Three-dimensional ocean state field generation type reconstruction method based on multi-source sparse observation constraint

Abstract

The application provides a three-dimensional marine state field generation type reconstruction method based on multi-source sparse observation constraint, relates to the field of marine observation, and specifically comprises the following steps: constructing an autoencoder and reconstructing a complete three-dimensional field from a hidden variable through a decoder; decoupling the three-dimensional marine state field into a vertical background hidden variable and a spatial anomaly hidden variable in a hidden space; constructing an observation constraint vertical background branch; generating a spatial anomaly hidden variable by adopting a conditional diffusion model; fusing the generated spatial anomaly hidden variable and the vertical background hidden variable to obtain a complete three-dimensional marine state field; generating a plurality of set reconstruction members to obtain a reconstruction result and an uncertainty distribution thereof; and evaluating the reconstruction result. The technical scheme of the application overcomes the problems in the prior art that a model background field needs to be used as a prior constraint, the system is complex to construct, the calculation cost is high, and it is difficult to fully express the multi-solution and uncertainty of the marine state field possibly existing under a sparse observation condition.

Description

Technical Field

[0001] This invention relates to the field of ocean observation, specifically to a generative reconstruction method for three-dimensional ocean state fields based on multi-source sparse observation constraints. Background Technology

[0002] The three-dimensional state field of the ocean is a crucial source of information for characterizing its internal structure and evolution. However, due to limitations in observation methods and the complexity of the marine environment, it is usually difficult to directly obtain a complete and continuous three-dimensional state field from real ocean observations.

[0003] Reconstructing sparse ocean observations not only requires addressing insufficient spatial coverage and missing vertical information, but also necessitates the rational utilization of temporal continuity information contained in nearby observations. This is crucial for restoring a stable, continuous, and physically plausible three-dimensional ocean state field even under conditions of incomplete or insufficient observations at the target time. Existing research has developed various methods for ocean field reconstruction under sparse observation conditions, including objective analysis, optimal interpolation, empirical orthogonal functions, numerical data assimilation, and machine learning and deep learning. Traditional statistical interpolation and low-dimensional modal methods offer advantages such as theoretical clarity and relatively simple implementation. However, they typically rely on pre-defined correlation scales, covariance structures, or historical master modes, limiting their ability to represent complex nonlinear structures and small-to-medium scale processes such as fronts, eddies, upwellings, and thermocline fluctuations, and leading to over-smoothing of reconstruction results. Numerical data assimilation methods can combine observational information with the dynamic model background field to form a relatively consistent ocean state estimate. However, they usually depend on a robust numerical model system, high-quality background field, well-defined error covariance, and substantial computational resources, resulting in high implementation costs in high-resolution, multi-source heterogeneous observation, and rapid reconstruction scenarios. In recent years, deep learning methods have been able to learn complex spatial, vertical, and temporal relationships from a large number of historical samples and integrate conditional information such as land-sea masking, latitude and longitude, topography, and multi-source observations, providing a new technical approach for 3D ocean field reconstruction. However, existing methods still have room for improvement in areas such as unified representation of multi-source heterogeneous observations, information fusion of temporally discontinuous observations, collaborative recovery of horizontal spatial structure and vertical background structure, computational efficiency of high-dimensional 3D field reconstruction, and uncertainty representation. In particular, joint modeling of large areas, high resolution, multiple depth layers, and multiple time slices significantly increases computational and storage overhead, while simple dimensionality reduction or excessive compression may lose local small-scale structures, vertical layering features, and regional differences. At the same time, many deterministic reconstruction methods mainly output single results, making it difficult to characterize the reconstruction reliability of sparsely observed regions, complex topographic regions, and vertically insufficient depth layers.

[0004] Therefore, there is a need for a generative reconstruction method for three-dimensional ocean state fields based on multi-source sparse observation constraints that fully utilizes spatial, vertical, and temporal information, can directly reconstruct continuous three-dimensional fields from observations, and takes into account computational efficiency, structural stability, and uncertainty. Summary of the Invention

[0005] The main objective of this invention is to provide a generative reconstruction method for three-dimensional ocean state fields based on multi-source sparse observation constraints, in order to solve the problems in existing technologies that require a pattern background field as a priori constraint, have complex system construction, high computational cost, and are difficult to fully express the multiple solutions and uncertainties that may exist in the ocean state field under sparse observation conditions.

[0006] To achieve the above objectives, this invention provides a generative reconstruction method for three-dimensional ocean state fields based on multi-source sparse observation constraints, specifically including the following steps: S1 acquires historical three-dimensional ocean state field data, multi-source sparse ocean observation data, and static auxiliary condition data for the target sea area, and performs data processing.

[0007] S2 constructs an observation window based on the target date or target time, and uses the ocean state variables from satellite remote sensing, profile observation, fixed-point observation and mobile platform observation within the observation window as input conditions for the automatic encoder.

[0008] S3 constructs an autoencoder to compress the complete three-dimensional ocean state field from the original physical space to the latent space, and then reconstructs the complete three-dimensional field from the latent variables through a decoder.

[0009] S4 decouples the three-dimensional ocean state field into vertical background latent variables and spatial anomaly latent variables in the latent space, which are used to characterize the large-scale vertical stratification structure and local spatial variation structure of the ocean field, respectively.

[0010] S5 uses underwater gliders, buoys, or underwater gliders to observe the background profile, and uses the observation mask, depth coverage, and error information corresponding to the background profile to construct the vertical background branch of the observation constraints, which is used to estimate or correct the vertical background latent variables.

[0011] S6 employs a conditional diffusion model, using multi-source sparse observations, static auxiliary conditions, and vertical background latent variables as constraints to generate spatial anomaly latent variables.

[0012] S7, the generated spatial anomaly latent variables are fused with the vertical background latent variables and input into the decoder of the autoencoder to obtain the complete three-dimensional ocean state field corresponding to the target time or target time window.

[0013] S8 generates multiple sets of reconstructed members by performing multiple diffusion samplings under the same observation conditions, and calculates the set mean and set dispersion to obtain the reconstruction result and its uncertainty distribution.

[0014] S9 uses root mean square error, mean absolute error, systematic bias, correlation coefficient, and depth-layer index to evaluate the numerical accuracy, vertical stability, and spatial structure consistency of the reconstruction results.

[0015] Furthermore, step S1 specifically includes the following steps: S1.1, select historical three-dimensional ocean state field data of the target sea area as training samples, including: temperature, salinity, density, sound speed, and current velocity; for the temperature field, the target three-dimensional temperature field... for: ; in, Indicates the length of the time window. Indicates the vertical depth layer number. and These represent the height and width of the horizontal spatial grid, respectively.

[0016] S1.2, Acquire the set of multi-source sparse ocean observation data within the target sea area and target time window. : ; in, Indicates the first One observation value, Indicates horizontal spatial position. Indicates the observation time. Indicates the depth of observation. Indicates the source or type of observation. This indicates the level of observation error or the reliability of the observation. Indicates the number of observations.

[0017] Furthermore, step S1 also includes the following steps: S1.3, Obtain the static environmental conditions corresponding to the target sea area, including: land-sea cover, latitude and longitude, topography, water depth, and distance from the coastline. for: ; in, This represents the number of channels for a static condition variable.

[0018] S1.4 is a collection of sparse observations from different sources, at different times, at different depths, and with different spatial distributions. Mapped to a unified spatiotemporal depth grid, forming observation tensors, observation mask tensors, observation type tensors, and observation error tensors; let the unified conditional inputs be: ; in, Represents the observation tensor; Represents the observation mask tensor; The observation type encoding tensor; This represents the observation error or observation weight tensor. This indicates static environmental conditions.

[0019] S1.5 uses a normalization formula to standardize the historical three-dimensional ocean state field data and multi-source sparse ocean observation data of the target sea area.

[0020] Furthermore, the observation window in step S2 for: ; in, For the target time, and These represent the available time range before and after the target time.

[0021] Furthermore, step S3 specifically includes: ; in, For the target three-dimensional temperature field, Represented as a latent space. The reconstructed field obtained by the decoder, For encoder, For decoders.

[0022] Furthermore, step S4 specifically includes the following steps: S4.1 decomposes the three-dimensional field into vertical background and spatial anomaly. For the temperature field, calculate the spatially averaged vertical profile at each time and depth: ; in, Indicates the first The moment, the first Spatial average vertical background value at each depth layer; Represents the effective set of ocean grids. Indicates the number of effective ocean grids; This indicates the time index within the time window. Indicates the vertical depth layer index. Indicates the vertical position index of the horizontal spatial grid. Indicates the horizontal position index of the horizontal spatial grid. Represents the three-dimensional ocean state field At any moment Depth layer Horizontal grid position The value of the state variable at that location.

[0023] The corresponding spatial anomaly field is: ; in, This indicates a local spatial anomaly relative to the vertical background.

[0024] S4.2, in the latent space, the encoder output is designed to include two types of latent variables: ; in, Represents the vertical background latent variable; Represents hidden variables with spatial anomalies.

[0025] Basic Reconstruction Loss for Autoencoder Training Represented as: ; Alternatively, the basic reconstruction loss during autoencoder training can be expressed in the form of mean squared error. : ; in, This represents the decoder mapping function in an autoencoder.

[0026] Furthermore, step S5 specifically includes the following steps: S5.1, let the initial estimate of the background profile obtained from vertical observation be... The corresponding observation coverage mask is Through vertical background branches Obtain the estimates of vertical background latent variables : ; in, This indicates vertical observation error or weighting information. This indicates static environmental conditions.

[0027] Vertical background branch It is a trainable neural network. Its function is to encode the corrected vertical background profile, observation coverage information, observation error information, and static environmental conditions into estimates of vertical background latent variables.

[0028] S5.2, To avoid excessive vertical background correction leading to unreasonable layering structures, a constrained residual correction method is adopted: ; in, This is an estimate of the vertical background profile. For residual correction networks, This is the residual amplitude control coefficient. This is the activation function.

[0029] Furthermore, step S6 specifically includes the following steps: S6.1, let the real space anomalous latent variables be... During the forward noise addition process of the diffusion model, it gradually moves towards Add Gaussian noise: ; in, Indicates the number of diffusion steps. The number of diffusion steps is Real-space anomaly hidden variables, Indicates that in the given first Step space anomaly hidden variable Under the conditions, obtain the first Step-by-step noise spatial anomaly latent variable The general distribution of positive diffusion conditions, Indicates the first Step noise intensity, It is the identity matrix. It follows a multivariate Gaussian distribution.

[0030] Based on the properties of the diffusion process, the noise addition result at any step is obtained. : ; in, , Indicates the first Signal retention coefficient for each diffusion step; , As of the date The cumulative information retention coefficient for each diffusion step; , To and Standard Gaussian noise with the same dimensions.

[0031] S6.2, Conditional Diffusion Network by diffusion steps Multi-source observation conditions Vertical background latent variable estimates and static environmental conditions Given the input, predict the noise term: .

[0032] S6.3, the training objective of the diffusion model is to minimize the error between the actual noise and the predicted noise: ; in, This represents the predicted loss for diffuse noise. Represents the real-space outlier latent variables corresponding to the training samples. diffusion steps and standard Gaussian noise Find the expected value.

[0033] S6.4, In the inference phase, firstly, based on the multi-source observation conditions within the target time window... And obtained from the vertical background branch Subsequently, initial spatial outlier latent variables were sampled from a standard Gaussian distribution. : ; Then, by using a conditional diffusion model to perform stepwise reverse denoising, the estimated values ​​of the generated spatial anomaly latent variables are obtained. The backsampling process is represented as: ; in, for The conditional probability distribution of back diffusion, This represents the inverse mean predicted by the diffusion network. This represents the variance of the backsampling.

[0034] Furthermore, step S7 specifically includes the following steps: S7.1 After completing the reverse denoising, the generated vertical background latent variable estimates are fused with the spatial anomaly latent variable estimates: .

[0035] S7.2, input to the decoder to obtain the complete three-dimensional ocean state field: ; in, This refers to the 3D reconstruction result corresponding to the target time or target time window.

[0036] S7.3, Let the target time be... The conditional input consists of observations within the vicinity of the target time: ; in, Indicates time Corresponding multi-source observation conditions; Indicates the target time Constructed set of multi-time observation conditions; Alternatively, a causal window that includes only the period before and at the target time can be used: ; in, Indicates the time window radius or window length.

[0037] S7.4 Utilize multi-time observation information within the window to generate a three-dimensional ocean state field corresponding to the target time. : ; in, This represents a generative reconstruction model composed of a vertical background branch, a conditional diffusion model, and a decoder.

[0038] Furthermore, step S8 specifically includes the following steps: S8.1, let the first... The reconstruction result obtained from the second sampling is The number of samples in the set is Then the set mean is: .

[0039] S8.2, ensemble uncertainty is represented by ensemble standard deviation: ; in, This represents the final set of averaged reconstructed fields. This represents the uncertainty estimate in terms of corresponding spatial location, depth layer, and time.

[0040] S8.3, the total training loss is expressed as: ; in, The vertical background constraint loss is defined as the true vertical background. and vertical background estimates The mean square error between them and These are the weighting coefficients.

[0041] The present invention has the following beneficial effects: Under multi-source sparse ocean observation conditions, this invention does not rely on a complete numerical model background field as input. Instead, it learns the statistical structure and physical morphology priors of the three-dimensional field from historical ocean state samples through a conditional generative model. Under the joint constraints of satellite remote sensing, vertical profiling, fixed-point observations, mobile platform observations, and static environmental conditions, it directly generates a continuous three-dimensional ocean state field corresponding to the target time or target time window. Therefore, compared with traditional data assimilation methods that rely on numerical model background fields and complex error covariance settings, this method can reduce the dependence on model system and background field quality and improve its applicability in scenarios with sparse observations, discontinuous observations, or difficult-to-obtain background fields.

[0042] Meanwhile, this method maps the high-dimensional 3D ocean state field to the latent space and then diffuses it to generate the state, avoiding the high GPU memory, high storage, and high computational overhead caused by directly modeling in the original 3D physical space. This is beneficial for improving the training and inference efficiency of large-area, high-resolution, and multi-depth layer reconstruction tasks. Furthermore, the latent space distinguishes between vertical background structures and spatial anomaly structures, enabling stable representation of vertical layering information such as the mixing layer, thermocline, and deep background state. Local spatial structures such as fronts, vortices, small- and medium-scale disturbances, and horizontal gradients can also be effectively recovered, thus balancing the rationality of vertical structures with the integrity of spatial details.

[0043] Furthermore, multi-source observations and observations within adjacent time windows are unified as generation conditions, enabling observations from different sources, with different spatial distributions, different depth coverages, and different error characteristics to jointly constrain the 3D field reconstruction. This processing method utilizes both the large-scale surface information from satellite observations and the vertical structure information provided by in-situ observations, and supplements the constraint gaps caused by insufficient observations at the target time through observations at adjacent time points, thereby enhancing the reconstruction stability under dynamic sparsity and temporal discontinuity observation conditions. Because the diffusion model has random sampling capabilities, multiple 3D state field samples that meet the observation constraints and have reasonable structures can be generated under the same observation conditions, further yielding the ensemble mean, ensemble dispersion, or spatial uncertainty distribution, providing richer information support for marine environmental analysis, observation system evaluation, and subsequent data assimilation. Attached Figure Description

[0044] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 A flowchart of a three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints is shown.

[0045] Figure 2 The actual sea surface temperature field of a certain study area is shown.

[0046] Figure 3 The temperature field of a study area after reconstruction using the method provided by this invention is shown.

[0047] Figure 4 The results of vertical temperature profile reconstruction obtained using the method provided in this invention are shown. Detailed Implementation

[0048] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] like Figure 1 The method for generative reconstruction of three-dimensional ocean state fields based on multi-source sparse observation constraints, as shown, specifically includes the following steps: S1 acquires historical three-dimensional ocean state field data, multi-source sparse ocean observation data, and static auxiliary condition data for the target sea area, and performs data processing, including: ensuring the consistency and usability of data from different sources through time matching, spatial alignment, data cleaning, observation mask construction, and normalization.

[0050] S2 constructs an observation window based on the target date or target time, and uses the ocean state variables from satellite remote sensing, profile observation, fixed-point observation and mobile platform observation within the observation window as input conditions for the automatic encoder.

[0051] S3 constructs an autoencoder to compress the complete three-dimensional ocean state field from the original physical space to the latent space, and then reconstructs the complete three-dimensional field from the latent variables through a decoder.

[0052] S4 decouples the three-dimensional ocean state field into vertical background latent variables and spatial anomaly latent variables in the latent space, which are used to characterize the large-scale vertical stratification structure and local spatial variation structure of the ocean field, respectively.

[0053] S5 uses on-site observations from underwater gliders, buoys, and underwater gliders to obtain background profiles. It then uses the observation mask, depth coverage, and error information corresponding to the background profiles to construct vertical background branches constrained by observations, which are used to estimate or correct the hidden variables of the vertical background.

[0054] S6 employs a conditional diffusion model, using multi-source sparse observations, static auxiliary conditions, and vertical background latent variables as constraints to generate spatial anomaly latent variables.

[0055] S7, the generated spatial anomaly latent variables are fused with the vertical background latent variables and input into the decoder of the autoencoder to obtain the complete three-dimensional ocean state field corresponding to the target time or target time window.

[0056] S8 generates multiple sets of reconstructed members by performing multiple diffusion samplings under the same observation conditions, and calculates the set mean and set dispersion to obtain the reconstruction result and its uncertainty distribution.

[0057] S9 uses root mean square error, mean absolute error, systematic bias, correlation coefficient, and depth-layer index to evaluate the numerical accuracy, vertical stability, and spatial structure consistency of the reconstruction results.

[0058] Specifically, step S1 includes the following steps: S1.1, select historical three-dimensional ocean state field data of the target sea area as training samples, including: temperature, salinity, density, sound speed, and current velocity; for the temperature field, the target three-dimensional temperature field... for: ; in, Indicates the length of the time window. Indicates the vertical depth layer number. and These represent the height and width of the horizontal spatial grid, respectively.

[0059] S1.2, Based on the actual observation system or observation simulation system, acquire a set of multi-source sparse ocean observation data for the target sea area and the target time window. : ; in, Indicates the first One observation value, Indicates horizontal spatial position. Indicates the observation time. Indicates the depth of observation. Indicates the source or type of observation. This indicates the level of observation error or the reliability of the observation. Indicates the number of observations.

[0060] The types of observations include: satellite remote sensing observations, used to provide constraints on the state of the sea surface or near-surface; profile observations such as Argo, CTD, and XBT, used to provide vertical temperature or other variable profile constraints; fixed-point observations such as moored moorings and buoys, used to provide continuous or intermittent time series constraints at fixed locations; and observations from mobile platforms such as gliders, AUVs, and shipborne underway observations, used to provide profile or point constraints distributed along a trajectory.

[0061] Specifically, step S1 also includes the following steps: S1.3, Obtain the static environmental conditions corresponding to the target sea area, including: land-sea cover, latitude and longitude, topography, water depth, and shoreline distance, to provide geographic location, land-sea boundary, and topographic modulation information. Static conditions for: ; in, This represents the number of channels for a static condition variable.

[0062] S1.4 is a collection of sparse observations from different sources, at different times, at different depths, and with different spatial distributions. Mapped to a unified spatiotemporal depth grid, forming observation tensors, observation mask tensors, observation type tensors, and observation error tensors; let the unified conditional inputs be: ; in, This represents the observation tensor; unobserved locations can be filled with zeros or preset default values. This represents the observation mask tensor, used to identify whether an observation exists in the corresponding grid. This represents the observation type encoding tensor, used to distinguish different sources such as satellites, buoys, and underwater gliders; This represents the observation error or observation weight tensor. This represents static environmental conditions. Through this unified coding method, different observation sources can all serve as constraints on the generative model and participate in the 3D field reconstruction.

[0063] S1.5, the historical three-dimensional ocean state field data and multi-source sparse ocean observation data of the target sea area are standardized using a normalization formula. The normalization formula is: ; in, and They represent the data on the training set, respectively. The mean and standard deviation, This is the normalized data. To avoid leakage of statistical information, the normalized statistic is calculated only from the samples during the training period; the validation and testing periods are not included in the statistic estimation.

[0064] Specifically, the observation window in step S2 for: ; in, For the target time, and These represent the available time range before and after the target time; in practice, a multi-day window ending with the target date can also be used, such as a three-day window.

[0065] Specifically, due to the high dimensionality of the original three-dimensional ocean field, direct diffusion generation in physical space would result in significant memory and computational overhead. Therefore, this invention first constructs an autoencoder to map the complete three-dimensional ocean state field to the latent space, and then recovers the three-dimensional field through a decoder. Step S3 specifically involves: ; in, For the target three-dimensional temperature field, Represented as a latent space. The reconstructed field obtained by the decoder, For encoder, For decoders.

[0066] Specifically, step S4 includes the following steps: S4.1, To adapt to the physical structure characteristics of the three-dimensional ocean field, this invention further decomposes the three-dimensional field into a vertical background and a spatial anomaly. For the temperature field, the spatially averaged vertical profile at each time and depth is calculated: ; in, Indicates the first The moment, the first Spatial average vertical background value at each depth layer; Represents the effective set of ocean grids. Indicates the number of effective ocean grids; This indicates the time index within the time window. Indicates the vertical depth layer index. Indicates the vertical position index of the horizontal spatial grid. Indicates the horizontal position index of the horizontal spatial grid. Represents the three-dimensional ocean state field At any moment Depth layer Horizontal grid position The value of the state variable at that location.

[0067] The corresponding spatial anomaly field is: ; in, This indicates a local spatial anomaly relative to the vertical background.

[0068] S4.2, in the latent space, the encoder output is designed to include two types of latent variables: ; in, Represents the vertical background latent variable, used to characterize vertical structures such as the mixing layer, thermocline layer, and deep background state; It represents spatial anomaly latent variables, used to characterize spatial structures such as fronts, vortices, small- and medium-scale disturbances, and horizontal gradients.

[0069] Basic Reconstruction Loss for Autoencoder Training Represented as: ;Right now: ; Alternatively, the basic reconstruction loss during autoencoder training can be expressed in the form of mean squared error. : ;Right now: ; in, This represents the decoder mapping function in an autoencoder, used to map vertical background latent variables. and spatial anomalies and hidden variables Mapping back to the original physical space yields the reconstructed field. .

[0070] In actual training, depth-weighted loss, gradient loss, or mask constraint loss can also be added to enhance the reconstruction capability of the sea surface, thermocline, or key depth layers.

[0071] Specifically, the vertical background structure has a significant impact on the physical plausibility of the three-dimensional ocean field. Since in-situ observations from moorings, buoys, and underwater gliders can provide profile information at different depths, this invention utilizes vertical observations to construct an estimate of the background vertical structure and generate corresponding vertical background latent variables.

[0072] Step S5 specifically includes the following steps: S5.1, let the initial estimate of the background profile obtained from vertical observation be... The corresponding observation coverage mask is Through vertical background branches Obtain the estimates of vertical background latent variables : ; in, This indicates vertical observation error or weighting information. This indicates static environmental conditions.

[0073] S5.2, To avoid excessive vertical background correction leading to unreasonable layering structures, a constrained residual correction method is adopted: ; in, This is an estimate of the vertical background profile. For residual correction networks, This is the residual amplitude control coefficient. This is the activation function used to limit the correction range. This allows us to constrain the vertical background using the observation profile while avoiding disruption of the existing layered structure provided by the vertical observations during the generation process.

[0074] Specifically, the diffusion model of this invention is mainly used to generate spatial anomaly latent variables. By generating only the spatial anomaly portion and leaving the vertical background structure to be handled by the observation constraint branch, the generation difficulty can be reduced and the stability of the vertical structure can be improved.

[0075] Step S6 specifically includes the following steps: S6.1, let the real space anomalous latent variables be... During the forward noise addition process of the diffusion model, it gradually moves towards Add Gaussian noise: ; in, Indicates the number of diffusion steps. The number of diffusion steps is Real-space anomaly hidden variables, Indicates that in the given first Step space anomaly hidden variable Under the conditions, obtain the first Step-by-step noise spatial anomaly latent variable The general distribution of positive diffusion conditions, Indicates the first Step noise intensity, It is the identity matrix. It follows a multivariate Gaussian distribution;

[0076] Based on the properties of the diffusion process, the noise addition result at any step is obtained. : ; in, , Indicates the first Signal retention coefficient for each diffusion step; , As of the date The cumulative information retention coefficient for each diffusion step; , To and Standard Gaussian noise with the same dimensions.

[0077] S6.2, Conditional Diffusion Network by diffusion steps Multi-source observation conditions Vertical background latent variable estimates and static environmental conditions Given the input, predict the noise term: .

[0078] S6.3, the training objective of the diffusion model is to minimize the error between the actual noise and the predicted noise: ; in, This represents the predicted loss for diffuse noise. Represents the real-space outlier latent variables corresponding to the training samples. diffusion steps and standard Gaussian noise Find the expected value.

[0079] S6.4, In the inference phase, firstly, based on the multi-source observation conditions within the target time window... And obtained from the vertical background branch Subsequently, initial spatial outlier latent variables were sampled from a standard Gaussian distribution. : ; Then, by using a conditional diffusion model to perform stepwise reverse denoising, the estimated values ​​of the generated spatial anomaly latent variables are obtained. The backsampling process is represented as: ; in, for The conditional probability distribution of back diffusion, This represents the inverse mean predicted by the diffusion network. This represents the variance of the backsampling.

[0080] Specifically, step S7 includes the following steps: S7.1 After completing the reverse denoising, the generated vertical background latent variable estimates are fused with the spatial anomaly latent variable estimates: .

[0081] S7.2, input to the decoder to obtain the complete three-dimensional ocean state field: ; in, This refers to the 3D reconstruction result corresponding to the target time or target time window.

[0082] Through this conditional diffusion training process, the model learns the ability to gradually generate reasonable spatial anomaly latent variables from random noise under multi-source sparse observations and vertical background constraints.

[0083] S7.3 To address the issues of discontinuity in ocean observation over time and insufficient observation at target times, this invention employs multiple time windows as model inputs.

[0084] Let the target time be The conditional input consists of observations within the vicinity of the target time: ; in, Indicates time The corresponding multi-source observation conditions include the observation value tensor, the observation mask tensor, the observation type coding tensor, and the observation error tensor; Indicates the target time Construct a multi-time observation condition set; or use a causal window that only includes the period before and at the target time: ; in, Indicates the time window radius or window length.

[0085] S7.4 Utilize multi-time observation information within the window to generate a three-dimensional ocean state field corresponding to the target time. : ; in, This represents a generative reconstruction model composed of a vertical background branch, a conditional diffusion model, and a decoder. Through a multi-time window design, the model can utilize the temporal continuity information in nearby observations, improving reconstruction stability under conditions of missing or sparse observations at the target time.

[0086] Specifically, because the conditional diffusion model has random sampling capability, multiple three-dimensional ocean state field samples can be generated by sampling multiple times under the same observation conditions.

[0087] Step S8 specifically includes the following steps: S8.1, let the first... The reconstruction result obtained from the second sampling is The number of samples in the set is Then the set mean is: .

[0088] S8.2, ensemble uncertainty is represented by ensemble standard deviation: ; in, This represents the final set of averaged reconstructed fields. This represents the uncertainty estimate corresponding to spatial location, depth layer, and time. This uncertainty distribution can be used to identify the reconstruction reliability of sparsely observed regions, regions with insufficient vertical constraints, and regions with strong small- to medium-scale activity.

[0089] S8.3 The training process of this invention can be divided into three stages: autoencoder training, latent variable statistics, and conditional diffusion model training.

[0090] During the autoencoder training phase, complete 3D ocean state field samples are used to train the encoder and decoder, enabling them to reconstruct the 3D field from the latent space and back to the 3D field with minimal loss. ; The goal of this phase is to ensure that the latent space representation can fully preserve the key vertical structure and spatial anomaly structure of the three-dimensional ocean field.

[0091] In the latent variable statistics phase, the mean, standard deviation, and other statistics of spatial outlier latent variables and vertical background latent variables are calculated using the training set samples. These statistics are then used for latent variable standardization in subsequent diffusion training. For any latent variable... Its standardized form is: ; in, and These are the mean and standard deviation of the latent variables in the training set, respectively. For standardization .

[0092] During the training phase of the conditional diffusion model, a pre-trained encoder is fixed or used in combination to encode the training samples as spatial anomalous latent variables. And input the conditions for constructing multi-source sparse observations of the corresponding samples. The model learns by adding and denoising, generating spatial anomaly latent variables under observation conditions and vertical background constraints. The total training loss is expressed as: ;

[0093] in, The vertical background constraint loss is defined as the true vertical background. and vertical background estimates The mean square error between them and These are the weighting coefficients. If the autoencoder and diffusion model are trained in stages, the corresponding losses can also be optimized separately.

[0094] During the training phase, based on a complete and realistic three-dimensional ocean state field The true vertical background is calculated according to the spatial averaging formula in S4.1. The vertical background branch obtains the vertical background estimate based on sparse vertical observations. Vertical background constraint loss Defined as the mean square error between the two: ; in, Indicates the length of the time window. Indicates the vertical depth layer number.

[0095] Specifically, in step S9, to evaluate the numerical accuracy, spatial structure consistency, and vertical structure rationality of the 3D reconstruction results, indicators such as root mean square error, mean absolute error, bias, and correlation coefficient can be used. The root mean square error is defined as: ; Mean absolute error is defined as: ; Deviation is defined as: ; The correlation coefficient is defined as: ; in, Represents the actual value. Indicates the reconstructed value. Indicates the number of valid grid points. and These represent the average values ​​of the actual and reconstructed values, respectively. These metrics can be calculated across the entire 3D field, at different depths, within different time windows, and in key regions to comprehensively evaluate the model's reconstruction accuracy, vertical structural stability, and spatial structural recovery capability.

[0096] In one specific embodiment, this invention is used to reconstruct the upper ocean three-dimensional temperature field based on multi-source sparse pseudo-observations. The complete ground truth sample uses the daily three-dimensional temperature field output from historical ocean models. Pseudo-observations are generated by sampling from this temperature field to simulate actual ocean observation systems, including satellite sea surface temperature observations, Argo vertical temperature profiles, moored observations, and glider observations. Simultaneously, the model input also includes static environmental conditions such as land-sea masking, latitude and longitude, and topography. The goal of this embodiment is to recover the continuous three-dimensional temperature field corresponding to the target date based on sparse observations of the target date and its neighboring dates without inputting the complete numerical model background field. Temperature normalized statistics, autoencoder training samples, latent variable statistics, and diffusion model training samples are all constructed solely from training year data to avoid leakage of validation and testing year information. The model uses a continuous three-day window as input each time, for example, for the target date. ,enter , and Sparse observations and static conditions over three days, with a primary assessment of the target date. The reconstruction results allow us to utilize observation information from nearby dates to alleviate the problem of insufficient daily observations.

[0097] In model implementation, an autoencoder is first trained to map the three-day, multi-depth 3D temperature field to the latent space, representing it as vertical background latent variables and spatial anomaly latent variables. The vertical background latent variables characterize the spatially averaged vertical temperature structure, while the spatial anomaly latent variables characterize local spatial variations relative to the background profile. Subsequently, the vertical background latent variables are estimated and corrected by the profile branch under observation constraints, while the spatial anomaly latent variables are generated by a conditional diffusion model under multi-source sparse observation constraints. The two are then fused and decoded to recover the complete 3D temperature field. In one implementation, the latent space includes 16 spatial anomaly channels and 38 vertical profile channels, totaling 54 channels; this channel setting is merely an example and can be adjusted based on the number of depth layers, target variables, and computational resources. During inference, the model constructs a unified conditional input based on observations within a three-day window of the target date, observation masks, observation types, observation errors, and static environmental conditions, generating the vertical background latent variables and spatial anomaly latent variables, and then decodes them to obtain the reconstructed 3D temperature field. By performing multiple diffusion samplings on the same input conditions, multiple set members can be obtained. The set mean and set standard deviation are then calculated to represent the reconstruction results and their uncertainties.

[0098] In the test implementation, the area near the Xisha Islands (latitude 17°N–18°N, longitude 111°E–112°E) can be selected as the evaluation area to reconstruct and evaluate the daily target dates for the validation and test sets. Evaluation metrics include root mean square error, mean absolute error, systematic bias, correlation coefficient, and depth-layer indices. The system can output results such as the true field, reconstructed field, error field, uncertainty field, observation location overlay map, and vertical profile comparison map for different depth layers.

[0099] The above embodiments are merely illustrative of one specific implementation of the present invention and do not limit the scope of protection of the present invention. The present invention can also be extended to other ocean state variables such as salinity, density, sound speed, and current velocity, as well as three-dimensional ocean field reconstruction tasks under different sea areas, different depth ranges, different time window lengths, and different observation combinations.

[0100] Figure 2 and Figure 3 This is a comparison of the sea surface temperature reconstruction results of the study area on January 28, 2018, in this embodiment. Figure 2 For a real temperature field, Figure 3 The image shows the average reconstruction results of the model ensemble, with colors representing temperature magnitudes and longitude and latitude as the horizontal and vertical axes, respectively. It can be seen that the model reconstruction results generally reproduce the spatial distribution characteristics of the transition from low temperatures in the northwest to high temperatures in the southeast within the study area, and can effectively characterize the main temperature gradients and the distribution range of warm water. This indicates that the method provided by this invention can recover a relatively continuous spatial structure of ocean temperature under sparse observation constraints. Figure 4This paper presents the reconstructed vertical temperature profile at latitude 17.500°N and longitude 111.500°E on January 28, 2018, obtained using the method provided in this invention. The black curve represents the actual temperature profile, the blue curve represents the model ensemble mean reconstruction result, and the light blue shading represents the range of the ensemble mean within one standard deviation. It can be seen that the model-reconstructed profile generally matches the actual profile well, accurately reproducing the temperature decrease trend from the sea surface to a depth of 300 m and the vertical variation characteristics near the thermocline. Furthermore, the ensemble uncertainty is small, indicating that the method provided in this invention has good reconstruction capability and stability for vertical temperature structures.

[0101] This invention proposes a method for reconstructing a three-dimensional ocean field based on latent space diffusion generation. By combining multi-source sparse ocean observations with a latent space generation model of the ocean state field, it reconstructs a continuous three-dimensional ocean state field directly from observational data such as satellite remote sensing, vertical profiles, fixed points, and mobile platforms without relying on the background field input of a complete numerical model. This invention further decouples the latent space representation into vertical background latent variables and spatial anomaly latent variables, enabling the model to maintain the stability of vertical stratification structures such as mixing layers and thermoclines, while also recovering spatial details such as fronts, vortices, and small- to medium-scale disturbances. Simultaneously, leveraging the conditional generation and multiple sampling capabilities of the diffusion model, this invention can generate physically reasonable complete three-dimensional fields under conditions of sparse observations, temporal discontinuities, or localized missing data, and provides ensemble uncertainty estimation. This provides an efficient, flexible, and highly generalizable new technological approach for ocean data reconstruction, observation system evaluation, and marine environmental analysis.

[0102] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A generative reconstruction method for three-dimensional ocean state fields based on multi-source sparse observation constraints, characterized in that, Specifically, the steps include the following: S1: Acquire historical three-dimensional ocean state field data, multi-source sparse ocean observation data, and static auxiliary condition data of the target sea area, and perform data processing. S2, construct an observation window based on the target date or target time, and use the ocean state variables from satellite remote sensing, profile observation, fixed point observation and mobile platform observation within the observation window as input conditions for the automatic encoder; S3, construct an autoencoder to compress the complete three-dimensional ocean state field from the original physical space to the latent space, and reconstruct the complete three-dimensional field from the latent variables through a decoder; S4 decouples the three-dimensional ocean state field into vertical background latent variables and spatial anomaly latent variables in the latent space, which are used to characterize the large-scale vertical stratification structure and local spatial variation structure of the ocean field, respectively. S5 uses underwater gliders, buoys or underwater gliders to observe the background profile, and uses the observation mask, depth coverage and error information corresponding to the background profile to construct the vertical background branch of the observation constraint, which is used to estimate or correct the vertical background latent variables. S6 adopts a conditional diffusion model, using multi-source sparse observations, static auxiliary conditions, and vertical background latent variables as constraints to generate spatial anomaly latent variables; S7, the generated spatial anomaly latent variables are fused with the vertical background latent variables and input into the decoder of the autoencoder to obtain the complete three-dimensional ocean state field corresponding to the target time or target time window. S8 generates multiple sets of reconstructed members by performing multiple diffusion samplings under the same observation conditions, and calculates the set mean and set dispersion to obtain the reconstruction result and its uncertainty distribution; S9 uses root mean square error, mean absolute error, systematic bias, correlation coefficient, and depth-layer index to evaluate the numerical accuracy, vertical stability, and spatial structure consistency of the reconstruction results.

2. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Step S1 specifically includes the following steps: S1.1, select historical three-dimensional ocean state field data of the target sea area as training samples, including: temperature, salinity, density, sound speed, and current velocity; for the temperature field, the target three-dimensional temperature field... for: ； in, Indicates the length of the time window. Indicates the vertical depth layer number. and These represent the height and width of the horizontal spatial grid, respectively. S1.2, Acquire the set of multi-source sparse ocean observation data within the target sea area and target time window. : ； in, Indicates the first One observation value, Indicates horizontal spatial position. Indicates the observation time. Indicates the depth of observation. Indicates the source or type of observation. This indicates the level of observation error or the reliability of the observation. Indicates the number of observations.

3. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 2, characterized in that, Step S1 also includes the following steps: S1.3, Obtain the static environmental conditions corresponding to the target sea area, including: land-sea cover, latitude and longitude, topography, water depth, and distance from the coastline. for: ； in, This represents the number of channels for a static condition variable. S1.4 is a collection of sparse observations from different sources, at different times, at different depths, and with different spatial distributions. Mapped to a unified spatiotemporal depth grid, forming observation tensors, observation mask tensors, observation type tensors, and observation error tensors; let the unified conditional inputs be: ； in, Represents the observation tensor; Represents the observation mask tensor; The observation type encoding tensor; This represents the observation error or observation weight tensor. Indicates static environmental conditions; S1.5 uses a normalization formula to standardize the historical three-dimensional ocean state field data and multi-source sparse ocean observation data of the target sea area.

4. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Observation window in step S2 for: ； in, For the target time, and These represent the available time range before and after the target time.

5. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Step S3 is as follows: ； in, For the target three-dimensional temperature field, Represented as a latent space. The reconstructed field obtained by the decoder, For encoder, For decoders.

6. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Step S4 specifically includes the following steps: S4.1 decomposes the three-dimensional field into vertical background and spatial anomaly. For the temperature field, calculate the spatially averaged vertical profile at each time and depth: ； in, Indicates the first The moment, the first Spatial average vertical background value at each depth layer; Represents the effective set of ocean grids. Indicates the number of effective ocean grids; This indicates the time index within the time window. Indicates the vertical depth layer index. Indicates the vertical position index of the horizontal spatial grid. Indicates the horizontal position index of the horizontal spatial grid. Represents the three-dimensional ocean state field At any moment Depth layer Horizontal grid position The state variable value at that location; The corresponding spatial anomaly field is: ； in, Indicates a local spatial anomaly relative to the vertical background; S4.2, in the latent space, the encoder output is designed to include two types of latent variables: ； in, Represents the vertical background latent variable; Indicates spatially anomalous hidden variables; Basic Reconstruction Loss for Autoencoder Training Represented as: ； Alternatively, the basic reconstruction loss during autoencoder training can be expressed in the form of mean squared error. : ； in, This represents the decoder mapping function in an autoencoder.

7. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Step S5 specifically includes the following steps: S5.1, let the initial estimate of the background profile obtained from vertical observation be... The corresponding observation coverage mask is Through vertical background branches Obtain the estimates of vertical background latent variables : ； in, This indicates vertical observation error or weighting information. Indicates static environmental conditions; S5.2, To avoid excessive vertical background correction leading to unreasonable layering structures, a constrained residual correction method is adopted: ； in, This is an estimate of the vertical background profile. For residual correction networks, This is the residual amplitude control coefficient. This is the activation function.

8. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Step S6 specifically includes the following steps: S6.1, let the real space anomalous latent variables be... During the forward noise addition process of the diffusion model, it gradually moves towards Add Gaussian noise: ； in, Indicates the number of diffusion steps. The number of diffusion steps is Real-space anomaly hidden variables, Indicates that in a given number Step space anomaly hidden variable Under the conditions, obtain the first Step-by-step noise spatial anomaly latent variable The general distribution of positive diffusion conditions, Indicates the first Step noise intensity, It is the identity matrix. It follows a multivariate Gaussian distribution; Based on the properties of the diffusion process, the noise addition result at any step is obtained. : ； in, , Indicates the first Signal retention coefficient for each diffusion step; , As of the date The cumulative information retention coefficient for each diffusion step; , To and Standard Gaussian noise of the same dimension; S6.2, Conditional Diffusion Network by diffusion steps Multi-source observation conditions Vertical background latent variable estimates and static environmental conditions Given the input, predict the noise term: ； S6.3, the training objective of the diffusion model is to minimize the error between the actual noise and the predicted noise: ； in, This represents the predicted loss for diffuse noise. Represents the real-space outlier latent variables corresponding to the training samples. diffusion steps and standard Gaussian noise Find the expected value; S6.4, In the inference phase, firstly, based on the multi-source observation conditions within the target time window... And obtained from the vertical background branch Subsequently, initial spatial outlier latent variables were sampled from a standard Gaussian distribution. : ； Then, by using a conditional diffusion model to perform stepwise reverse denoising, the estimated values ​​of the generated spatial anomaly latent variables are obtained. The backsampling process is represented as: ； in, for The conditional probability distribution of back diffusion, This represents the inverse mean predicted by the diffusion network. This represents the variance of the backsampling.

9. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Step S7 specifically includes the following steps: S7.1 After completing the reverse denoising, the generated vertical background latent variable estimates are fused with the spatial anomaly latent variable estimates: ； S7.2, input to the decoder to obtain the complete three-dimensional ocean state field: ； in, The 3D reconstruction result corresponding to the target time or target time window; S7.3, Let the target time be... The conditional input consists of observations within the vicinity of the target time: ； in, Indicates time Corresponding multi-source observation conditions; Indicates the target time Constructed set of multi-time observation conditions; Alternatively, a causal window that includes only the period before and at the target time can be used: ； in, Indicates the time window radius or window length; S7.4 Utilize multi-time observation information within the window to generate a three-dimensional ocean state field corresponding to the target time. : ； in, This represents a generative reconstruction model composed of a vertical background branch, a conditional diffusion model, and a decoder.

10. The three-dimensional ocean state field generative reconstruction method based on multi-source sparse observation constraints according to claim 1, characterized in that, Step S8 specifically includes the following steps: S8.1, let the first... The reconstruction result obtained from the second sampling is The number of samples in the set is Then the set mean is: ； S8.2, ensemble uncertainty is represented by ensemble standard deviation: ； in, This represents the final set of averaged reconstructed fields. This represents an estimate of the uncertainty in the corresponding spatial location, depth layer, and time. S8.3, the total training loss is expressed as: ; in, The vertical background constraint loss is defined as the true vertical background. and vertical background estimates The mean square error between them and These are the weighting coefficients.

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