Star material surface charging potential calculation method based on Bayesian PINN
By constructing a Bayesian physical information neural network and integrating electrostatic field equations with a Bayesian inference framework, the efficiency and accuracy issues of calculating surface charging potential of spacecraft materials were solved, achieving efficient and reliable potential prediction and uncertainty quantification, which is applicable to spacecraft design and safety assessment.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2025-12-31
- Publication Date
- 2026-04-10
Smart Images
Figure CN121835409A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of aircraft application technology, and more specifically, to a method for calculating the surface charging potential of space-borne materials based on Bayesian PINN. Background Technology
[0002] In the fields of spacecraft design and space environment effect assessment, accurately calculating the charging potential of spacecraft materials on their surfaces under space plasma conditions is crucial for preventing electrostatic discharge, ensuring spacecraft electrical safety, and extending their lifespan. Currently, calculation methods in this field mainly rely on three technical approaches, but all three have significant limitations: Numerical simulation methods, such as the finite element method or the boundary element method, can handle complex geometries, but they consume huge amounts of computational resources and are particularly inefficient when solving three-dimensional transient or nonlinear problems, making them difficult to use for large-scale design parameter scanning or rapid evaluation.
[0003] Analytical solutions rely on highly simplified geometric and physical assumptions (such as infinitely large planes and homogeneous materials), which cannot truly reflect the complex surface structure, material inhomogeneity, and dynamic space environment of spacecraft. As a result, the accuracy and reliability of their calculation results are insufficient in practical engineering applications.
[0004] While experimental measurement methods can provide direct data, space environment simulation experimental equipment is expensive and time-consuming, and it is difficult to reproduce the real multi-scale and multi-physics coupling conditions in space, so it cannot be widely used as a conventional design tool.
[0005] In recent years, machine learning-based surrogate model methods have been introduced to improve computation speed. However, purely data-driven models rely heavily on high-quality, comprehensive training data, and their predictions often lack physical consistency guarantees, which may lead to predictions that violate basic physical laws. In scenarios where data is scarce or extrapolation is required, their reliability drops sharply.
[0006] Therefore, there is an urgent need in this field for a new computational method that can ensure both computational efficiency and physical consistency, and provide uncertainty quantification analysis of the computational results, in order to support the requirements for precision and reliability in spacecraft material selection, protection design, and on-orbit safety assessment. Summary of the Invention
[0007] The problem solved by this invention is one or more of the aforementioned related technical problems.
[0008] To address the above problems, this invention provides a method for calculating the surface charging potential of space-borne materials based on Bayesian PINN, comprising: A physical information neural network is constructed, and the Bayesian physical information neural network model is trained by integrating the constraints of the electrostatic field equation with the Bayesian inference framework to obtain a trained Bayesian physical information neural network model. Obtain spatial coordinate data of the surface of the material used in the target star; The spatial coordinate data is input into the trained Bayesian physical information neural network model to obtain the predicted potential distribution on the surface of the target star material and the corresponding confidence interval.
[0009] Optionally, the training process of the Bayesian physical information neural network model includes: Step T1: Acquire training data, including historical spatial coordinate data of the surface of the space-borne material and corresponding potential measurement data or simulation data; Step T2: Construct the physical information neural network. The input of the physical information neural network is spatial coordinate data, and the output is the corresponding potential prediction value. Step T3: The electrostatic field equation and boundary conditions are introduced as physical constraints into the loss function of the physical information neural network; Step T4: Introduce the Bayesian inference framework and perform posterior distribution estimation on the network parameters of the physical information neural network to achieve uncertainty quantification. Step T5: Train the physical information neural network based on the training data, optimize the network parameters of the physical information neural network, and obtain the trained Bayesian physical information neural network model.
[0010] Optionally, in step T4, the network parameters are sampled a posteriori based on the Markov chain Monte Carlo method.
[0011] Optionally, in step T5, spatial coordinate data for calculating the loss function is dynamically selected based on an adaptive sampling strategy.
[0012] Optionally, the loss function includes a physical residual term based on the electrostatic field equation and a regularization term introduced by Bayesian inference.
[0013] Optionally, the physical residual terms of the electrostatic field equations include: ; Where N is the number of training data points, and i is the i-th training data point. Let ε be the potential, ρ be the dielectric constant of the material, ρ be the charge density, and ▽ be the gradient operator.
[0014] Optionally, the electrostatic field equations include: ; in, Let ε(r) be the potential, ε(r) be the dielectric constant of the material at point r, ρ(r) be the charge density, and ▽ be the gradient operator.
[0015] Optionally, the boundary conditions include at least one of potential boundary conditions or electric field boundary conditions.
[0016] Optionally, the neural network includes at least one hidden layer and a ReLU activation function.
[0017] The beneficial effects of the Bayesian PINN-based method for calculating the surface charging potential of space-borne materials in this invention are: By constructing and applying a physical information neural network (Bayesian PINN) that integrates the physical constraints of electrostatic field equations with a Bayesian inference framework, we have achieved efficient and high-precision calculation of the surface charging potential of space-borne materials and simultaneously provided the quantification of the uncertainty of the prediction results. Its beneficial effects are mainly reflected in the following aspects: First, it significantly improves the accuracy and reliability of calculations. The model incorporates the fundamental laws of electrostatics during training, ensuring that the prediction results strictly conform to physical laws and avoiding the physical inconsistencies that may occur with purely data-driven models. Second, it enables uncertainty assessment of potential predictions. With the help of a Bayesian inference framework, the model not only outputs a single potential distribution value but also provides the confidence interval for each prediction point, thereby providing risk perception capabilities for the electrical safety design of spacecraft materials and helping engineers make more robust decisions under conditions of multiple uncertainties such as material properties and space environment. Third, it has superior applicability and computational efficiency. Once the model training is completed, for new material surface geometries or boundary conditions, only spatial coordinates need to be input to quickly obtain the potential distribution and confidence interval, avoiding the cumbersome process of remodeling and large-scale calculations required by traditional numerical methods for each new problem. It is especially suitable for rapid analysis and design iteration in complex spacecraft surfaces and variable space environment scenarios.
[0018] To address the above problems, this invention provides a device for calculating the surface charging potential of space-borne materials based on Bayesian PINN, comprising: The construction unit is used to construct a Bayesian physical information neural network model. The Bayesian physical information neural network model is trained by integrating the constraints of the electrostatic field equation with the Bayesian inference framework to obtain a trained Bayesian physical information neural network model. The acquisition unit is used to acquire spatial coordinate data of the surface of the target star's material. The processing unit is used to input the spatial coordinate data into the trained Bayesian physical information neural network model to obtain the potential distribution prediction results and corresponding confidence intervals on the surface of the target star material.
[0019] The Bayesian PINN-based surface charging potential calculation device for space-borne materials described in this invention has the same advantages over existing technologies as the Bayesian PINN-based surface charging potential calculation method for space-borne materials, and will not be repeated here. Attached Figure Description
[0020] Figure 1 This is a flowchart illustrating a method for calculating the surface charging potential of space-borne materials based on Bayesian PINN, according to an embodiment of the present invention. Figure 2 This is a flowchart illustrating the training process of a Bayesian physical information neural network model according to an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the change of the loss function during model training according to an embodiment of the present invention; Figure 4 This is a schematic diagram showing the comparison between a potential distribution prediction result and actual experimental measurement data according to an embodiment of the present invention. Detailed Implementation
[0021] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.
[0022] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.
[0023] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.
[0024] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".
[0025] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.
[0026] Traditional methods share a common shortcoming: they cannot provide a quantitative assessment of the uncertainty of the calculation results. In practical engineering, material parameters, space environment parameters, and boundary conditions all exhibit a certain degree of uncertainty or variability. Traditional methods can only provide deterministic, single numerical results, lacking a measure of the reliability of the results. This makes it difficult for designers to make robust decisions when facing potential risks.
[0027] To address the problems existing in the aforementioned related technologies, embodiments of the present invention provide a method for calculating the surface charging potential of space-borne materials based on Bayesian PINN.
[0028] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for calculating the surface charging potential of space-borne materials based on Bayesian PINN, comprising: Step S100: Construct a physical information neural network. Train the Bayesian physical information neural network model by fusing electrostatic field equation constraints with a Bayesian inference framework to obtain a trained Bayesian physical information neural network model.
[0029] Specifically, this step aims to create and optimize a Bayesian Physics-Informed Neural Network (PINN) model specifically for calculating the surface charging potential of spaceborne materials. This process is not simply data fitting, but rather the construction of a deep learning framework that integrates prior physical knowledge with the ability to quantify Bayesian uncertainty. Its core process can be summarized as follows: Physical Information Neural Network (PINN) framework established: First, a computational model with a feedforward neural network as its core is constructed, whose input is the spatial coordinates of the material surface (such as x, y, z).
[0030] The key is to directly encode the governing equations (such as the Poisson equation) and boundary conditions (such as surface potential or electric field constraints) describing the electrostatic field as strong constraints into the loss function of the neural network. This means that during training, the network not only learns to fit limited observation or simulation data, but its output (predicted potential) is also forced to approximately satisfy the basic physical laws across the entire computational domain.
[0031] Introduction and Integration of Bayesian Inference Framework: Based on the aforementioned PINN framework, Bayesian inference is introduced. Specifically, the weights and biases of the neural network are treated as random variables, and a reasonable prior probability distribution is set for them.
[0032] The goal of training shifts from finding a single “optimal” set of parameters to estimating the complete posterior probability distribution of these parameters given training data (such as partially known potential points) and physical constraints. This is typically achieved through approximation algorithms such as Markov Chain Monte Carlo (MCMC) or variational inference.
[0033] Therefore, what is obtained after training is not a deterministic network with fixed weights, but a probabilistic model that can characterize the uncertainty of parameters.
[0034] Among them, model training and optimization: the model is trained using data (which can come from high-fidelity numerical simulation or ground experiments) containing partial coordinate points on the surface of space-use materials and their corresponding potential values.
[0035] Ultimately, a "trained" Bayesian PINN model was obtained. This model not only learned the complex mapping relationship from spatial coordinates to electrical potential, but also embedded physical conservation laws and had the ability to quantify and predict uncertainty through the posterior distribution of parameters.
[0036] The Bayesian PINN-based model building and training method implemented in this step brings significant and multi-layered innovative benefits: First, it fundamentally ensures the physical consistency and extrapolation reliability of the model. By embedding the electrostatic field equation as a hard constraint into the learning process, it ensures that even in regions with sparse or unseen data, the model's predictions strictly follow physical laws, effectively overcoming the "physical illusion" problem that may arise from traditional pure data-driven models. Second, this method achieves, for the first time in this computational field, the endogenous quantification of result uncertainty. Thanks to the Bayesian framework, the model can directly output the confidence interval of the potential prediction value, thereby elevating the calculation result from a single deterministic value to probabilistic information containing confidence assessment, providing a crucial basis for risk assessment and robust decision-making in spacecraft safety design. Finally, this method demonstrates excellent computational efficiency and wide applicability. Once the model is trained, for any new material surface geometry or working condition, only the coordinates need to be input to instantly obtain high-precision potential distribution and uncertainty assessment, avoiding the repeated modeling and high computational costs required by traditional numerical methods for each new problem. It is especially suitable for engineering scenarios where complex spacecraft systems require a large number of rapid working condition analyses during the design and on-orbit management phases.
[0037] Step S200: Obtain the spatial coordinate data of the surface of the target star material.
[0038] Specifically, this involves a crucial preparatory step in applying a pre-trained Bayesian physical information neural network model for potential calculation. The core of this process lies in providing the model with spatial geometric information about the object being analyzed. Specifically, "obtaining spatial coordinate data of the target spacecraft's material surface" refers to extracting the geometric coordinates of all discrete points on the surface of the target spacecraft component (such as a solar panel substrate, antenna reflector, or satellite outer shell) that require potential calculation, based on its specific three-dimensional shape.
[0039] Data content: Coordinate data is typically organized as an array or point cloud, containing the three-dimensional coordinates of each point (such as X, Y, Z values in a Cartesian coordinate system). These points need to be dense enough to capture the geometric features of the surface (such as curvature, bumps, and depressions).
[0040] Data Sources and Processing: Coordinate data can be directly exported from computer-aided design (CAD) models of spacecraft parts, or obtained by meshing and extracting nodes from physical or high-fidelity simulation models. For example, for a satellite antenna with a complex shape, its CAD model surface can be discretized into a triangular mesh, and then the coordinates of all mesh vertices can be collected to form the input dataset.
[0041] These coordinate data constitute the sole input variable of the neural network model. Based on these coordinate points, the model will use the learned physical laws and mapping relationships to calculate and output the predicted potential value and confidence level at each corresponding point.
[0042] The standardized data acquisition process defined in this step lays the foundation for the efficient and widespread application of the Bayesian PINN model and produces direct beneficial effects: it greatly improves the engineering applicability and automation level of the potential calculation method. By explicitly using "spatial coordinate data" as a unified and single input interface, this method can directly interface with existing spacecraft digital design processes (such as CAD systems) or 3D measurement data, without needing to re-derive formulas or construct complex simulation meshes for components of different shapes. This achieves rapid, one-click calculation from geometric models to potential distribution results. This not only significantly reduces the cumbersome preprocessing time (modeling, mesh generation) and professional barriers in traditional numerical methods, but also ensures that the calculation method can flexibly adapt to various surface morphologies of spacecraft materials, ranging from simple flat plates to complex curved surfaces. It provides spacecraft designers with a highly convenient, universal, and repeatable quantitative analysis tool during the selection, optimization, and safety assessment stages.
[0043] Step S300: Input the spatial coordinate data into the trained Bayesian physical information neural network model to obtain the predicted potential distribution of the target star material surface and the corresponding confidence interval.
[0044] Specifically, the core of this process is to utilize a pre-trained Bayesian Physical Information Neural Network (PINN) model to efficiently and intelligently solve for the physical field and perform uncertainty analysis on the input target geometric information. The set of spatial coordinate points representing the surface morphology of the target material, obtained in step S200, is used as a set of input vectors and fed into the pre-trained Bayesian PINN model in batches. Through forward propagation of its internal neural network, the model synchronously calculates and outputs two key scalars for each coordinate point: one is the predicted potential value at that point (i.e., the potential distribution); the other is the confidence interval corresponding to the predicted value (usually expressed as standard deviation or a specific quantile interval, such as the 95% confidence band). For example, for a complex spacecraft component containing tens of thousands of surface points, the model can complete the calculation for all points within seconds, directly generating a potential distribution cloud map covering the entire surface with error bands, intuitively displaying the high and low potential regions and the confidence range of their predictions.
[0045] This process achieves an input-results-instantaneous application model, realizing an instantaneous and reliable mapping from complex physical problems to intuitive quantitative results. It also embeds a professional risk warning function into engineering calculations for the first time. Through a single forward calculation, this method not only outputs a high-precision full-field potential distribution but, more importantly, simultaneously provides the confidence interval for each prediction point. This essentially provides designers with a "reliability map of the calculation results." This elevates traditional deterministic simulation to probabilistic assessment, enabling engineers to clearly identify which areas have highly reliable predictions and which areas have significant uncertainty due to lack of data or high physical complexity. This allows for targeted focus on high-risk areas during material selection, protection design, or fault diagnosis, leading to more comprehensive and robust engineering decisions and greatly enhancing the predictability and scientific rigor of spacecraft on-orbit safety management.
[0046] In this embodiment, by constructing and applying a physical information neural network (Bayesian PINN) that integrates the physical constraints of the electrostatic field equation with the Bayesian inference framework, efficient and high-precision calculation of the surface charging potential of space-use materials is achieved, and the uncertainty quantification of the prediction results is provided simultaneously. Its beneficial effects are mainly reflected in the following aspects: First, it significantly improves the accuracy and reliability of calculations. The model incorporates the fundamental laws of electrostatics during training, ensuring that the prediction results strictly conform to physical laws and avoiding the physical inconsistencies that may occur with purely data-driven models. Second, it enables uncertainty assessment of potential predictions. With the help of a Bayesian inference framework, the model not only outputs a single potential distribution value but also provides the confidence interval for each prediction point, thereby providing risk perception capabilities for the electrical safety design of spacecraft materials and helping engineers make more robust decisions under conditions of multiple uncertainties such as material properties and space environment. Third, it has superior applicability and computational efficiency. Once the model training is completed, for new material surface geometries or boundary conditions, only spatial coordinates need to be input to quickly obtain the potential distribution and confidence interval, avoiding the cumbersome process of remodeling and large-scale calculations required by traditional numerical methods for each new problem. It is especially suitable for rapid analysis and design iteration in complex spacecraft surfaces and variable space environment scenarios.
[0047] Optionally, such as Figure 2 As shown, the training process of the Bayesian physical information neural network model includes: Step T1: Acquire training data, including historical spatial coordinate data of the surface of the space-borne material and corresponding potential measurement data or simulation data; Step T2: Construct a physical information neural network. The input of the physical information neural network is spatial coordinate data, and the output is the corresponding potential prediction value. Step T3: The electrostatic field equation and boundary conditions are introduced as physical constraints into the loss function of the physical information neural network; Step T4: Introduce the Bayesian inference framework and perform posterior distribution estimation on the network parameters of the physical information neural network to achieve uncertainty quantification. Step T5: Train the physical information neural network based on the training data, optimize the network parameters of the physical information neural network, and obtain the trained Bayesian physical information neural network model.
[0048] Optionally, in step T4, the network parameters are sampled a posteriori based on the Markov chain Monte Carlo method.
[0049] Optionally, in step T5, spatial coordinate data for calculating the loss function is dynamically selected based on an adaptive sampling strategy.
[0050] Optionally, the loss function includes a physical residual term based on the electrostatic field equation and a regularization term introduced by Bayesian inference.
[0051] Optionally, the physical residual terms of the electrostatic field equations include: ; Where N is the number of training data points, and i is the i-th training data point. Let ε be the potential, ρ be the dielectric constant of the material, ρ be the charge density, and ▽ be the gradient operator.
[0052] Optionally, the electrostatic field equations include: ; in, Let ε(r) be the potential, ε(r) be the dielectric constant of the material at point r, ρ(r) be the charge density, and ▽ be the gradient operator.
[0053] Optionally, the boundary conditions include at least one of potential boundary conditions or electric field boundary conditions.
[0054] Optionally, the neural network includes at least one hidden layer and a ReLU activation function.
[0055] Specifically, the training process of the Bayesian physical information neural network model aims to build an intelligent computing model that can accurately predict the surface potential of materials used in spacecraft and quantify the uncertainty of prediction. Its core lies in the deep integration of physical laws, observation data and Bayesian probability framework.
[0056] Acquiring training data lays the data foundation for model learning. Training data mainly includes two categories: first, historical spatial coordinate data of the surface of space-use materials, i.e., positional information (such as three-dimensional coordinates) of a series of points representing the geometry of the material surface, collected from existing design models or experiments; second, the true potential values corresponding to these coordinate points. These true values can come from high-precision ground-based experimental measurements (such as potential probe measurements in simulated space plasma environments) or from validated high-fidelity numerical simulation results (such as detailed electrostatic simulations using the finite element method). For example, the coordinates of the surface mesh nodes of a CAD model of a satellite radome can be used as input, and professional simulation software can be called to calculate its surface potential under a specific space environment as the output label, together forming a training sample set.
[0057] Constructing a physical information neural network is the basic computational architecture for building models. A feedforward neural network is constructed where the input layer is explicitly designed to receive spatial coordinate data (e.g., x, y, z), and the output layer is designed to provide the predicted potential value corresponding to that coordinate point. The hidden layers of the network are responsible for learning the complex nonlinear mapping relationship between geometric space and the potential field.
[0058] Introducing physical constraints is crucial to ensuring the model is "physically correct." The fundamental physical laws describing the problem—such as electrostatic equations (e.g., Poisson's equation)—and specific boundary conditions (e.g., known surface potential or normal electric field)—are encoded as mandatory constraints and incorporated into the neural network's loss function. This means that during training, the model must not only strive to fit a limited number of training data points, but its predicted output at any point in the computational domain must also satisfy these physical laws as closely as possible. The loss function calculates the residual between the network's predicted solution and the physical equations, and incorporates this residual as part of the optimization objective.
[0059] A Bayesian inference framework is introduced to inject "uncertainty perception" into the model. The weights and biases of the neural network constructed in step T2 are no longer treated as fixed, deterministic values, but rather as random variables following a certain prior distribution. Using Bayesian inference methods (such as a feasible implementation based on Markov Chain Monte Carlo (MCMC) sampling technique), the probabilistic perception of these parameters is updated using training data (observational information) and physical constraints (prior knowledge), ultimately obtaining the posterior probability distribution of the network parameters. This distribution fully characterizes all possibilities of the model parameters and their confidence levels under given information and constraints, thus providing a mathematical foundation for quantifying the uncertainty of model predictions.
[0060] Model training and optimization is a process of integrating the above elements and iteratively optimizing. Based on prepared training data, the neural network, which integrates physical constraints and the Bayesian framework, is trained. Optimization algorithms (such as gradient-based optimizers) adjust the network parameters by minimizing the total loss function (typically including data fitting error, physical residuals, and Bayesian regularization terms). An optional augmentation strategy is to use adaptive sampling, which dynamically adjusts the spatial coordinates used to calculate the physical constraint loss during training, based on the model's performance in different regions of the computational domain (such as the magnitude of physical residuals or prediction variance). Sampling density is increased preferentially in regions where the model is difficult to learn or where uncertainty is high, thereby improving training efficiency and final accuracy. After training, a "trained" Bayesian physical information neural network model is obtained. This model has internalized the physical laws of electrostatic fields and possesses the ability to make probabilistic predictions based on the posterior distribution of parameters.
[0061] In some embodiments, a physical model is defined: The fundamental physical equations for the surface charging problem of spacecraft materials are established, including electrostatic field equations and boundary conditions. It is assumed that the spacecraft material surface has different charge distributions, considering parameters such as the material's conductivity and dielectric constant, and the influence of an external electric field is considered. The electrostatic field equations are used as constraints, and potential boundary conditions are set on the material surface. ; where n is the normal vector of the material surface.
[0062] The core of this embodiment lies in constructing a neural network that integrates the aforementioned physical model with Bayesian inference.
[0063] Construct a fully connected feedforward neural network. Its input layer nodes correspond to spatial coordinates r = (x, y, z); the output layer is a scalar, i.e., the predicted potential value at that point; there are 3 hidden layers, each with 64 neurons; the ReLU activation function is used to allow the model to learn complex relationships; the output layer is the potential value. .
[0064] Loss function design: The loss function L is the key to driving network learning and consists of two parts: the physical residual term of the electrostatic field equation and the regularization term introduced by Bayesian inference.
[0065] The loss function is: ;in, Representing the physical residuals of the electrostatic field equations: This is the loss term introduced by Bayesian inference (the regularization term introduced by Bayesian inference), which controls the quantification of model uncertainty. In the Bayesian Physical Information Neural Network framework, the regularization term... It is the core mathematical carrier for the model's ability to quantify uncertainty. Its introduction transforms traditional deterministic neural network training into a probabilistic inference process. Simply put, It originates from the prior probability distribution applied to the weight parameters of the neural network.
[0066] The introduction of Bayesian inference: A Bayesian inference framework is introduced based on PINN. Through a sampling strategy, the uncertainty of model parameters is estimated using Bayesian methods, and the uncertainty of the potential calculation results is inferred through the posterior distribution. Specifically, the network weights are sampled using the Markov Chain Monte Carlo (MCMC) method to obtain the confidence interval of the calculation results.
[0067] Within the Bayesian framework, the goal is to infer the posterior distribution of model parameters from given data: ; in, These are the model parameters, representing the network's weights and biases; D is the observed data (such as experimental or simulated data). It is the posterior distribution, representing the parameter given data D. The probability distribution; It is the likelihood function, which represents the likelihood of a given set of parameters. When, the probability of data D; It is the prior distribution of the parameters, representing the distribution of the parameters in the absence of observed data.
[0068] Due to calculation This marginal likelihood is computationally very complex, so Bayesian inference is usually approximated by sampling methods (such as Markov chain Monte Carlo MCMC) to approximate the posterior distribution.
[0069] For Bayesian inference, the purpose of MCMC is to obtain information from the posterior distribution. Samples are drawn from the middle. The core idea of the MCMC method is to construct a Markov chain such that the stationary distribution of the chain equals the posterior distribution. The Metropolis-Hastings algorithm is used to iteratively generate samples that conform to the target posterior distribution.
[0070] First, choose an initial value. Based on the current parameter value Generate candidate parameter samples It is typically generated using a proposed distribution (such as a normal distribution): ; in, From the current state (Current parameter value) to new state The probability distribution of (candidate samples), p(θ|D) represents the probability distribution of model parameters θ given all observed data D.
[0071] Then, calculate the probability of acceptance. That is, the decision to accept a candidate sample is based on the ratio of the current posterior probability to the posterior probability of the candidate sample. ; If accepted, then ; If you refuse, then keep .
[0072] Repeat the above steps until convergence. After multiple iterations, the resulting sample sequence... , ...will approach the target posterior distribution .
[0073] Model training and evaluation: The training process: Data preparation: Generate or collect the data required for training, including configuration points, boundary points, and possibly a small number of measured potential data points for physical loss calculation.
[0074] Adaptive sampling: During training, the density of configuration points in areas with large physical residuals can be dynamically increased based on the current loss distribution to improve training efficiency.
[0075] Optimization solution: Use stochastic gradient descent (SGD) or Adam optimizers to minimize the total loss function. If MCMC is used, execute the corresponding sampling algorithm.
[0076] Model evaluation: Evaluate the trained model on independent test sets (such as high-precision simulation results or experimental data not used in training). Key evaluation metrics include root mean square error (RMSE) of predicted potentials, mean absolute error (MAE), and degree of uncertainty calibration (such as examining the coverage probability of confidence intervals).
[0077] After training, the Bayesian PINN model becomes a surrogate model that can be used for rapid prediction, taking as input an arbitrary set of coordinate points on the surface of the target star's material. The model performs forward computation and directly outputs the predicted mean and standard deviation (or confidence interval) of the potential at each point.
[0078] The visualization output generates a surface potential distribution cloud map with uncertainty bands, providing an intuitive and reliable quantitative basis for the electrical safety design and analysis of spacecraft materials.
[0079] The Bayesian PINN model constructed through the aforementioned systematic training process fundamentally bridges the gap between physical reliability and data-driven learning. By embedding the electrostatic field equations and their boundary conditions as hard constraints into the neural network, it ensures that even in regions not covered by training data or under extrapolation conditions, the model's predictions strictly adhere to basic physical conservation laws, effectively eliminating potential physical errors from pure black-box models and significantly improving generalization ability and reliability. Secondly, this process achieves endogenous quantification of the uncertainties in complex physical field calculations. Using the Bayesian inference framework, the model probabilistically represents the uncertainties of parameters and predictions, so that the final output is no longer a single potential value, but a probability distribution with confidence intervals. This elevates the calculation results to the decision support level of "prediction + reliability assessment," helping spacecraft designers identify high-risk areas and make more robust design choices when facing inherent uncertainties in material properties and environmental parameters. Finally, this method demonstrates outstanding intelligent optimization characteristics and computational economy. For example, the adaptive sampling strategy can guide the model to focus efficiently on difficult-to-learn physical regions, achieving higher accuracy with less data and computational resources. Once the model is trained, when performing potential analysis on new geometries, it can instantly obtain high-precision solutions and uncertainty maps across the entire field with just forward propagation. This avoids the repetitive modeling and massive computation required by traditional numerical methods for each new problem, providing a powerful, efficient, and reliable tool for rapid iterative design of spacecraft and real-time assessment of on-orbit safety status.
[0080] In some embodiments, the method for calculating the surface charging potential of space-borne materials based on Bayesian PINN is experimentally verified. The method proposed in this invention can accurately calculate the surface potential of space-borne materials under complex electric field distributions and material properties. For example... Figure 3 As shown, this is a schematic diagram illustrating the changes in the loss function during model training; according to Figure 3 It can be seen that during the training process, the total loss function decreases rapidly and tends to stabilize as the number of iterations increases, indicating that the method has a good convergence effect and a high convergence speed during the training process, and has a good learning effect on the calculation of material surface potential.
[0081] like Figure 4 The diagram shows a comparison between the predicted potential distribution obtained from the Bayesian PINN-based method for calculating the surface charging potential of space-grade materials and actual experimental measurement data. Specifically, the potential prediction results of the method on the test set are compared with high-fidelity numerical simulation (or experimental) results. The two methods show a high degree of agreement and a low error distribution, verifying the calculation accuracy of the method. Furthermore, the confidence interval provided by the model effectively covers most of the prediction error, demonstrating the effectiveness of its uncertainty quantification capability. Figure 4The curves / data points corresponding to Ba-PINN Pre represent the predicted potential distribution results obtained by the surface charging potential calculation method of space-use materials based on Bayesian PINN, while the curves / data points corresponding to ExactSol represent the actual experimental measurement data.
[0082] This invention provides a device for calculating the surface charging potential of space-borne materials based on Bayesian PINN, comprising: The construction unit is used to construct a Bayesian physical information neural network model. The Bayesian physical information neural network model is trained by integrating the constraints of the electrostatic field equation with the Bayesian inference framework to obtain a trained Bayesian physical information neural network model. The acquisition unit is used to acquire spatial coordinate data of the surface of the target star's material. The processing unit is used to input the spatial coordinate data into the trained Bayesian physical information neural network model to obtain the potential distribution prediction results and corresponding confidence intervals on the surface of the target star material.
[0083] This invention provides a Bayesian PINN-based device for calculating the surface charging potential of space-borne materials, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the Bayesian PINN-based method for calculating the surface charging potential of space-borne materials as described above when the computer program is executed.
[0084] This invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the method for calculating the surface charging potential of space-borne materials based on Bayesian PINN as described above.
[0085] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.
Claims
1. A method for calculating the surface charging potential of a space material based on Bayesian PINN, characterized in that, The method comprises the steps of: constructing a physical information neural network, training the Bayesian physical information neural network model by fusing electrostatic field equation constraints and a Bayesian inference framework, and obtaining a trained Bayesian physical information neural network model; acquiring spatial coordinate data of a target space material surface; inputting the spatial coordinate data into the trained Bayesian physical information neural network model to obtain a potential distribution prediction result of the target space material surface and a corresponding confidence interval.
2. The Bayesian PINN-based material surface charging potential calculation method for satellites according to claim 1, characterized in that, The training process of the Bayesian physical information neural network model comprises: Step T1: acquiring training data, including historical spatial coordinate data of a space material surface and corresponding potential measurement data or simulation data; Step T2: constructing the physical information neural network, wherein the input of the physical information neural network is spatial coordinate data, and the output is a corresponding potential prediction value; Step T3: introducing electrostatic field equations and boundary conditions as physical constraints into the loss function of the physical information neural network; Step T4: introducing the Bayesian inference framework to realize uncertainty quantification by performing posterior distribution estimation on the network parameters of the physical information neural network; Step T5: training the physical information neural network based on the training data, optimizing the network parameters of the physical information neural network, and obtaining the trained Bayesian physical information neural network model.
3. The Bayesian PINN-based material surface charging potential calculation method for satellites according to claim 2, characterized in that, In step T4, the network parameters are sampled based on the Markov chain Monte Carlo method.
4. The Bayesian PINN-based material surface charging potential calculation method for satellites according to claim 2, characterized in that, In step T5, based on an adaptive sampling strategy, spatial coordinate data used to calculate the loss function is dynamically selected.
5. The Bayesian PINN-based method for calculating the surface charging potential of a space material according to claim 2, wherein, The loss function comprises a physical residual term based on the electrostatic field equation and a regularization term introduced by the Bayesian inference.
6. The Bayesian PINN-based material surface charging potential calculation method for satellites according to claim 5, characterized in that, The physical residual term of the electrostatic field equation Comprising: ； where N is the number of training data, i is the ith training data, is the electric potential, ε is the dielectric constant of the material, p is the charge density, and V is the gradient operator.
7. The Bayesian PINN-based material surface charging potential calculation method for space application according to claim 2, wherein, The electrostatic field equation comprises: ； wherein is the electric potential, ε(r) is the dielectric constant of the material at r, p(r) is the charge density, and ▽ is the gradient operator.
8. The Bayesian PINN-based material surface charging potential calculation method for satellites according to claim 2, characterized in that, The boundary conditions comprise at least one of a potential boundary condition or an electric field boundary condition.
9. The Bayesian PINN-based material surface charging potential calculation method for satellites according to claim 2, characterized in that, The physical information neural network comprises at least one hidden layer and a ReLU activation function.
10. A Bayesian PINN-based space material surface charging potential calculation device, characterized by, The method comprises the steps of: constructing a unit for constructing a Bayesian physical information neural network model, training the Bayesian physical information neural network model by fusing electrostatic field equation constraints and a Bayesian inference framework, and obtaining a trained Bayesian physical information neural network model; an acquisition unit for acquiring spatial coordinate data of a target space material surface; a processing unit for inputting the spatial coordinate data into the trained Bayesian physical information neural network model to obtain a potential distribution prediction result of the target space material surface and a corresponding confidence interval.