042] In addition, the logic instructions in the above-mentioned memory 530 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0043] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the method for inverting the asteroid gravity field and internal structure based on machine learning provided by the above-mentioned methods, the method comprising: obtaining a measured gravity field dataset and a terrain dataset of a sample planet, preprocessing the measured gravity field dataset and the terrain dataset to obtain a training set and a test set; constructing a planetary deep neural gravity field model, the planetary deep neural gravity field model comprising a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics and the planetary internal structure characteristics; using the training set to train the planetary deep neural gravity field model to obtain an initially trained planetary deep neural gravity field model; using the initially trained planetary deep neural gravity field model to invert the test set to obtain a trained planetary deep neural gravity field model; inputting the measured gravity field data and terrain data of the planet to be measured into the trained planetary deep neural gravity field model, and outputting the inversion result of the planetary gravity field and internal structure. The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0044] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for inverting the gravity field and internal structure of an asteroid based on machine learning, characterized in that: include: Acquire a measured gravity field dataset and a terrain dataset of a sample planet, and preprocess the measured gravity field dataset and the terrain dataset to obtain a training set and a test set; Constructing a planetary deep neural gravity field model, wherein the planetary deep neural gravity field model includes a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics, and the planetary internal structure characteristics; Using the training set to train the planetary deep neural gravity field model to obtain an initially trained planetary deep neural gravity field model; Inverting the test set using the initially trained planetary deep neural gravity field model to obtain a trained planetary deep neural gravity field model; The measured gravity field data and topographic data of the planet to be measured are input into the trained planetary deep neural gravity field model, and the inversion results of the planetary gravity field and internal structure are output.

2. The method for inverting the gravity field and internal structure of an asteroid based on machine learning according to claim 1, characterized in that: Preprocessing the measured gravity field dataset and the terrain dataset to obtain a training set and a test set includes: Formatting the measured gravity field dataset and the terrain dataset into PyTorch tensors and performing dimensionless processing; The processed data is divided into the training set and the test set according to a preset division ratio.

3. The method for inverting the gravity field and internal structure of an asteroid based on machine learning according to claim 1, characterized in that: Construct a deep neural gravity field model of the planet, including: A deep neural network is used to obtain a relationship function between gravitational acceleration and position, wherein the relationship function has solutions outside the planet, on the surface of the planet, and inside the planet and is differentiable for any order; Determine the external gravity field characteristics of the planet, the surface shape characteristics of the planet, and the internal structure characteristics of the planet by using the automatic differentiation characteristics of the deep neural network; The loss function is constructed which is jointly constrained by the external gravity field characteristics of the planet, the surface shape characteristics of the planet and the internal structure characteristics of the planet.

4. The method for inverting the gravity field and internal structure of an asteroid based on machine learning according to claim 1, characterized in that: The loss function includes: Determine that the planetary deep neural gravity field model is a fully connected network based on a sinusoidal activation function, and the loss function for: in, 、 、 、 is the weight of each constraint, is the external observation constraint, is the loss function constrained by the physical law, is the range density constraint loss function, is the spherical harmonic coefficient constraint loss function, is the expression of the fully connected network, is the number of spherical harmonic coefficients, , are the minimum and maximum values ​​of the internal density constraints, respectively. is the constrained interior density of the asteroid, is the straight-line distance from the asteroid surface to the observation point, is the measured spherical harmonic coefficient vector, Predict the spherical harmonic coefficient vector for the network.

5. The method for inverting the gravity field and internal structure of an asteroid based on machine learning according to claim 4, characterized in that: The planetary deep neural gravity field model is trained using the training set to obtain an initially trained planetary deep neural gravity field model, including: Without considering the spherical harmonic coefficient constraint, the internal density is constrained to the average density, and a pre-trained model representing the gravity field of a homogeneous asteroid is obtained; Spherical harmonic coefficient constraints and normal density change constraints are added to the pre-trained model, and the internal density range constraints are adjusted to ~ ; When the loss function When the minimum is reached, the training ends and the initially trained planetary deep neural gravity field model is obtained.

6. A system for inverting the gravity field and internal structure of an asteroid based on machine learning, characterized in that: include: An acquisition module is used to acquire a measured gravity field dataset and a terrain dataset of a sample planet, and preprocess the measured gravity field dataset and the terrain dataset to obtain a training set and a test set; A construction module for constructing a planetary deep neural gravity field model, wherein the planetary deep neural gravity field model includes a loss function jointly constrained by the planetary external gravity field characteristics, the planetary surface shape characteristics, and the planetary internal structure characteristics; A training module, used to train the planetary deep neural gravity field model using the training set to obtain an initially trained planetary deep neural gravity field model; An inversion module, used to invert the test set using the initially trained planetary deep neural gravity field model to obtain a trained planetary deep neural gravity field model; The output module is used to input the measured gravity field data and terrain data of the planet to be measured into the trained planetary deep neural gravity field model, and output the inversion results of the planetary gravity field and internal structure.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the method for inverting the gravity field and internal structure of an asteroid based on machine learning as described in any one of claims 1 to 5 is implemented.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for inverting the gravity field and internal structure of an asteroid based on machine learning as described in any one of claims 1 to 5 is implemented.

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