Spatial optical communication turbulence time sequence prediction model training method, phase compensation method and electronic equipment

Abstract

This application provides a training method, phase compensation method, and electronic device for a time-series prediction model of turbulence in space optical communication. The method includes: acquiring distorted spot intensity data from multiple frames of historical moments collected by the receiver in a space optical communication system, and constructing a historical spot intensity sequence based on a preset sliding window; performing multiple rounds of self-supervised learning steps on a spatiotemporal prediction network, including: inputting the historical spot intensity sequence into a 3D convolutional neural network in the spatiotemporal prediction network to generate a predicted phase screen for the target prediction moment; converting it into predicted spot intensity using an angular spectral transmission model, and acquiring the actual detected spot intensity at the target prediction moment; constructing a loss function and calculating the target loss value to update the parameters of the spatiotemporal prediction network; if the model converges, outputting the spatiotemporal prediction network as a time-series prediction model for turbulence in space optical communication. This application can solve the problems of significant lack of temporal dimension information and response lag in existing technologies.

Description

Technical Field

[0001] This invention relates to the field of optical communication technology, and in particular to a training method, phase compensation method, and electronic device for a spatial optical communication turbulence timing prediction model. Background Technology

[0002] In the field of computational phase imaging, traditional methods such as the Gerchberg-Saxton iterative algorithm, the Hybrid Input-Output (HIO) method, and the Transport of Intensity Equation (TIE) mainly rely on mathematical iteration or multiple image inputs. These methods have high computational costs, limited imaging speed, and are prone to getting trapped in local optima under strong turbulence or weak physical constraints, resulting in insufficient phase stability of the reconstructed image. In recent years, although supervised deep learning has been introduced into wavefront recovery, such schemes heavily rely on massive amounts of high-quality labeled data for model training. Due to the extremely complex distribution of underwater turbulence, the acquisition of experimental data is not only time-consuming and labor-intensive, but the generalization ability of trained models is often limited when faced with unseen turbulence distributions.

[0003] Current physics-driven models, such as PhysenNet, have achieved high-precision phase retrieval under single-frame speckle patterns, but existing research is generally limited to static inversion of underwater turbulent phase in a single frame. In real-world space-optical communication or underwater dynamic imaging scenarios, the turbulent field is not static but exhibits significant temporal evolution characteristics. The current mainstream temporal processing approach is to first use a single-frame recovery algorithm to acquire a series of continuous phase screens, and then use these as inputs to a neural network to learn the mapping relationship between adjacent frames, thereby predicting the phase at the next moment. Due to the lack of direct modeling of the dynamic evolution characteristics of turbulence, the system cannot utilize the deep correlation of phase screen evolution over time, resulting in only post-event recovery. Limited by the physical time consumption generated by detector acquisition, computer processing, and control link feedback, the real-time turbulent state has already shifted when the compensation system (such as a space-optical modulator) performs its actions, resulting in a system delay in the compensation effect. Simply relying on a two-stage structure of recovery first and prediction later can easily cause the static recovery error in the first stage to accumulate continuously in the temporal prediction. This discrete processing logic is difficult to capture the nonlinear coherence of the turbulent field in high-dimensional spatiotemporal dimensions. Summary of the Invention

[0004] In view of this, embodiments of the present invention provide a training method, a phase compensation method, and an electronic device for a space optical communication turbulence timing prediction model, in order to eliminate or improve one or more defects existing in the prior art.

[0005] One aspect of the present invention provides a method for training a time-series prediction model for turbulence in space optical communication, the method comprising: The system acquires distorted light spot intensity data from multiple historical frames collected by the receiver in a space optical communication system, and constructs a historical light spot intensity sequence corresponding to the distorted light spot intensity of multiple historical frames based on a preset sliding window; wherein, the distorted light spot intensity is formed by the influence of underwater turbulent channel on optical transmission; Based on the historical light spot intensity sequence, a pre-defined spatiotemporal prediction network undergoes multiple rounds of self-supervised learning. The self-supervised learning steps include: inputting the historical light spot intensity sequence into a 3D convolutional neural network within the spatiotemporal prediction network, causing the 3D convolutional neural network to generate a prediction phase screen corresponding to the target prediction time; then, enabling the angular spectral transmission model in the spatiotemporal prediction network to convert the prediction phase screen into predicted light spot intensity and obtain the actual detected light spot intensity at the target prediction time; constructing a loss function based on the predicted light spot intensity and the actual detected light spot intensity and calculating a target loss value; and updating the parameters of the spatiotemporal prediction network based on the target loss value. If the convolutional neural network prediction model converges, the spatiotemporal prediction network will be used as the spatial optical communication turbulence time series prediction model for output.

[0006] In some embodiments of the present invention, acquiring the distorted light spot intensity data of multiple historical moments collected by the receiver in the space optical communication system includes: The original phase screen sequence is generated using a preset spatial power spectrum model; Generate the target phase screen sequence based on the Taylor hypothesis and the time phase shift factor; The light spot intensity corresponding to the target phase screen sequence is extracted to obtain light spot intensity data.

[0007] In some embodiments of the present invention, the spatial power spectrum model includes: the Nikishov power spectrum model, used to characterize temperature fluctuations, salinity fluctuations, and the cross-correlation between temperature fluctuations and salinity fluctuations.

[0008] In some embodiments of the present invention, the mathematical form of the spatial power spectrum model includes: in, Represents the spatial frequency vector. Indicates the turbulent kinetic energy dissipation rate. Indicates the fluctuation dissipation rate. This represents the ratio of the contribution of salinity to temperature to the fluctuation of refractive index. The Kolmogorov scale is indicated. The decay operator represents the dissipation region. , , All of these represent dimensionless parameters, where T represents temperature and S represents salinity.

[0009] In some embodiments of the present invention, the spatiotemporal prediction network includes: The encoder layer is used to extract the spatiotemporal feature vector of the historical spot intensity sequence using 3D convolution and downsampling operations; Pooling layers are used to pool the spatiotemporal feature vectors in both spatial and temporal dimensions to reduce data redundancy; The bottleneck layer is used to map the pooled spatiotemporal feature vectors to obtain abstract features. The decoder layer is used to restore the abstract features by employing 3D transposed convolution operations and upsampling operations to obtain multi-channel features; The output layer is used to fuse the multi-channel features using 3D convolution to obtain the predicted phase screen.

[0010] In some embodiments of the present invention, the angular spectral transmission model is used to perform the following steps: A zero-fill operation to simulate the diffraction diffusion effect is performed on the predicted phase screen to obtain a zero-filled phase screen; The Gerchberg-Saxton algorithm and the hybrid input-output algorithm are alternately applied to the zero-filled phase screen to optimize the phase distribution of the phase screen, resulting in an optimized phase screen. The optimized phase screen is combined with the prior amplitude distribution of the transmitter probe beam to construct a complex amplitude. The complex amplitude is transformed to the angular spectrum domain using Fourier transform, multiplied with the angular spectrum transfer function, and then inverse Fourier transform is performed to obtain the propagated complex amplitude distribution. The propagated complex amplitude distribution is centrally clipped and returned to the effective observation area; The predicted spot intensity is calculated based on the complex amplitude distribution after trimming.

[0011] In some embodiments of the present invention, the step of constructing a loss function based on the predicted spot intensity and the actual detected spot intensity and calculating the target loss value includes: Based on the predicted spot intensity and the training labels, a spatial loss function, a frequency domain loss function, and a support domain loss function are constructed; wherein, the spatial loss function is used to measure the difference between the predicted spot intensity and the actual detected spot intensity in pixel space; the frequency domain loss function is used to measure the difference between the predicted spot intensity and the actual detected spot intensity in spectral distribution; and the support domain loss function is used to measure the residual energy in the non-effective aperture region; The loss values ​​corresponding to each loss function are calculated and then weighted and summed to obtain the target loss value.

[0012] The second aspect of this application provides a phase compensation method based on a space optical communication turbulence time series prediction model, comprising: To obtain the system processing latency in a space optical communication system; The target compensation time is determined based on the current time and the system processing delay. Obtain the historical distorted light spot intensities of multiple consecutive frames prior to the current moment, and form a historical light spot intensity sequence; The historical light spot intensity sequence is input into the space optical communication turbulence time series prediction model to generate the prediction phase screen for the target prediction time; wherein, the space optical communication turbulence time series prediction model is trained by the space optical communication turbulence time series prediction model training method. The predicted phase screen is loaded onto the spatial light modulator to perform feedforward phase compensation on the beam. A third aspect of this application provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computer program.

[0013] A fourth aspect of this application provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method described thereon.

[0014] A fifth aspect of this application provides a computer program product comprising a computer program that, when executed by a processor, implements the method described herein.

[0015] This application provides a training method for a temporal prediction model of turbulence in space optical communication. The method includes: acquiring distorted light spot intensity data of multiple frames of historical moments collected by a receiver in a space optical communication system; constructing a historical light spot intensity sequence corresponding to the distorted light spot intensity of the multiple frames of historical moments based on a preset sliding window; wherein the distorted light spot intensity is formed by the influence of underwater turbulence channel on optical transmission; and performing multiple rounds of self-supervised learning steps on a preset spatiotemporal prediction network based on the historical light spot intensity sequence. The self-supervised learning steps include: inputting the historical light spot intensity sequence into the 3D model of the spatiotemporal prediction network. A 3D convolutional neural network is used to generate a prediction phase screen corresponding to the target prediction time. Then, the angular spectral transmission model in the spatiotemporal prediction network converts the prediction phase screen into a prediction spot intensity and obtains the actual detected spot intensity at the target prediction time. A loss function is constructed based on the predicted spot intensity and the actual detected spot intensity, and the target loss value is calculated. The parameters of the spatiotemporal prediction network are updated based on the target loss value. If the convolutional neural network prediction model converges, the spatiotemporal prediction network is used as a spatial optical communication turbulence time series prediction model for output. By constructing a sliding time window input structure, the spatiotemporal prediction network can extract temporal gradient features from continuous historical frames, enabling early prediction of the turbulence phase at the target moment and improving the accuracy of feedforward compensation in dynamic environments. Utilizing a 3D convolutional neural network to slide and extract features along the depth direction (time axis) to capture the coherence and evolution of the turbulent field in the spatiotemporal dimension, it can correct instantaneous errors in single-frame observations in strongly turbulent or rapidly evolving underwater scenarios, making the phase recovery process more robust and obtaining higher-fidelity wavefront information. The predicted light spot recovered through the angular spectral transmission model is consistent with the actual... By observing the differences between light spots, the network is driven to spontaneously learn the turbulence evolution function. The training process only requires light spot intensity data and does not require the phase screen ground truth value, which is difficult to obtain directly, thus greatly reducing the difficulty and cost of dataset construction. By integrating the alternating mapping mechanism of mixed input and output with the GS algorithm in the preprocessing process, and introducing a zero-filling module and support domain penalty term, the network is effectively guided to solve the phase wrapping problem caused by phase abrupt changes and suppress phase noise generated in non-physical regions, ensuring the integrity and accuracy of phase recovery and improving the phase compensation accuracy of space optical communication systems in dynamic turbulent environments.

[0016] Additional advantages, objectives, and features of this application will be set forth in part in the description which follows, and will in part become apparent to those skilled in the art upon review of the following description, or may be learned by practice of the application. The objectives and other advantages of this application can be realized and obtained by means of the structures specifically pointed out in the specification and drawings.

[0017] Those skilled in the art will understand that the purposes and advantages that can be achieved with this application are not limited to those specifically described above, and that the above and other purposes that this application can achieve will be more clearly understood from the following detailed description. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, do not constitute a limitation thereof. The components in the drawings are not drawn to scale but are merely for illustrating the principles of this application. For ease of illustration and description of certain parts of this application, corresponding portions in the drawings may be enlarged, i.e., may appear larger relative to other components in an exemplary device actually manufactured according to this application. In the drawings: Figure 1 This is a flowchart illustrating the training method for a spatial optical communication turbulence time-series prediction model in one embodiment of this application.

[0019] Figure 2 This is a schematic diagram illustrating the generation of an underwater turbulent phase screen based on Taylor freezing theory, as exemplified in this application.

[0020] Figure 3 This is a schematic diagram of the architecture of a spatiotemporal prediction network as exemplified in this application.

[0021] Figure 4 This is a flowchart illustrating an example of the angular spectrum transmission model in this application.

[0022] Figure 5 This is a flowchart illustrating a phase compensation method based on a spatial optical communication turbulence timing prediction model in one embodiment of this application.

[0023] Figure 6 This is a flowchart illustrating the turbulence phase timing prediction and feedforward compensation based on a physical information neural network, as exemplified in this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the embodiments and accompanying drawings. Here, the illustrative embodiments and their descriptions are used to explain this application, but are not intended to limit it.

[0025] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the structures and / or processing steps closely related to the scheme according to this application are shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0026] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, element, step, or component, but does not exclude the presence or addition of one or more other features, elements, steps, or components.

[0027] It should also be noted that, unless otherwise specified, the term "connection" in this article can refer not only to a direct connection, but also to an indirect connection involving an intermediary.

[0028] In the following description, embodiments of the present application will be illustrated with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar parts, or the same or similar steps.

[0029] Therefore, in order to solve the problems of significant lack of time-series information and response lag in the existing technology, the embodiments of this application provide a training method for a space optical communication turbulence time-series prediction model, a phase compensation method based on the space optical communication turbulence time-series prediction model, an electronic device, a computer-readable storage medium, and a computer program product, so as to improve the phase compensation accuracy of the space optical communication system in a dynamic turbulence environment.

[0030] The following examples will provide a detailed description.

[0031] Based on this, embodiments of this application provide a method for training a space optical communication turbulence timing prediction model that can be executed by a space optical communication turbulence timing prediction model training device. See [link to relevant documentation]. Figure 1 The method specifically includes the following: Step 100: Obtain the distorted spot intensity data of multiple historical moments collected by the receiver in the space optical communication system, and construct the historical spot intensity sequence corresponding to the distorted spot intensity of multiple historical moments based on a preset sliding window; wherein, the distorted spot intensity is formed by the influence of the underwater turbulent channel on optical transmission.

[0032] Specifically, the Nikishov-Grigoriev power spectrum (a classic spatial power spectrum model describing the random fluctuations in the refractive index of seawater in ocean turbulence) is used to obtain distorted spot intensity data from multiple historical frames collected at the receiver in a space optical communication system. A physical constraint neural network is then combined to design a time-series prediction method for space optical communication turbulence. By introducing precise statistical characteristics of turbulent physical evolution at the data source, a high degree of simulation and accurate prediction of dynamic channels is achieved. The sliding window length is defined as... (i.e., historical observation step size). For each target time... Extract its preorder cipher. Frame distortion spot intensity Composition of input vector: This serialization process expands a single spatial intensity feature into a spatiotemporal joint feature. In addition to using the beam amplitude (intensity) recorded by a CCD detector as input, residual slope or residual phase data measured by a wavefront sensor (such as a Hartmann sensor) can also be input.

[0033] Step 200: Perform multiple rounds of self-supervised learning on a preset spatiotemporal prediction network based on the historical spot intensity sequence. The self-supervised learning steps include: inputting the historical spot intensity sequence into a 3D convolutional neural network in the spatiotemporal prediction network to generate a prediction phase screen corresponding to the target prediction time; then, enabling the angular spectral transmission model in the spatiotemporal prediction network to convert the prediction phase screen into predicted spot intensity and obtain the actual detected spot intensity at the target prediction time; constructing a loss function based on the predicted spot intensity and the actual detected spot intensity and calculating the target loss value; and updating the parameters of the spatiotemporal prediction network based on the target loss value.

[0034] It should also be noted that, Corresponding true light spot intensity Set as training labels. Self-supervised learning is achieved through a physical constraint layer, thus eliminating the need to directly obtain the difficult-to-measure ground truth value of the phase screen during training.

[0035] Specifically, using 3D convolution operators in the spatial dimension ( ) and time dimension ( Feature mapping is performed simultaneously on the spatial dimension (height). Traditional 2D U-Net convolutional kernels only perform feature mapping on the spatial dimension (height). The 2D convolutional architecture slides across the width of the input data, and its network design does not explicitly model the temporal dependencies between the input data. Even when multiple frames of light spot images are stacked as input in the channel dimension, 2D convolution still treats different time frames as equivalent multi-channel features during computation, failing to distinguish the temporal order and thus unable to establish temporal phase reconstruction. Therefore, compared to 2D U-Net, the 3D architecture can more effectively capture the dynamic correlation of turbulent phase screens as they translate and evolve over time.

[0036] Understandably, the core objective of existing physical embedded neural network methods is to achieve high-precision reconstruction of the turbulence phase at the current or past moment. Their physical constraint layers are primarily used to verify whether the network output satisfies the optical propagation laws within the same time step. However, in real-world dynamic turbulent environments, even with sufficiently high reconstruction accuracy from the physical model, the turbulence state itself has already evolved by the time the phase calculation is completed and used for compensation. This inevitably leads to a servo lag effect, limiting the system's real-time compensation performance.

[0037] It should be noted that a cross-time-step physical constraint mechanism is introduced into the angular spectrum propagation modeling. Specifically, the angular spectrum propagation operator incorporates the predicted phase and historical time-series observed light spots into the physical propagation and residual feedback process, allowing the physical layer to impose continuous constraints on the turbulence evolution process. This physical embedding layer minimizes the difference between the predicted and actual observed light intensities, driving the network to learn the nonlinear dynamic mapping relationship of the turbulence phase evolution over time, thereby achieving feedforward prediction of the turbulence phase at future moments. The target loss value is backpropagated via a differentiable physics module. Since the operators are continuously differentiable, the gradient can directly act on the front-end network parameters across the physical layer, achieving label-free self-supervised learning. Under conditions satisfying the far-field approximation or a specific propagation distance, Fresnel diffraction operators can be used instead of angular spectrum propagation to simplify the computational complexity in specific scenarios.

[0038] Step 300: If the convolutional neural network prediction model converges, the spatiotemporal prediction network is used as the spatial optical communication turbulence time series prediction model for output.

[0039] Understandably, it is possible not only to predict the current moment. It can also directly predict future moments. To accommodate greater system lag.

[0040] As described above, the spatial optical communication turbulence temporal prediction model training method provided in this application, by constructing a sliding time window input structure, enables the spatiotemporal prediction network to extract temporal gradient features from continuous historical frames, achieving early prediction of the turbulence phase at the target time and improving the feedforward compensation accuracy in dynamic environments. Utilizing a 3D convolutional neural network to slide and extract features along the depth direction (time axis) to capture the coherence and evolution of the turbulence field in the spatiotemporal dimension, it can correct instantaneous errors in single-frame observations in strongly turbulent or rapidly evolving underwater scenarios, making the phase recovery process more robust and obtaining higher-fidelity wavefront information. The difference between the predicted light spot recovered by the over-angle spectral transmission model and the actual observed light spot drives the network to spontaneously learn the turbulence evolution function. The training process only requires light spot intensity data and does not require the phase screen ground truth value, which is difficult to obtain directly, thus greatly reducing the difficulty and cost of dataset construction. By integrating the alternating mapping mechanism of mixed input and output with the GS algorithm in the preprocessing process, and introducing a zero-filling module and support domain penalty term, the network is effectively guided to solve the phase wrapping problem caused by phase abrupt changes and suppress phase noise generated in non-physical regions, ensuring the integrity and accuracy of phase recovery and improving the phase compensation accuracy of space optical communication systems in dynamic turbulent environments.

[0041] To further improve the phase compensation accuracy of space optical communication systems under dynamic turbulent environments, in a training method for a space optical communication turbulent time-series prediction model provided in this application embodiment, step 100, which involves acquiring distorted light spot intensity data from multiple historical frames collected by the receiver in the space optical communication system, specifically includes the following: Step 110: Generate the original phase screen sequence using the preset spatial power spectrum model.

[0042] Step 120: Generate the target phase screen sequence based on the Taylor hypothesis and the time phase shift factor.

[0043] Step 130: Extract the light spot intensity corresponding to the target phase screen sequence to obtain light spot intensity data.

[0044] Specifically, in order to generate a phase screen sequence that evolves over time, a transverse wind speed (or flow velocity) vector is introduced. Based on Taylor's Frozen Turbulence Hypothesis, it is assumed that the turbulent field changes over extremely short time intervals. The internal spatial structure remains relatively stable, shifting only with the flow field. This is achieved by introducing a time phase shift factor in the spatial frequency domain. This enables the phase screen to evolve smoothly over time. Here, j represents the imaginary unit. Represents the spatial frequency vector. This represents the lateral flow velocity or wind speed vector. Indicates the time step of sampling. This represents the phase difference between different spatial frequency components due to spatial displacement.

[0045] In one example, a schematic diagram of underwater turbulent phase screen generation based on Taylor's freezing theory is shown below. Figure 2 As shown, where, The target time is represented by n, which is a positive integer. T represents temperature and S represents salinity.

[0046] To further improve the phase compensation accuracy of space optical communication systems under dynamic turbulent environments, in a space optical communication turbulent time series prediction model training method provided in this application embodiment, the space power spectrum model specifically includes the following content in step 110: The Nikishov power spectrum model is used to characterize temperature fluctuations, salinity fluctuations, and the cross-correlation between temperature fluctuations and salinity fluctuations.

[0047] Specifically, to establish a dynamic channel model that conforms to the statistical laws of real physical environments (such as oceans or special atmospheres), the Nikishov-Grigoriev model is used to characterize the refractive index fluctuations of turbulent media, unlike traditional single-parameter spectra.

[0048] To further improve the phase compensation accuracy of space optical communication systems under dynamic turbulent environments, in a space optical communication turbulent time series prediction model training method provided in this application embodiment, the mathematical form of the space power spectrum model in step 110 specifically includes the following: in, Represents the spatial frequency vector. Indicates the turbulent kinetic energy dissipation rate. Indicates the fluctuation dissipation rate. This represents the ratio of the contribution of salinity to temperature to the fluctuation of refractive index. The Kolmogorov scale is indicated. The decay operator represents the dissipation region. , , All of these represent dimensionless parameters, where T represents temperature and S represents salinity.

[0049] Specifically , , Both represent dimensionless parameters describing the proportion of the contribution of temperature and salinity to the fluctuation of refractive index. TS represents the coupling of temperature and salinity. satisfy x and y represent the horizontal and vertical directions of the vector in the plane, respectively; It determines the intensity of turbulence; Fluctuation dissipation rate; This represents the minimum vortex size at which viscous dissipation begins to dominate; the attenuation operator in the dissipation region. Defined as: This model comprehensively considers temperature fluctuations, salinity (or humidity) fluctuations, and their cross-correlation. Its mathematical form not only incorporates traditional energy level and dissipation level characteristics but also uses mean square temperature dissipation rate. Kinetic energy dissipation rate and Kolmogorov microscale These parameters precisely characterize the spectral evolution at high spatial frequencies.

[0050] To further improve the phase compensation accuracy of space optical communication systems under dynamic turbulent environments, in a space optical communication turbulent time-series prediction model training method provided in this application embodiment, step 200 of the spatiotemporal prediction network specifically includes the following: The encoder layer is used to extract the spatiotemporal feature vector of the historical spot intensity sequence using 3D convolution and downsampling operations; Pooling layers are used to pool the spatiotemporal feature vectors in both spatial and temporal dimensions to reduce data redundancy; The bottleneck layer is used to map the pooled spatiotemporal feature vectors to obtain abstract features. The decoder layer is used to restore the abstract features by employing 3D transposed convolution operations and upsampling operations to obtain multi-channel features; The output layer is used to fuse the multi-channel features using 3D convolution to obtain the predicted phase screen.

[0051] Specifically, the encoder aims to compress the high-dimensional pixel information of the original image into a deep feature vector carrying the core evolutionary laws through layer-by-layer downsampling. Each layer employs 3D convolution operations. Unlike traditional 2D convolution, the 3D convolution kernel slides along the depth direction (time axis), directly extracting temporal gradient features between frames. The initial layer has 64 channels, which is then increased to 128. A 3D max-pooling layer is then added, performing max-pooling simultaneously in both spatial and temporal dimensions. This step reduces data redundancy and expands the receptive field of subsequent layers, enabling them to capture larger-scale vortex structure features in the turbulent field. The bottom layer of the encoder architecture incorporates a 3D bottleneck layer, achieving the highest feature abstraction level. This layer consists of 3D convolutional blocks with 256 and 512 channels respectively, used to lock in the most critical nonlinear turbulent dynamics representation.

[0052] Then, the decoder uses upsampling to restore the abstract feature vectors to a predicted phase field with the same size as the input. 3D transposed convolutions with a stride of 2 are performed to progressively restore the spatial resolution of the feature maps from low to high dimensions. Skip connections directly concatenate feature maps from corresponding layers in the encoding path to the decoding path. This design compensates for information loss caused by pooling operations by preserving high-frequency spatial details in the original observed signal. Furthermore, the feature maps concatenated by the deep fusion mechanism are processed again through 3D convolutional blocks, reducing the number of channels back to 128 and 64 respectively, achieving depth alignment between spatial location information and temporal prediction logic. The last layer of the network uses a kernel size of... The 3D convolutional kernel fuses multi-channel features into a single-channel continuous phase value. The network output is the target prediction time. phase screen This exogenous property enables spatiotemporal prediction networks to predict and compensate for beam distortion before turbulence changes occur.

[0053] In one example, the Physics-Enhanced Spatio-Temporal Prediction Network (PE-STPN) has the following structure diagram: Figure 3 As shown.

[0054] To further improve the phase compensation accuracy of space optical communication systems under dynamic turbulent environments, in a space optical communication turbulent time series prediction model training method provided in this application embodiment, in step 200, the angular spectrum transmission model is used to perform the following steps: Step 210: Perform a zero-fill operation on the predicted phase screen to simulate the diffraction diffusion effect, and obtain the zero-filled phase screen; Step 220: Alternately execute the Gerchberg-Saxton algorithm and the mixed input-output algorithm on the zero-filled phase screen to optimize the phase distribution of the phase screen and obtain the optimized phase screen; Step 230: Combine the optimized phase screen with the prior amplitude distribution of the transmitter probe beam to construct a complex amplitude; Step 240: Transform the complex amplitude to the angular spectrum domain using Fourier transform, multiply it with the angular spectrum transfer function, and then perform inverse Fourier transform to obtain the propagated complex amplitude distribution; Step 250: Perform center clipping on the propagated complex amplitude distribution to return it to the effective observation area; Step 260: Calculate the predicted spot intensity based on the trimmed complex amplitude distribution.

[0055] Specifically, before angular spectrum transmission, the target time prediction phase screen output by the spatiotemporal prediction network in the spatial support domain... First, we enter the zero-padding module. In this module, the original... The signal of a certain size (support domain) is embedded in the center of a larger computational grid, while the amplitudes of the remaining peripheral regions (non-support domain) are forced to zero. This zero-filling operation expands the frequency domain sampling rate, effectively simulating the diffraction and diffusion effects of a beam propagating in free space, and avoiding spectral aliasing and numerical reflection caused by an excessively narrow computational domain. To address the local convergence problem in phase retrieval, the preprocessing integrates an alternating mapping mechanism between the HIO and GS algorithms. In the GS loop stage, incorrectly predicted amplitudes are directly replaced with the known prior amplitudes of the probe beam at the transmitter, while preserving the predicted phase. In the HIO loop stage, negative feedback parameters are introduced outside the support domain. (Values ​​range from 0.5 to 1), using a combination of historical iteration values ​​and current predicted values ​​to correct the signal and break free from local minima. Through the negative feedback constraints provided by the HIO algorithm in the non-supporting domain, the network can be effectively guided to solve the phase wrapping problem caused by phase abrupt changes, resulting in a final recovered phase distribution that exceeds [the specified range]. It can still maintain physical continuity within a certain range.

[0056] It should also be noted that in the angular spectrum propagation evolution process driven by the physical model, the predicted phase is multiplied by the system's preset amplitude distribution to synthesize the complex amplitude at the transmitter. The complex field spectrum is then transformed into the angular spectral domain via a fast Fourier transform (FFT). The complex field spectrum and coherent transfer function are then discussed. Multiply the samples and perform an inverse Fourier transform (IFFT) to restore them to the spatial domain. After center cropping to regress the effective observation area, take the square of the complex field amplitude to obtain the predicted spot intensity. .

[0057] To further improve the phase compensation accuracy of space optical communication systems under dynamic turbulent environments, in a space optical communication turbulent time-series prediction model training method provided in this application embodiment, step 200, which involves constructing a loss function based on the predicted spot intensity and the actual detected spot intensity and calculating the target loss value, specifically includes the following: Step 270: Construct a spatial loss function, a frequency domain loss function, and a support domain loss function based on the predicted spot intensity and the training label; wherein, the spatial loss function is used to measure the difference between the predicted spot intensity and the actual detected spot intensity in pixel space; the frequency domain loss function is used to measure the difference between the predicted spot intensity and the actual detected spot intensity in spectral distribution; and the support domain loss function is used to measure the residual energy in the non-effective aperture region; Step 280: Calculate the loss value corresponding to each loss function and sum them by weight to obtain the target loss value.

[0058] Specifically, to ensure the physical accuracy of the predicted phase, a joint evaluation system covering both spatial and frequency dimensions was established in the spatial-frequency domain multi-constraint loss function module. Spatial domain consistency loss ( Predicting light intensity through calculation Target light intensity measured by detector The mean square error forces the network-generated phase to reconstruct the observed spot morphology. Frequency domain energy distribution loss ( The predicted spectrum is extracted from the complex field at the receiver using a second Fourier transform. and the actual frequency domain distribution Alignment is performed. This constraint captures high-frequency components defined by the Nikishov-Grigoriev spectrum, significantly enhancing the reconstruction fidelity of the phase screen's fine structure. Support domain energy penalty term ( By quantizing the residual energy within the zero-fill region, the optical field energy is forced to concentrate within the effective aperture, suppressing phase noise generated in non-physical regions. The final result is the sum of multiple constraint losses. (i.e., the target loss value).

[0059] In one example, a closed-loop architecture comprising a spatiotemporal prediction network PE-STPN (i.e., a spatiotemporal 3D U-Net network) and differentiable physical constraint modules, namely an angular spectrum transmission model, is shown below. Figure 4 As shown.

[0060] Based on the above-described embodiment of the training method for the turbulence timing prediction model in space optical communication, this application also provides an embodiment of a phase compensation method based on the space optical communication turbulence timing prediction model, see [link to embodiment]. Figure 5 The phase compensation method based on the spatial optical communication turbulence time series prediction model specifically includes the following: Step 010: Obtain the system processing delay in the space optical communication system; Step 020: Determine the target compensation time based on the current time and the system processing delay; Step 030: Obtain the historical distortion spot intensities of multiple consecutive frames prior to the current moment, and form a historical spot intensity sequence; Step 040: Input the historical light spot intensity sequence into the space optical communication turbulence time series prediction model to generate the prediction phase screen for the target prediction time; wherein, the space optical communication turbulence time series prediction model is trained by the space optical communication turbulence time series prediction model training method. Step 050: Load the predicted phase screen onto the spatial light modulator to perform feedforward phase compensation on the beam.

[0061] Specifically, the network input is a three-dimensional temporal tensor, whose dimensions are represented as follows: This tensor is composed of , and The input consists of historical observations of the light spot intensity over three consecutive time points. This input method preserves the time-series information of the light spot flicker. By comparing the intensity fluctuation distribution between different frames, the network can infer the nonlinear evolution trend of the lateral wind speed vector and phase distortion of the turbulent medium. Furthermore, the angular spectrum propagation model is integrated into the closed-loop prediction and compensation path of deep learning.

[0062] In one example, a schematic diagram of the entire process of turbulence phase timing prediction and feedforward compensation based on a physical information neural network is shown below. Figure 6 As shown. This modeling process covers time... Historical observation sampling, physical information neural network time-series prediction to time The entire process of advanced phase compensation is described. By embedding a differentiable physical constraint layer into the network, it is possible not only to learn the temporal evolution dynamics of turbulence, but also to guide the network to output a predicted phase screen that conforms to the laws of wave optics through multi-dimensional physical criteria. Thus, the actual future phase screen can be realized. High-fidelity matching.

[0063] It should also be noted that high-quality predictive phase screens The beam is loaded into a spatial light modulator (SLM) to perform wavefront conjugate compensation. After being focused by a Fourier lens, the beam forms a diffraction-limited compensated focal spot at the receiver. The time-dependent wavefront conjugate compensation is then applied. The ability to extrapolate ahead can offset the computational latency of the hardware system.

[0064] To further illustrate the embodiments of the above-described training method for the space optical communication turbulence time series prediction model and the phase compensation method based on the space optical communication turbulence time series prediction model, this application also provides a specific application example of the training and compensation method for the space optical communication turbulence time series prediction model. Specifically, it includes the following: Existing technologies suffer from significant loss of temporal information and response lag. Due to the lack of modeling capabilities for the dynamic evolution of turbulence, the models cannot utilize the correlation of phase screen evolution over time, and can only achieve post-event phase recovery based on single-frame observations. In practical applications, limited by the physical time consumption of hardware processing and link feedback, the real-time turbulence state has already shifted by the time the compensation system executes its actions, causing the compensation effect to deteriorate drastically with system delay.

[0065] The core objective of this application example is to construct a nonlinear temporal prediction framework based on a sliding time window. By introducing a series of consecutive historical observation sequences with temporal correlation as joint input, a deep neural network is used to deeply mine the coherence and nonlinear evolution laws of the turbulent field in the spatiotemporal dimensions. This application example aims to overcome the limitations of traditional single-frame recovery models in the temporal dimension, achieving early prediction and feedforward compensation of the turbulent phase at the target time. This fundamentally offsets the time delay caused by transmission links and signal processing, significantly improving the phase compensation accuracy of space optical communication systems in dynamic turbulent environments.

[0066] This application presents an innovative architecture that combines prior physical knowledge with deep temporal feature extraction. Its core principle lies in leveraging the spatiotemporal correlation of atmospheric turbulence over short timescales to elevate traditional static single-frame reconstruction to dynamic sequence evolution prediction.

[0067] Existing turbulence phase retrieval and prediction methods typically use single-frame light intensity or single-frame phase screens as input at the data level, only recovering static turbulence within a single frame. A few methods involve time series, but these are mostly sequential processes of recovering phase frame by frame followed by time regression. The data sampling itself does not include turbulence dynamics assumptions; the time dimension is merely treated as a passive index, not as a component of physical constraints. This results in models that can only learn surface statistical correlations and cannot characterize the true evolution mechanism of turbulence. In contrast, this application example captures the evolutionary dynamics of the turbulent field by constructing a sliding time window. At the input end, the system no longer relies on distortion information at a single moment but maps the distorted light spot intensity sequence of k consecutive historical moments to a high-dimensional feature space. The neural network integrates a temporal feature extraction module, aiming to uncover the phase evolution patterns hidden in the light spot intensity fluctuations, thereby overcoming the limitation that a single frame image cannot represent time trends. Based on the historical observation evolution logic, the network actively predicts the transmitter turbulence phase screen at the current moment (or extrapolates to future moments based on system delays). Subsequently, an Angular Spectrum Multiplying (Angular Spectrum Multiplying) physical constraint layer was introduced to substitute the predicted phase information into the Fresnel diffraction model for forward propagation simulation. This process establishes a closed-loop mechanism of observation sequence, phase prediction, physical backpropagation, and residual feedback: by minimizing the difference between the predicted spot recovered by the physical constraint layer and the spot at the actual target time, the network is driven to spontaneously learn the nonlinear evolution function of turbulent phase change with time interval. This design ensures that the prediction results not only conform to the statistical distribution of the neural network but also strictly follow the physical laws of electromagnetic wave propagation, thus providing a high-precision wavefront compensation reference while meeting the system's real-time requirements.

[0068] This application also provides an electronic device, which may include a processor, a memory, a receiver, and a transmitter. The processor is used to execute the space optical communication turbulence time series prediction model training method and / or the phase compensation method based on the space optical communication turbulence time series prediction model mentioned in the above embodiments. The processor and the memory can be connected via a bus or other means, taking a bus connection as an example. The receiver can be connected to the processor and the memory via wired or wireless means.

[0069] The processor can be a central processing unit (CPU). The processor can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or combinations of the above types of chips.

[0070] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the space optical communication turbulence timing prediction model training method and / or the phase compensation method based on the space optical communication turbulence timing prediction model in the embodiments of this application. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions, and modules stored in the memory, thereby implementing the space optical communication turbulence timing prediction model training method and / or the phase compensation method based on the space optical communication turbulence timing prediction model in the above method embodiments.

[0071] The memory may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0072] The one or more modules are stored in the memory. When executed by the processor, they execute the training method for the spatial optical communication turbulence timing prediction model and / or the phase compensation method based on the spatial optical communication turbulence timing prediction model in the embodiment.

[0073] In some embodiments of this application, the user equipment may include a processor, a memory, and a transceiver unit. The transceiver unit may include a receiver and a transmitter. The processor, memory, receiver, and transmitter may be connected via a bus system. The memory is used to store computer instructions, and the processor is used to execute the computer instructions stored in the memory to control the transceiver unit to send and receive signals.

[0074] As one implementation method, the functions of the receiver and transmitter in this application can be implemented by transceiver circuits or dedicated transceiver chips, and the processor can be implemented by dedicated processing chips, processing circuits or general-purpose chips.

[0075] As another implementation approach, the server provided in this application embodiment can be implemented using a general-purpose computer. That is, the program code implementing the processor, receiver, and transmitter functions is stored in memory, and the general-purpose processor implements the processor, receiver, and transmitter functions by executing the code in memory.

[0076] This application also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps of the aforementioned training method for a space optical communication turbulence timing prediction model and / or a phase compensation method based on the space optical communication turbulence timing prediction model. The computer-readable storage medium can be a tangible storage medium, such as random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, floppy disks, hard disks, removable storage disks, CD-ROMs, or any other form of storage medium known in the art.

[0077] This application also provides a computer program product, specifically including a computer program that, when executed by a processor, implements the steps of the space optical communication turbulence time series prediction model training method and / or the phase compensation method based on the space optical communication turbulence time series prediction model mentioned in the foregoing embodiments.

[0078] Those skilled in the art will understand that the exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application. When implemented in hardware, it can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. The programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave.

[0079] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0080] In this application, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or in place of features of other embodiments.

[0081] The above description is merely a preferred embodiment of this application and is not intended to limit this application. For those skilled in the art, various modifications and variations can be made to the embodiments of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A training method for a time-series prediction model of turbulence in space optical communication, characterized in that, The method includes: The system acquires distorted light spot intensity data from multiple historical frames collected by the receiver in a space optical communication system, and constructs a historical light spot intensity sequence corresponding to the distorted light spot intensity of multiple historical frames based on a preset sliding window; wherein, the distorted light spot intensity is formed by the influence of underwater turbulent channel on optical transmission; Based on the historical light spot intensity sequence, a pre-defined spatiotemporal prediction network undergoes multiple rounds of self-supervised learning. The self-supervised learning steps include: inputting the historical light spot intensity sequence into a 3D convolutional neural network within the spatiotemporal prediction network, causing the 3D convolutional neural network to generate a prediction phase screen corresponding to the target prediction time; then, enabling the angular spectral transmission model in the spatiotemporal prediction network to convert the prediction phase screen into predicted light spot intensity and obtain the actual detected light spot intensity at the target prediction time; constructing a loss function based on the predicted light spot intensity and the actual detected light spot intensity and calculating a target loss value; and updating the parameters of the spatiotemporal prediction network based on the target loss value. If the convolutional neural network prediction model converges, the spatiotemporal prediction network will be used as the spatial optical communication turbulence time series prediction model for output.

2. The training method for a space optical communication turbulence time series prediction model according to claim 1, characterized in that, The acquisition of distorted light spot intensity data from multiple historical moments collected by the receiver in the space optical communication system includes: The original phase screen sequence is generated using a preset spatial power spectrum model; Generate the target phase screen sequence based on the Taylor hypothesis and the time phase shift factor; The light spot intensity corresponding to the target phase screen sequence is extracted to obtain light spot intensity data.

3. The training method for a space optical communication turbulence time series prediction model according to claim 2, characterized in that, The spatial power spectrum model includes the Nikishov power spectrum model, which is used to characterize temperature fluctuations, salinity fluctuations, and the cross-correlation between temperature fluctuations and salinity fluctuations.

4. The training method for a space optical communication turbulence time series prediction model according to claim 1, characterized in that, The mathematical form of the spatial power spectrum model includes: in, Represents the spatial frequency vector. Indicates the turbulent kinetic energy dissipation rate. Indicates the fluctuation dissipation rate. This represents the ratio of the contribution of salinity to temperature to the fluctuation of refractive index. The Kolmogorov scale is indicated. The decay operator represents the dissipation region. , , All of these represent dimensionless parameters, where T represents temperature and S represents salinity.

5. The training method for a space optical communication turbulence time series prediction model according to claim 1, characterized in that, The spatiotemporal prediction network includes: The encoder layer is used to extract the spatiotemporal feature vector of the historical spot intensity sequence using 3D convolution and downsampling operations; Pooling layers are used to pool the spatiotemporal feature vectors in both spatial and temporal dimensions to reduce data redundancy; The bottleneck layer is used to map the pooled spatiotemporal feature vectors to obtain abstract features. The decoder layer is used to restore the abstract features by employing 3D transposed convolution operations and upsampling operations to obtain multi-channel features; The output layer is used to fuse the multi-channel features using 3D convolution to obtain the predicted phase screen.

6. The training method for a space optical communication turbulence time series prediction model according to claim 1, characterized in that, The angular spectral transmission model is used to perform the following steps: A zero-fill operation to simulate the diffraction diffusion effect is performed on the predicted phase screen to obtain a zero-filled phase screen; The Gerchberg-Saxton algorithm and the hybrid input-output algorithm are alternately applied to the zero-filled phase screen to optimize the phase distribution of the phase screen, resulting in an optimized phase screen. The optimized phase screen is combined with the prior amplitude distribution of the transmitter probe beam to construct a complex amplitude. The complex amplitude is transformed to the angular spectrum domain using Fourier transform, multiplied with the angular spectrum transfer function, and then inverse Fourier transform is performed to obtain the propagated complex amplitude distribution. The propagated complex amplitude distribution is centrally clipped and returned to the effective observation area; The predicted spot intensity is calculated based on the complex amplitude distribution after trimming.

7. The training method for a space optical communication turbulence time series prediction model according to claim 1, characterized in that, The step of constructing a loss function based on the predicted light spot intensity and the actual detected light spot intensity and calculating the target loss value includes: Based on the predicted spot intensity and the training labels, a spatial loss function, a frequency domain loss function, and a support domain loss function are constructed; wherein, the spatial loss function is used to measure the difference between the predicted spot intensity and the actual detected spot intensity in pixel space; the frequency domain loss function is used to measure the difference between the predicted spot intensity and the actual detected spot intensity in spectral distribution; and the support domain loss function is used to measure the residual energy in the non-effective aperture region; The loss values ​​corresponding to each loss function are calculated and then weighted and summed to obtain the target loss value.

8. A phase compensation method based on a time-series prediction model of turbulence in space optical communication, characterized in that, include: To obtain the system processing latency in a space optical communication system; The target compensation time is determined based on the current time and the system processing delay. Obtain the historical distorted light spot intensities of multiple consecutive frames prior to the current moment, and form a historical light spot intensity sequence; The historical light spot intensity sequence is input into the space optical communication turbulence time series prediction model to generate the prediction phase screen for the target prediction time; wherein, the space optical communication turbulence time series prediction model is trained by the space optical communication turbulence time series prediction model training method according to any one of claims 1 to 7; The predicted phase screen is loaded onto the spatial light modulator to perform feedforward phase compensation on the beam.

9. 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 computer program, it implements the training method for the space optical communication turbulence timing prediction model as described in any one of claims 1 to 7, and / or implements the phase compensation method based on the space optical communication turbulence timing prediction model as described in any one of claims 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the training method for the spatial optical communication turbulence timing prediction model as described in any one of claims 1 to 7, and / or implements the phase compensation method based on the spatial optical communication turbulence timing prediction model as described in any one of claims 8.

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