An ocean multi-source data fusion method based on adaptive fourier neural process

Abstract

The application provides a marine multi-source data fusion method based on an adaptive Fourier neural process, and relates to the technical field of data fusion, and specifically comprises the following steps: preprocessing marine variable field data. An ensemble background field is adaptively generated for any time point. The background field, true value and observation value are organized into a standardized data set for training of an adaptive Fourier neural process model. An AFNP model is constructed, which comprises a background field encoder, an observation field encoder, a neural Fourier operator, an adaptive alignment fusion module and a decoder, and finally a prediction result of the true field is output by the decoder. The AFNP model is supervised end-to-end trained, a nonlinear relationship between the background field and the observation field is learned, and the true marine state field is reconstructed. The technical scheme of the application overcomes the problems of dependence on linear hypothesis and Gaussian error in the prior art, physical uninterpretability of a deep learning model, and poor boundary adaptability of a spectral domain method.

Description

Technical Field

[0001] The present invention relates to the field of data fusion, and in particular to a method for fusion of ocean multi-source data based on adaptive Fourier neural process. Background Art

[0002] Marine environmental monitoring relies on the collaborative integration of multi-source heterogeneous data, including satellite remote sensing, buoy observations, and numerical model outputs.

[0003] In recent years, machine learning technology has opened up new paths for ocean data fusion. However, existing deep learning solutions still have three core flaws: First, the ability to extract spatial features is insufficient. Standard convolution operations are limited by local receptive fields and cannot effectively capture the large-scale spatial correlation and cross-regional teleconnection characteristics of the ocean temperature and salinity fields, resulting in weak characterization capabilities for key structures such as ocean current fronts and eddies. Second, there is a lack of physical constraints. Purely data-driven black box models are prone to overfitting, and the generated results often violate physical laws such as mass conservation and thermodynamic equilibrium. In areas with sparse observations, they may output physically unexplainable solutions. Third, the fusion mechanism for multi-source heterogeneous data is rigid. Existing methods usually simply splice observation and background field data, fail to establish a dynamic weight allocation mechanism, and are unable to adaptively handle changes in observation network density and fluctuations in background field uncertainty. Performance degrades sharply in scenarios with sparse observations.

[0004] The ocean observation network has inherent limitations. The spatial coverage of fixed buoys, cruise measurements and remote sensing satellites is extremely uneven, and the vast open sea has long been data-deficient. Existing fusion methods are too sensitive to observation density: when the number of effective observation points is lower than the critical threshold, traditional interpolation methods (such as optimal interpolation) will produce a "hole effect" in the unobserved sea area, and deep learning models, due to the lack of prior knowledge guidance, often output overly smoothed or distorted physical fields. More seriously, there are systematic defects in the background field construction process. The mainstream approach relies on the output of a single numerical model as the background field, but the model itself has problems with parameterization scheme errors and initial value sensitivity. Although the ensemble method is introduced to generate multi-member background fields, traditional random sampling or fixed time window selection strategies are difficult to capture the transient characteristics of the ocean system, resulting in insufficient representativeness of the background field ensemble and distortion of the error covariance matrix estimation.

[0005] To improve large-scale feature extraction capabilities, some studies have attempted to introduce spectral domain methods. The Fourier Neural Operator (FNO) models in the frequency domain through global convolution, theoretically possessing the advantage of capturing long-range spatial correlations. However, existing spectral domain methods face three challenges in ocean scenarios: First, they lack adaptability to complex land-ocean boundaries. The standard Fourier transform requires a regular rectangular domain, which cannot effectively handle complex boundary conditions such as coastline tortuosity and island distribution, resulting in "spurious signals" in nearshore fusion results. Second, multi-scale feature fusion fails. Ocean processes encompass a wide spectrum of scales, ranging from kilometer-scale eddies to hundred-kilometer-scale circulations. Fourier basis functions with fixed truncated modes struggle to account for features at different scales, often resulting in over-filtering of small-scale processes. Finally, the observation information injection mechanism is inefficient. Existing methods simply treat observations as additional channels and fail to establish adaptive correction mechanisms in the spectral space. Observation errors are easily propagated and amplified in the frequency domain.

[0006] Therefore, there is a need for an ocean multi-source data fusion method based on adaptive Fourier neural process that can effectively fuse multi-member background fields and sparse observation data. Summary of the Invention

[0007] The main purpose of the present invention is to provide an ocean multi-source data fusion method based on adaptive Fourier neural process to solve the problems in the existing technology of dependence on linear assumptions and Gaussian errors, physical uninterpretability of deep learning models, and poor boundary adaptability of spectral domain methods.

[0008] To achieve the above object, the present invention provides a method for fusion of ocean multi-source data based on adaptive Fourier neural process, which specifically comprises the following steps:

[0009] S1, preprocessing of ocean variable field data, ocean data includes: background field, true value and observation value.

[0010] S2, adaptively generate a background field set for any time point.

[0011] S3, organizes the background field, true value and observation value into a standardized dataset for training the adaptive Fourier neural process AFNP model.

[0012] S4, construct the AFNP model, which includes: background field encoder, observation field encoder, neural Fourier operator, adaptive alignment fusion module and decoder. Finally, the decoder outputs the prediction result of the real field.

[0013] S5, supervised end-to-end training of the AFNP model is performed to learn the nonlinear relationship between the background field and the observation field and reconstruct the real ocean state field.

[0014] Step S4 specifically includes the following steps:

[0015] S4.1, construct background field encoder and observation field encoder, and extract local spatial features.

[0016] S4.2, introduce the Fourier neural operator to perform frequency domain enhancement on the extracted local spatial features:

[0017] ;

[0018] ;

[0019] in, is the Fourier neural operator, is the local spatial feature of the background field extracted by the background encoder, is the local spatial feature of the observation field extracted by the observation encoder, is the frequency domain enhancement result of the background field, is the frequency domain enhancement result of the observation field.

[0020] S4.3, design an adaptive alignment fusion module to learn spatially variable alignment weights.

[0021] S4.4, the fused features are input into the decoder and mapped back to the ocean state estimation field.

[0022] Furthermore, step S1 specifically includes the following steps:

[0023] S1.1, align the background field, ground truth, and observations in the same dimension and time series through spatiotemporal truncation.

[0024] S1.2, map the ocean variable field data on the true value grid to the background field grid through spatial interpolation.

[0025] S1.3, generate a land mask based on the background field to eliminate the interference of land areas on ocean analysis, that is, the land area is 1 and the ocean area is 0.

[0026] Furthermore, step S2 is specifically as follows:

[0027] Assume that the observation time series is , for each time step , build contains Background field collection of members , calculated as:

[0028] ;

[0029] in, is the number of set members, For the The background field of each member.

[0030] Furthermore, step S3 specifically includes the following steps:

[0031] S3.1, set Indicates the Members at time Time, grid point The background field of the target variable, Indicates time Time, grid point The observed value of Indicates time Time, grid point The truth value of .

[0032] S3.2, yes 、 and Standardization was performed separately, and z-score normalization was used. The formula is:

[0033] ;

[0034] in, 、 are the mean and standard deviation of the background fields of all members at all time steps, respectively; 、 is the mean and standard deviation of all time step observations; 、 is the mean and standard deviation of the true value at all time steps, For the Members at time Time, grid point The background field after the target variable is standardized, and Time Time, grid point The observed and true values ​​after standardization.

[0035] S3.3, after normalization, the input-output pair of the adaptive Fourier neural process AFNP model at a single time step is:

[0036] ;

[0037] in, is the input field, is the output field, is the standardized background field set, and They are Normalized observation field and truth field of the full grid at all times.

[0038] S4.1.1, all standardized background field members are stacked in the channel dimension and input into the background encoder, and the background encoder extracts the local spatial features of the background field. :

[0039] ;

[0040] in, is the convolutional coding network of the background field, are the channel dimension, the number of grid rows and the number of grid columns, respectively. For the Members at time The background field after the target variable is standardized at the moment.

[0041] S4.1.2, input the standardized observation field into the observation encoder to obtain the local spatial features of the observation field extracted by the observation encoder :

[0042] ;

[0043] in, is the convolutional encoding network of the observation field.

[0044] Furthermore, in step S4.2:

[0045] S4.2.1, for any spatial feature , do a two-dimensional fast Fourier transform:

[0046] ;

[0047] in, represents the frequency domain Fourier coefficient, represents the spatial domain input features, and are the transverse wavenumber index and longitudinal wavenumber index in the Fourier domain, is the natural exponential function, Is an imaginary unit.

[0048] S4.2.2, Learning Complex Weight Kernels in the Frequency Domain , row-by-row and wavenumber-by-wavenumber enhancement:

[0049] ;

[0050] in, Represents the frequency domain coefficient after weight modulation.

[0051] S4.2.3, perform inverse Fourier transform to restore to the spatial domain:

[0052] ;

[0053] in, is the output of the inverse transform in the spatial domain after modulation, is the inverse Fourier transform.

[0054] Furthermore, in step S4.3, an adaptive alignment fusion module is designed to learn spatially variable alignment weights as follows:

[0055] ;

[0056] ;

[0057] in, To be learnable Convolution kernel; Indicates splicing in the channel dimension; Sigmoid activation function, the output weight is [0,1]; represents the alignment similarity weight matrix feature; is the fused feature; Represents element-wise product.

[0058] Furthermore, step S4.4 inputs the fused features into the decoder and maps them back to the ocean state estimation field as follows:

[0059] ;

[0060] in, For the decoder, is the normalized ocean prediction field predicted at a certain grid point.

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

[0062] S5.1, assuming that the training data contains multiple time steps, denoted as , for each time step, the prediction field output by the AFNP model is:

[0063] ;

[0064] in, Represents the forward inference function of the pre-trained AFNP model.

[0065] S5.2, in order to measure the consistency between the predicted field and the real field, the training adopts the mean square error loss function, which is defined as:

[0066] ;

[0067] in, is the loss function, is the total number of training time steps, Indicates that at time step , grid points The true ocean state value after denormalization, For the time step , grid points The denormalized AFNP model predictions.

[0068] S5.3, in mean square error loss Based on this, L2 regularization is introduced, and the total loss is:

[0069] ;

[0070] in, is the total loss, represents the set of all learnable parameters in the AFNP model, represents the L2 norm, is the regularization coefficient.

[0071] S5.4, using the adaptive moment estimation optimizer to optimize the parameter set Perform iterative updates. In each iteration, the model calculates the gradient of the current batch , and update the parameters by gradient descent:

[0072] ;

[0073] in, Indicates the AFNP model parameters at the iteration, is the learning rate of the current iteration.

[0074] S5.5, the predicted value By denormalizing and restoring to the original physical quantity, the prediction result is finally output:

[0075] ;

[0076] in, is the predicted physical field after restoration.

[0077] The present invention has the following beneficial effects:

[0078] The ocean data fusion method based on the adaptive Fourier neural process provided by the application can sufficiently fuse a multi-member background field set and sparse observation information, effectively overcome problems such as single background field, low interpolation precision, local distortion and systematic deviation caused by sparse observation in traditional data assimilation methods, through double feature interaction and consistency alignment in the time and space domains and the frequency domain. The method uses multi-member information to enhance the expression ability of the background field to complex non-stationary ocean processes, introduces a neural Fourier operator to adaptively learn spatial patterns under different wave number components, and enhances the capturing ability of the model to mesoscale eddies, fronts and local abnormal processes. Meanwhile, through a feature similarity-based alignment fusion mechanism, dynamic weighting between the background field and the observation field is automatically realized point by point, the influence of background bias on reconstruction precision is significantly reduced, and the consistency between the prediction field and the observation is ensured. The method provided by the application adopts an end-to-end joint training strategy, minimizes the global mean square error as a whole and combines parameter regularization, avoids overfitting, and has excellent generalization performance. Compared with the traditional ensemble average method, the method of the application shows lower root mean square error (RMSE) in experimental verification, can flexibly adapt to different spatial resolutions and observation densities, is computationally efficient, easy to deploy in ocean environment monitoring and real-time prediction services, and has high technical advancement and wide engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0079] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the drawings needed in the specific embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor. In the drawings:

[0080] Figure 1 A flowchart of an ocean multi-source data fusion method based on an adaptive Fourier neural process of the application is shown.

[0081] Figure 2 A real field is shown.

[0082] Figure 3 An observation field is shown.

[0083] Figure 4 A background field is shown.

[0084] Figure 5 A background field error is shown.

[0085] Figure 6 A prediction field of a traditional method is shown.

[0086] Figure 7 A prediction field error of a traditional method is shown.

[0087] Figure 8 The predicted fields of the AFNP model are shown.

[0088] Figure 9 The predicted field error of the AFNP model is shown. DETAILED DESCRIPTION

[0089] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0090] like Figure 1 The method for fusion of ocean multi-source data based on adaptive Fourier neural process shown in FIG. 1 includes the following steps:

[0091] S1, preprocessing of ocean variable field data, ocean data includes: background field, true value and observation value.

[0092] S2, adaptively generate a background field set for any time point.

[0093] S3, organizes the background field, true value and observation value into a standardized dataset for training the adaptive Fourier neural process AFNP model.

[0094] S4, construct the AFNP model, which includes: background field encoder, observation field encoder, neural Fourier operator, adaptive alignment fusion module and decoder. Finally, the decoder outputs the prediction result of the real field.

[0095] S5, supervised end-to-end training of the AFNP model is performed to learn the nonlinear relationship between the background field and the observation field and reconstruct the real ocean state field.

[0096] Specifically, step S1 includes the following steps:

[0097] S1.1, align the background field, ground truth, and observations in the same dimension and time series through spatiotemporal truncation.

[0098] S1.2, map the ocean variable field data (such as sea surface temperature) on the true value grid to the background field grid through spatial interpolation.

[0099] S1.3, generate a land mask based on the background field to eliminate unnecessary interference of land areas on ocean analysis, that is, the land area is 1 and the ocean area is 0.

[0100] Data preprocessing is a fundamental step in ocean data fusion methods, aiming to transform raw, heterogeneous data into a standardized format that can be processed by the model. This step processes three core data sources: numerical simulation data (background fields), reanalysis data (true values), and observations. First, a spatiotemporal truncation is performed to ensure that all data sources are aligned in the same dimension and time series. To enable comparison, fusion, and supervised learning of reanalysis and numerical simulation data on a unified grid, the ocean variable fields (such as sea surface temperature) on the reanalysis grid are mapped to the numerical simulation grid through spatial interpolation.

[0101] Subsequently, a land mask was generated based on the numerical simulation data to eliminate unnecessary interference from land areas in the ocean analysis, with land areas being assigned a value of 1 and ocean areas being assigned a value of 0. In actual processing, the input values ​​for masked points in the grid were set to missing values ​​or zero in subsequent analysis and training to avoid spurious effects from physical process modeling.

[0102] Specifically, constructing a representative background field set is crucial for improving the accuracy of subsequent assimilation and reconstruction. This method adaptively generates a background field set for any given time point, balancing temporal consistency and diversity. This method effectively captures the uncertainty of the background field and provides rich prior information for the adaptive Fourier neural process.

[0103] Step S2 is specifically as follows:

[0104] Assume that the observation time series is , for each time step , build contains Background field collection of members , calculated as:

[0105] ;

[0106] in, is the number of set members, For the The background field of each member is usually a two-dimensional grid, such as the sea surface temperature field. This set contains not only the model output at the current time, but also historical model outputs from adjacent or random times to reflect the spatiotemporal correlation of the physical field and the time-varying nature of the model error.

[0107] For each time step , the background field set consists of two parts: the background field at the current moment and Each member is selected from the model output at a given moment to simulate the time-varying nature of the background error. This selection can be done in two ways: random selection and sequential selection. The random selection strategy involves randomly selecting the background field at the current moment (which serves as the first member of the ensemble, ensuring consistency with the current observation moment) from any past moment in the past. Each member is selected at a different moment in the past. This approach maximizes temporal diversity and simulates potential random perturbations and external influences on the background error. If the available historical data at a given moment is insufficient to meet the required number of members, the earliest available historical field is reused to fill the gap, ensuring a constant number of members. The sequential selection strategy involves selecting the model output from several time points immediately preceding the current moment, in addition to the current moment in the past. If the historical data preceding a given moment is insufficient to provide a sufficient number of consecutive time points, the data from the earliest available time point is used to fill the gap. This ensures that the members of the ensemble are closely aligned in time, preserving the smooth temporal evolution of the background field. It is more suitable for scenarios with strong continuous dynamics and the need for temporal consistency.

[0108] Specifically, constructing a training dataset: After building the background field set, the background field, simulated observations, and ground truth data must be organized into a standardized dataset suitable for training the Adaptive Fourier Neural Process (AFNP) model. The core of this step is to ensure consistent input and output scaling through consistent normalization, promoting efficient model learning, and constructing an appropriate partitioning of training, validation, and test data to ensure generalization.

[0109] Step S3 specifically includes the following steps:

[0110] S3.1, set Indicates the Members at time Time, grid point The background field of the target variable (e.g. sea surface temperature), Indicates time Time, grid point Observed values ​​(missing values ​​if there are no observation points), Indicates time Time, grid point The true value of (can be provided by reanalysis data).

[0111] S3.2, since model training is sensitive to the numerical distribution of input data, 、 and Standardization was performed separately, and z-score normalization was used. The formula is:

[0112] ;

[0113] in, 、 are the mean and standard deviation of all member background fields at all time steps, respectively; 、 is the mean and standard deviation of all time step observations; 、 is the mean and standard deviation of the true value of all time steps, For the Members at time Time, grid point The target variable (e.g. sea surface temperature) is the normalized background field. and Time Time, grid point The observed and true values ​​after standardization.

[0114] S3.3, after normalization, the input-output pair of the adaptive Fourier neural process AFNP model at a single time step is:

[0115] ;

[0116] in, is the input field, is the output field, For complete, multi-member, full-grid, same time step The standardized background field set at the moment, and They are Normalized observation field and truth field of the full grid at all times.

[0117] To ensure data time series integrity and prevent information leakage, the time series is partitioned chronologically: 70% of the data is used as a training set for gradient updates, 20% as a validation set for selecting optimal hyperparameters, and 10% as a test set for evaluating generalization capabilities. The resulting training dataset contains not only a complete set of spatiotemporal background field information, but also sparse observations and their corresponding true values, with a uniform distribution of values. This fully meets the requirements of the subsequent AFNP model for learning the nonlinear relationship between background fields, observations, and true values. This standardization and partitioning strategy significantly improves the model's convergence and predictive stability, laying a solid foundation for achieving high-precision ocean data fusion.

[0118] Specifically, construct the AFNP model: after constructing the Background field collection of members and observation sites Afterwards, in order to overcome the problems of the traditional numerical model, such as the insufficient description of complex mesoscale and small-scale ocean dynamic process, sparse observation and noise, the AFNP model is adopted to realize the dynamic coupling and non-local correction of the background field and the observation information.

[0119] Step S4 specifically comprises the following steps:

[0120] S4.1, constructing a background field encoder and an observation field encoder, and extracting local spatial features.

[0121] S4.2, in order to make up for the limitation of the local convolution receptive field, a Fourier neural operator is introduced after encoding to enhance the extracted local spatial features in the frequency domain:

[0122] ;

[0123] ;

[0124] wherein, the Fourier neural operator is, the background field local spatial feature extracted through the background encoder is, the observation field local spatial feature extracted through the observation encoder is, the frequency domain enhancement result of the background field is, the frequency domain enhancement result of the observation field is. This step ensures adaptive emphasis on key wavenumber signals (such as mesoscale and small-scale eddies, fronts, etc.), while suppressing noise wavenumbers and improving feature expression.

[0125] S4.3, in order to overcome the inconsistency between the background field and the observation field, the adaptive alignment fusion module is designed to learn the spatially variable alignment weight and dynamically balance the two information sources.

[0126] S4.4, the fused features are input into the decoder to map back to the ocean state estimation field.

[0127] Specifically, step S4.1 specifically comprises the following steps:

[0128] S4.1.1, the standardized background field member set is stacked in the channel dimension and input into the background encoder, and the background field local spatial feature is extracted through the background encoder :

[0129] ;

[0130] wherein, the convolution type encoding network of the background field is, channel dimension, grid row number and grid column number, respectively, is the standardized background field of the target variable (e.g., sea surface temperature) of the th member at the time instant. is the standardized background field of the target variable (e.g., sea surface temperature) of the th member at the time instant. denotes a tensor of the form, each element of which is a real number, where is the channel dimension, used to carry multi-scale, multi-modal features in the encoder, is the grid row number, corresponding to the number of points in the spatial dimension of the latitude direction, is the grid column number, corresponding to the number of points in the spatial dimension of the longitude direction.

[0131] S4.1.2, input the standardized observation field into the observation encoder to obtain the observation field local spatial feature extracted by the observation encoder :

[0132] ;

[0133] wherein, is the convolutional encoding network of the observation field. and share parameters.

[0134] Specifically, in step S4.2:

[0135] S4.2.1, for any spatial feature, do two-dimensional fast Fourier transform:

[0136] ;

[0137] wherein, denotes the Fourier coefficient in the frequency domain, denotes the input feature in the spatial domain, and are the transverse wave number index (longitude direction) and the longitudinal wave number index (latitude direction) in the Fourier domain, respectively, is the natural exponential function, is the imaginary unit.

[0138] S4.2.2, learn the complex weight kernel in the frequency domain , enhance row by row and wave number by wave number:

[0139] ;

[0140] wherein, denotes the frequency domain coefficient after weight modulation.

[0141] S4.2.3, perform inverse Fourier transform to restore to the spatial domain:

[0142] ​​​ ;

[0143] in, is the output of the inverse transform in the spatial domain after modulation, is the inverse Fourier transform.

[0144] Specifically, step S4.3 designs an adaptive alignment fusion module to learn spatially variable alignment weights as follows:

[0145] ;

[0146] ;

[0147] in, To be learnable Convolution kernel; Indicates splicing in the channel dimension; Sigmoid activation function, the output weight is [0,1]; Represents the alignment similarity weight matrix, which determines point by point whether to use background features or observation features; is the fused feature; Represents element-wise product.

[0148] Specifically, step S4.4 inputs the fused features into the decoder and maps them back to the ocean state estimation field as follows:

[0149] ;

[0150] in, For the decoder, is the normalized ocean prediction field predicted at a certain grid point.

[0151] Specifically, after the model is built, supervised end-to-end training of the AFNP model is required to fully learn the nonlinear relationship between the background field set and the observed field, and accurately reconstruct the true ocean state field. The training process aims to minimize the deviation between the predicted value and the normalized true value. At the same time, the optimizer and scheduler gradually adjust the parameters to ensure the convergence and generalization of the model.

[0152] Step S5 specifically includes the following steps:

[0153] S5.1, assuming that the training data contains multiple time steps, denoted as , for each time step, the prediction field output by the AFNP model is:

[0154] ;

[0155] in, Represents the forward inference function of the pre-trained AFNP model.

[0156] S5.2, in order to measure the consistency between the predicted field and the real field, the training adopts the mean square error loss function, which is defined as:

[0157] ;

[0158] in, is the loss function, is the total number of training time steps, Indicates that at time step , grid points The true ocean state value after denormalization, For the time step , grid points The denormalized AFNP model predictions.

[0159] S5.3, in order to impose additional constraints on high-frequency noise and local errors, the mean square error loss Based on this, L2 regularization is introduced, and the total loss is:

[0160] ;

[0161] in, is the total loss, represents the set of all learnable parameters in the AFNP model, represents the L2 norm, is the regularization coefficient, which is used to balance prediction accuracy and parameter complexity.

[0162] S5.4, during training, the adaptive moment estimation optimizer is used to optimize the parameter set Perform iterative updates. In each iteration, the model calculates the gradient of the current batch , and update the parameters by gradient descent:

[0163] ;

[0164] in, Indicates the AFNP model parameters at the iteration, is the learning rate of the current iteration.

[0165] During the training process, an adaptive learning rate scheduler is used to dynamically adjust the learning rate within the entire training round. The learning rate curve usually increases first and then decreases, thereby accelerating convergence and avoiding falling into local optimality. After each round of training, if the validation set loss does not decrease significantly for several rounds, the early termination mechanism is triggered to prevent overfitting. After the training is completed, the parameter set with the minimum loss on the validation set is saved. .

[0166] S5.5, the predicted value By denormalizing and restoring to the original physical quantity, the prediction result is finally output:

[0167] ;

[0168] in, is the predicted physical field after restoration (such as sea surface temperature).

[0169] At this point, the AFPN model has achieved consistent fusion of background field sets and observation fields, spatial non-local information interaction, and high-fidelity reconstruction of the real state field through end-to-end supervised training.

[0170] Figure 2-Figure 9 The comparison of the prediction results of the sea surface temperature field between the method of the present invention and the traditional method in the same sea area and at the same time (taking January 1, 2019 as an example) is shown. Figure 2-Figure 9 It can be seen that under the same observation conditions, the AFNP method effectively reduces the systematic deviations and local errors in the background field and traditional methods, reducing the overall RMSE from 0.42°C for the background field and 0.40°C for the traditional method to 0.31°C. Compared to the background field without fusion of observation information, the adaptive Fourier neural process method described in this invention can reduce the root mean square error (RMSE) of the predicted field by approximately 26%. Compared to the prediction results of the traditional interpolation method, the RMSE is further reduced by approximately 22%, verifying the significant effectiveness and advantages of the present invention in fusing background field sets with sparse observation information.

[0171] The present invention proposes an adaptive Fourier neural process fusion method, which effectively breaks through the limitations of the existing framework through multi-dimensional collaborative innovation: first, a dual-channel coupling architecture driven by physical mechanisms and data is established, and the background field set encoder is used to capture the uncertainty of numerical patterns, and the observation feature encoder is used to extract the spatial correlation of sparse observations. The contribution of the two types of information sources is adaptively reconciled through a learnable dynamic weight allocation mechanism, which significantly alleviates the performance degradation problem in sparse observation scenarios; second, a mask-enhanced spectral domain fusion core is designed, and the land boundary mask and multi-scale modal truncation mechanism are embedded in the Fourier neural operator to overcome the frequency domain artifact problem caused by complex coastlines while retaining the cross-scale characteristics of the ocean field; third, an end-to-end differentiable fusion system is constructed, which integrates background field generation, observation information injection, physical field reconstruction and uncertainty quantification into a unified framework, and realizes efficient error correction in the spectral space through the adaptive Fourier layer, which not only avoids the iterative calculation bottleneck of traditional assimilation, but also ensures that the output results meet the fluid dynamics constraints. This technology addresses key bottlenecks such as the traditional methods' reliance on linear assumptions and Gaussian errors, the physical inability of deep learning models, and the poor boundary adaptability of spectral domain methods. It provides an efficient and reliable solution for multi-source heterogeneous data fusion in complex ocean environments. The proposed ocean data fusion method, based on an adaptive Fourier neural process, can effectively fuse multi-member background fields and sparse observation data, achieving high-precision ocean temperature field reconstruction through deep neural networks.

[0172] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for fusion of ocean multi-source data based on adaptive Fourier neural process, characterized by: The specific steps include: S1, preprocessing the ocean variable field data, the ocean data includes: background field, true value and observation value; S2, adaptively generates a background field set for any time point; S3, organizes the background field, ground truth and observation values ​​into a standardized dataset for training the adaptive Fourier neural process AFNP model; S4, constructing the AFNP model, which includes: background field encoder, observation field encoder, neural Fourier operator, adaptive alignment fusion module and decoder. Finally, the decoder outputs the prediction result of the real field. S5, supervised end-to-end training of the AFNP model to learn the nonlinear relationship between the background field and the observation field and reconstruct the true ocean state field; Step S4 specifically includes the following steps: S4.1, construct background field encoder and observation field encoder, and extract local spatial features; S4.2, introduce the Fourier neural operator to perform frequency domain enhancement on the extracted local spatial features: ； ； in, is the Fourier neural operator, is the local spatial feature of the background field extracted by the background encoder, is the local spatial feature of the observation field extracted by the observation encoder, is the frequency domain enhancement result of the background field, is the frequency domain enhancement result of the observation field; S4.3, design an adaptive alignment fusion module to learn spatially variable alignment weights; S4.4, the fused features are input into the decoder and mapped back to the ocean state estimation field.

2. The method for fusion of ocean multi-source data based on adaptive Fourier neural process according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S1.1, align the background field, ground truth, and observations in the same dimension and time series by spatiotemporal interception; S1.2, mapping the ocean variable field data on the true value grid to the background field grid through spatial interpolation; S1.3, generate a land mask based on the background field to eliminate the interference of land areas on ocean analysis, that is, the land area is 1 and the ocean area is 0.

3. The method for fusion of ocean multi-source data based on adaptive Fourier neural process according to claim 1 is characterized in that: Step S2 is specifically as follows: Assume that the observation time series is , for each time step , build contains Background field collection of members , calculated as: ； in, is the number of set members, For the The background field of each member.

4. The method for fusion of ocean multi-source data based on adaptive Fourier neural process according to claim 1, characterized in that: Step S3 specifically includes the following steps: S3.1, set Indicates the Members at time Time, grid point The background field of the target variable, Indicates time Time, grid point The observed value of Indicates time Time, grid point The truth value of S3.2, yes 、 and Standardization was performed separately, and z-score normalization was used. The formula is: ； in, 、 are the mean and standard deviation of the background fields of all members at all time steps, respectively; 、 is the mean and standard deviation of all time step observations; 、 is the mean and standard deviation of the true value of all time steps, For the Members at time Time, grid point The background field after the target variable is standardized, and Time Time, grid point Standardized observed values ​​and true values; S3.3, after normalization, the input-output pair of the adaptive Fourier neural process AFNP model at a single time step is: ； in, is the input field, is the output field, is the standardized background field set, and They are Normalized observation field and truth field of the full grid at all times.

5. The method for fusion of ocean multi-source data based on adaptive Fourier neural process according to claim 4 is characterized in that: Step S4.1 specifically includes the following steps: S4.1.1, all standardized background field members are stacked in the channel dimension and input into the background encoder, and the background encoder extracts the local spatial features of the background field. : ； in, is the convolutional coding network of the background field, are the channel dimension, the number of grid rows and the number of grid columns, respectively. For the Members at time The background field after the target variable at the moment is standardized; S4.1.2, input the standardized observation field into the observation encoder to obtain the local spatial features of the observation field extracted by the observation encoder : ； in, is a convolutional encoding network for the observation field.

6. The method for fusion of ocean multi-source data based on adaptive Fourier neural process according to claim 5 is characterized in that: In step S4.2: S4.2.1, for any spatial feature , do a two-dimensional fast Fourier transform: ； in, represents the frequency domain Fourier coefficient, represents the spatial domain input features, and are the transverse wavenumber index and longitudinal wavenumber index in the Fourier domain, is the natural exponential function, is an imaginary unit; S4.2.2, Learning Complex Weight Kernels in the Frequency Domain , row-by-row and wavenumber-by-wavenumber enhancement: ； in, Represents the frequency domain coefficient after weight modulation; S4.2.3, perform inverse Fourier transform to restore to the spatial domain: ； in, is the output of the inverse transform in the spatial domain after modulation, is the inverse Fourier transform.

7. The method for ocean multi-source data fusion based on adaptive Fourier neural process according to claim 6 is characterized in that: Step S4.3 designs an adaptive alignment fusion module to learn spatially variable alignment weights: ； ； in, To be learnable Convolution kernel; Indicates splicing in the channel dimension; Sigmoid activation function, the output weight is [0,1]; represents the alignment similarity weight matrix feature; is the fused feature; Represents element-wise product.

8. The method for ocean multi-source data fusion based on adaptive Fourier neural process according to claim 7 is characterized in that: Step S4.4 inputs the fused features into the decoder and maps them back to the ocean state estimation field as follows: ； in, For the decoder, is the normalized ocean prediction field predicted at a certain grid point.

9. The method for ocean multi-source data fusion based on adaptive Fourier neural process according to claim 8, characterized in that: Step S5 specifically includes the following steps: S5.1, assuming that the training data contains multiple time steps, denoted as , for each time step, the prediction field output by the AFNP model is: ； in, Represents the forward reasoning function of the pre-trained AFNP model; S5.2, in order to measure the consistency between the predicted field and the real field, the training adopts the mean square error loss function, which is defined as: ； in, is the loss function, is the total number of training time steps, Indicates that at time step , grid points The true ocean state value after denormalization, For the time step , grid points The predicted value of the AFNP model after denormalization; S5.3, in mean square error loss Based on this, L2 regularization is introduced, and the total loss is: ； in, is the total loss, represents the set of all learnable parameters in the AFNP model, represents the L2 norm, is the regularization coefficient; S5.4, using the adaptive moment estimation optimizer to optimize the parameter set Perform iterative updates. In each iteration, the model calculates the gradient of the current batch , and update the parameters by gradient descent: ； in, Indicates the AFNP model parameters at the iteration, is the learning rate of the current iteration; S5.5, the predicted value By denormalizing and restoring to the original physical quantity, the prediction result is finally output: ； in, is the predicted physical field after restoration.

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