A physically constrained deep generative wave field probability forecasting method

Abstract

A physical constraint deep generative wave field probabilistic prediction method belongs to the field of wave prediction, and a single-point or multi-point buoy historical wave observation sequence is input to construct effective wave height, average wave period and wave direction characteristics; sea state characteristics are extracted through a buoy condition coding network, a latent variable posterior and a conditional prior distribution are constructed, reparameterization sampling is combined with a two-dimensional field generation network to realize multi-step two-dimensional wave field generation prediction; during the training process, time continuity, spatial smoothness, wave direction continuity and reasonable energy change constraints are introduced to improve the physical consistency of the prediction results; in the reasoning stage, multiple random samplings of the latent variable are performed to obtain a prediction sample set of the two-dimensional wave height field, wave period field and wave direction field, and the mean field, uncertainty field and quantile field are output to realize the extension prediction from discrete buoy observation to continuous two-dimensional wave field, and the method has multi-step prediction, probabilistic prediction and good physical rationality, and is suitable for fine prediction and risk assessment of wave field in complex sea areas.

Description

Technical Field

[0001] This invention relates to the field of wave prediction technology, and in particular to a multi-step probabilistic prediction method for two-dimensional wave fields based on buoy observation, latent variable probabilistic modeling and physical constraints. It can be used to generate predictions of two-dimensional wave fields at multiple future times in a target sea area based on single-point or multi-point buoy wave observation data, and output the probability distribution results of wave height field, wave period field and wave direction field. Background Technology

[0002] Wave fields are important parameter fields describing the marine dynamic environment. Their spatial distribution and temporal evolution are of great significance for marine disaster early warning, shipping safety, offshore engineering construction, marine resource development, and marine environmental protection. Two-dimensional wave fields typically include elements such as significant wave height, mean wave period, and mean wave direction. Traditional methods for obtaining two-dimensional wave fields mainly rely on numerical model simulation, satellite remote sensing inversion, and interpolation of field observation data.

[0003] While existing numerical wave models can provide relatively complete spatial field information, they typically rely on external drivers such as wind fields, boundary conditions, and water depth topography, resulting in significant computational resource consumption. Their real-time performance and cost-effectiveness are limited, especially in complex nearshore waters or local high-resolution scenarios. Satellite remote sensing, although offering good spatial coverage, still faces limitations in revisit cycles, weather conditions, and nearshore applicability. In-situ buoys can provide high temporal resolution and high-precision point wave observations, but they only reflect local sea state information and cannot directly provide the two-dimensional wave field distribution for the entire region.

[0004] In recent years, deep learning technology has been used to reconstruct two-dimensional environmental fields based on sparse observations. However, most existing methods focus on deterministic predictions, that is, directly outputting a single result, which is difficult to express the ambiguity and uncertainty of future sea states. At the same time, existing methods mostly focus on single-time spatial reconstruction and lack the ability to predict the continuous evolution of two-dimensional wave fields over multiple future times. On the other hand, if only data-driven networks are relied upon for learning, it is easy to produce prediction results with small numerical errors but that do not conform to the laws of wave propagation, spatiotemporal smoothness, or physical evolution, especially in extreme sea states, areas affected by complex topography, or scenarios with sparse observations.

[0005] Therefore, there is an urgent need for a two-dimensional wave field prediction method that can make full use of single-point or multi-point buoy observation information and take into account future multi-step prediction capabilities, probabilistic prediction capabilities and physical consistency constraints, so as to improve the accuracy, stability and reliability of two-dimensional wave field prediction in local sea areas. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-step probabilistic prediction method for two-dimensional wave fields based on buoy conditional encoding, latent variable probabilistic modeling, two-dimensional field generation, and physical constraints, in order to solve the following problems existing in the prior art: 1) Buoy observations are single points or a small number of discrete points, making it difficult to directly infer the two-dimensional wave field of the entire sea area; 2) Existing deep learning methods mostly output single deterministic results, making it difficult to characterize the uncertainty of future wave fields; 3) Existing methods mostly focus on field reconstruction at the same time moment, lacking the ability to jointly predict the continuous evolution of two-dimensional wave fields at multiple future times; 4) Purely data-driven prediction results lack physical constraints, which are prone to problems such as unreasonable local oscillations or insufficient physical consistency.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for probabilistic prediction of wave fields generated by physically constrained depth includes the following steps:

[0009] 1) Obtain wave observation data of single or multiple buoys in the target sea area at continuous historical moments, and construct a historical observation input sequence of buoys; the wave observation data shall include at least the significant wave height, mean wave period and mean wave direction;

[0010] 2) Encode the average wave direction using sine and cosine components, and construct a two-dimensional wave field label for the future time period based on the historical input time period; the two-dimensional wave field label for the future time period includes at least a two-dimensional significant wave height field, a two-dimensional average wave period field, and a two-dimensional wave direction code;

[0011] 3) Input the buoy historical observation input sequence into the buoy conditional coding network to extract the conditional vector representing the current sea state evolution;

[0012] 4) During the training phase, based on the conditional vector and the two-dimensional wave field labels for future time periods, a latent variable posterior network is constructed to obtain the latent variable posterior distribution; at the same time, a latent variable conditional prior network is constructed based on the conditional vector to obtain the latent variable conditional prior distribution.

[0013] 5) The latent variables are sampled from the posterior distribution of the latent variables using a reparameterized sampling method, and the latent variables and the conditional vector are input into a two-dimensional field generation network to generate two-dimensional wave field prediction results for multiple future time periods;

[0014] 6) During model training, a joint loss function is constructed, including reconstruction loss, latent variable distribution constraint loss, and physical constraint loss, to impose physical consistency constraints on the two-dimensional wave field prediction results;

[0015] 7) Based on the joint loss function, the buoy conditional encoding network, the latent variable posterior network, the latent variable conditional prior network, and the two-dimensional field generation network are jointly trained to obtain a two-dimensional wave field probability prediction model.

[0016] The present invention also includes the following steps:

[0017] 8) During the inference phase, the buoy historical observation input sequence is input into the trained two-dimensional wave field probability prediction model. Multiple random samplings are performed through the latent variable conditional prior distribution to obtain a two-dimensional wave field sample set for multiple future times. Based on the sample set, the mean prediction result and uncertainty characterization result of the two-dimensional wave field are output.

[0018] In step 1), let the number of buoys be... The historical input time length is Then the first The historical observation sequence of each buoy is represented as follows:

[0019]

[0020] in, Indicates the first Each buoy at time The observation vector;

[0021] When using only a single-point buoy, the input sequence is a historical observation time series of a single buoy; when using multiple-point buoys, the input sequence is a combination of historical observation sequences of multiple buoys.

[0022] In step 2), the average wave direction is... When encoding, use and The cosine and sine components of the wave direction are respectively characterized to eliminate the discontinuity of the angle variable between 0° and 360°;

[0023] Simultaneously, based on numerical models, reanalysis products, post-report data, or high-resolution gridded reference fields, two-dimensional wave field labels for future time periods corresponding to training samples are constructed.

[0024] The future time period two-dimensional wave field label includes the future A two-dimensional wave field sequence at each moment:

[0025]

[0026] Among them, the two-dimensional wave field at each moment It is a four-channel grid tensor, corresponding to: wave height field, wave period field, wave direction cosine field, and wave direction sine field.

[0027] In step 3), the buoy conditional coding network is used to extract the temporal evolution features and joint state features among multiple buoys from the historical observation input sequence of the buoys, and outputs a fixed-dimensional conditional vector. .

[0028] In step 4), the posterior distribution of the latent variable is expressed as: The latent variable conditional prior distribution is expressed as: ;in, As a latent variable, Labels for two-dimensional wave fields in the future time period. For conditional vectors, For latent variables, posterior network parameters, The conditional prior network parameters are latent variables;

[0029] The latent variable posterior network is used to receive two-dimensional wave field labels and condition vectors for future time periods, and output the mean and variance parameters of the latent variable posterior distribution.

[0030] The latent variable conditional prior network is used to receive the conditional vector and output the mean and variance parameters of the latent variable conditional prior distribution.

[0031] Both the latent variable posterior distribution and the latent variable conditional prior distribution are represented by parameterized Gaussian distributions, and the mean parameter and variance parameter are output respectively.

[0032] In step 5), the two-dimensional field generation network generates data based on latent variables. With condition vector The combined input, output the future The two-dimensional effective wave height field, two-dimensional average wave period field, and two-dimensional wave direction coding field at each moment are used to realize the mapping from discrete buoy historical observations to future continuous two-dimensional wave fields.

[0033] In step 6), the reconstruction loss is used to constrain the difference between the predicted two-dimensional wave field and the two-dimensional wave field label for future time periods, and the latent variable distribution constraint loss is used to constrain the difference between the latent variable posterior distribution and the latent variable conditional prior distribution.

[0034] The physical constraint loss includes at least one of the following:

[0035] Temporal continuity constraints are used to constrain the smoothness of field evolution between adjacent prediction times;

[0036] Spatial smoothness constraints are used to constrain local anomalous oscillations in a two-dimensional mesh space.

[0037] Wave direction continuity constraint is used to constrain the wave direction encoding results to satisfy the unit circle consistency; the wave direction continuity constraint is achieved by constraining the predicted wave direction cosine component and wave direction sine component to satisfy the unit circle relationship.

[0038] The energy change rationality constraint is used to constrain the overall wave energy change at each predicted time in the future to meet a preset reasonable range; the energy change rationality constraint is based on the spatial average square value of the two-dimensional effective wave height field at each predicted time in the future to construct an overall energy characterization quantity, and the constraint term is constructed based on the change of the overall energy characterization quantity between adjacent times.

[0039] The joint loss function is a weighted sum of reconstruction loss, latent variable distribution constraint loss, and physical constraint loss.

[0040] In step 8), during the inference phase, the condition vector is obtained solely using the buoy's historical observation input sequence. And based on the latent variable conditional prior distribution Multiple random samplings were performed to obtain multiple latent variable samples;

[0041] The multiple latent variable samples are respectively input into the two-dimensional field generation network to generate multiple future two-dimensional wave field prediction samples;

[0042] Based on the multiple future two-dimensional wave field prediction samples, at least one of the following fields is calculated for each future time: mean field, variance field, standard deviation field, quantile field, or confidence interval field of the two-dimensional effective wave height field, two-dimensional average wave period field, and two-dimensional wave direction field, as the probability prediction output result.

[0043] The two-dimensional wave-direction field is obtained by inverting the predicted wave-direction cosine component field and wave-direction sine component field using inverse trigonometric functions.

[0044] Compared with the prior art, the beneficial effects achieved by the technical solution of this invention are:

[0045] 1. Achieving spatial expansion prediction of two-dimensional wave fields from single-point or small number of buoy observations: This invention can generate two-dimensional wave fields of target sea areas at multiple future times using historical observation information from single-point or multi-point buoys, thereby breaking through the limitation of traditional buoys that can only reflect local single-point sea conditions and realizing the expansion from discrete point observation to continuous spatial field prediction.

[0046] 2. Achieve joint prediction of two-dimensional wave fields in multiple future steps: Unlike methods that only reconstruct space at a single moment, this invention can jointly output the two-dimensional wave height field, periodic field and wave direction field at multiple consecutive future moments, which has significant spatiotemporal prediction capabilities and is more suitable for marine forecasting and early warning business scenarios.

[0047] 3. Possesses probabilistic prediction capabilities and can output uncertainty information: This invention obtains a prediction sample set of the future two-dimensional wave field through latent variable probabilistic modeling and multiple random sampling. It can output not only the mean field, but also the variance field, quantile field, or confidence interval field, thereby quantifying the prediction uncertainty and improving the credibility and risk expression capability of the forecast results.

[0048] 4. Introducing physical constraints to improve the physical consistency of prediction results: This invention introduces one or more of the following constraints during the training process: temporal continuity constraint, spatial smoothness constraint, wave direction continuity constraint, and energy change rationality constraint. This can effectively reduce the local abnormal oscillations, time abrupt changes, or physical inconsistencies that are prone to occur in pure data-driven models, and improve the stability and physical rationality of prediction results.

[0049] 5. Adaptability to missing observations and changes in the number of buoys: The buoy condition coding method of this invention can adapt to single-point or multi-point buoy inputs, and can handle scenarios with missing buoys or changes in the number of stations, thus having strong engineering applicability and promotion capabilities.

[0050] 6. Applicable to refined wave field prediction in complex sea areas: This invention does not rely entirely on high-cost real-time calculations of all-physical numerical models. It can quickly generate future multi-step two-dimensional wave fields based on existing buoy observations. It is especially suitable for refined wave forecasting and decision support in complex sea areas such as nearshore areas, straits, and areas around islands and reefs. Attached Figure Description

[0051] Figure 1 This is a flowchart of the overall process of a two-dimensional wave field multi-step probability prediction method for physically constrained depth generation according to the present invention. Detailed Implementation

[0052] To make the technical problems, technical solutions and beneficial effects of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments, but the present invention is not limited thereto.

[0053] This invention includes the following technical main lines:

[0054] 1. Perform conditional encoding on historical wave observation sequences of single-point or multi-point buoys to extract contextual condition vectors that characterize the evolution of local sea conditions;

[0055] 2. Based on the concept of conditional variational probability modeling, we construct the prior and posterior distributions of latent variables, and use the latent variables to describe the various possible evolution scenarios of the future two-dimensional wave field under the same buoy observation conditions;

[0056] 3. Input the conditional features and latent variables into the two-dimensional field generation network to generate two-dimensional wave fields at multiple future time points;

[0057] 4. Introduce physical constraints during the training process to constrain the spatiotemporal continuity, wave direction continuity, or rationality of energy changes in the prediction results;

[0058] 5. During the reasoning process, the latent variables are sampled multiple times to form a prediction sample set for the future two-dimensional wave field, and then the mean field, variance field and quantile field are output to realize the probability prediction of the two-dimensional wave field.

[0059] In the preferred embodiment:

[0060] 1. The buoy observations include one or more of the following: significant wave height, mean wave period, and mean wave direction;

[0061] 2. The average wave direction is encoded using a sine and cosine method to eliminate the problem of periodic discontinuity in the angle variable;

[0062] 3. The aforementioned multi-step future prediction includes predictions of the future. The two-dimensional wave height field, two-dimensional periodic field and two-dimensional wave direction field at each moment are jointly output;

[0063] 4. The physical constraints include one or more of the following: temporal continuity constraints, spatial smoothness constraints, wave direction continuity constraints, and energy change rationality constraints.

[0064] Example 1

[0065] See Figure 1 This embodiment of a multi-step probability prediction method for two-dimensional wave fields generated by physical constraint depth includes the following steps:

[0066] 1. Data Construction

[0067] Taking a specific area of ​​the target sea area as the research scope, a regular two-dimensional grid is constructed with a grid size of [size missing]. Data was acquired from three buoy stations deployed in the area. The buoy observation elements included wave height field. Wave periodic field Harmony wave direction field Meanwhile, high-resolution two-dimensional wave field reference data corresponding to the same time period in this region was obtained from the ECMWF ReAnalysisv5 (ERA5) product of the European Centre for Medium-Range Weather Forecasts (ECMWF) and used as the label field for model training.

[0068] In this embodiment, the most recent Using historical observation sequences of buoys within the region as input, predict future... A two-dimensional wave field sequence. The input time interval is 1 hour, and the output time interval is the same as the input.

[0069] The two-dimensional wave field label for each future moment includes four channels: wave height field. Wave periodic field Wave towards cosine field , wave towards sine field Among them, wave direction field Sine and cosine encoding is used to eliminate the discontinuity of the direction variable at 0° and 360°.

[0070] Considering that buoy observations may experience data gaps at certain times during actual operation due to communication interruptions, sensor malfunctions, or sea state interference, this embodiment further processes the missing data in the buoy's historical observation sequence. Specifically, for the wave height field... Synchronous field For short-term missing values, linear interpolation in the time dimension is used for completion; when the missing value occurs at the boundary of the input time window and two-sided interpolation is not possible, forward or backward filling is used for completion. For wave field... For missing measurements, it is preferable to first convert them into wave-directed cosine fields. Sine Field Then, linear interpolation or boundary filling is performed on the cosine field and the sine field respectively to avoid the discontinuity error near 0° and 360° caused by directly interpolating the angle.

[0071] Furthermore, to preserve the auxiliary role of missing measurement information in model discrimination, a missing measurement mask sequence is constructed synchronously with the completed buoy historical observation sequence, wherein the effective observation position is recorded as 1, and the missing and completed position is recorded as 0; the missing measurement mask sequence can be used as an additional input and sent to the buoy conditional coding network together with the buoy historical observation sequence.

[0072] In this embodiment, when a buoy is within the input time window When the proportion of missing data within a time window exceeds a preset threshold, the observation quality of that time window is deemed insufficient. Preferably, when the proportion of missing data exceeds 50%, the corresponding sample is discarded, or in a multi-buoy scenario, only the data of the remaining valid buoys is retained to participate in subsequent conditional coding and prediction, so as to enhance the model's adaptability to scenarios with missing data for some buoys and changes in the number of stations.

[0073] In this embodiment, the historical observation sequence of the buoy and the two-dimensional wave field labels for future time periods are standardized. For the wave height field and wave period field, standardization based on training set statistics is used; for the wave direction field, it is first converted into a wave direction cosine field and a wave direction sine field, and its bounded properties are used directly as network input.

[0074] In this embodiment, the standardized data from the locations of the three buoys for 10 years from 2014 to 2023 are divided into training, validation, and test sets in a ratio of 7:2:1, according to the chronological order. That is, the data from 2014 to 2020 (7 years) is used as the training set, the data from 2021 to 2022 (2 years) is used as the validation set, and the data from 2023 is used as the test set.

[0075] 2. Buoy Condition Coding

[0076] Each buoy in continuous The observed sequences are input into a gated recurrent unit network (GRU, 2 layers) with shared parameters. Single buoy time-series feature representations are extracted, and the three buoy features are aggregated using max pooling to obtain a unified buoy condition vector. .

[0077] 3. Latent variable probability modeling

[0078] During the training phase, the future Two-dimensional wave field label With buoy condition vector The latent variable posterior network (preferably a spatiotemporal convolutional network ConvLSTM, 3 layers, each with a kernel size of 3×3) is input together to output the mean parameters of the latent variable posterior distribution. and variance parameter Construct the posterior distribution of the latent variables:

[0079]

[0080] in, For the posterior distribution of latent variables, For latent variables, posterior network parameters, As a latent variable, Labels for two-dimensional wave fields in the future time period. For conditional vectors, It follows a Gaussian distribution (normal distribution). It is an identity matrix.

[0081] Meanwhile, based on buoy condition vector The input latent variable conditional prior network (in this embodiment, a multilayer perceptron network MLP, with 2 layers and 20 neurons per layer) is used to output the mean parameter of the latent variable conditional prior distribution. and variance parameter Construct the conditional prior distribution of latent variables:

[0082]

[0083] in, For latent variables, conditional prior distribution, These are the latent variable conditional prior network parameters.

[0084] Latent variables are sampled from the posterior distribution using a reparameterization method:

[0085]

[0086] in, For Hadamard product, Let be a random vector that follows a standard normal distribution with a mean of 0 and a variance of 1.

[0087] 4. Future generation of two-dimensional wave fields

[0088] latent variables obtained from sampling With buoy condition vector Input the spatiotemporal generation network together Output the future Two-dimensional wave field prediction sequence :

[0089]

[0090] The spatiotemporal generation network is used to simultaneously model the two-dimensional spatial structure and the future temporal evolution relationship. In this embodiment, a convolutional neural network cascade structure is used (5 layers, each layer has a convolutional kernel size of 3×3). Batch normalization, activation and max pooling operations are used. The network outputs a four-channel two-dimensional tensor sequence for the next 6 hours, corresponding to wave height, wave period, wave direction cosine and wave direction sine.

[0091] 5. Loss Function Design

[0092] In this embodiment, the total training loss function Defined as:

[0093]

[0094] in:

[0095] (1) Reconstruction losses

[0096] Used to constrain the error between the predicted two-dimensional wave field and the actual two-dimensional wave field:

[0097]

[0098] (2) KL divergence loss

[0099] Used to constrain the consistency between the posterior and prior distributions:

[0100]

[0101] in, Kullback–Leibler divergence is used to measure the probability distribution. and The similarity between them.

[0102] (3) Temporal continuity constraints

[0103] Used to constrain the smoothness of changes between adjacent prediction times:

[0104]

[0105] (4) Spatial smoothness constraint

[0106] Used to suppress local anomalous oscillations in the prediction field:

[0107]

[0108] (5) Wave direction consistency constraint

[0109] This is used to ensure that the wave direction coding results satisfy the unit circle relationship:

[0110]

[0111] in, and These are the wave-direction cosine component and the wave-direction sine component in the predicted output, respectively.

[0112] (6) Constraints on the rationality of energy changes

[0113] Let the spatial average wave energy index of the study sea area at each prediction time be:

[0114]

[0115] in, For the predicted time The study of the average spatial energy of the sea area , These represent the total number of pixels for the height and the total number of pixels for the width of the research sea area, respectively. For the predicted time The study of marine space The square of the wave height at the pixel location.

[0116] The rationality constraint of energy change is defined as follows:

[0117]

[0118] , , , These are the loss functions. , , , , The weights are determined by the loss function. Through joint training using the loss function described above, the model can learn the probability distribution of the future two-dimensional wave field while improving the spatiotemporal continuity and physical rationality of the prediction results.

[0119] 6. Test reasoning and probabilistic prediction output

[0120] During the testing and actual reasoning phases, only the most recent input is considered. The historical observation sequence of the buoy is used to obtain the condition vector through the buoy condition coding network. Then, the latent variable conditional prior distribution is constructed through a latent variable conditional prior network (in this embodiment, a multilayer perceptron network MLP is preferred, with 2 layers and 20 neurons per layer):

[0121]

[0122] A set of latent variable samples is obtained by performing 20 random samplings from the prior distribution:

[0123]

[0124] Each latent variable sample is input into the spatiotemporal generation network to obtain a set of two-dimensional wave field samples for the study sea area:

[0125]

[0126] This sample set constitutes a prediction sample set for the future two-dimensional wave field. Further calculations can be made for: the mean value of the two-dimensional wave height field at each future time, the mean value of the two-dimensional wave period field at each future time, the mean value of the two-dimensional wave direction field at each future time, the uncertainty field corresponding to each grid point, and the quantile field or confidence interval field for each grid point. The two-dimensional wave direction field can be obtained by inverting the predicted wave direction cosine and sine fields using inverse trigonometric functions. The two-dimensional wave height and two-dimensional wave period fields are then recovered to actual physical quantities through inverse normalization. This enables probabilistic prediction of the future two-dimensional wave field in the target sea area.

[0127] In this embodiment, 2023 was selected as the test period. The ERA5 two-dimensional wave field data of the gridded sea area is used as the agreed true value during the test period, and the uncertainty / quantile output index is used to evaluate the wave field probability prediction capability of the method of the present invention.

[0128] This invention's method can stably output two-dimensional wave height, two-dimensional wave period, and two-dimensional wave direction fields for multiple future moments in a target sea area, and simultaneously provide corresponding uncertainty characterization results. Compared with deterministic prediction methods that do not introduce latent variable probabilistic modeling, this invention's method can better reflect the diversified evolution trends of future wave fields; compared with generative models that do not introduce physical constraints, this invention's method performs better in suppressing local anomalous oscillations, ensuring the continuity of temporal evolution, and demonstrating the rationality of spatial field distribution. In summary, this invention's method can achieve extended predictions from discrete point observations to continuous two-dimensional wave fields in the future, relying only on a small number of historical buoy observations. It is suitable for refined wave field forecasting and decision support in complex sea areas such as nearshore areas, straits, and areas surrounding islands and reefs, and has significant engineering application value.

Claims

1. A method for probabilistic prediction of wave fields generated by physically constrained depth, characterized in that, Includes the following steps: 1) Obtain wave observation data of single or multiple buoys in the target sea area at continuous historical moments, and construct a historical observation input sequence of buoys; the wave observation data shall include at least the significant wave height, mean wave period and mean wave direction; 2) Encode the average wave direction using sine and cosine components, and construct a two-dimensional wave field label for the future time period based on the historical input time period; the two-dimensional wave field label for the future time period includes at least a two-dimensional significant wave height field, a two-dimensional average wave period field, and a two-dimensional wave direction code; 3) Input the buoy historical observation input sequence into the buoy conditional coding network to extract the conditional vector representing the current sea state evolution; 4) During the training phase, based on the conditional vector and the two-dimensional wave field labels for future time periods, a latent variable posterior network is constructed to obtain the latent variable posterior distribution; at the same time, a latent variable conditional prior network is constructed based on the conditional vector to obtain the latent variable conditional prior distribution. 5) The latent variables are sampled from the posterior distribution of the latent variables using a reparameterized sampling method, and the latent variables and the conditional vector are input into a two-dimensional field generation network to generate two-dimensional wave field prediction results for multiple future time periods; 6) During model training, a joint loss function is constructed, including reconstruction loss, latent variable distribution constraint loss, and physical constraint loss, to impose physical consistency constraints on the two-dimensional wave field prediction results; 7) Based on the joint loss function, the buoy conditional encoding network, the latent variable posterior network, the latent variable conditional prior network, and the two-dimensional field generation network are jointly trained to obtain a two-dimensional wave field probability prediction model.

2. The wave field probability prediction method for physically constrained depth generation as described in claim 1, characterized in that, It also includes the following steps: 8) During the inference phase, the buoy historical observation input sequence is input into the trained two-dimensional wave field probability prediction model. Multiple random samplings are performed through the latent variable conditional prior distribution to obtain a two-dimensional wave field sample set for multiple future times. Based on the sample set, the mean prediction result and uncertainty characterization result of the two-dimensional wave field are output.

3. The wave field probability prediction method for physically constrained depth generation as described in claim 1, characterized in that: In step 1), let the number of buoys be... The historical input time length is Then the first The historical observation sequence of each buoy is represented as follows: in, Indicates the first Each buoy at time The observation vector; When using only a single-point buoy, the input sequence is a historical observation time series of a single buoy; when using multiple-point buoys, the input sequence is a combination of historical observation sequences of multiple buoys.

4. The wave field probability prediction method for physically constrained depth generation as described in claim 1, characterized in that: In step 2), the average wave direction is... When encoding, use and The cosine and sine components of the wave direction are respectively characterized to eliminate the discontinuity of the angle variable at 0° and 360°; Simultaneously, based on numerical models, reanalysis products, post-report data, or high-resolution gridded reference fields, two-dimensional wave field labels for future time periods corresponding to training samples are constructed. The future time period two-dimensional wave field label includes the future A two-dimensional wave field sequence at each moment: Among them, the two-dimensional wave field at each moment It is a four-channel grid tensor, corresponding to: wave height field, wave period field, wave direction cosine field, and wave direction sine field.

5. The wave field probability prediction method for physically constrained depth generation as described in claim 1, characterized in that: In step 3), the buoy conditional coding network is used to extract the temporal evolution features and joint state features among multiple buoys from the historical observation input sequence of the buoys, and outputs a fixed-dimensional conditional vector. .

6. The wave field probability prediction method for physically constrained depth generation as described in claim 1, characterized in that: In step 4), the posterior distribution of the latent variable is expressed as: The latent variable conditional prior distribution is expressed as: ;in, As a latent variable, Labels for two-dimensional wave fields in the future time period. For conditional vectors, For latent variables, posterior network parameters, The conditional prior network parameters are latent variables; The latent variable posterior network is used to receive two-dimensional wave field labels and condition vectors for future time periods, and output the mean and variance parameters of the latent variable posterior distribution. The latent variable conditional prior network is used to receive the conditional vector and output the mean and variance parameters of the latent variable conditional prior distribution. Both the latent variable posterior distribution and the latent variable conditional prior distribution are represented by parameterized Gaussian distributions, and the mean parameter and variance parameter are output respectively.

7. The wave field probability prediction method for physically constrained depth generation as described in claim 1, characterized in that: In step 5), the two-dimensional field generation network generates data based on latent variables. With condition vector The combined input, output the future The two-dimensional effective wave height field, two-dimensional average wave period field, and two-dimensional wave direction coding field at each moment are used to realize the mapping from discrete buoy historical observations to future continuous two-dimensional wave fields.

8. The wave field probability prediction method for physically constrained depth generation as described in claim 1, characterized in that: In step 6), the reconstruction loss is used to constrain the difference between the predicted two-dimensional wave field and the two-dimensional wave field label for future time periods, and the latent variable distribution constraint loss is used to constrain the difference between the latent variable posterior distribution and the latent variable conditional prior distribution. The physical constraint loss includes at least one of the following: Temporal continuity constraints are used to constrain the smoothness of field evolution between adjacent prediction times; Spatial smoothness constraints are used to constrain local anomalous oscillations in a two-dimensional mesh space. Wave direction continuity constraint is used to constrain the wave direction encoding results to satisfy the unit circle consistency; the wave direction continuity constraint is achieved by constraining the predicted wave direction cosine component and wave direction sine component to satisfy the unit circle relationship. The energy change rationality constraint is used to constrain the overall wave energy change at each predicted time in the future to meet a preset reasonable range; the energy change rationality constraint is based on the spatial average square value of the two-dimensional effective wave height field at each predicted time in the future to construct an overall energy characterization quantity, and the constraint term is constructed based on the change of the overall energy characterization quantity between adjacent times. The joint loss function is a weighted sum of reconstruction loss, latent variable distribution constraint loss, and physical constraint loss.

9. The wave field probability prediction method for physically constrained depth generation as described in claim 2, characterized in that: In step 8), during the inference phase, the condition vector is obtained solely using the buoy's historical observation input sequence. And based on the latent variable conditional prior distribution Multiple random samplings were performed to obtain multiple latent variable samples; Multiple latent variable samples are input into a two-dimensional field generation network to generate multiple future two-dimensional wave field prediction samples. Based on the multiple future two-dimensional wave field prediction samples, at least one of the following fields is calculated for each future time: mean field, variance field, standard deviation field, quantile field, or confidence interval field of the two-dimensional effective wave height field, two-dimensional average wave period field, and two-dimensional wave direction field, as the probability prediction output result.

10. The wave field probability prediction method for physically constrained depth generation as described in claim 9, characterized in that: The two-dimensional wave-direction field is obtained by inverting the predicted wave-direction cosine component field and wave-direction sine component field using inverse trigonometric functions.

Images