A multi-source meteorological data fusion prediction method and system based on a Fourier neural operator, an electronic device, and a storage medium

Abstract

The application relates to the technical field of computers and discloses a multi-source meteorological data fusion prediction method and system based on a Fourier neural operator, an electronic device and a storage medium, which comprises the following steps: acquiring multiple meteorological element data from different meteorological sources; integrating the meteorological element data to form a multi-channel input function and inputting the multi-channel input function to a promotion layer for processing; obtaining a first feature representation and inputting the first feature representation to a core Fourier layer to obtain a second feature representation; processing the second feature representation through a projection layer, performing nonlinear transformation and dimension reduction mapping on a feature vector, and obtaining a bump prediction function describing the spatial distribution of bump intensity in a target geographical area; and outputting the bump prediction function as the final prediction result of the flight bump of an airplane. The application can improve the accuracy and practicability of flight bump prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computers, and in particular to a multi-source meteorological data fusion prediction method and system based on a Fourier neural operator, an electronic device and a storage medium. BACKGROUND

[0002] Atmospheric turbulence (turbulence) encountered by an aircraft during flight is an important factor that threatens aviation safety and affects passenger comfort. Therefore, accurate prediction of flight turbulence is a key challenge in the field of aviation meteorology. Currently, meteorological forecasting agencies can provide a variety of meteorological data sources from different numerical prediction models and different regions, such as equivalent turbulence degree (EDR) data, wind speed, air pressure, etc.

[0003] However, the turbulence prediction systems and methods in the prior art face many technical bottlenecks in processing these multi-source meteorological data. In terms of data fusion, existing systems mostly use simple weighted averaging or linear regression methods, which are difficult to effectively capture the complex nonlinear interactions and coupling relationships between multi-source data, resulting in limited prediction accuracy. In terms of spatial dependence modeling, traditional methods and deep learning models based on convolutional neural networks (CNN) can process spatial data, but their receptive fields are limited and it is difficult to efficiently capture long-range spatial correlations between weather conditions in remote geographical regions (such as the influence of oceanic air currents on continental routes). In terms of technical architecture, existing models (such as CNN, visual Transformer, etc.) essentially rely on discrete and fixed resolution grid data, which cannot adapt to the actual situation of different resolutions of data from different sources. If the resolution of the input data changes, the model often needs to be retrained or interpolated, which not only has high computational cost, but also introduces additional errors.

[0004] Therefore, the present application provides a multi-source meteorological data fusion prediction method based on a Fourier neural operator to solve the above technical problems. SUMMARY

[0005] The purpose of the present application is to provide a multi-source meteorological data fusion prediction method based on a Fourier neural operator, a system, an electronic device and a storage medium, to solve the technical problems that the prior art cannot fundamentally handle multi-source, high-dimensional, continuous meteorological data, has limitations, and has low prediction accuracy.

[0006] To solve the above technical problems, the present application provides a multi-source meteorological data fusion prediction method based on a Fourier neural operator, comprising:

[0007] Obtaining a plurality of meteorological element data from different meteorological sources, and integrating the meteorological element data to form a multi-channel input function, wherein the multi-channel input function is used to represent the continuous spatial distribution of the meteorological state in the target geographical region;

[0008] processing the multi-channel input function through a lifting layer to perform non-linear transformation and dimension expansion on the feature vector at each spatial position in the multi-channel input function to obtain a first feature representation;

[0009] inputting the first feature representation into a kernel Fourier layer, converting the first feature representation to a frequency domain through Fourier transform, modulating the frequency spectrum using a learnable Fourier kernel parameter to capture global spatial dependency, and returning to the spatial domain through inverse Fourier transform to obtain a second feature representation;

[0010] processing the second feature representation through a projection layer to perform non-linear transformation and dimension reduction mapping on the feature vector to obtain a bump prediction function describing the spatial distribution of bump intensity in the target geographic area;

[0011] outputting the bump prediction function as the final prediction result of the aircraft flight bump condition, wherein the prediction result has a resolution-independent characteristic to adapt to input data of different spatial resolutions and provide corresponding prediction output.

[0012] In some embodiments, a plurality of meteorological element data from different meteorological sources is obtained, and the meteorological element data is integrated to form a multi-channel input function, wherein the multi-channel input function is used to represent the continuous spatial distribution of meteorological conditions in the target geographic area, further comprising:

[0013] receiving equivalent bump degree data from at least two independent meteorological data sources, wherein the equivalent bump degree data is used to represent atmospheric turbulence intensity;

[0014] receiving auxiliary meteorological variable data, the auxiliary meteorological variable data including one or more of wind speed, air pressure, or temperature;

[0015] registering and aligning the equivalent bump degree data and the auxiliary meteorological variable data in a spatial coordinate system;

[0016] splicing the registered equivalent bump degree data and the auxiliary meteorological variable data along the feature channel dimension to form the multi-channel input function.

[0017] In some embodiments, the multi-channel input function is processed through a lifting layer to perform non-linear transformation and dimension expansion on the feature vector at each spatial position in the multi-channel input function to obtain a first feature representation, further comprising:

[0018] extracting the feature vector of the multi-channel input function at each spatial coordinate position;

[0019] using a multi-layer perceptron network in the lifting layer to independently perform a non-linear transformation on the feature vector of each position;

[0020] mapping the feature vector from the original input dimension to a higher dimensional feature space through the non-linear transformation;

[0021] reorganizing the transformed feature vectors of all spatial positions according to the original spatial structure to generate the first feature representation.

[0022] In some embodiments, the first feature representation is input into a core Fourier layer, the first feature representation is converted to the frequency domain through Fourier transform, a learnable Fourier kernel parameter is used to modulate the frequency spectrum to capture global spatial dependence, and then inverse Fourier transform is performed to return to the spatial domain to obtain a second feature representation, further comprising:

[0023] applying Fourier transform to the input first feature representation to convert from the spatial domain to the frequency domain to obtain a corresponding frequency spectrum representation;

[0024] in the frequency domain, performing point-by-point multiplication operation of the learnable Fourier kernel parameter and the frequency spectrum representation;

[0025] applying inverse Fourier transform to the modulated frequency spectrum to convert from the frequency domain back to the spatial domain to obtain a spatial domain feature map;

[0026] fusing the spatial domain feature map and the input first feature representation through a residual connection, and applying a non-linear activation function for transformation to output the second feature representation.

[0027] In some embodiments, the learnable Fourier kernel parameter is used to weight and fuse the influence of different meteorological sources and geographical regions in the frequency domain, and is learned through a training process, which can capture the contribution of different spatial frequency components to the prediction of the bump, and realize the modeling of long-distance spatial dependence.

[0028] In some embodiments, the second feature representation is processed through a projection layer to perform non-linear transformation and dimensionality reduction mapping on the feature vector to obtain a bump prediction function describing the spatial distribution of bump intensity in the target geographical region, further comprising:

[0029] extracting the feature vector of the second feature representation at each spatial coordinate position;

[0030] using a multi-layer perceptron network in the projection layer to independently perform a non-linear transformation on the feature vector of each position;

[0031] mapping the feature vector to a one-dimensional output space through the non-linear transformation to obtain the predicted bump intensity of the corresponding spatial position;

[0032] reorganize the predicted values of all spatial positions according to the original spatial structure to generate the bumpiness prediction function.

[0033] In some embodiments, the bumpiness prediction function is output as the final prediction result of the aircraft flight bumpiness condition, further comprising:

[0034] The bumpiness prediction function is represented in the form of a two-dimensional spatial distribution map, where each spatial position corresponds to a predicted bumpiness intensity value.

[0035] The two-dimensional spatial distribution map is provided as a bumpiness prediction product for a flight route or area.

[0036] The prediction product automatically adjusts the resolution of the output prediction according to the different spatial resolution of the input meteorological data.

[0037] Based on the same concept, the present application also provides a multi-source meteorological data fusion prediction system based on Fourier neural operator, comprising:

[0038] A multi-channel input function construction module is configured to obtain multi-channel input function data from different meteorological sources, and integrate the meteorological element data to form a multi-channel input function, wherein the multi-channel input function is used to represent the continuous spatial distribution of the meteorological state in the target geographical area.

[0039] A first feature representation generation module is configured to process the multi-channel input function through a lifting layer, and perform nonlinear transformation and dimension expansion on the feature vector at each spatial position in the multi-channel input function to obtain a first feature representation.

[0040] A second feature representation generation module is configured to input the first feature representation into a core Fourier layer, convert the first feature representation to the frequency domain through Fourier transform, use a learnable Fourier kernel parameter to modulate the frequency spectrum to capture global spatial dependence, and then return to the spatial domain through inverse Fourier transform to obtain a second feature representation.

[0041] A bumpiness prediction function generation module is configured to process the second feature representation through a projection layer, perform nonlinear transformation and dimension reduction mapping on the feature vector to obtain a bumpiness prediction function describing the spatial distribution of bumpiness intensity in the target geographical area.

[0042] A prediction result output module is configured to output the bumpiness prediction function as the final prediction result of the aircraft flight bumpiness condition, wherein the prediction result has the characteristic of being independent of the resolution of the input data, so as to adapt to input data of different spatial resolutions and provide corresponding prediction output.

[0043] Based on the same concept, the application also provides an electronic device, comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete communication with each other through the communication bus; the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the Fourier neural operator-based multi-source meteorological data fusion prediction method.

[0044] Based on the same concept, the application also provides a computer readable storage medium storing a computer program executable by an electronic device, and when the computer program runs on the electronic device, the electronic device executes the steps of the Fourier neural operator-based multi-source meteorological data fusion prediction method.

[0045] Compared with the prior art, the application has the beneficial effects that:

[0046] The application discloses a Fourier neural operator-based multi-source meteorological data fusion prediction method and system, an electronic device and a storage medium, which adopts a neural operator paradigm that learns "function to function" mapping instead of processing discrete points on a specific grid, so that the trained model can directly process input data with different resolutions from training. Low-resolution historical data can be used to efficiently train the model, which can be directly applied to high-resolution real-time prediction data without the need for retraining or model adjustment, improving the flexibility and application efficiency of the model, and avoiding the loss of accuracy caused by data interpolation.

[0047] It has the ability to model global spatial dependencies, and through core operations in the Fourier frequency domain space, it can efficiently modulate the spectrum using a learnable Fourier kernel, capturing long-range correlations between all points in the entire meteorological field at once.

[0048] It combines physical mechanisms and data-driven methods to make the prediction results more physically consistent and reliable, and has better generalization ability in extreme scenarios not covered by the training data.

[0049] It improves the efficiency of multi-source data fusion, and unifies multiple sources of meteorological data (such as multiple EDR data sources, wind fields and pressure fields) as a multi-channel continuous function for end-to-end learning, automatically optimizes the fusion weights and methods of different sources and variables through learnable network parameters, and overcomes the limitations of traditional linear fusion methods to form a more accurate prediction field with more information. BRIEF DESCRIPTION OF DRAWINGS

[0050] Other features, objects and advantages of the application will become more apparent through reading the detailed description of the non-limiting embodiments made by referring to the following drawings:

[0051] Figure 1 is a flowchart of a method for multi-source meteorological data fusion and prediction based on a Fourier neural operator according to some embodiments of the present application;

[0052] Figure 2 is a structural diagram of a system for multi-source meteorological data fusion and prediction based on a Fourier neural operator according to some embodiments of the present application;

[0053] Figure 3 is a structural diagram of an electronic device according to some embodiments of the present application;

[0054] In the figure, 710 is a processor; 720 is a memory; 730 is an input device; and 740 is an output device. DETAILED DESCRIPTION

[0055] In order to make the purposes, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0056] The terms used in the embodiments of the present application are only for the purpose of describing the specific embodiments, and are not intended to limit the present application. The singular forms "a", "an" and "the" used in the embodiments of the present application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. "Multiple" generally includes at least two.

[0057] It should be understood that the term "and / or" used herein is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " herein generally represents an "or" relationship between the front and rear associated objects.

[0058] It should be understood that although the terms first, second, third, etc. can be used in the embodiments of the present application, these descriptions should not be limited to these terms. These terms are only used to distinguish the description. For example, without departing from the scope of the embodiments of the present application, the first can also be called the second, and similarly, the second can also be called the first.

[0059] Depending on the context, the word "if' can be interpreted to mean "when" or "upon" or "in response to determining" or "in response to detecting," generally or as used in this document. Similarly, the phrase "if it is determined" or "if [a stated condition or event] is detected" can be interpreted to mean "upon determining" or "in response to determining" or "upon detecting [the stated condition or event]" or "in response to detecting [the stated condition or event]," generally or as used in this document.

[0060] It is also to be noted that the terms "comprising," "including," and any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0061] It is particularly noted that symbols and / or numbers present in the description, if not marked in the description of the figures, are not figure references.

[0062] Reference Figure 1 A multi-source meteorological data fusion prediction method based on a Fourier neural operator includes:

[0063] S101, obtaining multiple meteorological element data from different meteorological sources, and integrating the meteorological element data to form a multi-channel input function, wherein the multi-channel input function is used to represent a continuous spatial distribution of meteorological states in a target geographical area;

[0064] S102, processing the multi-channel input function through a lifting layer, performing nonlinear transformation and dimension expansion on the feature vector at each spatial position in the multi-channel input function, and obtaining a first feature representation;

[0065] S103, inputting the first feature representation into a core Fourier layer, converting the first feature representation to a frequency domain through a Fourier transform, modulating the frequency spectrum using a learnable Fourier kernel parameter to capture global spatial dependence, and returning to the spatial domain through an inverse Fourier transform to obtain a second feature representation;

[0066] S104, processing the second feature representation through a projection layer, performing nonlinear transformation and dimension reduction mapping on the feature vector, and obtaining a bumpiness prediction function describing the spatial distribution of bumpiness intensity in the target geographical area;

[0067] S105, outputting the bumpiness prediction function as a final prediction result of the aircraft flight bumpiness, wherein the prediction result has a resolution-independent characteristic to adapt to input data of different spatial resolutions and provide corresponding prediction output.

[0068] Specifically, in the embodiments of the present application, multiple meteorological element data from different meteorological sources are obtained, including equivalent bumpiness degree data and other related meteorological variables, and these data are integrated in the spatial domain to form a multi-channel input function, which is used to represent the continuous spatial distribution of meteorological states in the target geographical area. The multi-channel input function is input into the lifting layer, and the feature vectors at each spatial position in the input function are nonlinearly transformed and dimensionally expanded by the learnable parameter structure set in the lifting layer to obtain a first feature representation. The first feature representation is input into the core Fourier layer, in which the spatial domain features are converted to the frequency domain by Fourier transform, and the frequency spectrum representation is modulated by the learnable Fourier kernel parameters to capture the global dependency between different meteorological sources and geographical space. The modulated frequency spectrum is converted back to the spatial domain by inverse Fourier transform, and combined with residual connection and nonlinear activation processing to output a second feature representation. The second feature representation is input into the projection layer, and the features at each spatial position are nonlinearly transformed and dimensionally mapped by the learnable parameter structure set in the projection layer to map them to a single-dimensional output space representing the bumpiness intensity, thereby generating a bumpiness prediction function describing the spatial distribution of bumpiness intensity in the target geographical area. The bumpiness prediction function is output as a prediction result of the aircraft flight bumpiness, and the result has a resolution-independent characteristic, which can adapt to input data of different spatial resolutions and automatically adjust the output.

[0069] For example, for a 100km x 100km rectangular airspace region, to perform the prediction of the turbulence, the equivalent turbulence intensity data from three different meteorological sources are obtained, as well as the wind speed and air pressure, two auxiliary meteorological variables, which together constitute the input function of 5 channels. Each channel covers the region and is discretized into a 100 x 100 grid of points with a resolution of 1 km. The input function is processed by a lifting layer, in which a multilayer perceptron structure with 2 hidden layers is used to non-linearly map the 5-dimensional original feature vector of each position to a 64-dimensional feature, generating a first feature representation with a dimension of 64 x 100 x 100. The first feature representation is input into a 4-layer core Fourier layer, which performs the following operations: perform a fast Fourier transform to obtain a frequency domain representation; element-wise multiply with a set of learnable complex weight kernels in the frequency domain to modulate the spectrum; perform an inverse fast Fourier transform to restore to the spatial domain; and generate an output feature through a residual connection and a GELU activation function. After 4 layers of processing, a second feature representation is obtained, which maintains a dimension of 64 x 100 x 100. The second feature representation is processed by a projection layer, which uses a 3-layer perceptron network to non-linearly map the 64-dimensional feature vector of each position to a scalar value representing the turbulence intensity, outputting a 100 x 100 prediction grid, with each grid point representing the predicted turbulence intensity at that location, with a unit of m² / s³. During training, 0.5 km resolution data can be used, while during prediction, 1 km or 2 km resolution data can be directly input without adjusting the model or retraining, and the corresponding resolution turbulence prediction map is directly output.

[0070] In some applications, multiple meteorological element data from different meteorological sources are obtained, and the meteorological element data are integrated to form a multi-channel input function, wherein the multi-channel input function is used to represent the continuous spatial distribution of the meteorological state in the target geographical region, including receiving equivalent turbulence intensity data from at least two independent meteorological data sources, wherein the equivalent turbulence intensity data is used to represent the atmospheric turbulence intensity; receiving auxiliary meteorological variable data, the auxiliary meteorological variable data including at least one or more of wind speed, air pressure, or temperature; registering and aligning the equivalent turbulence intensity data and the auxiliary meteorological variable data in a spatial coordinate system; and splicing the registered equivalent turbulence intensity data and the auxiliary meteorological variable data along the feature channel dimension to form the multi-channel input function.

[0071] It can be understood that equivalent roughness data is obtained from at least two independent meteorological data sources, which is used to quantitatively characterize the atmospheric turbulence intensity. At the same time, auxiliary meteorological variable data is obtained from the meteorological observation system, at least including one or more physical quantities such as wind speed, air pressure or temperature. The obtained equivalent roughness data and auxiliary meteorological variable data are registered in the same spatial coordinate system to ensure the accurate alignment of different data sources in the spatial grid. The spatially registered equivalent roughness data and auxiliary meteorological variable data are spliced and integrated along the characteristic channel dimension to form a unified multi-channel input function, which fully characterizes the continuous spatial distribution of meteorological state in the target geographical area.

[0072] For example, equivalent roughness data from two independent meteorological sources, global forecast system and regional numerical model, is obtained, with a spatial resolution of 0.25°x0.25° and a coverage range of 110°-120°E, 30°-40°N. At the same time, three auxiliary meteorological variable data, wind speed, air pressure and temperature, are obtained in this region, with the same spatial resolution and range as the equivalent roughness data. All data are uniformly interpolated to a regular latitude and longitude grid of 0.25°x0.25° by bilinear interpolation method to realize spatial registration and alignment. The equivalent roughness data from two sources is taken as two independent channels, and is spliced with the wind speed, air pressure and temperature three auxiliary variable channels to finally form an input function containing five channels, which is represented as a 5x40x40 data array in space, where 40x40 corresponds to 40 grid points in longitude and 40 grid points in latitude.

[0073] In some applications, the multi-channel input function is processed through a lifting layer to perform nonlinear transformation and dimension expansion on the feature vector at each spatial position in the multi-channel input function to obtain a first feature representation, including extracting the feature vector at each spatial coordinate position of the multi-channel input function; using a multi-layer perceptron network in the lifting layer to independently perform nonlinear transformation on the feature vector at each position; mapping the feature vector from the original input dimension to a higher dimensional feature space through the nonlinear transformation; reorganizing all transformed feature vectors at different spatial positions according to the original spatial structure to generate the first feature representation.

[0074] It can be understood that the feature vector at each spatial coordinate position of the multi-channel input function is extracted, which contains the numerical information of all input channels at the position. The feature vector at each spatial position is independently subjected to nonlinear transformation using a preset multi-layer perceptron network in the lifting layer, which includes a hidden layer and a nonlinear activation function. Through the nonlinear transformation process, the feature vector at each position is mapped from the original input dimension to a higher dimensional feature space, realizing the expansion and enrichment of the feature dimension. The transformed feature vectors of all spatial positions are recombined and arranged according to the spatial structure of the original input function to generate the first feature representation which retains the original spatial relationship.

[0075] For example, the input function is a 100x100 spatial grid data containing 5 channels, and each spatial position corresponds to a 5-dimensional feature vector. The lifting layer uses a multi-layer perceptron network with two hidden layers, where the first hidden layer contains 32 neurons and uses ReLU activation function, and the second hidden layer contains 64 neurons and uses ReLU activation function. The network independently performs nonlinear transformation on the 5-dimensional input feature vector at each position, and outputs a 64-dimensional feature vector. Through this transformation process, the original 5x100x100 input data is converted into a 64x100x100 first feature representation, where the feature dimension is expanded from 5 to 64, while the spatial dimension 100x100 remains unchanged, retaining the spatial structure information of the original data.

[0076] In some applications, the first feature representation is input into the core Fourier layer, the first feature representation is converted into the frequency domain through Fourier transform, the frequency spectrum is modulated using learnable Fourier kernel parameters to capture global spatial dependence, and then inverse Fourier transform is performed to return to the spatial domain to obtain the second feature representation, including applying Fourier transform to the input first feature representation to convert from the spatial domain to the frequency domain to obtain the corresponding frequency spectrum representation; in the frequency domain, the learnable Fourier kernel parameters are multiplied point by point with the frequency spectrum representation; the modulated frequency spectrum is subjected to inverse Fourier transform to convert from the frequency domain back to the spatial domain to obtain the spatial domain feature map; the spatial domain feature map and the input first feature representation are fused through a residual connection, and a nonlinear activation function is applied for transformation to output the second feature representation.

[0077] It can be understood that the Fourier transform is applied to the input first feature representation to convert from the spatial domain to the frequency domain to obtain the corresponding complex spectrum representation. In the frequency domain, the learnable Fourier kernel parameter is multiplied point by point with the spectrum representation to realize the modulation of the spectrum and the capture of the global spatial dependence. The inverse Fourier transform is applied to the modulated spectrum to convert from the frequency domain back to the spatial domain to obtain the processed spatial domain feature map. The obtained spatial domain feature map is fused with the input first feature representation through a residual connection, and a nonlinear activation function is applied to the fusion result to output the enhanced second feature representation.

[0078] For example, the input first feature representation is a 64x100x100 data array, and a two-dimensional fast Fourier transform is performed thereon to obtain a 64x100x100 complex spectrum representation. In the frequency domain, the learnable Fourier kernel parameter (dimension 64x50x50, corresponding to the low-frequency components reserved after Fourier transform) is multiplied point by point with the spectrum representation. The inverse Fourier transform is applied to the modulated spectrum to convert it back to a 64x100x100 spatial domain feature map. The feature map is added element by element with the original input first feature representation through a residual connection, and then a GELU nonlinear activation function is applied to the addition result to transform it, outputting a second feature representation with a dimension of 64x100x100. During the entire processing process, the Fourier kernel parameter is learned through the training process and is specially used to capture the global spatial dependence between different meteorological variables.

[0079] In some applications, the learnable Fourier kernel parameter is used to weight and fuse the effects of different meteorological sources and geographical regions in the frequency domain, and is learned through the training process to capture the contribution of different spatial frequency components to the prediction of the bump, and to model the long-distance spatial dependence.

[0080] It can be understood that the Fourier kernel parameter is used to adaptively weight and fuse the effects of different meteorological sources and geographical regions in the frequency domain, and the parameter value is learned through the model training process. The kernel parameter can effectively identify and capture the contribution difference of different spatial frequency components to the prediction result of the bump, and accurately model the long-distance spatial dependence in the meteorological data. Through the modulation operation in the frequency domain, the parameter can establish the correlation between the meteorological conditions of remote geographical regions, thereby enhancing the global spatial perception ability of the model.

[0081] For example, in the setting of 64 feature channels, the Fourier kernel parameter is a complex-valued tensor of dimension 64 x 50 x 50, where 50 x 50 corresponds to the dimension of low-frequency components reserved after Fourier transform. The parameter is randomly initialized at the beginning of training, with the range of initial real part set to -0.1 to 0.1, and the range of initial imaginary part also set to -0.1 to 0.1. Through the backpropagation algorithm, the parameter gradually learns the contribution weights of different meteorological sources (such as global forecast systems and regional numerical models) at different spatial frequencies during the training process. After training is completed, the kernel parameter can automatically identify the importance difference of low-frequency components (such as large-scale weather systems) and high-frequency components (such as local turbulent features) to the prediction of turbulence, and effectively model the spatial dependence within a range of 1000 km. In the inference process, the learned kernel parameter is stored in 32-bit floating-point precision, and complex multiplication is performed with the input frequency spectrum in the frequency domain. The calculation process is executed in parallel on the GPU, and the single operation time is less than 5 ms.

[0082] In some applications, the second feature representation is processed through a projection layer to perform nonlinear transformation and dimension reduction mapping on the feature vectors to obtain a turbulence prediction function describing the spatial distribution of turbulence intensity within the target geographical region, including extracting the feature vectors of the second feature representation at each spatial coordinate position; using a multi-layer perceptron network in the projection layer to independently perform nonlinear transformation on the feature vectors of each position; mapping the feature vectors to a one-dimensional output space through the nonlinear transformation to obtain the predicted turbulence intensity of the corresponding spatial position; and recombining the predicted values of all spatial positions according to the original spatial structure to generate the turbulence prediction function.

[0083] It can be understood that the feature vectors of the second feature representation at each spatial coordinate position are extracted, and the feature vectors contain high-dimensional feature information processed by the core Fourier layer. The multi-layer perceptron network in the projection layer is used to independently perform nonlinear transformation on the feature vectors of each spatial position, and the network includes multiple hidden layers and nonlinear activation functions. Through the nonlinear transformation process, the high-dimensional feature vectors of each position are mapped to a one-dimensional output space to obtain the predicted turbulence intensity value of the corresponding spatial position. The predicted turbulence intensity values of all spatial positions are recombined and arranged according to the spatial structure of the original second feature representation to generate a turbulence prediction function that fully describes the spatial distribution of turbulence intensity within the target geographical region.

[0084] For example, the input second feature representation is a data array of 64x100x100, each spatial location corresponds to a 64-dimensional feature vector. The projection layer adopts a multi-layer perceptron network with two hidden layers, where the first hidden layer contains 32 neurons and uses ReLU activation function, the second hidden layer contains 16 neurons and uses ReLU activation function, and the output layer is a single neuron using linear activation function. This network independently performs a nonlinear transformation on the 64-dimensional input feature vector of each location, and outputs a scalar value representing the intensity of the bump. Through this transformation process, the original 64x100x100 second feature representation is converted into a 100x100 bump prediction function, where each grid point value represents the predicted bump intensity at that location, with the unit of m² / s³. The entire processing process maintains the original spatial structure, and the output result can be directly used for flight route bump warning and flight planning.

[0085] In some applications, the bump prediction function is output as the final prediction result of the aircraft flight bump, including representing the bump prediction function in the form of a two-dimensional spatial distribution map, where each spatial location corresponds to a predicted bump intensity value; providing the two-dimensional spatial distribution map as a bump prediction product for a flight route or a region; the prediction product automatically adjusts the resolution of the output prediction according to the different spatial resolution of the input meteorological data.

[0086] It can be understood that the bump prediction function is represented in the form of a two-dimensional spatial distribution map, where each spatial location corresponds to a predicted bump intensity value, forming a complete spatial visualization expression. The two-dimensional spatial distribution map is provided as a bump prediction product for a flight route or a specific region, which can be directly applied to aviation operations and flight decision support. The prediction product has the ability to automatically adjust the resolution of the output prediction according to the different spatial resolution of the input meteorological data, without manual intervention or model retraining, ensuring the consistency of the prediction result with the input data in spatial scale.

[0087] For example, when the spatial resolution of the input meteorological data is 0.25°x0.25°, the output bump prediction function automatically generates a 256x256 two-dimensional spatial distribution map, covering the region of 110°-120°E, 30°-40°N. Each grid point corresponds to a predicted bump intensity value within an area of about 25 km², with an intensity value range of 0-0.4 m² / s³, and areas with an intensity value exceeding 0.2 m² / s³ are marked as moderate to severe bump areas. When the input data resolution changes to 0.5°x0.5°, an automatically output 128x128 prediction map is generated, covering the same geographical range, and each grid point corresponds to a predicted value within an area of about 100 km². The prediction product is output in GeoTIFF format, containing complete geographic coordinate information, and can be directly integrated into a flight management system or an electronic flight bag to provide decision support for route planning and real-time avoidance.

[0088] Another embodiment of the present application is described below, which is a multi-source meteorological data fusion prediction method based on Fourier neural operator:

[0089] In this embodiment, the problem is defined as learning an operator from one function space to another function space . Input function: a multi-channel function representing the distribution of EDR data from different sources and other meteorological variables in space.

[0090] ;

[0091] wherein, is the geographical coordinate, is the number of input features.

[0092] Output function: the actual turbulence field to be predicted.

[0093] ;

[0094] Training the neural operator , realize the mapping:

[0095] .

[0096] 2. Model architecture

[0097] The model consists of the following core components:

[0098] Lifting layer: use a multi-layer perceptron (MLP) to lift each point of the input function to a higher-dimensional representation .

[0099] ;

[0100] wherein, is a learnable parameter.

[0101] Core Fourier layer: consists of iterative layers. The calculation formula of the th layer to the +1th layer is:

[0102] ;

[0103] wherein:

[0104] is the input of the th layer.

[0105] and are the Fourier transform and inverse Fourier transform, respectively.

[0106] is a learnable Fourier kernel that performs a multiplication operation on the Fourier coefficients in the frequency domain.

[0107] is a linear transformation for residual connection.

[0108] is a nonlinear activation function (e.g., GELU).

[0109] Projection layer: After going through core layers, use another MLP to project the final high-dimensional representation back to the desired output dimension.

[0110] ;

[0111] where are learnable parameters.

[0112] Formula parameter details:

[0113] : a two-dimensional spatial coordinate vector representing any specific location within a geographical area.

[0114] Input function of the model. It is a vector-valued function that contains a dimensional feature vector at each geographical location . represents the number of EDR forecast data from different meteorological sources and other meteorological variables.

[0115] : the intermediate representation of the model's layer, which is a high-dimensional feature vector. Between different layers of the model, the feature vector contains processed and fused information.

[0116] : output function of the model, i.e., the desired prediction of the turbulence field. It is a single-valued spatial function.

[0117] : parameters of the lifting layer (Lifting Layer). A small feedforward neural network (MLP) that maps each input feature vector to a higher-dimensional intermediate representation .

[0118] : The total set of learnable parameters of the model. This includes the parameters of all layers, specifically the weights of the lifting layers , the Fourier kernels in the core layers , and the parameters of the linear transformations , and the weights of the projection layer .

[0119] : Fourier Kernel, a learnable parameter matrix. It performs point-wise multiplication with the data in the frequency domain, learning the global interactions of different meteorological sources.

[0120] : Parameters of the linear transformation. A small linear layer (usually implemented as convolution) used for residual connections, allowing the model to learn global relationships while preserving local information.

[0121] : Parameters of the Projection Layer. Another small feed-forward neural network (MLP) responsible for mapping the final intermediate representation back to the final prediction output .

[0122] and : Fourier Transform and Inverse Fourier Transform. Non-learnable mathematical operators responsible for converting data from spatial domain (original grid) to frequency domain and vice versa.

[0123] : Non-linear activation function (e.g., GELU). Allows the model to learn and represent more complex non-linear relationships.

[0124] : Point-wise multiplication is denoted in the formula. The multiplication here is done in the frequency domain, representing the operation of the Fourier Kernel on the data.

[0125] Implementation process and examples:

[0126] Suppose we are predicting the turbulence in a 100x100 geographical area. There are EDR data from three meteorological sources (A, B, C), as well as wind speed and air pressure data for the region.

[0127] Input function : Represented as a 5-channel (3 EDR sources + wind speed + air pressure) function, which has a value at each geographical location .

[0128] This input function can be materialized as a 5x100x100 data matrix.

[0129] Output function example:

[0130] Output function is a single-channel function representing the final bump prediction for that region.

[0131] ;

[0132] This output can be materialized as a 1x100x100 data matrix.

[0133] The whole task is to learn an operator that can transform a 5x100x100 input matrix into a 1x100x100 output matrix.

[0134] Data processing flow: from low-dimensional input to high-dimensional features:

[0135] Lifting Layer is the first gate that data enters the model. It is used to transform features and receives raw, low-dimensional data from different meteorological sources.

[0136] Example: the input is 5 raw features for each geographical location. The lifting layer uses a small neural network to transform these 5 features into a high-dimensional feature vector, for example, 64-dimensional.

[0137] ;

[0138] The original 5x100x100 matrix is transformed into a high-dimensional feature representation of 64x100x100.

[0139] Core Fourier Layers receive the high-dimensional data output by the lifting layer and begin the core calculations:

[0140] Connection between spatial domain and frequency domain: the first step in the core layer is to use the Fourier transform to convert data from the spatial domain to the frequency domain.

[0141] Connection between Fourier kernel and global learning: in the frequency domain, the learnable Fourier kernel performs point-wise multiplication with the data. This is equivalent to the model weighting and blending the contributions of different meteorological sources and different geographical regions in the frequency domain.

[0142] Prediction generation: from abstract features to concrete results:

[0143] Inverse Fourier transform is the last step of the core layer, which converts the processed data from the frequency domain back to the spatial domain, making it a spatial field that can be understood and contains prediction information.

[0144] The projection layer is the final output stage of the model. The highly abstract high-dimensional features output by the core layer are projected back into a single-valued bump prediction to generate an intuitive and usable bump prediction map.

[0145] Example: After processing by the core layer, the data is still a 64x100x100 high-dimensional feature representation. The projection layer uses a small neural network to project the 64-dimensional features back to a single-dimensional final prediction value.

[0146] ;

[0147] Finally, a 1x100x100 prediction matrix, i.e. a bump prediction map, is obtained.

[0148] For the method steps disclosed in the above embodiments, the method steps are described as a series of action combinations for the purpose of simple description, but those skilled in the art should know that the embodiments of the present application are not limited by the order of the described actions, because according to the embodiments of the present application, certain steps can be performed in other order or simultaneously. Secondly, those skilled in the art should know that the embodiments described in the specification are all preferred embodiments, and the actions involved are not necessarily required by the embodiments of the present application.

[0149] As shown in Figure 2 , the present application also provides a multi-source meteorological data fusion prediction system based on Fourier neural operator, comprising:

[0150] A multi-channel input function construction module 201 is configured to obtain multiple meteorological element data from different meteorological sources, and integrate the meteorological element data to form a multi-channel input function, wherein the multi-channel input function is used to represent the continuous spatial distribution of meteorological states in a target geographical area;

[0151] A first feature representation generation module 202 is configured to process the multi-channel input function through a lifting layer, and perform nonlinear transformation and dimension expansion on the feature vector at each spatial position in the multi-channel input function to obtain a first feature representation;

[0152] A second feature representation generation module 203 is configured to input the first feature representation into a core Fourier layer, convert the first feature representation to a frequency domain through Fourier transform, use a learnable Fourier kernel parameter to modulate the frequency spectrum to capture global spatial dependence, and then return to the spatial domain through inverse Fourier transform to obtain a second feature representation;

[0153] The bump prediction function generation module 204 is configured to process the second feature representation through a projection layer, perform nonlinear transformation and dimension reduction mapping on the feature vector, and obtain a bump prediction function describing the spatial distribution of bump intensity in the target geographic region.

[0154] The prediction result output module 205 is configured to output the bump prediction function as the final prediction result of the aircraft flight bump condition, wherein the prediction result has a resolution-independent characteristic to adapt to input data of different spatial resolutions and provide corresponding prediction output.

[0155] It is worth noting that, although only some basic function modules are disclosed in the embodiments of the present application, it does not mean that the composition of the system is limited to only the above basic function modules. On the contrary, the meaning expressed in the embodiments is that on the basis of the above basic function modules, those skilled in the art can add one or more function modules to form infinite embodiments or technical solutions in combination with the prior art, that is, the system is open rather than closed, and the protection scope of the claims of the present application cannot be limited to the disclosed basic function modules. At the same time, in order to facilitate description, the above device is described as various units and modules. Of course, when implementing the present application, the functions of the units and modules can be implemented in the same software and / or hardware.

[0156] As shown in Figure 3 The present application also provides an electronic device, comprising: a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete mutual communication through the communication bus; the memory stores a computer program, when the computer program is executed by the processor, the processor executes the steps of a multi-source meteorological data fusion prediction method based on a Fourier neural operator.

[0157] Figure 3 is a structural schematic diagram of an electronic device provided by an embodiment of the present application. As shown in the structure Figure 3 The electronic device provided in the embodiment of the present application includes one or more processors 710 and a memory 720; the processor 710 in the electronic device can be one or more, Figure 3 The memory 720 is used to store one or more programs; the one or more programs are executed by the one or more processors 710, so that the one or more processors 710 implement a multi-source meteorological data fusion prediction method based on a Fourier neural operator as described in any one of the embodiments of the present application.

[0158] The electronic device can also include an input device 730 and an output device 740.

[0159] The processor 710, the memory 720, the input device 730 and the output device 740 in the electronic device can be connected through a bus or other means, Figure 3 The bus connection is taken as an example.

[0160] The memory 720 in the electronic device can be used to store one or more programs as a computer readable storage medium, which can be a software program, a computer executable program and a module, such as program instructions / modules of the method for fusing and predicting multi-source meteorological data based on a Fourier neural operator provided in the embodiments of the present application. The processor 710 executes various functions and data processing of the electronic device by running the software program, instructions and modules stored in the memory 720, that is, implements the method for fusing and predicting multi-source meteorological data based on a Fourier neural operator in the above method embodiments.

[0161] The memory 720 can include a program storage area and a data storage area, wherein the program storage area can store an operating system and at least one application required by a function; the data storage area can store data created according to the use of the electronic device, etc. In addition, the memory 720 can include a high-speed random access memory, and can also include a non-volatile memory, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state memory device. In some examples, the memory 720 can further include a memory remotely arranged with respect to the processor 710, which can be connected to the device through a network. Examples of the above network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network and a combination thereof.

[0162] The input device 730 can be used to receive input digital or character information, and generate key signal input related to user settings and function control of the electronic device. The output device 740 can include a display device such as a display screen.

[0163] The present application also provides a computer readable storage medium storing a computer program executable by an electronic device, which causes the electronic device to execute the steps of the method for fusing and predicting multi-source meteorological data based on a Fourier neural operator when the computer program runs on the electronic device.

[0164] In particular, a computer storage medium of embodiments of the present application can employ any combination of one or more computer readable medium or media. The computer readable medium can be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In this embodiment, the computer readable storage medium can be any tangible medium that contains or stores a program used by an instruction execution system, apparatus, or device to function or to be combined with the instruction execution system, apparatus, or device.

[0165] Finally, it should be noted that the above embodiments are merely used to illustrate the technical solutions of the present application, rather than limit the present application; even though the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced equivalently; and these modifications or replacements do not cause the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A multi-source meteorological data fusion prediction method based on a Fourier neural operator, characterized in that, The method comprises: obtaining multiple meteorological element data from different meteorological sources, and integrating the meteorological element data to form a multi-channel input function, wherein the multi-channel input function is used to represent a continuous spatial distribution of meteorological states in a target geographical area; processing the multi-channel input function through a lifting layer, performing nonlinear transformation and dimension expansion on a feature vector at each spatial position in the multi-channel input function to obtain a first feature representation; inputting the first feature representation into a core Fourier layer, converting the first feature representation to a frequency domain through Fourier transform, modulating the frequency spectrum using a learnable Fourier kernel parameter to capture global spatial dependence, and returning to the spatial domain through inverse Fourier transform to obtain a second feature representation; processing the second feature representation through a projection layer, performing nonlinear transformation and dimension reduction mapping on the feature vector to obtain a bump prediction function describing the spatial distribution of bump intensity in the target geographical area; outputting the bump prediction function as the final prediction result of the aircraft flight bump condition, wherein the prediction result has a resolution-independent characteristic to adapt to input data of different spatial resolutions and provide corresponding prediction output; wherein the feature vector at each spatial coordinate position of the multi-channel input function is extracted; using a multi-layer perceptron network in the lifting layer to independently perform nonlinear transformation on the feature vector at each position; mapping the feature vector from the original input dimension to a higher-dimensional feature space through the nonlinear transformation; reorganizing the feature vectors of all spatial positions after transformation according to the original spatial structure to generate the first feature representation; wherein the Fourier transform is applied to the input first feature representation to convert from the spatial domain to the frequency domain to obtain a corresponding frequency spectrum representation; in the frequency domain, the learnable Fourier kernel parameter is multiplied point by point with the frequency spectrum representation; applying inverse Fourier transform to the modulated frequency spectrum to convert from the frequency domain to the spatial domain to obtain a spatial domain feature map; fusing the spatial domain feature map and the input first feature representation through a residual connection and applying a nonlinear activation function for transformation to output the second feature representation; wherein the feature vector at each spatial coordinate position of the second feature representation is extracted; using a multi-layer perceptron network in the projection layer to independently perform nonlinear transformation on the feature vector at each position; mapping the feature vector to a one-dimensional output space through the nonlinear transformation to obtain the predicted bump intensity of the corresponding spatial position; reorganizing the predicted values of all spatial positions according to the original spatial structure to generate the bump prediction function. 2.The multi-source meteorological data fusion prediction method based on Fourier neural operator according to claim 1, wherein obtaining multiple meteorological element data from different meteorological sources, and integrating the meteorological element data to form a multi-channel input function, wherein the multi-channel input function is used to represent a continuous spatial distribution of meteorological states in a target geographical area, further comprising: receiving equivalent bump degree data from at least two independent meteorological data sources, wherein the equivalent bump degree data is used to represent atmospheric turbulence intensity; receiving auxiliary meteorological variable data, which includes one or more of wind speed, air pressure, or temperature; aligning the registered equivalent roughness data and the auxiliary meteorological variable data in a spatial coordinate system; stitching the registered equivalent roughness data and the auxiliary meteorological variable data along a characteristic channel dimension to form the multi-channel input function. 3.The multi-source meteorological data fusion prediction method based on Fourier neural operator of claim 1, wherein, The learnable Fourier kernel parameter is used to weight and fuse the influences of different meteorological sources and geographical regions in the frequency domain, and is learned through a training process, which can capture the contributions of different spatial frequency components to roughness prediction and realize modeling of long-distance spatial dependence. 4.The multi-source meteorological data fusion prediction method based on Fourier neural operator of claim 1, wherein, outputting the roughness prediction function as a final prediction result of aircraft flight roughness, further comprising: representing the roughness prediction function in the form of a two-dimensional spatial distribution map, wherein each spatial position corresponds to a predicted roughness intensity value; providing the two-dimensional spatial distribution map as a roughness prediction product for a flight route or region; The prediction product automatically adjusts the resolution of the output prediction according to the different spatial resolution of the input meteorological data.

5. A multi-source meteorological data fusion prediction system based on Fourier neural operator, used for the multi-source meteorological data fusion prediction method based on Fourier neural operator in claim 1, characterized in that, comprising: a multi-channel input function construction module configured to obtain multiple meteorological element data from different meteorological sources, and integrate the meteorological element data to form a multi-channel input function, wherein the multi-channel input function is used to represent the continuous spatial distribution of meteorological conditions in a target geographical region; a first feature representation generation module configured to process the multi-channel input function through a lifting layer, perform nonlinear transformation and dimension expansion on the feature vector at each spatial position in the multi-channel input function, and obtain a first feature representation; a second feature representation generation module configured to input the first feature representation into a core Fourier layer, convert the first feature representation to the frequency domain through Fourier transform, use a learnable Fourier kernel parameter to modulate the frequency spectrum to capture global spatial dependence, and then return to the spatial domain through inverse Fourier transform to obtain a second feature representation; a roughness prediction function generation module configured to process the second feature representation through a projection layer, perform nonlinear transformation and dimension reduction mapping on the feature vector, and obtain a roughness prediction function describing the spatial distribution of roughness intensity in the target geographical region; a prediction result output module configured to output the roughness prediction function as a final prediction result of aircraft flight roughness, wherein the prediction result has a resolution-independent characteristic to adapt to input data of different spatial resolutions and provide corresponding prediction output.

6. An electronic device, comprising: comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, which stores a computer program executable by an electronic device, and when the computer program runs on the electronic device, the electronic device executes the steps of the method in any one of claims 1 to 4.

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