A deep neural process ocean data assimilation method for dynamic sparse observation

Abstract

The application provides a deep neural process ocean data assimilation method for dynamic sparse observation, relates to the field of ocean data processing, and specifically comprises the following steps: constructing a training data set; simulating the uneven and uncertain characteristics of actual observation through a Gaussian kernel diffusion; building an ocean assimilation network for sparse dynamic observation, outputting an analysis field and uncertainty estimation; using a reanalysis true value field as a supervision signal to perform end-to-end training on the ocean assimilation network model, and optimizing network parameters by jointly minimizing an error term and a structure constraint term. After training is completed, the background field and sparse observation in the test stage are input into the ocean assimilation network model for reasoning, so that an ocean state reconstruction field conforming to the actual physical quantity scale is obtained. The technical scheme of the application overcomes the problem in the prior art that the calculation feasibility, cross-scale correlation modeling and reliable uncertainty output cannot be considered under the realistic conditions that the observation is sparse and the spatiotemporal distribution dynamically changes.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ocean data processing, and particularly relates to a deep neural process ocean data assimilation method for dynamic sparse observation. BACKGROUND

[0002] Ocean prediction is highly sensitive to initial conditions, while the existing observation system presents the structural characteristics of "dense in the surface layer, sparse in the interior layer, and variable in space and time": satellite observations cover a wide range but only represent the surface layer, while moorings, Argo, gliders and ship sections can provide three-dimensional information, but there are problems such as sparse arrangement, position drift and intermittent observation, resulting in the observation field presenting dynamic, sparse and irregular characteristics. Under this background, traditional OI, 3DVar, 4DVar and EnKF methods generally face three types of bottlenecks in high-resolution and strong nonlinear scenarios: first, the cost of calculation and parameter adjustment is high, and it is difficult to quickly adapt to the time-varying observation density; second, the dependence on convection and the lack of long-range propagation representation make it easy to over-smooth or locally distort in complex areas such as fronts, eddies and near-shore areas; third, the method generally assumes fixed matching between observations and grid points, and needs to force the irregular observations to be gridded, resulting in information dilution and misrepresentation of confidence. Although the end-to-end deep learning assimilation in recent years has reduced the reasoning cost, it generally lacks physical consistency and incremental constraints, and the robustness and probability calibration of irregular and time-varying observations are still insufficient. Pure convolution is difficult to cover cross-scale dependence, pure attention is sensitive to local structure preservation and sample size, and graph networks introduce high engineering complexity. Therefore, the existing technology is still difficult to balance computational feasibility, cross-scale correlation modeling and reliable uncertainty output under the realistic conditions of sparse observation and dynamic spatiotemporal distribution.

[0003] Therefore, there is a need for a method of ocean data assimilation that can adapt to dynamic observations, efficiently utilize sparse observations, and uniformly output analysis mean and uncertainty. SUMMARY

[0004] The main purpose of the present application is to provide a deep neural process ocean data assimilation method for dynamic sparse observation, so as to solve the problem that the existing technology cannot balance computational feasibility, cross-scale correlation modeling and reliable uncertainty output under the realistic conditions of sparse observation and dynamic spatiotemporal distribution.

[0005] To achieve the above-mentioned purpose, the present application provides a deep neural process ocean data assimilation method for dynamic sparse observation, which specifically comprises the following steps:

[0006] S1, constructing a training data set, including: a true value field, a background field and an observation set.

[0007] S2, forming a continuous observation field and a confidence distribution of the observation field by Gaussian kernel diffusion, so as to simulate the uneven and uncertain characteristics of actual observation.

[0008] S3 constructs an ocean assimilation network for sparse dynamic observations, including a local feature extraction module and a global dependency modeling module. It integrates observation information with background information at multiple scales and outputs the analysis field and uncertainty estimates.

[0009] S4 uses the reanalysis ground truth field as a supervision signal to perform end-to-end training on the ocean assimilation network model. By jointly minimizing the error term and the structural constraint term, the network parameters are optimized to ensure that the prediction results are consistent with the real field in terms of amplitude and spatial gradient.

[0010] S5. After training, the background field from the testing phase and sparse observations are input into the ocean assimilation network model for inference. The analysis results are output and denormalized to obtain a reconstructed ocean state field that conforms to the actual physical quantity scale.

[0011] Furthermore, step S3 specifically includes the following steps:

[0012] S3.1, Input via local representation operator The local representation operator operates point-by-point on the original mesh, outputting locally equivariant features. :

[0013] .

[0014] S3.2, using the downsampling operator Will Compressed into fixed-dimensional subdomain features, and then overlaid with positional encoding. :

[0015] ;

[0016] in, These are features that have been downsampled and overlaid with positional encoding.

[0017] S3.3, after the global dependency operator deal with :

[0018] ;

[0019] in, These are the features after processing by the global dependency operator.

[0020] S3.4, through the upsampling operator Mapping back to the original mesh yields global features. :

[0021] .

[0022] S3.5, utilizing the gated fusion operator Adaptive integration of local isovariant features and global features:

[0023] ;

[0024] in, For confidence level field, Adaptive integration features.

[0025] S3.6, and Concatenated input decoding operator Output the residual increment and logarithmic standard deviation:

[0026] ;

[0027] in, for The mean field of the time step. Represents the residual. for The standard deviation field of the analysis at time point. It is a logarithmic function.

[0028] S3.7, to ensure numerical stability and positive definiteness, the residual increment and logarithmic standard deviation are calculated using the softplus function. Mapped to positive values:

[0029] ;

[0030] in, for The analysis standard field after mapping time to positive values. It is a positive constant.

[0031] S3.8, the probability distribution of the output analysis results at each grid point is as follows:

[0032] ;

[0033] in, Indicates the analysis field at the grid points The variable at that location, It follows a standard normal distribution.

[0034] The analysis of the mean follows the form of residual increments:

[0035] ;

[0036] in, Background field at grid points The variable at that location, This is a learnable scaling factor.

[0037] Furthermore, step S1 specifically includes the following steps:

[0038] S1.1, Truth Field Indicates reference ocean state, background field This represents a priori fields that are not constrained by observations.

[0039] S1.2, at each time step Randomly select the observation set from the truth field:

[0040] ;

[0041] in, Indicates time The set of observations For the first Spatial coordinates of each observation point For the observed values, This corresponds to the standard deviation of the observation error or the confidence level parameter. express The number of observations at any given time and the dynamic set of observations.

[0042] S1.3, the observed values ​​are expressed as:

[0043] ;

[0044] in, For observation operators, used to map from the truth field to the observation space. It is zero-mean Gaussian noise. This represents a Gaussian probability distribution.

[0045] S1.4 performs unified processing of the model output and reanalysis products in both time and space dimensions, including temporal registration, spatial clipping, and land-sea masking, to ensure that the background field, ground truth field, and observation data are aligned on the same spatiotemporal grid.

[0046] Furthermore, step S2 specifically includes the following steps:

[0047] S2.1, the design calculation is any point on the mesh as , No. The observation points are located at coordinates , Point Influence weight Defined as:

[0048] ;

[0049] in, The scale parameter of the diffusion nucleus; For the observation confidence weight function, It is a natural exponential function.

[0050] S2.2, the observed field value at each grid point is defined as the weighted average of all observations:

[0051] ;

[0052] in, For the first Any point on the grid The observed field values, To prevent stable terms with a denominator of zero, This represents the total number of grid cells.

[0053] S2.3, Confidence field for each grid point Defined as the accumulation of all weights:

[0054] .

[0055] S2.4, at each time step Will Mapped to time step Background Consistent gridded input triples :

[0056] .

[0057] in, for All moments A set of.

[0058] Furthermore, the loss function for step S4 is:

[0059] ;

[0060] in, , , These are the weighting coefficients for the three losses, For probability loss, For spatial structural loss, This represents the loss due to physical constraints.

[0061] Furthermore, step S5 specifically includes the following steps:

[0062] S5.1 For deterministic assimilation fields, the analytical mean is directly used as the predictor variable:

[0063] ;

[0064] in, Indicates at time step and grid points The results of the deterministic analysis at the location.

[0065] S5.2, if physical boundary or conservation constraints need to be satisfied, further apply the physical projection operator:

[0066] ;

[0067] in, Indicates at time step and grid points The analysis field after physical projection; This represents a projection function that imposes upper and lower limits and smoothing constraints on temperature, salinity, and energy.

[0068] S5.3, for ensemble or probabilistic forecasting applications, sample ensemble members from the predicted distribution:

[0069] ;

[0070] in, For the first The set member represents the th sampled from the analysis distribution. This is achieved through randomization; The random disturbance term follows a standard normal distribution. ; For collection member index, This represents the total number of members in the set.

[0071] S5.4, the confidence interval and the probability of exceeding the threshold are:

[0072] ;

[0073] in, For probability operators, It is the standard normal distribution function. For any threshold value.

[0074] The present invention has the following beneficial effects:

[0075] The adaptive fusion mechanism for sparse and dynamic observations in this invention breaks through the limitation of traditional assimilation requiring a fixed observation network, and realizes automatic adaptation and efficient fusion of time-varying, irregular, and multi-source observations. It can still stably reconstruct the continuous ocean state field under limited observation conditions.

[0076] This invention adopts an end-to-end intelligent assimilation and uncertainty modeling integrated framework: it directly learns the optimal fusion relationship between observation and background field in a data-driven manner, and outputs analysis results and their uncertainties, realizing rapid inference, reliable quantification and cross-scale information propagation, significantly improving computational efficiency and reliability.

[0077] This invention is robust and widely applicable. The method provided by this invention still performs stably in the absence of background or under sparse observation conditions, has excellent spatial extrapolation and temporal continuity, can be flexibly embedded into operational ocean analysis and prediction systems, and has good potential for engineering implementation and expansion.

[0078] In summary, this invention, based on a unified assimilation framework of adaptive observation coding and multi-scale information fusion, directly processes irregular and time-varying observations and outputs analysis results with uncertainty characterization. This invention does not rely on fixed grids or static error covariance, and can improve the accuracy and stability of the analysis field under sparse observation conditions while maintaining physical consistency, and reduce the overall computational cost. Attached Figure Description

[0079] 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:

[0080] Figure 1 A flowchart of a deep neural process ocean data assimilation method for dynamic sparse observations according to the present invention is shown.

[0081] Figure 2 The reanalysis truth field of the HYCOM ocean model in mixed coordinates is shown.

[0082] Figure 3 The distribution of sparse observation sample points for the HYCOM oceanographic model is shown.

[0083] Figure 4 The background field before assimilation is shown.

[0084] Figure 5 The difference between the background field and the real field before assimilation is shown.

[0085] Figure 6 The analytical field after assimilation using the method provided by this invention is shown.

[0086] Figure 7 The error distribution diagram after assimilation using the method provided by the present invention is shown. Detailed Implementation

[0087] 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.

[0088] Example 1

[0089] like Figure 1 The method for assimilating deep neural process ocean data for dynamic sparse observations, as shown, specifically includes the following steps:

[0090] S1, construct the training dataset, including: ground field, background field and observation set.

[0091] S2 uses Gaussian kernel diffusion to form a continuous observation field and its confidence distribution to simulate the non-uniformity and uncertainty of actual observations. Based on the latitude and longitude coordinates of the observation points, several effective grid points are randomly selected from the true field and random noise is superimposed to generate a sparse observation set. A continuous observation field and its confidence distribution are then formed through Gaussian kernel diffusion to simulate the non-uniformity and uncertainty of actual observations.

[0092] S3 constructs an ocean assimilation network for sparse dynamic observations, including a local feature extraction module and a global dependency modeling module. It integrates observation information with background information at multiple scales and outputs the analysis field and uncertainty estimates.

[0093] S4 uses the reanalysis ground truth field as a supervision signal to perform end-to-end training on the ocean assimilation network model. By jointly minimizing the error term and the structural constraint term, the network parameters are optimized to ensure that the prediction results are consistent with the real field in terms of amplitude and spatial gradient.

[0094] S5. After training, the background field from the testing phase and sparse observations are input into the ocean assimilation network model for inference. The analysis results are output and denormalized to obtain a reconstructed ocean state field that conforms to the actual physical quantity scale.

[0095] This invention proposes an ocean assimilation method for sparse, dynamic observation networks. It employs a unified framework of "observation set - gridded representation - probabilistic fusion," incorporating local and global spatial dependencies, adaptive weights, and uncertainty quantification into the same process. The method can operate independently (relying solely on observations) or be embedded as an incremental corrector into operational systems when a pattern background field exists.

[0096] Specifically, in this invention, the ocean state reconstruction problem is formalized as an optimal estimation problem constrained by dynamic sparse observations. Before implementing assimilation inference under sparse dynamic observation conditions, this invention first needs to construct a training sample system that reflects the true ocean state, background error, and observation distribution characteristics. The training data consists of three parts: a ground truth field, a background field, and a dynamic observation set, used to simulate the "state reconstruction under finite observation constraints" process in actual operations.

[0097] Step S1 specifically includes the following steps:

[0098] S1.1, Truth Field The reference ocean state can be derived from high-resolution reanalysis data or numerical model output, background field. The background field represents the a priori field that is not constrained by observations. The difference between the true field and the true field ( This describes the statistical characteristics of the mode error or assimilation increment.

[0099] S1.2, at each time step Randomly select the observation set from the truth field:

[0100] ;

[0101] in, Indicates time The set of observations For the first The spatial coordinates (such as latitude and longitude) of each observation point. For the observed values, This corresponds to the standard deviation of the observation error or the confidence level parameter. express The number of observations at any given time and the dynamic set of observations can change dynamically over time to simulate the time-varying characteristics of non-fixed observations such as buoys, moorings, or gliders. To more closely resemble the real ocean observation environment, the training phase can... Values ​​are randomly selected within a preset range to cover different observation scenarios ranging from sparse to relatively dense.

[0102] S1.3, the observed values ​​are expressed as:

[0103] ;

[0104] in, For observation operators, used to map from the truth field to the observation space. Zero-mean Gaussian noise is used to characterize the observation error. This represents a Gaussian probability distribution.

[0105] S1.4 performs unified processing of the model output and reanalysis products in both time and space dimensions, including temporal registration, spatial clipping, and land-sea masking, to ensure that the background field, ground truth field, and observation data are aligned on the same spatiotemporal grid, providing consistent input for assimilation modeling.

[0106] Through the above process, a series of samples can be generated. This sample system not only includes the spatial distribution characteristics of background errors but also reflects the dynamic changes in the number, location, and errors of observation points over time. This enables the model to learn during the training phase how to fuse multi-source information and recover a continuous ocean state field under irregular, time-varying observation conditions. This design ensures the model's adaptability to dynamic sparse observations in practical operations, providing a solid data foundation for subsequent probabilistic fusion and uncertainty modeling.

[0107] Specifically, after constructing the training samples, to enable the model to directly handle observation inputs with irregular spatiotemporal distribution and dynamically changing quantities, this invention employs a kernel diffusion-based gridded representation method for observation sets. This method eliminates the need for forced interpolation or resampling of observation points; instead, it diffuses the information of each observation point in a Gaussian kernel manner within a continuous space, thus representing the discrete observation set... Converted to an observation field with the same resolution as the background field. With confidence field Step S2 specifically includes the following steps:

[0108] S2.1, the design calculation is any point on the mesh as , No. The observation points are located at coordinates , Point Influence weight Defined as:

[0109] ;

[0110] in, The scale parameter of the diffusion kernel (measured by grid cell distance) controls the spatial radius of influence of the observed information; For the observation confidence weight function, we can take... or ( (This is a balance coefficient) used to adjust the weights based on the magnitude of the observation error. It is a natural exponential function.

[0111] S2.2, the observed field value at each grid point is defined as the weighted average of all observations:

[0112] ;

[0113] in, For the first Any point on the grid The observed field values, To prevent stable terms with a denominator of zero, This represents the total number of grid cells.

[0114] S2.3, Confidence field for each grid point Defined as the accumulation of all weights:

[0115] .

[0116] The confidence field reflects the spatial distribution of local observation density and confidence. When observations are sparse in a certain area,... When the confidence level is low, the model will rely more on the background field and contextual information during subsequent assimilation; when the observations are dense or the confidence level is high, This significantly increases the constraints on observation.

[0117] S2.4, at each time step Will Mapped to time step Background Consistent gridded input triples :

[0118] ;

[0119] in, for All moments A set of.

[0120] This design enables the model to simultaneously receive background field and sparse observation information under a unified spatial representation, and to explicitly obtain the spatial distribution and confidence level of the observations. Unlike traditional fixed interpolation or mask input methods, the method provided by this invention maintains the input dimension and numerical stability even when the number and location of observations change over time, thus laying an adaptive observation representation foundation for subsequent probabilistic fusion and uncertainty modeling.

[0121] Subsequently, an input sample consisting of three channels—background field, observation field, and confidence field—was constructed and divided into training, validation, and test sets to ensure temporal independence and sample representativeness. An ocean assimilation network for sparse dynamic observations was built, comprising a local feature extraction module and a global dependency modeling module, to achieve multi-scale fusion of observational and background information and output the analysis field and its uncertainty estimate.

[0122] Specifically, step S3 includes the following steps:

[0123] S3.1, the input of this invention is a triple after unified meshing. This triple shares the same resolution spatially, enabling the model to simultaneously receive background prior and sparse observation information within the same representation domain. First, in the local feature extraction module, the input... via local representation operator The processing is used to extract local spatial correlation and gradient features; the local representation operator operates point-by-point on the original grid, outputting local isovariant features. :

[0124] ;

[0125] Among them, the local representation operator Convolution, radial basis functions, wavelets, or finite volume filtering can be used to capture dynamic features such as neighborhood smoothness, local gradients, and frontal structures.

[0126] In the global dependency modeling module, global dependency operators are used. Establish long-range spatial connections.

[0127] S3.2, using the downsampling operator Will Compressed into fixed-dimensional subdomain features, and then overlaid with positional encoding. :

[0128] ;

[0129] in, These are features that have been downsampled and overlaid with positional encoding.

[0130] S3.3, after the global dependency operator deal with :

[0131] ;

[0132] in, Features are those processed by the global dependency operator; operator It can be implemented by self-attention (Transformer), integral kernel mapping, spectral domain attention, etc., and is used to aggregate long-range dependencies in the downsampled domain and reversibly map them back to the original domain, thereby capturing the cross-scale correlation and nonlocal dynamic structure of the ocean field.

[0133] S3.4, through the upsampling operator Mapping back to the original mesh yields global features. :

[0134] .

[0135] Specifically, step S3 also includes the following steps:

[0136] S3.5, utilizing the gated fusion operator Adaptive integration of local isovariant features and global features:

[0137] ;

[0138] in, The confidence field is used to adjust the fusion weights. If observations are sparse or confidence is low, the model relies more on background and global features; if observations are dense or confidence is high, the influence of local features is strengthened. Thus, the model achieves adaptive information fusion that dynamically changes with the distribution of observations in space. Adaptive integration features.

[0139] S3.6, and Concatenated input decoding operator Output the residual increment and logarithmic standard deviation:

[0140] ;

[0141] in, for The mean field of the time step. Represents the residual. for The standard deviation field of the analysis at time point. It is a logarithmic function.

[0142] S3.7, to ensure numerical stability and positive definiteness, the residual increment and logarithmic standard deviation are calculated using the softplus function. Mapped to positive values:

[0143] ;

[0144] in, for The analysis standard field after mapping time to positive values. It is a positive constant used to prevent the standard deviation from being too small or zero.

[0145] S3.8, the probability distribution of the output analysis results at each grid point is as follows:

[0146] ;

[0147] in, Indicates the analysis field at the grid points The variable at that position represents the assimilation result. It follows a standard normal distribution.

[0148] The analysis of the mean follows the form of residual increments:

[0149] ;

[0150] in, Background field at grid points The variable at that location, It is a learnable scaling factor used to adjust the correction magnitude and maintain dynamic-thermal consistency.

[0151] This structured mapping from input triples to probabilistic analysis distributions enables this invention to stably achieve error correction and uncertainty quantification of the background field under sparse, dynamic observation conditions. Local operators ensure detail and gradient preservation, global dependency operators capture large-scale flow system structures, gated fusion adaptively allocates the contributions of observations and the background based on confidence levels, and residual increment design ensures the physical rationality and continuity of the correction results. Through this coherent information flow path, the model achieves full-process assimilation inference from dynamic observation inputs to probabilistic analysis outputs within a single framework.

[0152] Specifically, the loss function for step S4 is:

[0153] ;

[0154] in, , , These are the weighting coefficients for the three losses, used to balance the relative importance of the three constraints in the optimization process. For probability loss, used to characterize the statistical consistency between the model's output distribution and the true value field, Gaussian negative log-likelihood or continuous rank probability scoring can be used to simultaneously optimize the analysis mean. With variance ; To mitigate spatial structure loss, the continuity and stability of high-gradient regions such as fronts and vortices are maintained by constraining the consistency between the analytical field and the true field in terms of spatial gradient or local energy distribution. To address the physical constraint loss, a differentiable physical operator is introduced. Constraining the dynamic-thermal consistency (such as energy conservation, mass balance, or momentum continuity) prevents the analytical field from deviating from a physically feasible solution.

[0155] After obtaining the above probability distribution, various recovery strategies can be used to generate analysis results that are usable for business purposes.

[0156] Specifically, step S5 includes the following steps:

[0157] S5.1 For deterministic assimilation fields, the analytical mean is directly used as the predictor variable:

[0158] ;

[0159] in, Indicates at time step and grid points The deterministic analysis results at the location correspond to the maximum a posteriori estimate and minimum mean square error estimate under the Gaussian distribution, and can be directly used as the initial field of the numerical model.

[0160] S5.2, if physical boundary or conservation constraints need to be satisfied, further apply the physical projection operator:

[0161] ;

[0162] in, Indicates at time step and grid points The analysis field after physical projection, i.e. the corrected field after applying physical constraints; This represents a projection function that imposes upper and lower limits and smoothing constraints on physical quantities such as temperature, salinity, and energy.

[0163] S5.3, for ensemble or probabilistic forecasting applications, sample ensemble members from the predicted distribution:

[0164] ;

[0165] in, For the first The set member represents the th sampled from the analysis distribution. This is achieved through randomization; The random disturbance term follows a standard normal distribution. ; For collection member index, This represents the total number of members in the ensemble. This allows for the formation of an ensemble analysis field, supporting ensemble forecasting and uncertainty propagation.

[0166] S5.4, the confidence interval and the probability of exceeding the threshold are:

[0167] ;

[0168] in, For probability operators, It is the standard normal distribution function. For any threshold value.

[0169] Finally, error statistics and probability performance evaluation (such as RMSE and CRPS) are performed on the obtained analysis field to verify the applicability and stability of the method under different observation sparsity and regional conditions, thereby achieving high-precision ocean assimilation under sparse dynamic observation conditions.

[0170] Through the above steps, this invention achieves a complete assimilation inference process, from dynamic sparse observation input to probabilistic fusion, and then to deterministic or aggregated output. This design, within a unified framework, balances local accuracy, global consistency, and uncertainty characterization. It can operate as an independent observation-driven assimilation device or be embedded into existing ocean model systems, providing a universal assimilation technology path for high-resolution, real-time intelligent ocean forecasting.

[0171] Example 2

[0172] To verify the assimilation performance of the method provided in this invention under dynamic and sparse observation conditions, HYCOM 1 / 12° reanalysis data was selected as the ground truth, and the ROMS model output from the same region was used as the background field. The studied variable was sea surface temperature. At each time step (t), an observation set was randomly selected from the ground truth, and the number of observations was... The data is randomly varied within the range [0, 50] to simulate the non-fixed distribution of observations from buoys, moorings, or gliders. To enable the model to directly handle irregular, time-varying observation inputs, this invention employs an "observation set gridding" strategy based on Gaussian kernel diffusion, mapping sparse observations to continuous inputs with the same resolution as the background field. The three channels of the final model input correspond to the background prior, observation information, and confidence weights, respectively.

[0173] In the network design, the local representation operator employs a three-layer 5×5 convolutional structure to extract neighborhood smoothness and gradient information, and output local features. Subsequently, long-range spatial dependencies are established through multi-head self-attention. For the compressed feature sequences... The self-attention mechanism is calculated as follows:

[0174] ;

[0175] in, For the attention calculation function, These are query, key, and value matrices, used for attention calculation. The dot product matrix representing the query and the key reflects the similarity between spaces or features. For feature dimension, This is a normalization function used to map the attention weights to a probability distribution. Global features are obtained after passing through a feedforward network and upsampling operations. Then, compare with local features according to confidence level Gated fusion is performed. Model training employs a joint loss of heteroscedastic Gaussian negative log-likelihood and gradient consistency.

[0176] ;

[0177] in, For the true value field at time step and grid points Reference value at that location, The number of grid points used to calculate the loss. and These are the discrete gradient operators in the longitudinal and latitudinal directions, respectively. For balance coefficient, and They represent the fields predicted by the model in the analysis. and gradient of direction, and They represent the truth fields at... and The gradient in the direction is used as a reference for gradient consistency constraints. This represents the L1 norm, which is the sum of absolute values ​​used to measure the difference between gradient fields. This design achieves joint optimization of error and uncertainty while preserving the physical gradient structure.

[0178] like Figure 2 and Figure 3 These are the HYCOM reanalysis true field and its sparse observation sample point distribution, where the observation sample locations are randomly selected; for example... Figure 4 and Figure 5 The background field before assimilation and its difference from the true value; Figure 6 and Figure 7 The image shows the assimilated analytical field and its error distribution. It can be seen that the background field before assimilation exhibits significant cooling errors in the nearshore and continental slope regions. Figure 5 The root mean square error (RMSE) in the original model was 0.592 °C. After assimilation using this method, the overall structure significantly approximates the true value, and the vortex and frontal features are effectively recovered. Figure 7 The global RMSE decreased to 0.258 °C. The error distribution plot shows that the improved area extends from the neighborhood of the observation point to the entire study area, demonstrating the method's ability to achieve consistent global correction and error convergence under sparse observation conditions.

[0179] This embodiment can significantly reduce the global root mean square error even with a very small number of observation points, and maintains a continuous structure in the nearshore front and vortex regions. As the number of observation points increases, the root mean square error decreases monotonically, and the error converges and stabilizes; simultaneously, the variance field output by the model... The ability to adaptively increase in unobserved areas and converge in densely observed areas demonstrates excellent uncertainty calibration capabilities. This result proves that the framework proposed in this invention can achieve stable correction and reliable reconstruction of the ocean state field under conditions of sparse observations and dynamically changing distributions, possessing feasibility and potential for widespread application in practical ocean forecasting systems.

[0180] 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 method for assimilating deep neural process ocean data for dynamic sparse observation, characterized in that, Specifically, the steps include the following: S1, Construct the training dataset, including: ground field, background field and observation set; S2, through Gaussian kernel diffusion, forms a continuous observation field and a confidence distribution of the observation field to simulate the non-uniformity and uncertainty of actual observations; S3, constructs an ocean assimilation network for sparse dynamic observation, including: a local feature extraction module and a global dependency modeling module, which fuses observation information with background information at multiple scales and outputs the analysis field and uncertainty estimate; S4 uses the reanalysis true field as a supervision signal to train the ocean assimilation network model end-to-end. By jointly minimizing the error term and the structural constraint term, the network parameters are optimized to ensure that the prediction results are consistent with the real field in terms of amplitude and spatial gradient. S5. After training, the background field from the testing phase and sparse observations are input into the ocean assimilation network model for inference. The analysis results are output and denormalized to obtain the ocean state reconstruction field that conforms to the actual physical quantity scale. Step S3 specifically includes the following steps: S3.1, Input via local representation operator The local representation operator operates point-by-point on the original mesh, outputting locally equivariant features. : ； S3.2, using the downsampling operator Will Compressed into fixed-dimensional subdomain features, and then overlaid with positional encoding. : ； in, Features that have been downsampled and overlaid with position encoding; S3.3, after the global dependency operator deal with : ； in, Features are those processed by the global dependency operator; S3.4, through the upsampling operator Mapping back to the original mesh yields global features. : ； S3.5, utilizing the gated fusion operator Adaptive integration of local isovariant features and global features: ； in, For confidence level field, Adaptive integration of features; S3.6, and Concatenated input decoding operator Output the residual increment and logarithmic standard deviation: ； in, for The mean field of the time step. Represents the residual. for The standard deviation field of the analysis at time point. It is a logarithmic function; S3.7, to ensure numerical stability and positive definiteness, the residual increment and logarithmic standard deviation are calculated using the softplus function. Mapped to positive values: ； in, for The standard deviation field after mapping time to positive values ​​is analyzed. It is a positive constant; S3.8, Output the probability distribution of the analysis results at each grid point. for: ； in, Indicates the analysis field at the grid points The variable at that location, It follows a standard normal distribution; The analysis of the mean follows the form of residual increments: ； in, Background field at grid points The variable at that location, This is a learnable scaling factor.

2. The method for assimilating deep neural process ocean data for dynamic sparse observation as described in claim 1, characterized in that, Step S1 specifically includes the following steps: S1.1, Truth Field Indicates reference ocean state, background field Represents a priori fields that are not constrained by observations; S1.2, at each time step Randomly select the observation set from the truth field: ； in, Indicates time The set of observations For the first Spatial coordinates of each observation point For the observed values, This corresponds to the standard deviation of the observation error or the confidence level parameter. express The number of observations at any given time and the dynamic set of observations; S1.3, the observed values ​​are expressed as: ； in, For observation operators, used to map from the truth field to the observation space. It is zero-mean Gaussian noise. Represents a Gaussian probability distribution; S1.4 performs unified processing of the model output and reanalysis products in both time and space dimensions, including temporal registration, spatial clipping, and land-sea masking, to ensure that the background field, ground truth field, and observation data are aligned on the same spatiotemporal grid.

3. The method for assimilation of deep neural process ocean data for dynamic sparse observation as described in claim 1, characterized in that, Step S2 specifically includes the following steps: S2.1, the design calculation is any point on the mesh as , No. The observation points are located at coordinates , Point Influence weight Defined as: ； in, The scale parameter of the diffusion nucleus; For the observation confidence weight function, It is a natural exponential function; S2.2, the observed field value at each grid point is defined as the weighted average of all observations: ； in, For the observed values, For the first Any point on the grid The observed field values, To prevent stable terms with a denominator of zero, Total number of grid cells; S2.3, Confidence field for each grid point Defined as the accumulation of all weights: ； S2.4, at each time step Will Mapped to time step Background Consistent gridded input triples : ； in, for All moments A set of.

4. The method for assimilation of deep neural process ocean data for dynamic sparse observation as described in claim 1, characterized in that, The loss function for step S4 is: ； in, , , These are the weighting coefficients for the three losses, For probability loss, For spatial structural loss, This represents the loss due to physical constraints.

5. A method for assimilating deep neural process ocean data for dynamic sparse observation according to claim 1, characterized in that, Step S5 specifically includes the following steps: S5.1 For deterministic assimilation fields, the analytical mean is directly used as the predictor variable: ； in, Indicates at time step and grid points The results of the deterministic analysis at the location; S5.2, if physical boundary or conservation constraints need to be satisfied, further apply the physical projection operator: ； in, Indicates at time step and grid points The analysis field after physical projection; This represents a projection function that imposes upper and lower limits and smoothing constraints on temperature, salinity, and energy. S5.3, for ensemble or probabilistic forecasting applications, sample ensemble members from the predicted distribution: ； in, For the first The set member represents the th sampled from the analysis distribution. This is achieved through randomization; The random disturbance term follows a standard normal distribution. ; For collection member index, The total number of members in the set; S5.4, the confidence interval and the probability of exceeding the threshold are: ； in, For probability operators, It is the standard normal distribution function. For any threshold value.

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