Physical information constrained non-convex asteroid shape intelligent inversion method based on light variation curve

Abstract

According to the intelligent non-convex asteroid shape inversion method based on the optical variation curve and constrained by physical information, physical prior information is fused through a deep learning network (PINAS-Net), and rapid and accurate non-convex asteroid three-dimensional shape inversion is achieved. Specifically, light variation curve data and a scattering parameter c serve as input, features of all curves are extracted through a light variation curve feature extraction module (LCFEM), interaction features among multiple curves are captured through a Transform encoder, and 1024-dimensional global features are obtained; meanwhile, expanding a scalar scattering parameter c into 16-dimensional features, fusing the 16-dimensional features with global features, and importing the 16-dimensional features into the network as physical constraints; and rough point prediction is carried out based on the fused features, and a fine point cloud shape is obtained through a Transform decoder and three-layer up-sampling. The method provided by the invention is verified on observation data and simulation data of a plurality of asteroids (433 Eros, 9 Metis and 21 Luteria), and a reconstruction result is highly consistent with a reference model. Assessment indexes show that the intersection-to-union ratio (IoU) of the method for the non-convex region can reach 0.81, the Chamfer distance is 0.046, and compared with a traditional KTM method, the inversion speed and precision are remarkably improved. The method provides a new technical means for asteroid shape inversion and physical parameter estimation, and has an important planet defense value.

Description

Technical Field

[0001] This invention relates to the field of asteroid shape inversion, specifically to a method for inverting the three-dimensional shape of non-convex asteroids based on the fusion of light curve data and prior physical information. Background Technology

[0002] Asteroids preserve crucial information about the formation and evolution of the solar system, while also posing a potential impact threat to Earth. Therefore, accurately obtaining asteroid physical parameters (such as volume and density) is essential for scientific research and planetary defense. Among these parameters, asteroid shape is particularly critical, as it directly affects volumetric density estimation and is highly sensitive to thermal radiation effects (YORP, Yarkowski effect). Light curves are the primary data source for obtaining asteroid shape and rotation parameters. Existing research has established a mature theory and method for inverting convex shape light curves (hereinafter referred to as the KTM method), which has become the mainstream approach in the field. However, a significant number of asteroids in the solar system exhibit significant non-convexity, and their light curves at low solar phase angles can closely approximate those generated by convex models. This makes the shadowing effect of non-convex structures difficult to manifest in photometric data. Traditional inversion methods under the assumption of convexity struggle to capture non-convex features, but non-convex shapes affect the accuracy of volume estimation and further impact the accuracy of density and thermodynamic model predictions.

[0003] For the inversion of non-convex asteroid shapes, the SAGE method based on genetic algorithms has been proposed. This method uses random shape mutation iterative solutions to capture non-convex features in high-phase-angle data. However, such numerical iterative inversion methods have numerous parameters and extremely high computational complexity, making them unsuitable for processing large-scale sky survey data. In recent years, with the development of deep learning, it has become possible to quickly and accurately invert the 3D shape of asteroids from light curves. We propose a novel method that integrates physical information into a deep learning structure to achieve fast and accurate inversion of non-convex asteroid shapes. Summary of the Invention

[0004] To address the issues of low accuracy and long computation time in existing technologies for non-convex asteroid shape inversion, this invention proposes a deep learning method that incorporates physical priors—the Non-convex Asteroid Shape Inversion Network PINAS-Net.

[0005] A method for inverting the shape of a non-convex asteroid based on light curves and constrained by physical information includes the following steps: S1. Dataset Construction: Blender software was used to create 3D models of non-convex asteroids of different shapes. The Lommel–Seelige–Lambert scattering model was combined to simulate and generate a large number of light curves for training the PINAS-Net model. S2. Preprocessing and zero-filling of optical curves: The brightness of each optical curve is normalized and then filled with a simple zero vector to meet the fixed dimension requirements of the network input. S3. Physical Prior Labeling: Label the corresponding scattering parameter c (weighting factor of the scattering model) for each light curve, and use c as physical prior information and the light curve as input to the PINAS-Net network. S4. Constructing the PINAS-Net network: Build the PINAS-Net shape inversion network based on Transformer. The PINAS-Net structure is as follows: starting from the input layer, it sequentially passes through the optical curve feature extraction module, Transformer encoding module, coarse shape prediction module, Transformer decoding module, and Seedformer upsampling module; The light curve feature extraction module is used to extract local and global features of the light curve; the Transformer encoding module establishes long-range feature dependencies through a self-attention mechanism to generate an encoded feature sequence; the coarse shape prediction module generates a sparse shape point cloud of the asteroid based on the aggregated global features; the Transformer decoding module uses the query vector generated from the sparse point cloud to perform cross-attention interaction with the encoded feature sequence, and outputs an optimized point cloud feature sequence; the Seedformer decoding module uses the optimized feature sequence to guide the 3D point cloud to be upsampled step by step, and outputs the final 3D model of the asteroid. S5. Training and testing the PINAS-Net network: Input the light curve data obtained in step S2 and the scattering parameters obtained in step S3 into the PINAS-Net network. Train the network by calculating the geometric distance between the multi-level predicted point cloud and the real shape point cloud as the loss function to obtain the trained PINAS-Net network. Then, use the test set to verify the trained PINAS-Net network to obtain the final PINAS-Net network. S6. Shape Inversion and Evaluation: Input the light curve and scattering parameters of the asteroid to be inverted into the final PINAS-Net, output the three-dimensional point cloud model of the target asteroid, and evaluate the inversion accuracy using Chamfer distance, intersection-over-union ratio (IoU) of non-convex regions, and the fitting accuracy of the light curve.

[0006] Step 1 includes: S1.1 Construct a 3D shape library using existing convex models provided by the DAMIT website and non-convex models generated based on Blender scripts (generating various non-convex shapes by controlling random noise and geometric parameters); S1.2. For each shape model, under several randomly selected asteroid orbit conditions (Sun-Asteroid-Observer position), the Lommel-Seeliger and Lambert linear mixed scattering model is used to simulate and generate light curves. Scattering parameters are randomly sampled during generation to enhance data diversity, thereby obtaining a large-scale light curve sample. S1.3 Divide the light curve samples into training and test sets at a ratio of approximately 10:1.

[0007] The specific structures of the optical curve feature extraction module, Transformer encoding module, rough shape prediction module, Transformer decoding module, and Seedformer upsampling module are as follows: The light curve feature extraction module includes a cascaded input feature transformation unit, a max-pooling unit, and a global semantic interpolation unit. The input feature transformation unit uses a one-dimensional convolutional layer with a kernel size of 1 to map the feature dimension of each sampling point within each light curve in the input data from 7-dimensional to 8-dimensional and then to 256-dimensional. The temporal max-pooling unit performs max-pooling operations on the time dimension of each observation period block, compressing the 200-length temporal feature into a single feature and extracting the coordinates of the sun and earth as positional information. The global semantic interpolation unit calculates the mean of all valid light curve feature vectors in the current sample, transforms them through a fully connected layer to generate interpolated features, and fills the invalid zero-padding block positions with these interpolated features to form a complete feature tensor. Transformer encoding module: Contains physical parameter embedding layer and multi-layer stacked self-attention convolutional blocks; the self-attention convolutional blocks encode the superimposed positions of the feature node sequence and then perform long-range feature updates; at the end of the module, a global feature vector is generated through max pooling operation, and the scattering parameter feature vector mapped by the physical parameter embedding layer is concatenated to the end of the global feature vector to form global features; Rough Shape Prediction Module: Composed of a multi-layer fully connected neural network, it takes global features as input and directly regresses to predict the coordinates of a rough point cloud containing 224 points; The Transformer decoding module first constructs a query vector, which is composed of conditional global features and coarse point clouds. Then, through a multi-layer decoder block, it retrieves the encoded feature sequence (Key / Value) output by the Transformer encoding module using the query vector, and uses a cross-attention mechanism to output an optimized feature sequence containing geometric details. SeedFormer upsampling module: It adopts a cascaded multi-level upsampling structure. Each level uses the current sparse point cloud as the "seed point" and combines the optimized feature sequence output by the Transformer decoding module. Through feature expansion, local attention aggregation and coordinate offset regression, it generates a denser point cloud step by step according to a preset ratio.

[0008] The inversion accuracy is improved through explicit physical constraint mechanisms, which include: setting a physical parameter embedding layer, which includes a linear mapping layer and a normalization layer, to map the input scalar scattering parameters into a high-dimensional physical feature vector; before the network performs shape inversion, the physical feature vector is forced to be concatenated and fused with the global feature vector extracted from the light curve, so that the inputs of the rough shape prediction module and the Transformer decoding module both contain physical scattering information.

[0009] The loss function construction in step 5 includes: The point cloud similarity metric is defined using Chamfer distance, and Chamfer loss is calculated in the coarse, intermediate, and final output layers respectively, and the total loss is combined to train the network.

[0010] This invention introduces scattering parameters as physical information into the network, constraining the inversion process through physical information fusion, thereby ensuring that the obtained shape model conforms to physical laws and improving the reliability of the inversion. Specifically, this invention first constructs a model dataset and a light curve dataset, normalizes and fills the light curves to generate fixed-size input data; then, the light curves and scattering parameters are input into the PINAS-Net network. The network's Light Curve Feature Extraction (LCFEM) module independently processes each light curve, mapping 7-dimensional brightness and geometric information to a 256-dimensional feature vector and pooling it. The extracted curve features are interactively fused through a Transformer encoder to obtain a 1024-dimensional global light curve feature; simultaneously, the scalar scattering parameters are mapped to 16-dimensional physical features. After concatenating the scattering parameter features and the global light curve features, the Transformer decoder gradually generates the predicted shape: first, a coarse prediction of a 224-point point cloud is made, and then refined into a final 1024-point fine shape through three upsampling operations. During training, a loss function based on Chamfer distance is used to evaluate the errors between the coarse and refined shape point clouds and the real model. The method of this invention can directly predict non-convex shapes without complex iterative search, thereby greatly improving inversion efficiency.

[0011] Experimental verification using real observation data and simulated data has demonstrated that the method of this invention has achieved excellent results. For example... Figure 1As shown, in tests on the non-convex asteroid 433 Eros, the PINAS-Net reconstruction result has a distance of only 0.046 from the reference model Chamfer, and the intersection-over-union (IoU) of the non-convex region reaches 0.81, which is far superior to the traditional KTM method based on the convex assumption. The fitting error of the light curve is also improved. Tests on the main-belt asteroids 9 Metis and 21 Lutetia also obtained highly consistent shape reconstructions (Metis non-convex IoU=0.25, Chamfer=0.055; Lutetia non-convex IoU=0.50, Chamfer=0.050). In addition, tests on various simulated non-convex shapes (dumbbell, rod, sheet, etc.) show that the present invention can also effectively capture non-convex features.

[0012] The advantages of this invention are: breakthroughs in both inversion speed and accuracy, providing high-precision estimation of asteroid physical parameters, offering new technical means for asteroid shape inversion and physical parameter estimation, and having important planetary defense value. Attached Figure Description

[0013] Figure 1 The diagram illustrates the shape inversion results of the method of this invention for non-convex asteroids 433 Eros, 9 Metis, and 21 Lutetia. Figure (a) shows the shape inversion result of 433 Eros, with the upper half being the reference model and the lower half being the prediction model of this invention (Chamfer distance = 0.046, IoU = 0.81); (b) and (c) show the comparison between the reference model and the prediction model for 9 Metis (Chamfer = 0.055, IoU = 0.25) and 21 Lutetia (Chamfer = 0.050, IoU = 0.50), respectively.

[0014] Figure 2 The diagram illustrates the inversion results of the method of this invention on a partial non-convex asteroid model dataset. The diagram shows the 3D point cloud and mesh views of real asteroid models of different shapes (dumbbell-shaped, rod-shaped, sheet-shaped, and quasi-spherical) and the shapes predicted by this invention.

[0015] Figure 3 : Schematic diagram of the PINAS-Net deep learning network architecture. The diagram shows that the network of this invention receives standardized light curve data and scattering parameters, and outputs the three-dimensional point cloud shape of a non-convex asteroid through a hierarchical structure of light curve feature extraction module (LCFEM), Transformer encoder, scattering parameter feature module and Transformer decoder.

[0016] Figure 4: Schematic diagram of the Light Curve Feature Extraction Module (LCFEM). This module performs a one-dimensional convolution transformation on the 7-dimensional sampling information (brightness, solar coordinates, and observer coordinates) of a single light curve to obtain 256-dimensional features, and then performs max pooling to obtain a 256×1-dimensional tensor as the feature representation of the light curve. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0018] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0019] Please see Figure 1-4 A physical information-constrained intelligent inversion method for non-convex asteroid shapes based on light curves is proposed, which combines a Transformer network to construct a deep learning shape inversion model, PINAS-Net.

[0020] The specific process of the intelligent inversion method for non-convex asteroid shapes is as follows: Step 1: Constructing the training dataset. First, using the 3D modeling software Blender, a large number of asteroid shape models with different non-convex geometric features are randomly generated by writing scripts. For example... Figure 1 As shown, the number of models, the number of basic vertices, the level of detail, and the shape type (spherical, ellipsoidal, disk-shaped, rod-shaped, strongly non-convex, etc.) can be set in the script. To make the model more realistically resemble the surface of an asteroid, Perlin cloud noise is applied to the model surface to increase random details. Based on the eigenvalues ​​of the covariance matrix of the model geometry, its principal axis ratio can be calculated, and shape categories can be classified to obtain asteroid models with various non-convex shapes. Then, using these 3D models and the orbital parameters provided by the DAMIT database, the light curve under illumination conditions is simulated. The brightness is calculated according to the Lommel–Seeliger (LS) and Lambert (L) scattering models.

[0021] Where f(α) is the phase function, , Here, denoted by ...

[0022] Step 2: Preprocessing of Light Curves. For each simulated or observed light curve, first process the brightness values ​​of the sampling points... Divide by the average brightness of all sampling points on the light curve Normalization is achieved to obtain normalized brightness. Assuming each optical curve contains M sampling points, construct a sampling vector after normalization.

[0023] Since the actual number of optical curves and sampling points is not fixed, the data needs to be padded to fit the network input: for each curve containing... The light curve of each sampling point Add the blank at the end. zero vectors =(0,0,0,0,0,0,0), we get If a certain asteroid has fewer than 80 observed light curves, then add an array of all zeros: This brings the total to 80. The above filling process ensures that each input sample is uniform. Dimension. At this point, the entire input dataset can be represented as: (3) Provide a consistent, standardized input for PINAS-Net. For the representation of asteroid shapes, a 1024-point cloud is used to describe the shape, and the point set is represented as follows: .

[0024] Step 3: PINAS-Net Network Construction and Shape Prediction. The network structure is as follows: Figure 3 As shown, its main modules include: Light Curve Feature Extraction (LCFEM), Transformer encoder, scattering parameter feature module, and Transformer decoder. The specific process is as follows: First, the standardized light curve data... The data is input into the LCFEM in segments. The LCFEM performs feature transformation on the 7-dimensional sampled information of a single light curve: One-dimensional convolution is applied to expand the brightness and coordinate information into 256-dimensional features, followed by max pooling, representing the curve's features as a 256×1-dimensional tensor. The solar and observer coordinates (6-dimensional) of the light curve are independently expanded into 128-dimensional spatial features through convolution. After performing the above operations on each light curve, the 256×1 features of all light curves are stacked in the second dimension to form a light curve feature tensor with a dimension of 80×256. This tensor is then input into a multi-head self-attention Transformer encoder module, achieving interactive fusion of curve features under different observation geometries through an attention mechanism. The encoder outputs a 1024-dimensional global feature vector of the light curve (obtained by pooling the features of each curve). Simultaneously, the scattering parameter c is input into the scattering parameter feature module and mapped to a 16-dimensional feature vector using a simple fully connected network. The 1024-dimensional global features and 16-dimensional scattering features are concatenated to obtain a fused feature, which is used to physically constrain shape generation. Then, a Transformer decoder is used to decode and predict the fused feature: first, a coarse 3D point cloud of 224 points is predicted based on the fused feature; this coarse point cloud, along with the global features, is input into the decoder, and after three layers of upsampling, the final refined asteroid shape of 1024 points is iteratively generated. It is worth noting that the introduction of scattering parameters ensures that the shape output by the network conforms to physical constraints, thereby improving the accuracy of the inversion.

[0025] Step 4: Network Training and Loss Function Design. During network training, to balance computational efficiency and shape accuracy, the Chamfer distance is used as the loss function. The total loss is defined as follows:

[0026] in , and The Chamfer loss is calculated between the coarse point cloud, the first upsampled point cloud, and the final refined point cloud, respectively, and the ground truth point cloud. During training, the network was implemented using the PyTorch framework with the AdamW optimizer. The total number of training epochs was set to 400, the batch size for each iteration was 64, the initial learning rate was 0.001, and techniques such as synchronous BatchNorm were used to optimize training stability.

[0027] Step 5: Shape Inversion and Validation. The trained PINAS-Net is used to predict the shape of the target asteroid. This involves inputting the standardized light curve data and scattering parameters of the asteroid into the network to obtain a point cloud output representing its non-convex shape. The output point cloud can then be used for surface reconstruction (e.g., Poisson reconstruction) to obtain a 3D model. Experimental results show that the method of this invention can reconstruct non-convex surface features with high fidelity. For example, when inverting the actual asteroid 433 Eros, the reconstruction result of the model of this invention has a Chamfer distance of only 0.046 and an IoU of 0.81 in the non-convex region; the mean absolute error (MAE) of the light curve fitting is 0.047, which is less than 0.051 when using the KTM method for inversion. Experiments on 9 Metis and 21 Lutetia also yielded results highly consistent with the reference model (9 Metis Chamfer=0.055, IoU=0.25; 21 Lutetia Chamfer=0.050, IoU=0.50). Furthermore, the Chamfer distance is superior to traditional methods when measured on various simulated non-convex models. These results fully demonstrate the excellent performance and reliability of the physical information fusion method described in this invention for the inversion of non-convex asteroid shapes.

[0028] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for inverting the shape of a non-convex asteroid based on light curves with physical information constraints, comprising the following steps: S1. Dataset Construction: Blender software was used to create 3D models of non-convex asteroids of different shapes. The Lommel–Seelige–Lambert scattering model was combined to simulate and generate a large number of light curves for training the PINAS-Net model. S2. Preprocessing and zero-filling of optical curves: The brightness of each optical curve is normalized and then filled with a simple zero vector to meet the fixed dimension requirements of the network input. S3. Physical Prior Labeling: Label the corresponding scattering parameter c (weighting factor of the scattering model) for each light curve, and use c as physical prior information and the light curve as input to the PINAS-Net network. S4. Constructing the PINAS-Net network: Build the PINAS-Net shape inversion network based on Transformer. The PINAS-Net structure is as follows: starting from the input layer, it sequentially passes through the optical curve feature extraction module, Transformer encoding module, rough shape prediction module, Transformer decoding module, and Seedformer upsampling module; The light curve feature extraction module is used to extract local and global features of the light curve; the Transformer encoding module establishes long-range feature dependencies through a self-attention mechanism to generate an encoded feature sequence; the coarse shape prediction module generates a sparse shape point cloud of the asteroid based on the aggregated global features; the Transformer decoding module uses the query vector generated from the sparse point cloud to perform cross-attention interaction with the encoded feature sequence, and outputs an optimized point cloud feature sequence; the Seedformer decoding module uses the optimized feature sequence to guide the 3D point cloud to be upsampled step by step, and outputs the final 3D model of the asteroid. S5. Training and testing the PINAS-Net network: Input the light curve data obtained in step S2 and the scattering parameters obtained in step S3 into the PINAS-Net network. Train the network by calculating the geometric distance between the multi-level predicted point cloud and the real shape point cloud as the loss function to obtain the trained PINAS-Net network. Then, use the test set to verify the trained PINAS-Net network to obtain the final PINAS-Net network. S6. Shape Inversion and Evaluation: Input the light curve and scattering parameters of the asteroid to be inverted into the final PINAS-Net, output the three-dimensional point cloud model of the target asteroid, and evaluate the inversion accuracy using Chamfer distance, intersection-over-union ratio (IoU) of non-convex regions, and the fitting accuracy of the light curve.

2. The asteroid three-dimensional shape inversion method based on PINAS-Net network according to claim 1, characterized in that, Step 1 includes: S1.1 Construct a 3D shape library using existing convex models provided by the DAMIT website and non-convex models generated based on Blender scripts (generating various non-convex shapes through random noise and geometric parameter control). S1.

2. For each shape model, under several randomly selected asteroid orbit conditions (Sun-Asteroid-Observer position), the Lommel-Seeliger and Lambert linear mixed scattering model is used to simulate and generate light curves. Scattering parameters are randomly sampled during generation to enhance data diversity, thereby obtaining a large-scale light curve sample. S1.3 Divide the light curve samples into training and test sets at a ratio of approximately 10:

1.

3. The asteroid three-dimensional shape inversion method based on PINAS-Net network according to claim 1, characterized in that, The specific structures of the optical curve feature extraction module, Transformer encoding module, rough shape prediction module, Transformer decoding module, and Seedformer upsampling module are as follows: The light curve feature extraction module includes a cascaded input feature transformation unit, a max-pooling unit, and a global semantic interpolation unit. The input feature transformation unit uses a one-dimensional convolutional layer with a kernel size of 1 to map the feature dimension of each sampling point within each light curve in the input data from 7-dimensional to 8-dimensional and then to 256-dimensional. The temporal max-pooling unit performs max-pooling operations on the time dimension of each observation period block, compressing the 200-length temporal feature into a single feature and extracting the coordinates of the sun and earth as positional information. The global semantic interpolation unit calculates the mean of all valid light curve feature vectors in the current sample, transforms them through a fully connected layer to generate interpolated features, and fills the invalid zero-padding block positions with these interpolated features to form a complete feature tensor. The Transformer encoding module includes a physical parameter embedding layer and multiple stacked self-attention convolutional blocks. The self-attention convolutional blocks encode the superimposed positions of the feature node sequence and then perform long-range feature updates. At the end of the module, a global feature vector is generated through max pooling, and the scattering parameter feature vector mapped by the physical parameter embedding layer is concatenated to the end of the global feature vector to form global features. Rough Shape Prediction Module: Composed of a multi-layer fully connected neural network, it takes global features as input and directly regresses to predict the coordinates of a rough point cloud containing 224 points; The Transformer decoding module first constructs a query vector, which is composed of conditional global features and coarse point clouds. Then, through a multi-layer decoder block, it retrieves the encoded feature sequence (Key / Value) output by the Transformer encoding module using the query vector, and uses a cross-attention mechanism to output an optimized feature sequence containing geometric details. SeedFormer upsampling module: It adopts a cascaded multi-level upsampling structure. Each level uses the current sparse point cloud as the "seed point" and combines the optimized feature sequence output by the Transformer decoding module. Through feature expansion, local attention aggregation and coordinate offset regression, it generates a denser point cloud step by step according to a preset multiplier.

4. The method according to claim 3, characterized in that, The inversion accuracy is improved by using explicit physical constraint mechanisms, specifically including: setting a physical parameter embedding layer, which includes a linear mapping layer and a normalization layer, to map the input scalar scattering parameters into a high-dimensional physical feature vector; before the network performs shape inversion, the physical feature vector is forced to be concatenated and fused with the global feature vector extracted from the light curve, so that the inputs of the rough shape prediction module and the Transformer decoding module both contain physical scattering information.

5. The asteroid three-dimensional shape inversion method based on PINAS-Net network according to claim 1, characterized in that, The loss function construction in step 5 includes: The point cloud similarity metric is defined using Chamfer distance, and Chamfer loss is calculated in the coarse, intermediate, and final output layers respectively, and the total loss is combined to train the network.

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