A physical equation driven sea wave spectrum intelligent prediction method and system

Abstract

The application belongs to the technical field of marine prediction and artificial intelligence, and discloses a physical equation driven sea wave spectrum intelligent prediction method and system. The method disassembles a spectrum balance equation into a propagation term and a source term, models the propagation term and the source term respectively, divides the source term into different sub-source terms according to different physical mechanisms, constructs a source term sub-network for different sub-source terms, embeds a guide variable, realizes decoupling of a nonlinear physical process and construction of a high-fitting-degree multi-source driving expression mechanism, and realizes construction of a prediction strategy with long-term prediction stability and physical consistency through multi-step training combined with main peak offset constraint, energy conservation control and propagation gradient supervision. For engineering applications such as ship motion response with spectrum as input, the application avoids information gaps between single-element prediction and spectrum driving applications, realizes seamless connection from environment prediction to engineering calculation, and greatly improves the practicability of the application.

Description

Technical Field

[0001] This invention belongs to the field of interdisciplinary technology of marine forecasting and artificial intelligence, and in particular, it relates to a method and system for intelligent wave spectrum forecasting driven by physical equations. Specifically, it relates to a technology that achieves intelligent wave spectrum forecasting with physical consistency by driving neural network modeling through physical equations. Background Technology

[0002] Current intelligent forecasting in this field mostly relies on rapid regression of single scalar elements such as significant wave height, characteristic period, and peak frequency, using machine learning / deep learning to improve short-term numerical indicators in point-time series or gridded scenarios. While this approach is convenient for training and deployment, the output is limited to a few scalars, reflecting incomplete information and failing to represent the organization of wave energy and its structural changes over time. More importantly, many practical applications (such as RAO-based ship motion forecasting, offshore platform load assessment, fatigue and extreme response analysis, etc.) essentially use the wave spectrum as the driving force. An information gap exists between single-element forecasting and spectrum-driven applications, resulting in an incomplete or amplified error chain from environmental forecasting to engineering assessment.

[0003] Meanwhile, existing models mostly employ a purely data-driven, "black-box" deep architecture, lacking an alignment design and interpretable expression with physical mechanisms. They fail to explicitly incorporate constraints such as propagation terms and various source terms from the spectral balance equations, making it difficult to guarantee fundamental physical consistency such as energy conservation and consistent propagation direction. While these models may achieve small errors on conventional indicators, they cannot explain "why this forecast was made or which physical process is playing a dominant role," nor can they provide traceable and verifiable structural evidence under sudden sea state changes or extreme conditions. In high-risk decision-making scenarios such as route planning, operational window determination, and risk warning, this black-box characteristic, lacking physical constraints and structural interpretability, directly weakens the credibility and acceptability of the results.

[0004] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0005] (1) The output of existing intelligent wave forecasting methods is limited to single elements such as wave height, which does not reflect comprehensive information and makes it difficult to present the organization of wave energy and the structural changes that evolve over time.

[0006] (2) Many practical applications (such as RAO-based ship motion forecasting, offshore platform load assessment, fatigue and extreme response analysis, etc.) are essentially driven by the wave spectrum. There is an information gap between single-element forecasting and spectrum-driven applications, which leads to the link from environmental forecasting to engineering assessment being unclosed or the error being amplified.

[0007] (3) Existing “black box” models lack alignable design and interpretable expression of physical mechanisms, and do not explicitly incorporate many constraints in the spectral balance equations, making it difficult to guarantee the consistency of basic physics. This black box characteristic of lacking physical constraints and structural interpretation ability directly weakens the credibility and acceptability of the results. Summary of the Invention

[0008] To overcome the problems existing in related technologies, the present invention discloses an embodiment of a physical equation-driven intelligent wave spectrum forecasting method and system, the technical solution of which is as follows:

[0009] This invention is implemented as follows: a physical equation-driven intelligent wave spectrum prediction method, comprising the following steps:

[0010] S1, deconstruct the spectral equilibrium equation into propagation terms and source terms, and model the propagation terms and source terms separately;

[0011] S2, based on different physical mechanisms, divides the source terms into different sub-source terms; and constructs source term subnets for different sub-source terms, embedding guiding variables to achieve decoupling of nonlinear physical processes and construction of multi-source driven expression mechanisms with high fitting degree;

[0012] S3, through multi-step ground-based training combined with peak offset constraints, energy conservation control, and propagation gradient supervision, achieves the construction of a prediction strategy that ensures long-term prediction stability and physical consistency.

[0013] In step S1, the deconstruction of the spectral equilibrium equation includes:

[0014] The frequency spectrum energy density is obtained by using the spectral balance equation. Regarding time The partial derivatives are:

[0015] ;

[0016] ;

[0017] In the formula, For propagation; This is the group velocity vector, used to represent the direction of the propagation speed of spectral energy in physical space; The total source term includes wind energy input, nonlinear interaction, and dissipation processes. It is the total derivative. These are partial derivatives;

[0018] The propagation term and the source term are constructed as physical control modules and embedded in the deep learning framework; among them, the spectral propagation term is explicitly calculated using analytical formulas to maintain the physical interpretation capability of the structural change path.

[0019] Furthermore, in the spectral balance equation, the propagation term is used to control the spatial translation and structural transfer of the spectral shape, while the source term is used to control the energy accumulation and internal structural adjustment of the spectral shape.

[0020] Furthermore, the spectral propagation term is expanded as follows:

[0021] ;

[0022] In the formula, The gradient of spectral energy in space is a manifestation of energy transfer along the direction of propagation; The spatial divergence of the group velocity field reflects the local energy source and sink effect caused by spatial non-uniformity;

[0023] The propagation term is expressed as:

[0024] ;

[0025] In the formula, For propagation items, , For the group velocity direction component, These are partial derivatives;

[0026] in,

[0027] ;

[0028] In the formula, It is the acceleration due to gravity. The center frequency of the spectrum, The current wind direction angle;

[0029] From the current wind angle With the center frequency of the spectrum Jointly determined, The wind speed is 10m.

[0030] Furthermore, the gradient of spectral energy in space The spectral sequence input to the neural network model is used to calculate the partial derivative of the output spectral tensor with respect to the spatial coordinate input through an automatic differentiation mechanism, thereby obtaining the implicit spectral gradient changes in the network.

[0031] Spatial divergence of group velocity field Group velocity direction components obtained from wind speed field inversion Explicit calculation is performed using the central difference algorithm;

[0032] The specific method of the central difference algorithm is as follows:

[0033] ;

[0034] ;

[0035] In the formula, Latitude and longitude This represents the change in latitude and longitude.

[0036] In step S2, a multi-source driving expression mechanism for decoupling complex nonlinear physical processes and achieving high fitting degree is constructed, including:

[0037] Spectral source terms The local enhancement and dissipation processes controlling the spectrum, the spectral source terms originate from three physical mechanisms, expressed as follows:

[0038] ;

[0039] In the formula, As the energy injection is dominated by wind speed, the energy of the main peak of the control spectrum is enhanced; This is a spectral energy redistribution caused by the four-wave interaction process, which manifests as energy dispersing from the main peak to high and low frequencies; The spectral tail attenuation is caused by fragmentation, turbulence, and bottom friction mechanisms;

[0040] Constructing a multi-sub-network structure Three types of physical mechanisms are simulated, with the total source term being the sum of all sub-modules. Each sub-network has the same structure, including an input layer, a spectral embedding coding layer, a mechanism mapping layer, and an output layer. The input layer receives the frequency-direction spectrum and guiding variables of wind speed, wind direction, and water depth from the previous time step. The spectral embedding coding layer uses a three-layer one-dimensional convolutional network with 64, 128, and 128 channels respectively, kernel sizes of 5, 3, and 3, and a stride of 1. Each convolutional layer is followed by ReLU activation and layer normalization. The mechanism mapping layer uses a two-layer fully connected network with 256 and 128 hidden units, using ReLU activation. The output layer is a linear layer. The AdamW optimizer is used during training with a learning rate of 1×10⁻³ and weight decay of 1×10⁻³. 4 Batch size 32;

[0041] The subnetworks achieve coupled learning by sharing spectral variables, and adapt the source term structure to different wind and wave conditions by dynamically adjusting the proportion of different physical processes contributing to the spectral evolution.

[0042] Furthermore, total source item Represented as:

[0043] ;

[0044] In the formula, for Frequency spectral energy density at time , for The corresponding subnetwork, for The corresponding subnetwork, for The corresponding subnetwork, for The spectrum of waves at any moment It is the second spatial derivative.

[0045] In step S3, the construction of the prediction strategy to achieve long-term prediction stability and physical consistency includes:

[0046] Design a stepwise recursive mechanism to achieve continuous prediction closed-loop modeling, the expression of which is:

[0047] ;

[0048] ;

[0049] In the formula, For time number, for The spectrum of waves at any moment for The spectrum of waves at any moment For the time change, for The transmission of time, for The source item of time;

[0050] At each step, the outputs of the propagation and source terms submodules are recalculated to keep the spectral structure and physical drive updated synchronously. A stepwise supervision mechanism is adopted during the training phase, and the loss function is accumulated at multiple steps. Constraints of peak consistency and energy conservation are introduced during training.

[0051] Furthermore, the main peak consistency term constraints include:

[0052] Calculate the main peak frequencies of the predicted and true spectra. Direction of the main peak The expression is:

[0053] ;

[0054] ;

[0055] In the formula, The main peak frequency. From the direction of the main peak. For frequency, As direction, for and The wave spectrum below;

[0056] The peak consistency loss is defined as:

[0057] ;

[0058] In the formula, This results in a loss of consistency with the main peak.

[0059] Energy conservation term:

[0060] The expression for calculating the total spectral energy is:

[0061] ;

[0062] And constrain the difference between the predicted and the actual total energy, defined as:

[0063] ;

[0064] In the formula, ;

[0065] The final training objective function is:

[0066] ;

[0067] In the formula, All are weighting coefficients. For multi-step recursion steps, For total training losses, For the first Consistency loss of the main peak in the step For the first Total energy difference of the steps For the first The predicted total energy of the step, For the first The true total energy of a step It is a 2-norm.

[0068] Another object of the present invention is to provide a physical equation-driven intelligent wave spectrum forecasting system, which is used to regulate the physical equation-driven intelligent wave spectrum forecasting method. The system includes:

[0069] The spectral equilibrium equation deconstruction module is used to deconstruct the spectral equilibrium equation, which is divided into propagation terms and source terms, and the propagation terms and source terms are modeled separately.

[0070] The multi-mechanism source term modeling and driving expression module is used to divide source terms into different sub-source terms according to different physical mechanisms; and to construct source term subnets for different sub-source terms, embedding guiding variables to achieve decoupling of nonlinear physical processes and construction of multi-source driving expression mechanisms with high fitting degree.

[0071] The multi-step spectral prediction module with structural physical consistency is used to construct a prediction strategy that achieves long-term prediction stability and physical consistency through multi-step ground-pull training combined with peak shift constraints, energy conservation control, and propagation gradient supervision.

[0072] Combining all the above technical solutions, the beneficial effects of this invention are as follows:

[0073] First, this invention directly models and forecasts the wave spectrum. Compared to outputting only single scalar elements such as significant wave height and period, spectral-level forecasting can comprehensively present the distribution characteristics of wave energy in the frequency domain, intuitively reflecting the location of the main peak, energy concentration, and spectral shape changes, thus providing a more complete description of sea conditions. For engineering applications that use the spectrum as input, such as ship motion response and platform load assessment, this invention avoids the information gap between single-element forecasting and spectrum-driven applications, achieving seamless integration from environmental forecasting to engineering calculations and significantly improving the practicality of the application.

[0074] Secondly, this invention strictly adheres to the physical process during modeling. By introducing the propagation and source terms in the spectral balance equation, it ensures that the predicted results are consistent with the actual process in terms of energy conservation, propagation direction, and physical driving mechanism (see Table 1). This design enhances the physical reliability of the results, providing credible technical support for high-risk scenarios such as flight path planning and safety early warning.

[0075] Third, through the improved technical solution of this invention, the forecast results can directly output the wave spectrum distribution, which more comprehensively reflects the energy structure and evolution characteristics compared with predictions based on only a single element, enabling seamless integration in spectrum-driven applications such as ship motion forecasting; at the same time, the model, combined with the physical constraints of the spectral balance equation, ensures the consistency of the results in terms of energy conservation and propagation mechanism, greatly improving the interpretability and physical credibility of the forecast, thus possessing higher reliability and practical value in engineering applications and high-risk decision-making scenarios.

[0076] Fourth, this invention takes the wave spectrum as the direct prediction object and explicitly embeds the propagation term and multi-mechanism source term in the spectral balance equation into the model, so that the forecast results move from a few single scalars (significant wave height, characteristic period, peak frequency, etc.) to a complete spectral distribution, which makes up for the need for wave spectrum in engineering applications and forms a closed loop from environmental forecasting to engineering calculation.

[0077] Fifth, two types of technical biases have long existed in the industry: first, the belief that as long as the numerical error is small, it is acceptable, ignoring the consistency of the spectral evolution mechanism; second, the tendency to use uninterpretable black-box deep networks. This invention analyzes the spectral propagation term, decomposes source terms such as wind energy input / four-wave interaction / dissipation into separable mechanisms for parallel learning, and applies energy conservation and propagation consistency constraints in multi-step prediction. It overcomes the above biases at the design level and provides interpretable, traceable, and verifiable spectral-level predictions. Attached Figure Description

[0078] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure;

[0079] Figure 1 This is a flowchart of the physical equation-driven intelligent wave spectrum forecasting method provided in this embodiment of the invention;

[0080] Figure 2 This is a schematic diagram of the intelligent wave spectrum prediction method driven by physical equations provided in this embodiment of the invention. Detailed Implementation

[0081] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0082] The innovation of this invention lies in its ability to overcome the limitations of existing methods that only predict single wave elements. It directly uses the wave spectrum as the modeling and forecasting object, achieving a complete expression of energy distribution and spectral evolution. Simultaneously, it explicitly introduces propagation and source terms from the spectral equilibrium equation into the model, ensuring strict consistency between the forecast results and the physical process, guaranteeing energy conservation and consistency in propagation direction, thereby significantly improving the reliability and interpretability of the results. This invention provides an intelligent forecasting method and system capable of directly outputting a complete wave spectrum, supporting engineering applications such as ship motion that rely on spectral input. Furthermore, this invention provides an intelligent modeling mechanism that integrates physical constraints from the spectral equilibrium equation. This mechanism ensures consistency between the forecast results and physical laws, forming a core technological advantage that distinguishes it from traditional black-box prediction methods.

[0083] Example 1, such as Figure 1As shown, the physical equation-driven intelligent wave spectrum prediction method provided in this embodiment of the invention involves three technical aspects: deconstruction of the spectral equilibrium equation, multi-mechanism source term modeling and driving expression, and multi-step spectral prediction with structural physical consistency. Specifically, it includes the following steps:

[0084] S1, deconstruct the spectral equilibrium equation into propagation terms and source terms, and model the propagation terms and source terms separately;

[0085] The key to wave spectrum prediction driven by physical equations is to determine the frequency spectrum energy density. Regarding time Partial derivatives. Frequency spectrum energy density. Regarding time The partial derivatives can be obtained from the spectral equilibrium equations:

[0086] ;

[0087] ;

[0088] In the formula, For propagation; This is the group velocity vector, used to represent the direction of the propagation speed of spectral energy in physical space; The total source term includes wind energy input, nonlinear interaction, and dissipation processes. It is the total derivative. These are partial derivatives;

[0089] In this equation, the propagation term on the left controls the spatial translation and structural transfer of the spectral shape, while the source term on the right controls the energy accumulation and internal structural adjustment of the spectral shape.

[0090] The propagation term and the source term are constructed as physical control modules and embedded into the deep learning framework. Among them, the spectral propagation term is explicitly calculated using analytical formulas, preserving the physical interpretation capability of the structural change path.

[0091] The spectral propagation term can be expanded as follows:

[0092] ;

[0093] In the formula, The gradient of spectral energy in space is a manifestation of energy transfer along the direction of propagation; The spatial divergence of the group velocity field reflects the local energy source and sink effect caused by spatial non-uniformity;

[0094] Spectral energy gradient in space The spectral sequence input to the neural network model is used to calculate the partial derivatives of the output spectral tensor with respect to the spatial coordinate input through an automatic differentiation mechanism, accurately obtaining the spectral gradient changes implicit in the network. This method is transparent to the model structure, has continuous derivatives, and a controllable gradient propagation chain, making it suitable for propagation direction modeling and peak shift estimation.

[0095] Spatial divergence of group velocity field Group velocity direction components obtained from wind speed field inversion Explicit computation is performed on the discrete grid using the central difference operator:

[0096] ;

[0097] ;

[0098] In the formula, Latitude and longitude This represents the change in latitude and longitude.

[0099] This difference method is simple and stable, avoiding the problem of derivative oscillation amplification, and is suitable for spatial partial derivative estimation of the velocity field derived from external wind speed.

[0100] The propagation term is expressed as:

[0101] ;

[0102] In the formula, For propagation items, , For the group velocity direction component, These are partial derivatives;

[0103] in,

[0104] ;

[0105] In the formula, It is the acceleration due to gravity. The center frequency of the spectrum, The current wind direction angle;

[0106] From the current wind angle With the center frequency of the spectrum Jointly determined, The wind speed is 10m.

[0107] S2, based on different physical mechanisms, divides the source terms into different sub-source terms; and constructs source term subnets for different sub-source terms, embedding guiding variables to achieve decoupling of nonlinear physical processes and construction of multi-source driven expression mechanisms with high fitting degree;

[0108] ;

[0109] In the formula, As the energy injection is dominated by wind speed, the energy of the main peak of the control spectrum is enhanced; This is a spectral energy redistribution caused by the four-wave interaction process, which manifests as energy dispersing from the main peak to high and low frequencies; The spectral tail attenuation is caused by fragmentation, turbulence, and bottom friction mechanisms;

[0110] To demonstrate the physical separability and structural controllability of the source term mechanism, a multi-sub-network structure is constructed. Three types of physical mechanisms are simulated, with the total source term being the sum of all sub-modules. Each sub-network has the same structure, including an input layer, a spectral embedding coding layer, a mechanism mapping layer, and an output layer. The input layer receives the frequency-direction spectrum and guiding variables of wind speed, wind direction, and water depth from the previous time step. The spectral embedding coding layer uses a three-layer one-dimensional convolutional network with 64, 128, and 128 channels respectively, kernel sizes of 5, 3, and 3, and a stride of 1. Each convolutional layer is followed by ReLU activation and layer normalization. The mechanism mapping layer uses a two-layer fully connected network with 256 and 128 hidden units, using ReLU activation. The output layer is a linear layer. The AdamW optimizer is used during training with a learning rate of 1×10⁻³ and weight decay of 1×10⁻³. 4 Batch size 32;

[0111] The subnetworks achieve coupled learning by sharing spectral variables, and adapt the source term structure to different wind and wave conditions by dynamically adjusting the proportion of different physical processes contributing to the spectral evolution.

[0112] S3, through multi-step ground-based training combined with peak offset constraints, energy conservation control, and propagation gradient supervision, achieves the construction of a prediction strategy that ensures long-term prediction stability and physical consistency.

[0113] Spectral evolution exhibits continuous-time dependence, and single-step modeling cannot reflect the cumulative effects of the propagation path and the non-stationary response driven by the source term. This invention designs a stepwise recursive mechanism to achieve continuous prediction closed-loop modeling, expressed as:

[0114] ;

[0115] ;

[0116] In the formula, For time number, for The spectrum of waves at any moment for The spectrum of waves at any moment For the time change, for The transmission of time, for The source item of time;

[0117] At each step, the outputs of the propagation and source terms submodules are recalculated to keep the spectral structure and physical drive updated synchronously. A stepwise supervision mechanism is adopted during the training phase, and the loss function is accumulated at multiple steps. Constraints of peak consistency and energy conservation are introduced during training.

[0118] The main peak consistency term constraints include:

[0119] Calculate the main peak frequencies of the predicted and true spectra. Direction of the main peak The expression is:

[0120] ;

[0121] ;

[0122] In the formula, The main peak frequency. From the direction of the main peak. For frequency, As direction, for and The wave spectrum below;

[0123] The peak consistency loss is defined as:

[0124] ;

[0125] In the formula, This results in a loss of consistency with the main peak.

[0126] Energy conservation term:

[0127] The expression for calculating the total spectral energy is:

[0128] ;

[0129] And constrain the difference between the predicted and the actual total energy, defined as:

[0130] ;

[0131] In the formula, ;

[0132] The final training objective function is:

[0133] ;

[0134] In the formula, All are weighting coefficients. For multi-step recursion steps, For total training losses, For the first Consistency loss of the main peak in the step For the first Total energy difference of the steps For the first The predicted total energy of the step, For the first The true total energy of a step It is a 2-norm.

[0135] At each step, the outputs of the propagation and source terms submodules are recalculated to keep the spectral structure and physical drivers updated synchronously. A stepwise supervision mechanism is used during the training phase, and a sliding window method is introduced to construct samples to improve temporal generalization ability. The loss function is accumulated over multiple steps.

[0136] To ensure the physical rationality of the model's output spectral structure, constraints such as peak consistency terms, propagation structure terms, and energy conservation terms are introduced during training.

[0137] Example 2: The physical equation-driven intelligent wave spectrum forecasting system provided in this embodiment of the invention includes:

[0138] The spectral equilibrium equation deconstruction module is used to deconstruct the spectral equilibrium equation, which is divided into propagation terms and source terms, and the propagation terms and source terms are modeled separately.

[0139] The multi-mechanism source term modeling and driving expression module is used to divide source terms into different sub-source terms according to different physical mechanisms; and to construct source term subnets for different sub-source terms, embedding guiding variables to achieve decoupling of nonlinear physical processes and construction of multi-source driving expression mechanisms with high fitting degree.

[0140] The multi-step spectral prediction module with structural physical consistency is used to construct a prediction strategy that achieves long-term prediction stability and physical consistency through multi-step ground-pull training combined with peak shift constraints, energy conservation control, and propagation gradient supervision.

[0141] To further demonstrate the positive effects of the above embodiments, the present invention conducted the following experiment based on the above technical solution: the forecasting effect of the present invention in the Northwest Pacific Ocean was compared with the spatial distribution of the wave spectrum of the actual and predicted values. It can be seen that whether the forecast is made 6 hours or 12 hours in advance, the model can reproduce the position and intensity distribution of the main energy band well, and the forecast results are highly consistent with the actual observations, indicating that the method has an effective ability to characterize the spectral structure and energy evolution process.

[0142] Table 1. Beneficial effects of the present invention

[0143]

[0144] The comparative results show that the two methods are not significantly different in terms of overall spectral fitting error: the relative error of the wave spectrum for the physical equation-driven method is 4.3%, while that for the pure data-driven method is 4.7%, with the two values ​​being close. However, the difference is quite significant in indicators that better reflect physical rationality and engineering usability. The total energy conservation deviation of the physical equation-driven method is only 3.4%, while that of the pure data-driven method is as high as 38.9%, indicating that the latter cannot guarantee energy conservation; in terms of the main propagation direction error, the physical equation-driven method is only 5.7°, far better than the 19.6° of the pure data-driven method. This indicates that although the two are close in terms of surface numerical accuracy, only the physical equation-driven method can maintain the physical consistency and interpretability of spectral evolution, making it more suitable for high-risk application scenarios such as route planning and risk warning.

[0145] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A physically equation-driven intelligent sea wave spectrum forecasting method, characterized in that, The method comprises the following steps: S1, the spectral balance equation is decomposed into a propagation term and a source term, and the propagation term and the source term are modeled respectively; S2, according to different physical mechanisms, the source term is divided into different sub-source terms; and a source term sub-network is constructed for different sub-source terms respectively, and a guide variable is embedded to realize decoupling of the nonlinear physical process and construction of a high-fitting multi-source driving expression mechanism; S3, through multi-step training combined with main peak shift constraint, energy conservation control and propagation gradient supervision, a prediction strategy construction realizing long-term prediction stability and physical consistency is realized; In step S1, the spectral balance equation is decomposed, including: The partial derivative of the frequency spectrum energy density E with respect to time t is obtained by the spectral balance equation as: It is obtained that: where is the propagation term; c g is the group velocity vector, indicating the direction of the spectral energy propagation in physical space; S tot is the total source term, containing the wind energy input, nonlinear interactions and dissipation processes; is the full derivative, is the partial derivative; The propagation term and the source term are respectively constructed into physical control modules and embedded into a deep learning framework; wherein the spectral propagation term is explicitly calculated by an analytical formula, maintaining the ability of physical explanation to the structural change path; In step S2, the decoupling of the nonlinear physical process and the construction of the high-fitting multi-source driving expression mechanism are realized, including: Spectrum source term S tot The local enhancement and dissipation of the control spectrum are controlled by the spectrum source term S, which is derived from three physical mechanisms, and the expression is S tot = S in + S nl + S ds where S in is the energy injection dominated by wind speed, which enhances the energy at the peak of the control spectrum;S nl is the energy redistribution caused by four-wave interaction, which disperses the energy from the peak to high and low frequencies;S ds is the spectral decay caused by breaking, turbulence and bottom friction mechanisms;S tot is the total source term; Constructing multi-subnetwork structure F in ,F nl ,F ds , respectively simulate three kinds of physical mechanism, the total source term is the sum of each sub-module; each subnetwork structure is the same, which contains input layer, spectral embedding coding layer, mechanism mapping layer and output layer; among them, the input layer receives the frequency-direction spectrum and the guiding variables of wind speed, wind direction and water depth at the previous time, the spectral embedding coding layer adopts a 3-layer one-dimensional convolution network, the channel number is 64, 128 and 128 in turn, the convolution kernel size is 5, 3 and 3, and the step is 1, and the convolution layer is connected with RELU activation and layer normalization; the mechanism mapping layer adopts a 2-layer fully connected network, the hidden unit number is 256 and 128, the activation function is RELU, and the output layer is a linear layer; during training, the AdamW optimizer is adopted, the learning rate is 1×10 -3 , the weight decay is 1×10 -4 , and the batch size is 32; The sub-networks are coupled and learned through shared spectral variables, and the proportion of the contribution of different physical processes to the spectral evolution is dynamically adjusted to adapt to the source term structure under different wind wave conditions; In step S3, the construction of the prediction strategy realizing long-term prediction stability and physical consistency includes: A step-by-step recursive mechanism is designed to realize continuous prediction closed-loop modeling, and the expression is: E t+1 = E t + Δt · (-τ prop + S tot ) where t is the time, E t+1 is the sea spectrum at time t+1, E t+2 is the sea spectrum at time t+2, Δt is the time variation, is the propagation term at time t+1, is the source term at time t+1; The output of the propagation term and the source term sub-modules is recalculated at each step to keep the spectral structure and physical driving synchronous update; a step-by-step supervision mechanism is adopted in the training stage, and the loss function is accumulated at multiple time points; the main peak consistency term and the energy conservation term are introduced in the training.

2. The physically equation-driven intelligent sea wave spectrum forecasting method according to claim 1, characterized in that, In the spectral balance equation, the propagation term is used to control the spatial translation and structural transfer of the spectral shape, and the source term is used to control the energy accumulation and internal structure adjustment of the spectral shape.

3. The physically equation-driven intelligent sea wave spectrum forecasting method according to claim 1, wherein, The spectral propagation term is expanded as: where is the spatial gradient of the spectral energy, representing the energy transfer with the propagation direction; is the spatial divergence of the group velocity field, representing the local energy source-sink effect due to the spatial inhomogeneity; The propagation term is expressed as: In the formula, τ prop For the propagation term, (x,y) represents latitude and longitude, and (c) represents the propagation term. x ,c y () represents the component of the group velocity in the direction of the velocity. Wherein, where g is the acceleration due to gravity, f c is the spectral center frequency, θ ω is the current wind direction angle; is determined jointly with the spectral center frequency f c from the current wind direction angle θ ω = arctan2(v 10 , u 10 ) and the 10 m high wind speed (v x , u y ).

4. The physically equation-driven intelligent sea wave spectrum forecasting method according to claim 3, wherein, Gradient of spectral energy over space The spectral sequence input by the neural network model is calculated by an automatic differentiation mechanism to obtain the partial derivative of the output spectral tensor with respect to the spatial coordinate input, and the change of the spectral gradient change is obtained. Spatial divergence of the group velocity field The group velocity direction component (c x ,c y ) is calculated explicitly by a central difference algorithm. The specific method of the central difference algorithm is as follows: In the formula, (Δx, Δy) is the change of longitude and latitude.

5. The physically equation-driven intelligent sea wave spectrum forecasting method according to claim 1, wherein, Total source term S tot is represented as: where E t is the frequency spectrum energy density E, F in is S in the corresponding subnetwork, F nl is S nl the corresponding subnetwork, F ds is S ds the corresponding subnetwork, E t is the sea wave spectrum at time t, is the second spatial derivative.

6. The physically equation-driven intelligent sea wave spectrum forecasting method according to claim 1, wherein, The main peak consistency term constraint includes: The main peak frequency of the calculated prediction spectrum is compared to the main peak frequency of the real spectrum with the main peak direction The expression is: where f p is the dominant peak frequency, θ p is the dominant peak direction, f is the frequency, θ is the direction, and E(f, θ) is the wave spectrum at f and θ. The main peak consistency loss is defined as: In the formula, L peak is the loss of main peak consistency; The energy conservation term is: The expression for calculating the total energy of the spectrum is: E tot = ∫∫E(f, θ) df dθ And the difference between the predicted and the real total energy is constrained, defined as: wherein L energy is the total energy difference, is the predicted total energy, is the true total energy; The final training objective function is: wherein a, b, g are weight coefficients, k is the number of multi-step recursion, L is the total training loss, L peak (k) is the peak consistency loss of the kth step, L energy (k) is the total energy difference of the kth step, is the predicted total energy of the kth step, is the real total energy of the kth step, is the two-norm.

7. A physically equation-driven intelligent sea wave spectrum forecasting system, characterized in that, The system is used for regulating and controlling the intelligent sea wave spectrum prediction method driven by the physical equation in any one of claims 1-6, and the system comprises: A spectral balance equation decomposition module is used for decomposing the spectral balance equation into a propagation term and a source term, and modeling the propagation term and the source term respectively; A multi-mechanism source term modeling and driving expression module is used for dividing the source term into different sub-source terms according to different physical mechanisms; and a source term sub-network is constructed for different sub-source terms respectively, and a guide variable is embedded to realize decoupling of the nonlinear physical process and construction of a high-fitting multi-source driving expression mechanism; A multi-step spectral prediction module of structural physical consistency is used for realizing construction of a prediction strategy realizing long-term prediction stability and physical consistency through multi-step training combined with main peak shift constraint, energy conservation control and propagation gradient supervision.

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