Vertical atmospheric profile fine-grained processing method, system and device based on KAN network

Abstract

The present application relates to the technical field of atmospheric science and machine learning, and in particular to a vertical atmospheric profile fine-grained processing method, system and equipment based on a KAN network, to solve the problems of insufficient vertical resolution, poor physical consistency and mismatch of high-resolution observations of the existing NWP model; it comprises obtaining input data of the KAN network; the input data is nonlinearly mapped by a B-spline function in the KAN network to obtain control point parameters and bias terms of the B-spline function; physical knowledge constraints are introduced into the KAN network, the atmospheric physical law is converted into a constraint term of the loss function, and the output of the KAN network is constrained; the control point parameters and bias terms of the B-spline function are defined as training parameters of the KAN network, a pre-defined staged training strategy is adopted to train the training parameters of the KAN network in stages; the trained KAN network outputs atmospheric variable functions in a continuous height range, to realize the conversion of NWP coarse-grained profiles to high-resolution continuous vertical profiles.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of atmospheric science and machine learning, and particularly relates to a vertical atmospheric profile fine-grained processing method, system and equipment based on a KAN network. BACKGROUND

[0002] Numerical weather prediction (NWP) is the core support of modern meteorological services, and its prediction accuracy directly depends on the model's ability to represent the physical state of the atmosphere. In recent years, NWP models have made significant breakthroughs in horizontal resolution, such as the Global Forecast System (GFS) model of the National Oceanic and Atmospheric Administration (NOAA) with a horizontal resolution of about 28 kilometers, and the BCC-CSM (BCC-Climate System Model) of the China Meteorological Administration (CMA) with a maximum resolution of 30 kilometers. However, due to the limitations of computing resources and the complexity of physical parameterization schemes, the refinement of NWP models in the vertical direction has lagged far behind, resulting in an imbalance between horizontal refinement and vertical roughness.

[0003] Existing operational NWP models generally use a layered strategy, with relatively high vertical resolution in the planetary boundary layer (PBL) (about 100-200 meters) and reduced to about 500 meters in the upper troposphere. Related studies have shown that when the vertical grid spacing is greater than 200 meters, even if the horizontal resolution reaches 15 kilometers, the model solution will not converge, resulting in noise and false structures. This lack of vertical resolution is not simply a numerical roughness problem, but directly leads to the model's incorrect representation of atmospheric physical dynamics - for example, small-scale physical processes such as gravity waves and boundary layer turbulence, which are crucial to atmospheric circulation and weather systems, cannot be accurately analyzed, leading to wave distortion and ultimately affecting the reliability of downstream forecasts.

[0004] At the same time, the development of high-precision observation technology has highlighted the "resolution gap" between NWP model output and actual observations. The vertical resolution of sounding data can reach 10 meters, providing detailed vertical profiles of cloud structure; laser radar technology can achieve near-real-time high-altitude observations with 30-meter vertical resolution and 200-meter horizontal resolution. These observation tools can capture fine atmospheric structures that NWP model grids cannot resolve, while NWP models have vertical resolutions ranging from hundreds of meters to kilometers, which is orders of magnitude different from the above observation data.

[0005] To bridge this gap, the prior art often uses traditional interpolation methods (such as linear interpolation, cubic spline interpolation) to post-process the NWP output. However, as a continuous fluid, the atmosphere, traditional interpolation can only make a simple numerical connection between discrete grid points, and cannot essentially restore the continuous vertical structure that conforms to the physical law. For example, linear interpolation can only calculate the temperature at 500 meters as 284K between 100 meters (288K) and 1450 meters (280K), completely ignoring the nonlinear variation of temperature in the boundary layer, resulting in a lack of physical credibility in the output.

[0006] In addition, some studies attempt to use traditional neural networks (such as multi-layer perceptron MLP) for vertical downscaling, but MLP has significant defects: first, MLP uses a fixed activation function (such as ReLU), which is low in parameter efficiency, and the number of parameters needs to reach the order of 10^6 for the same performance, with high computational cost; second, MLP is a "black box" model, and the internal mechanism cannot be visualized, making it difficult for atmospheric scientists to understand the physical relationship learned by the model and making it difficult to use for scientific discovery; third, purely data-driven MLP is susceptible to the sparsity of observation data and may output physically unreasonable results (such as temperature mutation, wind speed exceeding the upper limit), making it difficult to meet the rigorous requirements of atmospheric science.

[0007] In summary, the prior art cannot simultaneously solve the problems of insufficient vertical resolution of NWP, lack of physical consistency, and poor interpretability, and there is an urgent need for a vertical atmospheric profile refinement scheme that takes into account accuracy, physical credibility, and interpretability. SUMMARY

[0008] To overcome the problems in the prior art, the present application provides a vertical atmospheric profile fine-grained processing method and system based on a KAN network and equipment. The emerging neural network architecture of Kolmogorov-Arnold Network (KAN) is used to bridge the vertical resolution gap between NWP models and high-resolution observations, providing more accurate atmospheric vertical structure information for weather forecasting and climate research.

[0009] To achieve the above-mentioned purposes, the present application adopts the following technical solutions:

[0010] In a first aspect, the present application provides a vertical atmospheric profile fine-grained processing method based on a KAN network, which comprises:

[0011] Obtaining input data of the KAN network; the input data includes the output of the NWP model on the coarse-grained vertical layer;

[0012] Nonlinearly mapping the input data through the B-spline function in the KAN network to learn the control point parameters and bias terms of the B-spline function;

[0013] The physical knowledge constraint is introduced into the KAN network, and the output of the KAN network is constrained by converting the atmospheric physical law into a constraint term of a loss function.

[0014] The control point parameters and the bias term of the B-spline function are defined as training parameters of the KAN network, and the training parameters of the KAN network are trained in stages by using a pre-defined training strategy in stages.

[0015] The trained KAN network outputs the continuous height range atmospheric variable function, and converts the coarse-grained atmospheric vertical profile into a high-resolution continuous vertical profile according to the following recursive relationship.

[0016] Optionally, the input data of the KAN network includes: receiving output data output by each coarse-grained vertical layer of the NWP model, auxiliary input data and physical prior data; wherein the output data includes coarse-grained atmospheric vertical profiles and vertical coordinate parameters corresponding to each coarse-grained vertical layer; the auxiliary input data includes surface auxiliary information; and the physical prior data includes physical prior variables;

[0017] The coarse-grained atmospheric vertical profile, the vertical coordinate parameter corresponding to each coarse-grained vertical layer, the surface auxiliary information and the physical prior variable are used as the input data of the KAN network.

[0018] Optionally, the coarse-grained atmospheric vertical profile includes: a temperature profile, a wind speed profile and a relative humidity profile.

[0019] The vertical coordinate parameter includes: air pressure and potential height.

[0020] The surface auxiliary information includes: surface terrain height and surface temperature.

[0021] The physical prior variable includes potential temperature, which is calculated from temperature, air pressure, dry air gas constant and constant-pressure specific heat capacity.

[0022] Optionally, the KAN network includes an input layer, a hidden layer, an output layer, and a B-spline function constituting layer connection.

[0023] The number of nodes of the input layer matches the dimension of the input data; the connection between the input nodes and the hidden nodes, and the connection between the hidden nodes and the output nodes are all composed of B-spline functions; the B-spline function is a k-order B-spline, the node vector of which covers the physical value interval of the corresponding input variable, and the node interval is set according to the vertical sensitivity difference of the input variable.

[0024] The output layer is used to output the continuous value of a single atmospheric variable at any target height.

[0025] Optionally, the constraint term of converting the atmospheric physical law into the loss function comprises:

[0026] reading an atmospheric physical law describing a hydrostatic balance law in a vertical direction of the atmosphere and an adiabatic variation law of potential temperature in vertical movement of the atmosphere;

[0027] calculating derivative terms corresponding to the hydrostatic balance law and the adiabatic variation law of potential temperature by a continuous derivative property of the B-spline function, and incorporating the derivative terms as constraint terms into the loss function to obtain the constraint terms in the loss function of the KAN network training;

[0028] The loss function comprises: a prediction error loss, a hydrostatic balance constraint loss, and an adiabatic variation constraint loss of potential temperature.

[0029] The constraint term of the loss function comprises: a hydrostatic balance constraint defined based on a derivative of the air pressure with respect to the height, and an adiabatic variation constraint of potential temperature defined based on a derivative of the potential temperature with respect to the height.

[0030] Optionally, the calculation of the derivative terms corresponding to the hydrostatic balance law and the adiabatic variation law of potential temperature comprises: obtaining the derivative of the air pressure with respect to the height and the derivative of the potential temperature with respect to the height by calculating a first-order derivative of a k-order B-spline function; wherein the first-order derivative of the k-order B-spline function is a linear combination of k-1 order spline functions.

[0031] Optionally, the control point parameters and the bias term of the B-spline function are defined as training parameters of the KAN network, and a pre-defined staged training strategy is adopted to train the training parameters of the KAN network in stages, comprising:

[0032] In the pre-training stage, NWP reanalysis data and its pseudo ground truth are used as training samples to learn the mapping relationship from coarse granularity to fine granularity; the NWP reanalysis data comprises vertical profile data with a specific horizontal resolution and a specific time resolution;

[0033] The coarse-grained atmospheric vertical profile data of the NWP reanalysis data is used as input data of the KAN network, and the profile data obtained by interpolating the coarse-grained atmospheric vertical profile data to fine-grained height is used as pseudo ground truth; the control point parameters and the bias term in the KAN network are pre-trained by minimizing the error between the predicted value of the KAN network and the pseudo ground truth.

[0034] In the fine-tuning stage, real observation profile data is used as training data; the real observation profile data comprises sounding data and lidar data; the coarse-grained atmospheric vertical profile of the NWP model is input into the pre-trained KAN network, and the control point parameters of the B-spline function in the KAN network are adjusted to minimize the error between the predicted value of the KAN network and the real observation value.

[0035] Optionally, the atmospheric variable function includes temperature, wind speed and relative humidity, and multiple KAN sub-networks can be called in parallel for the same input to output different variables respectively.

[0036] In a second aspect, the present application provides a vertical atmospheric profile fine-grained processing system based on KAN network, the system comprising:

[0037] a data acquisition module for acquiring input data of the KAN network; the input data including the output of the NWP model on the coarse-grained vertical layer;

[0038] a processing module for performing nonlinear mapping on the input data by the B-spline function in the KAN network, and learning the control point parameters and bias term of the B-spline function;

[0039] a constraint condition definition module for introducing physical knowledge constraints in the KAN network, and constraining the output of the KAN network by converting atmospheric physical laws into constraint terms of the loss function;

[0040] a training module for defining the control point parameters and bias term of the B-spline function as training parameters of the KAN network, and performing staged training on the training parameters of the KAN network by using a pre-defined staged training strategy;

[0041] a result output module for outputting the atmospheric variable function in the continuous height range by the trained KAN network, and converting the coarse-grained atmospheric vertical profile into a high-resolution continuous vertical profile.

[0042] In a third aspect, the present application provides an electronic device, the electronic device comprising:

[0043] at least one processor; and

[0044] a memory in communication with the at least one processor; wherein

[0045] the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the method of any one of the first aspect.

[0046] Compared with the closest prior art, the present application has the beneficial effects of:

[0047] (1) The vertical atmospheric profile fine-grained processing method, system and equipment based on the KAN network provided by the application take the KAN network as the core, combine the continuity and smoothness of the spline function, break through the limitations of the traditional interpolation method and the black box AI model, can convert the coarse-grained vertical profile output by the NWP model into high-resolution and continuous atmospheric vertical profile, effectively fill the resolution gap between the model output and high-precision observation, and improve the prediction accuracy in the vertical direction.

[0048] (2) The application integrates atmospheric physical knowledge constraints in the KAN network model, uses the analytical derivability of the spline function, converts the hydrostatic equilibrium law and the law of conservation of energy into constraint terms of the loss function, ensures that the model output conforms to the atmospheric physical law, avoids the occurrence of physically unreasonable prediction results such as temperature mutation and wind speed exceeding the upper limit, and improves the physical credibility of the results.

[0049] (3) The KAN network used by the application has good interpretability, by visualizing the shape of the spline function, researchers can directly observe how the model learns the fine-scale vertical physical relationship from the coarse-grained input, which helps to establish trust in the model, promotes debugging, and accelerates knowledge transfer in the field of atmospheric science, and provides support for scientific discovery. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the specific embodiments or prior art of the present application, the drawings needed in the specific embodiments or prior art description will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, each element or part is not necessarily drawn according to the actual scale.

[0051] Figure 1 is a flow chart of a vertical atmospheric profile fine-grained processing method based on the KAN network provided by the application;

[0052] Figure 2 is a schematic structural diagram of a vertical atmospheric profile fine-grained processing system based on the KAN network provided by the application;

[0053] Figure 3 is an internal structure diagram of an electronic device provided by the application. DETAILED DESCRIPTION

[0054] The embodiments of the technical solutions of the present application will be described in detail below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, therefore, only as an example, and cannot limit the protection scope of the present application.

[0055] It should be noted that the technical terms or scientific terms used in the present application should be understood as the general meanings understood by the skilled in the art, unless otherwise specified.

[0056] The present application provides a KAN network-based vertical atmospheric profile fine-grained processing method, system and device. In order to bridge the vertical resolution gap between NWP models and high-resolution observations, the present application proposes to use Kolmogorov-Arnold Network (KAN), a new neural network architecture.

[0057] Embodiment 1: Please refer to Figure 1 , Figure 1 A KAN (Kolmogorov-Arnold) network-based vertical atmospheric profile fine-grained acquisition method is provided for Embodiment 1 of the present application, which specifically includes the following steps:

[0058] S101: Obtain input data of the KAN network; the input data includes output of the NWP model on the coarse-grained vertical layer;

[0059] S102: Perform nonlinear mapping on the input data through the B-spline function in the KAN network, and learn to obtain the control point parameters and bias term of the B-spline function;

[0060] S103: Introduce physical knowledge constraints in the KAN network, and constrain the output of the KAN network by converting atmospheric physical laws into constraint terms of the loss function;

[0061] S104: Define the control point parameters and bias term of the B-spline function as the training parameters of the KAN network, and perform staged training on the training parameters of the KAN network using a pre-defined staged training strategy;

[0062] S105: Output the atmospheric variable function in the continuous height range through the trained KAN network, and convert the coarse-grained atmospheric vertical profile into a high-resolution continuous vertical profile.

[0063] In the above embodiment, the input data of the KAN network obtained in step S101 specifically includes: receiving output data, auxiliary input data and physical prior data output by each coarse-grained vertical layer of the NWP model; wherein the output data includes coarse-grained atmospheric vertical profiles and vertical coordinate parameters corresponding to each coarse-grained vertical layer; the auxiliary input data includes surface auxiliary information; and the physical prior data includes physical prior variables;

[0064] The coarse-grained atmospheric vertical profiles and the vertical coordinate parameters corresponding to each coarse-grained vertical layer, the surface auxiliary information and the physical prior variables are used as the input data of the KAN network.

[0065] In the above embodiment, the coarse-grained vertical profile of atmosphere includes a temperature profile, a wind speed profile, and a relative humidity profile.

[0066] The vertical coordinate parameter includes air pressure and potential height.

[0067] The ground surface auxiliary information includes ground surface terrain height and ground surface temperature.

[0068] The physical prior variable includes potential temperature, which is calculated from temperature, air pressure, dry air gas constant, and constant-pressure specific heat capacity.

[0069] In the above step S102, the KAN network is a multi-layer network architecture, which includes an input layer, a hidden layer, an output layer, and a B-spline function constituting inter-layer connection.

[0070] The number of nodes of the input layer matches the dimension of the input data; that is, the sum of the number of variables corresponding to the number of layers of temperature profile data, the number of layers of wind speed profile data, the number of layers of relative humidity profile data, and the number of variables corresponding to ground surface terrain height data and ground surface temperature data.

[0071] The connection between the input nodes and the hidden nodes, and the connection between the hidden nodes and the output nodes are both constituted by B-spline functions; the B-spline function is a k-order B-spline, each learnable B-spline function adopts a third-order B-spline function, and the number of control points of each B-spline function is set to 10-20. The nodes cover the physical value interval of the corresponding input variable, and the node interval is set differently according to the vertical sensitivity of the input variable.

[0072] The output layer is configured to output the continuous value of a single atmospheric variable at any target height.

[0073] The input layer receives 3L+2-dimensional input features, where L is the number of NWP vertical layers, 3L represents the values of temperature, wind speed, and relative humidity at each layer, and 2 represents the ground surface terrain height and the ground surface temperature.

[0074] The hidden layer is configured to set 2 nodes, and each input layer node is connected to a hidden layer node through a learnable B-spline function.

[0075] The output layer is configured to set 1 node, and output the continuous function value of the target atmospheric parameter at any height.

[0076] In the above embodiment, the spline function is a smooth piecewise function used to approximate complex, continuous, and multi-dimensional relationships, and in KANs, it is usually in the form of B-spline (B-Splines) as a learnable basis function. The core definition of B-spline is as follows:

[0077] Let the node vector be where , k is the degree of the spline (the degree of the polynomial is -1), then the B-spline basis function of degree k is defined by the following recursive relation:

[0078] When k = 1 (0th degree polynomial):

[0079]

[0080] When k > 1:

[0081]

[0082] (Note: when the denominator is 0, the corresponding item is 0)

[0083] i is the index of the basis function (used to distinguish different basis functions, such as the first, second, etc. basis function); k is the degree of the B-spline (related to the degree of the polynomial, k = 1 corresponds to the 0th degree polynomial, k = 2 corresponds to the 1st degree polynomial, and so on, the degree = the degree + 1);

[0084] x is the independent variable (input variable, input value of the basis function); t is the knot sequence, which is a set of ordered real numbers (usually arranged in ascending order), representing the segmentation points of the B-spline basis function.

[0085] is a specific element in the knot sequence, for example:

[0086] When k = 1, and define the non-zero interval of the basis function ; ;

[0087] When k > 1, is used to recursively calculate the high-order basis function, the denominator and determine the weight proportion of the basis function.

[0088] Each connected function in KAN , represents the connection function from the i th input neuron to the j th output neuron in KAN, which describes the non-linear mapping relationship between the two layers of neurons; represented by B-spline linear combination:

[0089]

[0090] where, The control point parameters are learnable, and are used for linear combination of B-spline basis functions. The number of basis functions is The number of basis functions is k The order of the B-spline basis function is

[0091] It is worth noting that the key role of the spline function in atmospheric modeling lies in the continuity and smoothness (perfectly capturing the continuous change of atmospheric variables with height, avoiding step-like artifacts), flexibility and controllability (tuning the accuracy by adjusting the node vector density without retraining), and compliance with physical laws.

[0092] In step S103, the atmospheric physical law is converted into a constraint term of the loss function, including:

[0093] The atmospheric physical law for describing the hydrostatic equilibrium law in the vertical direction of the atmosphere and the adiabatic change rule of the potential temperature in the vertical movement of the atmosphere is read;

[0094] By the continuous derivative characteristics of the B-spline function, the derivative terms corresponding to the hydrostatic equilibrium law and the adiabatic change rule of the potential temperature are calculated, and the derivative terms are integrated into the loss function as constraint terms, obtaining the constraint terms in the loss function of the KAN network training, and the expression is:

[0095]

[0096] Wherein: L data is the data fitting loss in the form of mean square error; L hydro is the hydrostatic equilibrium constraint term; L θ is the potential temperature conservation constraint term; λ1 and λ2 are hyperparameters for balancing the importance of each loss.

[0097] The loss function includes: prediction error loss, hydrostatic equilibrium constraint loss and adiabatic change constraint loss of potential temperature;

[0098] The constraint term of the loss function includes: the hydrostatic equilibrium constraint based on the derivative definition of the air pressure to the height, and the adiabatic change constraint of the potential temperature based on the derivative definition of the potential temperature to the height.

[0099] Specifically, the hydrostatic equilibrium constraint is calculated by the following formula:

[0100]

[0101] The adiabatic change constraint of the potential temperature is calculated by the following formula:

[0102]

[0103] Wherein, p is the air pressure, T is the temperature, θ is the potential temperature, g is the acceleration of gravity, R dg is the dry air gas constant, g d is the dry adiabatic lapse rate.

[0104] In the above embodiment, the derivative terms corresponding to the hydrostatic equilibrium law and the adiabatic variation law of potential temperature include: obtaining the derivative of air pressure with respect to height and the derivative of potential temperature with respect to height by calculating the first derivative of the k-th B-spline function; wherein the first derivative of the k-th B-spline function is a linear combination of k-1-th spline functions.

[0105] In step S104, the control point parameters and the bias term of the B-spline function are defined as the training parameters of the KAN network, and a pre-defined staged training strategy is used to train the training parameters of the KAN network, including: in the pre-training stage, using NWP reanalysis data and its pseudo-true value as training samples to learn the mapping relationship from coarse granularity to fine granularity; the NWP reanalysis data includes vertical profile data with a specific horizontal resolution and a specific time resolution;

[0106] The coarse-grained vertical profile of the NWP reanalysis data is used as the input data of the KAN network, and the profile data obtained by interpolating the coarse-grained vertical profile to fine-grained height is used as the pseudo-true value; the control point parameters and the bias term in the KAN network are pre-trained by minimizing the error between the predicted value of the KAN network and the pseudo-true value;

[0107] In the fine-tuning stage, real observation profile data is used as training data; the real observation profile data includes sounding data and lidar data;

[0108] The coarse-grained atmospheric vertical profile of the NWP model is input into the pre-trained KAN network, and the control point parameters of the B-spline function in the KAN network are adjusted to minimize the error between the predicted value of the KAN network and the real observation value; thus the training of the KAN network is completed.

[0109] After the training of the KAN network is completed, the embodiment further includes a verification step of the trained KAN network, which includes quantitative evaluation and qualitative verification; the quantitative evaluation uses two indicators of mean square error and mean absolute error to evaluate the prediction accuracy by calculating the difference between the predicted value of the trained KAN network and the observation value in the sounding data or the lidar data; the qualitative verification includes physical consistency check and scientific interpretability verification; the physical consistency check is used to verify whether the output atmospheric vertical profile meets the preset physical law, and the preset physical law includes that the temperature in the troposphere decreases with height, the temperature in the stratosphere increases with height, and the wind speed has no obvious non-physical jump; the scientific interpretability verification analyzes whether the physical relationship between the input variable and the target atmospheric variable conforms to the pre-physical expectation by visualizing the shape of the B-spline function.

[0110] In step S105, the atmospheric variable functions output by the trained KAN network include temperature, wind speed, and relative humidity, and multiple KAN sub-networks can be called in parallel for the same input to output different variables.

[0111] Embodiment 2: Based on the technical concept of the above method, a KAN network and B-spline function-based atmospheric vertical profile refinement (KAVAP) model framework is proposed, which is equivalent to the trained KAN network in Embodiment 1. The KAVAP model provides an innovative solution to the problem of insufficient vertical resolution of NWP by integrating KAN network, spline function, and physical knowledge constraints. It solves the problems of insufficient vertical resolution, poor physical consistency, and mismatch with high-resolution observations of existing NWP models. As a supplement to traditional NWP models, the KAVAP model enhances vertical prediction capability through hybrid and data-driven post-processing techniques. Its architecture design is as follows:

[0112] I. Input layer:

[0113] 1. Core input: NWP model output on coarse vertical layers, such as temperature profile of a certain grid point: ; where L is the number of vertical layers, T l is the temperature value of the l th layer, wind speed profile (unit: m / s), relative humidity profile (unit: %), and corresponding pressure p l (unit: hPa) or height z l (unit: m) of each layer.

[0114] Auxiliary input: surface terrain height z s (unit: m), surface temperature T s (unit: K), and other static or near-surface data to improve the refinement accuracy near the boundary layer.

[0115] Physical prior: potential temperature ;

[0116] where is the gas constant of dry air, is the specific heat capacity at constant pressure), and other variables with clear physical meaning to encode atmospheric thermodynamic properties in advance.

[0117] 2. KAN core layer: This embodiment uses a 3-layer KAN structure; in particular, the number of layers of the KAN network can also be determined according to specific circumstances.

[0118] The input layer dimension is 3L+2 (including L temperature, L wind speed, L humidity values, plus terrain height and surface temperature); the hidden layer is provided with 2 nodes, and each connection from input to hidden layer corresponds to a 3-order B-spline function (the node vector covers the physical range of input variables); the output layer is provided with 1 node, which represents a target variable (such as temperature) at a certain height z.

[0119] In the above embodiment, the calculation method of the hidden layer nodes h1 and h2 is as follows:

[0120]

[0121] wherein, x i represents the i-th variable of the input layer, f i,1 is a 3-order B-spline function from the i-th node of the input layer to the hidden layer node h1, f i,2 is a 3-order B-spline function from the i-th node of the input layer to the hidden layer node h2; b1 is the bias term of the hidden layer node h1, and the initial value is set to 0.1; b2 is the bias term of the hidden layer node h2, and the initial value is set to 0.1.

[0122] The output layer node takes temperature T(z) as an example, the calculation formula is as follows:

[0123]

[0124] wherein, f 1,out is a 3-order B-spline function from the hidden layer node h1 to the output layer node, f 2,out is a 3-order B-spline function from the hidden layer node h2 to the output layer node, is the output layer bias term.

[0125] Output layer: the output is the function of atmospheric variables at continuous height z, such as temperature profile T(z), wind speed profile V(z), etc. For any height z, the corresponding value can be directly obtained by KAN calculation without relying on discrete grid.

[0126] For example, when the input NWP temperature at 1000 hPa (z=100 m) is 288 K, the temperature at 850 hPa (z=1450 m) is 280 K, KAVAP can output the temperature at z=500 m as 285.3 K, and the temperature at z=1000 m as 282.1 K, etc.

[0127] For example, when the input NWP temperature at 1000 hPa (z=100 m) is 288 K, the temperature at 850 hPa (z=1450 m) is 280 K, KAVAP can output the temperature at z=500 m as 285.3 K, and the temperature at z=1000 m as 282.1 K, etc.

[0128] II. Incorporate the constraints of physical knowledge in the model, and convert the atmospheric physical law into a constraint term of the loss function of KAN network training:

[0129] Due to the sparsity of high-quality and high-resolution observation data in the field of atmospheric science, purely data-driven models may overfit or produce physically unreasonable predictions, such as temperature mutations and wind speed exceeding the upper limit. To address this, KAVAP employs a physical knowledge constraint method, which encodes physical laws into the loss function.

[0130] Taking the hydrostatic balance of the atmosphere in the vertical direction as an example, its differential form is:

[0131] where, p is the air pressure (unit: Pa), z is the height (unit: m), is the air density (unit: kg / m³), is the acceleration of gravity. Combined with the ideal gas law , it can be converted to: ;

[0132] where g is the acceleration of gravity, R d is the gas constant of dry air, representing the proportionality coefficient of dry air in the ideal gas law. KAN outputs the temperature T(z) and air pressure at z height, which need to satisfy this equation. Since the spline function has continuous derivatives (the derivative of a k order spline is k-1 order spline), the spline derivative of can be directly calculated by:

[0133]

[0134] where, is the first derivative of the B-spline function, c p is the specific heat capacity at constant pressure of dry air, i.e., the heat required to raise the temperature of unit mass of air by 1 K when the pressure remains constant.

[0135] In addition, the energy conservation constraint requires that the adiabatic change of the potential temperature in the vertical motion of the atmosphere satisfies: (without non-adiabatic processes such as radiation and phase change), and its vertical gradient constraint can be expressed as: ;

[0136] is the dry adiabatic lapse rate, is the derivative of the KAN output temperature and the B-spline function.

[0137] In one embodiment, the training of the KAVAP model is carried out in stages to make full use of various types of data:

[0138] 1. Training data sources:

[0139] Main data: NWP reanalysis data (e.g. CRA-40), containing vertical profiles with 30 km horizontal resolution and 6 hours temporal resolution, e.g. 10-layer temperature data at a certain time . Corresponding .

[0140] Ground truth: Radiosonde data (e.g. observations at a certain site at a certain time: T=288.2 K at z=0 m, T=287.5 K at z=200 m,..., T=269.8 K at z=5000 m) and lidar data (continuous temperature profiles with 30 m resolution).

[0141] 2. Training procedure:

[0142] First stage (pre-training): coarse-grained profiles from NWP reanalysis data are taken as input, and their interpolated profiles to fine-grained heights are used as pseudo ground truth to minimize the prediction error. For example, 10-layer data from NWP are input to KAN, and it is trained to predict temperature values at 100 layers (with 50 m interval).

[0143] Second stage (fine-tuning): at the observation points of radiosonde / lidar, the control point parameters of the spline function are adjusted to optimize the capture of high-resolution details, taking the observed data as ground truth. Due to the high efficiency of KAN parameters (e.g. only 10-20 control points are needed for each spline function), it can effectively deal with data sparsity.

[0144] KAVAP model can be used as a data assimilation tool, inspired by the idea of "Kolmogorov-Arnold Neural Interpolator" (KANI), to correct systematic biases in NWP through sparse observations. For example, when NWP predicts a temperature of 280 K at z=1000 m, but the radiosonde observation is 278 K, KAN can adjust the local spline function (correct the control point parameters in the corresponding height interval) to make the output fit the observation at that height, while maintaining the physical continuity of the overall profile.

[0145] 3. Verification of KAVAP model combining quantitative and qualitative methods:

[0146] Quantitative evaluation: Mean Squared Error (MSE): ;

[0147] where N is the number of observation points, is the KAVAP prediction value, is the radiosonde / lidar observation value.

[0148] Mean Absolute Error (MAE): . ​

[0149] Qualitative verification: Physical consistency check: Verify if the output profile satisfies basic laws, e.g. troposphere temperature decreases with height , stratosphere temperature increases with height , wind speed does not have non-physical jumps , based on atmospheric turbulent diffusion limit.

[0150] Scientific interpretability: Visualize the spline function , e.g. analyze the slope of the spline curve for "850 hPa temperature -> hidden layer 1", verify if it is consistent with the physical expectation that "low-level temperature rise will lead to temperature rise in the upper boundary layer".

[0151] Benchmark: Compare with traditional methods (linear interpolation, cubic spline interpolation) and MLP models, e.g. linear interpolation may calculate temperature at m as (288+280) / 2=284K, while KAVAP model learns the physical relationship and outputs closer to the observed 285.3K.

[0152] The inherent interpretability (non-post hoc) of KAN network is reflected in:

[0153] The spline function form directly reflects the physical relationship, e.g. if the spline function for "wind speed -> output layer" has an inflection point at V=10m / s, it may correspond to the critical value of boundary layer wind shear.

[0154] By pruning spline functions with small contributions (e.g. functions with control point absolute value less than 10 -3 ), the model can be simplified and the core physical processes can be highlighted, e.g. it is found that "700 hPa humidity" has a much higher weight on the tropopause temperature than other layers, revealing the vertical correlation of a specific meteorological system.

[0155] Further, the business feasibility analysis of the above scheme includes: although the derivative calculation of spline function is slightly more complex than matrix multiplication of MLP during KAN network training, the parameter efficiency reduces the total calculation amount. For example, a KAVAP model processing 50-layer NWP input, the total parameters (control points + bias terms) are about 10 4 , much less than the 10 6 parameters of an MLP with the same performance. In the inference stage, the fast evaluation of spline function (through pre-computed basis function table) can achieve millisecond-level response, suitable for embedding into business processes as NWP post-processing module to improve vertical resolution at low cost.

[0156] Based on the same inventive concept, the present application also provides a KAN network-based vertical atmospheric profile fine-grained processing system for implementing the above-mentioned KAN network-based vertical atmospheric profile fine-grained processing method. The implementation scheme for solving the problem provided by the system is similar to the implementation scheme described in the above-mentioned embodiment method, so the specific limitations in one or more KAN network-based vertical atmospheric profile fine-grained processing system embodiments provided below can refer to the limitations of the KAN network-based vertical atmospheric profile fine-grained processing method described above, and will not be repeated here.

[0157] In one embodiment, the KAN network-based vertical atmospheric profile fine-grained processing system provided by the present application embodiment includes a data acquisition module 210, a processing module 220, a constraint condition definition module 230, a training module 240, and a result output module 250, as shown in Figure 2

[0158] The data acquisition module 210 is configured to acquire input data of the KAN network, and the input data includes output of the NWP model on the coarse-grained vertical layer.

[0159] The processing module 220 is configured to perform nonlinear mapping on the input data by using the B-spline function in the KAN network, and learn the control point parameters and the bias term of the B-spline function.

[0160] The constraint condition definition module 230 is configured to introduce physical knowledge constraints in the KAN network, and constrain the output of the KAN network by converting atmospheric physical laws into constraint terms of the loss function.

[0161] The training module 240 is configured to define the control point parameters and the bias term of the B-spline function as training parameters of the KAN network, and perform stage-by-stage training on the training parameters of the KAN network by using a pre-defined stage-by-stage training strategy.

[0162] The result output module 250 is configured to output an atmospheric variable function in a continuous height range by using the trained KAN network, and convert the coarse-grained atmospheric vertical profile into a high-resolution continuous vertical profile.

[0163] In one embodiment, an electronic device, which can be a terminal, is provided, and an internal structure diagram of the electronic device can be as shown in Figure 3 ​As shown. The electronic device includes a processor, memory, communication interface, display screen, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements the fine-grained vertical atmospheric profile processing method based on the KAN network as described in any of steps S101 to S105. The display screen can be a liquid crystal display or an e-ink display. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the device's casing, or an external keyboard, touchpad, or mouse.

[0164] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0165] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0166] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0167] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the flow Figure 1 one or more flow or block Figure 1 one or more blocks or blocks specified in the flow.

[0168] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions that are executed on the computer or other programmable apparatus provide steps for implementing the flow Figure 1 one or more flow or block Figure 1 one or more blocks or blocks specified in the flow.

[0169] The above merely provides an embodiment of the present application, but is not intended to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the scope of the claims of the present application.

Claims

1. A vertical atmospheric profile fine-grained processing method based on KAN network, characterized in that, The method comprises: obtaining input data of the KAN network; the input data comprises output of an NWP model on coarse-grained vertical layers; nonlinearly mapping the input data through a B-spline function in the KAN network to learn control point parameters and bias terms of the B-spline function; introducing a physical knowledge constraint in the KAN network to constrain the output of the KAN network by converting atmospheric physical laws into a constraint term of a loss function; defining the control point parameters and bias terms of the B-spline function as training parameters of the KAN network, and training the training parameters of the KAN network in stages by using a pre-defined training strategy in stages; outputting an atmospheric variable function in a continuous height range by using the trained KAN network to convert coarse-grained atmospheric vertical profiles into high-resolution continuous vertical profiles; the pre-defined training strategy in stages comprises: in a pre-training stage, using NWP reanalysis data and pseudo-true values thereof as training samples to learn a mapping relationship from coarse-grained to fine-grained; the NWP reanalysis data comprises vertical profile data of a specific horizontal resolution and a specific time resolution; using coarse-grained atmospheric vertical profile data of the NWP reanalysis data as input data of the KAN network, and using profile data obtained by interpolating the coarse-grained atmospheric vertical profile data to a fine-grained height as pseudo-true values; pre-training control point parameters and bias terms in the KAN network by minimizing errors between predicted values of the KAN network and the pseudo-true values; in a fine-tuning stage, using real observation profile data as training data; the real observation profile data comprises sounding data and lidar data; inputting coarse-grained atmospheric vertical profiles of an NWP model into the pre-trained KAN network to adjust control point parameters of a B-spline function in the KAN network by taking minimizing errors between predicted values of the KAN network and real observation values as an objective.

2. The method of claim 1, wherein, The input data of the KAN network comprises: receiving output data, auxiliary input data and physical prior data output by each coarse-grained vertical layer of an NWP model; wherein the output data comprises coarse-grained atmospheric vertical profiles and vertical coordinate parameters corresponding to each coarse-grained vertical layer; the auxiliary input data comprises surface auxiliary information; and the physical prior data comprises physical prior variables; using the coarse-grained atmospheric vertical profiles, the vertical coordinate parameters corresponding to each coarse-grained vertical layer, the surface auxiliary information and the physical prior variables as input data of the KAN network.

3. The method of claim 2, wherein, The coarse-grained atmospheric vertical profiles comprise: temperature profiles, wind speed profiles and relative humidity profiles; The vertical coordinate parameters comprise: air pressure and potential height; The surface auxiliary information comprises: surface terrain height and surface temperature; The physical prior variables comprise potential temperature, which is calculated from temperature, air pressure, dry air gas constant and constant-pressure specific heat capacity.

4. The method of claim 2, wherein, The KAN network comprises an input layer, a hidden layer, an output layer and a B-spline function constituting interlayer connection. The number of nodes of the input layer matches the dimension of the input data; the connections between the input nodes and the hidden nodes, and between the hidden nodes and the output nodes are all composed of B-spline functions; the B-spline function is a k-order B-spline, the node vector of which covers the physical value interval of the corresponding input variable, and the node interval is set according to the vertical sensitivity difference of the input variable; The output layer is configured to output continuous values of a single atmospheric variable at any target height.

5. The method of claim 1, wherein, The constraint term of the loss function converted from the atmospheric physical law comprises: reading the atmospheric physical law describing the hydrostatic equilibrium law in the vertical direction of the atmosphere and the adiabatic change rule of the potential temperature in the vertical movement of the atmosphere; calculating the derivative term corresponding to the hydrostatic equilibrium law and the adiabatic change rule of the potential temperature through the continuous derivative characteristics of the B-spline function, and incorporating the derivative term as a constraint term into the loss function to obtain the constraint term in the loss function of the KAN network training; The loss function comprises: a prediction error loss, a hydrostatic equilibrium constraint loss, and a potential temperature adiabatic change constraint loss. The constraint term of the loss function comprises: a hydrostatic equilibrium constraint defined based on the derivative of the air pressure with respect to the height, and a potential temperature adiabatic change constraint defined based on the derivative of the potential temperature with respect to the height.

6. The method of claim 5, wherein, The calculation of the derivative term corresponding to the hydrostatic equilibrium law and the adiabatic change rule of the potential temperature comprises: obtaining the derivative of the air pressure with respect to the height and the derivative of the potential temperature with respect to the height by calculating the first derivative of the k-order B-spline function; wherein the first derivative of the k-order B-spline function is a linear combination of k-1 order spline functions.

7. The method of claim 1, wherein, The atmospheric variable function comprises temperature, wind speed, and relative humidity, and a plurality of KAN sub-networks can be called in parallel for the same input to output different variables.

8. A vertical atmospheric profile fine-grained processing system based on KAN network, characterized in that, The system comprises: a data acquisition module configured to acquire input data of the KAN network; the input data comprises output of an NWP model on a coarse-grained vertical layer; a processing module configured to perform nonlinear mapping on the input data through the B-spline function in the KAN network, and learn control point parameters and bias terms of the B-spline function; a constraint condition definition module configured to introduce physical knowledge constraints in the KAN network, and constrain the output of the KAN network by converting the atmospheric physical law into a constraint term of the loss function; a training module configured to define the control point parameters and the bias terms of the B-spline function as training parameters of the KAN network, and perform stage-by-stage training on the training parameters of the KAN network by using a pre-defined stage-by-stage training strategy; the pre-defined stage-by-stage training strategy comprises: in a pre-training stage, using NWP reanalysis data and pseudo ground truth as training samples to learn the mapping relationship from coarse-grained to fine-grained; the NWP reanalysis data comprises vertical profile data with a specific horizontal resolution and a specific time resolution; using coarse-grained atmospheric vertical profile data of the NWP reanalysis data as input data of the KAN network, and using profile data obtained by interpolating the coarse-grained atmospheric vertical profile data to fine-grained height as pseudo ground truth; pre-training the control point parameters and the bias terms in the KAN network by minimizing the error between the prediction value of the KAN network and the pseudo ground truth; In the fine-tuning stage, real observation profile data is used as training data; the real observation profile data includes sounding data and lidar data; the coarse-grained atmospheric vertical profile of the NWP model is input into the pre-trained KAN network, and the control point parameters of the B-spline function in the KAN network are adjusted to minimize the error between the predicted value of the KAN network and the real observation value; The result output module is configured to output an atmospheric variable function in a continuous height range by using the trained KAN network, and convert the coarse-grained atmospheric vertical profile into a high-resolution continuous vertical profile.

9. An electronic device, comprising: The electronic device includes: at least one processor; and a memory connected to the at least one processor in communication; wherein The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the method of any one of claims 1-7.

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