A method and system for predicting ocean three-dimensional temperature and salinity currents based on Fourier neural operators

Abstract

The present invention belongs to the fields of hydrology and oceanography, and specifically discloses a method and system for predicting three-dimensional ocean temperature-salinity currents based on a Fourier neural operator. The method comprises the following steps: obtaining ocean temperature data, ocean salinity data, and ocean current velocity data at different depths; constructing a three-dimensional ocean temperature-salinity current prediction model based on a Fourier neural operator architecture; inputting the ocean temperature data, ocean salinity data, and ocean current velocity data into the three-dimensional ocean temperature-salinity current prediction model, and outputting a three-dimensional ocean temperature-salinity current prediction result. The present invention solves the problems of high computational resource consumption and long time required for traditional numerical simulation of three-dimensional ocean temperature-salinity currents, improves prediction accuracy and efficiency, and provides strong support for marine scientific research and applications.

Description

Technical Field

[0001] The present invention belongs to the field of hydrology and ocean technology, and specifically relates to a method and system for predicting three-dimensional ocean temperature and salinity currents based on a Fourier neural operator. Background Art

[0002] Long-term changes in ocean temperature, salinity, and current structure are closely related to the climate, ecological environment, and marine operations in my country's coastal areas. Understanding the patterns of these changes is an important scientific foundation for ensuring the development of marine resources, improving the quality of the marine environment, and maintaining ecological balance. Furthermore, it is crucial for understanding ocean dynamics, climate systems, and ecosystems. Changes in seawater temperature and salinity directly affect ocean circulation, the global water cycle, and the evolution of the ocean-climate system, thereby affecting the ocean's ability to regulate global climate change. These changes are also closely linked to key ocean-atmosphere thermal processes, including the occurrence of marine heatwaves, the formation of thermoclines, the development of El Niño phenomena, and the generation of deep water. Therefore, accurately estimating the temperature and salinity fields within the ocean is crucial for understanding marine ecosystems, ocean dynamics, and climate change.

[0003] Currently, thermohaline current predictions rely primarily on numerical models and statistical methods. These methods typically simulate the behavior of the ocean environment based on a series of physical equations (such as the Navier-Stokes equations and energy transfer equations). Although these methods can provide useful predictions to a certain extent, they still have some inherent limitations: numerical simulations require a large amount of computing resources, especially when simulating in three dimensions and over long time scales; ocean observation data are often sparsely distributed and discontinuous, which poses a challenge to model calibration and validation; when predicting over long periods of time, errors within the model gradually accumulate, resulting in a decrease in prediction accuracy; and the nonlinear interactions in complex ocean phenomena are difficult to fully capture with traditional models. These methods are highly dependent on parameter settings and human cognitive capabilities, resulting in limited simulation effectiveness for complex ocean processes. In particular, in real-time predictions, traditional methods struggle to accurately predict extreme ocean events, and solving complex dynamic equations is challenging. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of large consumption of computing resources and long time in the research of traditional numerical simulation of ocean three-dimensional temperature-salinity flow, and propose a method and system for predicting ocean three-dimensional temperature-salinity flow based on Fourier neural operator.

[0005] The technical solution of the present invention is as follows: In a first aspect, a method for predicting three-dimensional ocean temperature and salinity currents based on a Fourier neural operator comprises the following steps:

[0006] S1. Obtain ocean temperature data, ocean salinity data, and ocean current data at different depths;

[0007] S2. Construct a three-dimensional ocean temperature and salinity flow prediction model based on the Fourier neural operator architecture;

[0008] S3. Input the ocean temperature data, ocean salinity data, and ocean velocity data into the ocean three-dimensional temperature-salinity flow prediction model, and output the ocean three-dimensional temperature-salinity flow prediction results.

[0009] The beneficial effects of the present invention are:

[0010] The present invention uses a three-dimensional ocean temperature-salinity current prediction model based on a Fourier neural operator architecture to learn from historical ocean temperature-salinity current data, thereby accurately and efficiently predicting the three-dimensional ocean temperature-salinity current conditions, providing strong support for marine scientific research and applications, and bringing significant technological progress to fields such as marine environmental monitoring, climate research, and marine resource management.

[0011] Preferably, the step S2 specifically includes the following sub-steps:

[0012] S21. Perform data cleaning, missing value filling, and normalization on the ocean temperature, salinity, and current data at different depths to obtain a four-dimensional ocean temperature and salinity current dataset.

[0013] S22. Construct a network model based on the Fourier neural operator, and input the four-dimensional ocean temperature-salinity flow data set into the network model based on the Fourier neural operator for training, to obtain a three-dimensional ocean temperature-salinity flow prediction model based on the Fourier neural operator architecture.

[0014] Preferably, the normalization process is specifically as follows: subtracting the mean of the data set from each data value and dividing by the standard deviation to obtain a four-dimensional ocean temperature and salinity flow data set; a constant 0.00001 is added to the standard deviation.

[0015] Preferably, the ocean three-dimensional temperature-salinity current prediction model described in step S2 includes a position encoding module, a lifting module, three stacked Fourier neural operator modules and a mapping module connected in sequence; the lifting module includes a fully connected layer and a linear layer connected in sequence; the mapping module includes a fully connected layer and a linear layer connected in sequence;

[0016] The position encoding module is used to receive ocean temperature data, ocean salinity data and ocean current data, perform position encoding on the ocean temperature data, ocean salinity data and ocean current data, and output a three-dimensional ocean temperature-salinity flow tensor with spatial information characteristics;

[0017] The upgrading module is used to receive the ocean three-dimensional temperature-salinity flow tensor with spatial information characteristics, perform dimension expansion on the tensor with spatial information characteristics, and output a high-dimensional coding tensor;

[0018] The Fourier neural operator module is used to receive the high-dimensional coding tensor, perform spatial mixing and channel mixing on the high-dimensional coding tensor, and output the mixed tensor;

[0019] The mapping module is used to receive the mixed tensor, perform feature decoding on the mixed tensor, and output target output features, namely, the ocean three-dimensional temperature and salinity flow prediction result.

[0020] Preferably, the three stacked Fourier neural operator modules each include a spatial mixing unit, a first normalization layer, a channel mixing unit, and a second normalization layer connected in sequence; the input end of the spatial mixing unit is also connected to the input end of the first residual connection unit, and the output end of the first residual connection unit is connected to the input end of the first normalization layer; the output end of the spatial mixing unit is also connected to the input end of the second residual connection unit, and the output end of the second residual connection unit is connected to the output end of the second normalization layer;

[0021] The spatial mixing unit includes a Fourier transform layer, two stacked linear layers, an inverse Fourier transform layer and an activation layer connected in sequence;

[0022] The channel mixing unit includes a fully connected layer and a linear layer connected in sequence.

[0023] Preferably, the step S3 specifically includes the following sub-steps:

[0024] S31. Position-encode the ocean temperature data, ocean salinity data, and ocean current data to obtain a three-dimensional ocean temperature-salinity current tensor with spatial information characteristics;

[0025] S32. Mapping the ocean three-dimensional temperature-salinity flow tensor with spatial information characteristics from low latitudes to a high-dimensional space to obtain a high-dimensional encoding tensor;

[0026] S33. Perform spatial mixing and channel mixing on the high-dimensional coded tensor based on Fourier transform to obtain a mixed tensor;

[0027] S34. Perform feature decoding on the mixed tensor to obtain the target output feature, i.e., the prediction result of the three-dimensional ocean temperature and salinity flow.

[0028] Preferably, the step S33 specifically includes the following sub-steps:

[0029] S331. Input the high-dimensional coding tensor into the Fourier neural operator module and reshape the high-dimensional coding tensor to obtain A tensor of shape where represents the number of channels of the high-dimensional encoding tensor, represents the number of latitude grid points, Indicates the number of longitude grid points;

[0030] S332. Along the horizontal direction Perform Fourier transform on the tensor of shape and retain the front part along the height direction of the tensor after Fourier transform. The frequency tensor and the preceding tensor along the width of the tensor The frequency tensor, A tensor of shape;

[0031] S333.Yes The tensor of shape is phase-adjusted, amplitude-adjusted, and inverse Fourier transformed and reshaped into A tensor of shape, completing spatial blending;

[0032] S334. Using learnable weights and nonlinear activation functions, A tensor of shape channels are mapped to the new A set of channels is constructed to complete channel mixing and obtain the mixed tensor.

[0033] Preferably, the step S34 specifically includes the following formula:

[0034] The mixed tensor is linearly mapped to the intermediate feature. The specific formula is:

[0035]

[0036] in, represents the intermediate features, represents the ReLU activation function, represents the weight matrix, represents the mixed tensor, represents the bias term;

[0037] Map the intermediate features to The target output feature of the channel is:

[0038]

[0039] in, represents the target output feature, represents the weight matrix, represents the bias term.

[0040] The beneficial effects of the above preferred solution are:

[0041] 1. A residual path is set up in the Fourier neural operator module to bypass the spatial and channel mixing parts, which can effectively compensate for the small-scale changes that may be caused by discarding high-frequency modes.

[0042] 2. Through spatial and channel mixing of Fourier neural network operator modules, the ocean three-dimensional temperature and salinity current prediction model can effectively learn relationships in the horizontal dimension (latitude-longitude), capture long-range dependencies with a smaller number of layers, and ignore high-frequency modes, thereby improving computational efficiency.

[0043] 3. In the position encoding module, position encoding technology based on sine and cosine functions is used, and two additional channels are introduced to represent the relative distance of grid points in the latitude and longitude directions. The ocean three-dimensional temperature-salinity flow grid data is position-encoded, giving the neural operator position perception capabilities, so that the input data has spatial information after encoding, effectively improving the prediction accuracy of the ocean three-dimensional temperature-salinity flow prediction model.

[0044] 4. Through activation function The nonlinear processing of the mapping module can better capture complex data forms and improve the accuracy of the ocean three-dimensional temperature and salinity flow prediction model.

[0045] In a second aspect, a system for predicting three-dimensional ocean temperature and salinity currents based on a Fourier neural operator is provided. The system includes a processor configured to execute the method for predicting three-dimensional ocean temperature and salinity currents based on a Fourier neural operator as described in the first aspect.

[0046] In a third aspect, a computer-readable storage medium stores computer instructions. In response to a computer reading the computer instructions in the storage medium, the computer executes the ocean three-dimensional temperature-salinity flow prediction method based on Fourier neural operator as described in the first aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Shown is a flow chart of the ocean three-dimensional temperature-salinity current prediction method based on Fourier neural operator provided in Example 1 of the present invention.

[0048] Figure 2 Shown is a structural diagram of the ocean three-dimensional temperature-salinity flow prediction model based on the Fourier neural operator architecture provided in Example 1 of the present invention.

[0049] Figure 3 Shown is the RMSE value of the east-west flow velocity predicted by the model provided in Example 3 of the present invention for 10 days.

[0050] Figure 4 Shown is the RMSE value of the north-south flow velocity predicted by the model provided in Example 3 of the present invention for 10 days.

[0051] Figure 5 Shown is the RMSE value of the ocean salinity predicted for 10 days by the model provided in Example 3 of the present invention.

[0052] Figure 6Shown is the RMSE value of the ocean temperature predicted for 10 days by the model provided in Example 3 of the present invention.

[0053] Figure 7 Shown is a visualization diagram of the actual value of ocean temperature for one day provided in Example 3 of the present invention.

[0054] Figure 8 Shown is a visualization of the one-day ocean temperature model prediction value provided in Example 3 of the present invention.

[0055] Figure 9 Shown is a visualization of the actual ocean temperature values ​​for two days provided in Example 3 of the present invention.

[0056] Figure 10 Shown is a visualization of the 2-day ocean temperature model prediction values ​​provided in Example 3 of the present invention.

[0057] Figure 11 Shown is a visualization of the actual ocean temperature values ​​for three days provided in Example 3 of the present invention.

[0058] Figure 12 Shown is a visualization of the 3-day ocean temperature model prediction values ​​provided in Example 3 of the present invention.

[0059] Figure 13 Shown is a visualization of the actual ocean temperature values ​​for four days provided in Example 3 of the present invention.

[0060] Figure 14 Shown is a visualization of the 4-day ocean temperature model prediction values ​​provided in Example 3 of the present invention. DETAILED DESCRIPTION

[0061] The exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the accompanying drawings are merely exemplary and are intended to illustrate the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0062] Example 1:

[0063] like Figure 1 As shown, a method for predicting three-dimensional ocean temperature and salinity flow based on Fourier neural operator includes the following steps:

[0064] S1. Obtain ocean temperature data, ocean salinity data, and ocean current data at different depths;

[0065] S2. Construct a three-dimensional ocean temperature and salinity flow prediction model based on the Fourier neural operator architecture;

[0066] S3. Input the ocean temperature data, ocean salinity data, and ocean velocity data into the ocean three-dimensional temperature-salinity flow prediction model, and output the ocean three-dimensional temperature-salinity flow prediction results.

[0067] In this embodiment, step S2 specifically includes the following sub-steps:

[0068] S21. Perform data cleaning, missing value filling, and normalization on the ocean temperature, salinity, and current data at different depths to obtain a four-dimensional ocean temperature and salinity current dataset.

[0069] S22. Construct a network model based on the Fourier neural operator, and input the four-dimensional ocean temperature-salinity flow data set into the network model based on the Fourier neural operator for training, to obtain a three-dimensional ocean temperature-salinity flow prediction model based on the Fourier neural operator architecture.

[0070] Among them, the number of channels of input data of the network model based on Fourier neural operator is is 44, assuming the spatial resolution is ,in represents the number of latitude grid points, represents the number of longitude grid points, then the input function size in tensor form is , the input data is normalized, specifically: the mean of the data set is subtracted from each data value and divided by the standard deviation to obtain a four-dimensional ocean temperature and salinity flow data set. The shape of the four-dimensional ocean temperature and salinity flow data set is: ,in, represents the sample size; a constant of 0.00001 is added to the standard deviation to ensure numerical stability and prevent division by 0.

[0071] In this embodiment, if Figure 2 As shown, the ocean three-dimensional temperature and salinity current prediction model described in step S2 includes a position encoding module, a lifting module, three stacked Fourier neural operator modules and a mapping module connected in sequence; the lifting module includes a fully connected layer and a linear layer connected in sequence; the mapping module includes a fully connected layer and a linear layer connected in sequence;

[0072] The position encoding module is used to receive ocean temperature data, ocean salinity data, and ocean current data, and position encode the ocean temperature data, ocean salinity data, and ocean current data to output a three-dimensional ocean temperature-salinity flow tensor with spatial information characteristics. The position encoding module adopts a position encoding technology based on sine and cosine functions, and introduces two additional channels to represent the relative distance of grid points in the latitude and longitude directions respectively. The position encoding module gives the neural operator position perception capabilities, so that the ocean temperature-salinity flow data has spatial information after being encoded.

[0073] The lifting module is used to receive the ocean three-dimensional temperature-salinity flow tensor with spatial information characteristics, expand the dimension of the tensor with spatial information characteristics, and output a high-dimensional encoding tensor, which is crucial for capturing complex interactions across multiple scales and features.

[0074] The Fourier neural operator module is used to receive the high-dimensional coded tensor, perform spatial mixing and channel mixing on the high-dimensional coded tensor, and output the mixed tensor; the Fourier neural operator module (FNO) is also provided with a residual path that bypasses the spatial mixing unit and the channel mixing unit to compensate for small-scale changes caused by discarding high-frequency modes;

[0075] The mapping module is used to receive the mixed tensor, perform feature decoding on the mixed tensor, and output target output features, namely, the ocean three-dimensional temperature and salinity flow prediction result.

[0076] In this embodiment, the three stacked Fourier neural operator modules each include a spatial mixing unit, a first normalization layer, a channel mixing unit, and a second normalization layer connected in sequence; the input end of the spatial mixing unit is also connected to the input end of the first residual connection unit, and the output end of the first residual connection unit is connected to the input end of the first normalization layer; the output end of the spatial mixing unit is also connected to the input end of the second residual connection unit, and the output end of the second residual connection unit is connected to the output end of the second normalization layer;

[0077] The spatial mixing unit includes a Fourier transform layer, two stacked linear layers, an inverse Fourier transform layer and an activation layer connected in sequence;

[0078] The channel mixing unit includes a fully connected layer and a linear layer connected in sequence;

[0079] The first residual connection unit and the second residual connection unit are both composed of linear layers.

[0080] In this embodiment, step S3 specifically includes the following sub-steps:

[0081] S31. Position-encode the ocean temperature data, ocean salinity data, and ocean current data to obtain a three-dimensional ocean temperature-salinity current tensor with spatial information characteristics;

[0082] S32. Map the ocean three-dimensional temperature-salinity flow tensor with spatial information characteristics from low latitude to high-dimensional space to obtain a high-dimensional coding tensor. The shape of the high-dimensional coding tensor is ,in, represents the number of channels of the high-dimensional encoding tensor, represents the number of latitude grid points, Indicates the number of longitude grid points;

[0083] S33. Perform spatial mixing and channel mixing on the high-dimensional coded tensor based on Fourier transform to obtain a mixed tensor;

[0084] S34. Perform feature decoding on the mixed tensor to obtain the target output feature, i.e., the prediction result of the three-dimensional ocean temperature and salinity flow.

[0085] In this embodiment, step S33 specifically includes the following sub-steps:

[0086] S331. Input the high-dimensional coding tensor into the Fourier neural operator module and reshape the high-dimensional coding tensor to obtain A tensor of shape where represents the number of channels of the high-dimensional encoding tensor, represents the number of latitude grid points, Indicates the number of longitude grid points;

[0087] S332. Along the horizontal direction The tensor of the shape is Fourier transformed, and the low-frequency part of the tensor is retained, that is, the front part along the height direction of the tensor after Fourier transform. The frequency tensor and the preceding tensor along the width of the tensor The frequency tensor, A tensor of shape to reduce the amount of data and highlight important low-frequency information;

[0088] S333. The tensor of shape is multiplied by the learning weights specific to the Fourier neural operator module to complete phase adjustment and amplitude adjustment, complete the inverse Fourier transform, return the inverse transformed tensor to the geographic coordinate system, and reshape it into A tensor of shape, completing spatial blending;

[0089] S334. Using learnable weights and nonlinear activation functions, A tensor of shape channels are mapped to the new A set of channels is constructed to complete channel mixing and obtain the mixed tensor.

[0090] In this embodiment, step S34 specifically includes the following formula:

[0091] The mixed tensor is linearly mapped to the intermediate feature. The specific formula is:

[0092]

[0093] in, represents the intermediate features, represents the ReLU activation function, express dimensional weight matrix, Represents intermediate features The number of channels, represents the mixed tensor, The number of channels is , represents the bias term;

[0094] Map the intermediate features to The target output feature of the channel is:

[0095]

[0096] in, represents the target output feature, express dimensional weight matrix, represents the bias term.

[0097] Example 2: A three-dimensional ocean temperature-salinity current prediction system based on Fourier neural operators, used to configure and execute the three-dimensional ocean temperature-salinity current prediction method based on Fourier neural operators in Example 1.

[0098] In this embodiment, the system can be an electronic device, including a memory, a processor, and a computer program stored on the memory and running on the processor. The processor executes the program to implement some or all steps of the ocean three-dimensional temperature-salinity flow prediction method based on Fourier neural operator as described in Example 1.

[0099] In this embodiment, the electronic device may include: a processor, a memory, a bus and a communication interface. The processor, the communication interface and the memory are connected through a bus. The memory stores a computer program that can be run on the processor. When the processor runs the computer program, it executes part or all of the steps of the ocean three-dimensional temperature and salinity flow prediction method based on the Fourier neural operator provided in the aforementioned embodiment 1 of this application.

[0100] The system in the embodiment of the present invention can also be a computer-readable storage medium, which stores a computer program. When the computer program is executed, some or all steps of the ocean three-dimensional temperature-salinity current prediction method based on Fourier neural operator as described in Example 1 are implemented.

[0101] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. Such program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device so that when the program code is executed by the processor or controller, the functions / operations specified in the flow chart and / or block diagram are implemented. The program code can be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0102] In the context of the present invention, machine-readable medium can be a tangible medium that can contain or store a program for use with an instruction execution system, device or equipment or used in combination with an instruction execution system, device or equipment. Machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. More specific examples of machine-readable storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0103] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0104] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (LAN), a wide area network (WAN), and the Internet.

[0105] A computer system may include a client and a server. The client and server are generally remote from each other and typically interact through a communication network. The client-server relationship arises through computer programs running on the respective computers and having a client-server relationship with each other. The server may be a cloud server, a server in a distributed system, or a server integrated with a blockchain.

[0106] Example 3:

[0107] On the basis of Example 1, the principle of the present invention is further illustrated based on the ocean temperature and salinity current data in the area of ​​5°N to 23°N and 108°E to 121°E in the South China Sea from 2010 to 2020.

[0108] The temperature data, salinity data, east-west flow velocity data, and north-south flow velocity data of 11 depth layers between 0.5 meters and 300 meters in the ocean area of ​​5°N to 23°N and 108°E to 121°E in the South China Sea from 2010 to 2020 were collected and organized, and these data were divided into a series of thermohaline flow grid data with specific geographic coordinates as the center.

[0109] The temperature and salinity flow data from 2010 to 2019 were used as training data and preprocessed, including data cleaning and missing value filling, to ensure data quality. At the same time, a three-dimensional ocean temperature and salinity flow prediction model based on the Fourier neural operator architecture was constructed, and the data starting from January 1, 2020 was used as a test set to evaluate the model performance.

[0110] The preprocessed samples are fed into a 3D ocean temperature and salinity current prediction model for training. First, the input samples are processed through a position encoding module to incorporate spatial information. Then, the lifting module expands the dimensionality. Third, the input is fed into three stacked Fourier Neural Operator (FNO) modules, which perform spatial blending and channel blending, extracting features through Fourier transforms and inverse transforms. Finally, a layer normalization layer is used to enhance the model's generalization capabilities.

[0111] After being processed by three stacked Fourier neural operator modules, the output values ​​of the three stacked Fourier neural operator modules are input into the fully connected layer for dimensionality reduction and feature mapping. The output values ​​of the fully connected layer are then input into the mapping module for regression classification. The output is the predicted value of the temperature and salinity flow state at the subsequent moment, and finally the model training is completed.

[0112] The data from 2020 is applied to the trained model to obtain the temperature-salinity flow data predicted by the ocean three-dimensional temperature-salinity flow prediction model. In this embodiment, after the data from January 1, 2020 is input into the model, the model prediction results are as follows: Figure 3 、 Figure 4 、 Figure 5 and Figure 6 As shown, the comparison between the predicted results and the true values ​​is Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 、 Figure 11 、 Figure 12 、 Figure 13 and Figure 14 As shown, it can be obtained that the model can accurately and quickly predict the subsequent thermohaline flow conditions.

[0113] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for predicting ocean three-dimensional temperature and salinity currents based on Fourier neural operators, characterized in that: The method comprises the following steps: S1. Obtain ocean temperature data, ocean salinity data, and ocean current data at different depths; S2. Construct a three-dimensional ocean temperature and salinity flow prediction model based on the Fourier neural operator architecture; S3. Inputting ocean temperature data, ocean salinity data, and ocean velocity data into the ocean three-dimensional temperature-salinity current prediction model, and outputting the ocean three-dimensional temperature-salinity current prediction result; The three-dimensional ocean temperature and salinity flow prediction model includes a position encoding module, a lifting module, three stacked Fourier neural operator modules and a mapping module connected in sequence; the lifting module includes a fully connected layer and a linear layer connected in sequence; the mapping module includes a fully connected layer and a linear layer connected in sequence; The position encoding module is used to receive ocean temperature data, ocean salinity data and ocean current data, perform position encoding on the ocean temperature data, ocean salinity data and ocean current data, and output a three-dimensional ocean temperature-salinity flow tensor with spatial information characteristics; The upgrading module is used to receive the ocean three-dimensional temperature-salinity flow tensor with spatial information characteristics, perform dimension expansion on the tensor with spatial information characteristics, and output a high-dimensional coding tensor; The three stacked Fourier neural operator modules are used to receive the high-dimensional coding tensor, perform spatial mixing and channel mixing on the high-dimensional coding tensor, and output the mixed tensor; The mapping module is used to receive the mixed tensor, perform feature decoding on the mixed tensor, and output target output features, namely, the three-dimensional ocean temperature and salinity flow prediction result; Each of the stacked Fourier neural operator modules includes a first residual connection unit, a second residual connection unit, and a spatial mixing unit, a first element-by-element addition unit, a first normalization layer, a channel mixing unit, a second normalization layer, and a second element-by-element addition unit connected in sequence; The input end of the spatial mixing unit and the input end of the first residual connection unit are both input ends of the Fourier neural operator module, the output end of the first residual connection unit is connected to the other input end of the first element-by-element addition unit; the output end of the first element-by-element addition unit is connected to the input end of the second residual connection unit; the output end of the second residual connection unit is connected to the other input end of the second element-by-element addition unit; the output end of the second element-by-element addition unit is the output end of the Fourier neural operator module; The spatial mixing unit includes a Fourier transform layer, two stacked linear layers, an inverse Fourier transform layer and an activation layer connected in sequence; The channel mixing unit includes a fully connected layer and a linear layer connected in sequence.

2. The method for predicting ocean three-dimensional temperature and salinity currents based on Fourier neural operators according to claim 1 is characterized in that: The step S2 specifically includes the following sub-steps: S21. Perform data cleaning, missing value filling, and normalization on the ocean temperature data, ocean salinity data, and ocean current data to obtain a four-dimensional ocean temperature and salinity current dataset. S22. Construct a network model based on the Fourier neural operator, and input the four-dimensional ocean temperature-salinity flow data set into the network model based on the Fourier neural operator for training, to obtain a three-dimensional ocean temperature-salinity flow prediction model based on the Fourier neural operator architecture.

3. The method for predicting ocean three-dimensional temperature and salinity currents based on Fourier neural operators according to claim 2 is characterized in that: The normalization process is specifically as follows: subtracting the mean of the data set from each data value and dividing by the standard deviation to obtain a four-dimensional ocean temperature and salinity flow data set; a constant 0.00001 is added to the standard deviation.

4. The method for predicting ocean three-dimensional temperature and salinity currents based on Fourier neural operators according to claim 1, characterized in that: The step S3 specifically includes the following sub-steps: S31. Position-encode the ocean temperature data, ocean salinity data, and ocean current data to obtain a three-dimensional ocean temperature-salinity current tensor with spatial information characteristics; S32. Mapping the ocean three-dimensional temperature-salinity flow tensor with spatial information characteristics from low latitudes to a high-dimensional space to obtain a high-dimensional encoding tensor; S33. Perform spatial mixing and channel mixing on the high-dimensional coded tensor based on Fourier transform to obtain a mixed tensor; S34. Perform feature decoding on the mixed tensor to obtain the target output feature, i.e., the prediction result of the three-dimensional ocean temperature and salinity flow.

5. The method for predicting three-dimensional ocean temperature and salinity currents based on Fourier neural operators according to claim 4 is characterized in that: The step S33 specifically includes the following sub-steps: S331. Input the high-dimensional coding tensor into three stacked Fourier neural operator modules to reshape the high-dimensional coding tensor to obtain A tensor of shape where represents the number of channels of the high-dimensional encoding tensor, represents the number of latitude grid points, Indicates the number of longitude grid points; S332. Along the horizontal direction Perform Fourier transform on the tensor of shape and retain the front part along the height direction of the tensor after Fourier transform. The frequency tensor and the preceding tensor along the width of the tensor The frequency tensor, A tensor of shape; S333.Yes The tensor of shape is phase-adjusted, amplitude-adjusted, and inverse Fourier transformed and reshaped into A tensor of shape, completing spatial blending; S334. Using learnable weights and nonlinear activation functions, A tensor of shape channels are mapped to the new A set of channels is constructed to complete channel mixing and obtain the mixed tensor.

6. The method for predicting ocean three-dimensional temperature and salinity currents based on Fourier neural operators according to claim 4, characterized in that: The step S34 specifically includes the following formula: The mixed tensor is linearly mapped to the intermediate feature. The specific formula is: ； in, represents the intermediate features, represents the ReLU activation function, represents the weight matrix, represents the mixed tensor, represents the bias term; Map the intermediate features to The target output feature of the channel is: ； in, represents the target output feature, represents the weight matrix, represents the bias term.

7. A three-dimensional ocean temperature and salinity current prediction system based on Fourier neural operator, characterized by: The method comprises a processor for executing the ocean three-dimensional temperature-salinity flow prediction method based on Fourier neural operator according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that The storage medium stores computer instructions. In response to the computer reading the computer instructions in the storage medium, the computer executes the ocean three-dimensional temperature-salinity flow prediction method based on Fourier neural operator according to any one of claims 1 to 6.

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