Chaotic sequence prediction method and meteorological prediction method based on fractional order ordinary differential neural network

Abstract

The invention discloses a chaotic sequence prediction method based on a fractional order ordinary differential neural network. The method comprises the following steps: selecting a fractional order chaotic system; obtaining corresponding input-output data and constructing a training data set; selecting a neural network to construct a chaotic sequence prediction initial model, and training to obtain a chaotic sequence prediction model; and adopting the obtained chaos sequence prediction model to predict continuous chaos sequences. The invention also discloses a meteorological prediction method comprising the chaotic sequence prediction method based on the fractional order ordinary differential neural network. Through the design, implementation and training of the neural network, not only is the prediction of the chaotic sequence and the meteorological prediction realized, but also the reliability is higher, the accuracy is better, and the interpretability is better.

Description

Technical Field

[0001] The present invention belongs to the field of digital signal processing, and particularly relates to a chaotic sequence prediction method and a meteorological prediction method based on a fractional-order ordinary differential neural network. Background Art

[0002] A large number of literature studies have shown that in the fields of laser communication, load prediction in power systems, data analysis in the financial industry, weather prediction, etc., chaotic nonlinear behaviors exist in the systems. Therefore, the analysis of chaotic characteristics and the prediction of evolution in the corresponding systems are of great significance.

[0003] Due to the high initial value sensitivity, nonlinearity, and long-term unpredictability of chaotic sequences, the analysis of the evolution prediction of chaotic sequences has become an extremely difficult task. At present, the prediction schemes for chaotic sequences usually adopt traditional machine learning methods, such as multi-layer perceptron (MLP), recurrent neural network (RNN), variant long short-term memory network (LSTM), and gated recurrent unit (GRU), etc. Although such prediction schemes have achieved certain effects, there are also some problems: these chaotic sequence prediction schemes based on traditional machine learning mostly use discrete data sets as training sets, which are difficult to handle continuous dynamic systems, and the trained models only learn the front-back correlation relationship of the sequences, and the physical meaning of the models lacks interpretability.

[0004] Similarly, in the process of meteorological prediction, due to the nonlinearity and long-term unpredictability of meteorological data, the existing meteorological prediction schemes often adopt meteorological prediction schemes based on chaotic sequence prediction. Therefore, the existing meteorological prediction schemes also have corresponding defects. Summary of the Invention

[0005] One of the purposes of the present invention is to provide a chaotic sequence prediction method based on a fractional-order ordinary differential neural network with high reliability, good accuracy, and good interpretability.

[0006] Another purpose of the present invention is to provide a meteorological prediction method including the chaotic sequence prediction method based on the fractional-order ordinary differential neural network.

[0007] The chaotic sequence prediction method based on the fractional-order ordinary differential neural network provided by the present invention includes the following steps:

[0008] S1. Select a fractional-order chaotic system;

[0009] S2. According to the fractional-order chaotic system selected in step S1, obtain the corresponding input-output data and construct a training data set;

[0010] S3. Select a neural network to construct an initial model for chaotic sequence prediction;

[0011] S4. Use the training data set obtained in step S2 to train the initial chaotic sequence prediction model constructed in step S3 to obtain a chaotic sequence prediction model;

[0012] S5. Use the chaotic sequence prediction model obtained in step S4 to predict continuous chaotic sequences.

[0013] The selected fractional-order chaotic system described in step S1 includes the following steps:

[0014] The selected fractional-order chaotic systems include 2-scroll fractional-order Chua chaotic system, fractional-order Lorenz system, fractional-order JerK system, and fractional-order Chen system.

[0015] The described step S1 specifically includes the following steps:

[0016] Select the fractional-order chaotic system as the 2-scroll fractional-order Chua chaotic system;

[0017] The 2-scroll fractional-order Chua chaotic system is expressed as

[0018]

[0019] where is the fractional-order first differential operator; α is the first parameter; y is the second state variable varying with time t; h(x) is a non-linear function, and h(x) = k·p·tanh(n·x), k is the third parameter, p is the fourth parameter, n is the fifth parameter, and x is the first state variable varying with time t; is the fractional-order second differential operator; z is the third state variable varying with time t; is the fractional-order third differential operator; β is the second parameter.

[0020] The step S2 of obtaining the corresponding input-output data according to the fractional-order chaotic system selected in step S1 and constructing a training data set specifically includes the following steps:

[0021] Based on the Adomian algorithm, solve the fractional-order chaotic system selected in step S1 to obtain the continuous evolution state (x, y, z) of the chaotic sequence corresponding to the target value and the derivative values of the corresponding continuous fractional-order differential operators at the corresponding state (x, y, z) to form the corresponding training data set; where the mapping behavior characterizes the dynamic equation of the corresponding fractional-order chaotic system.

[0022] The step S3 of selecting a neural network to construct an initial chaotic sequence prediction model includes the following steps:

[0023] Selected neural networks, including an N-layer fully connected layer model, an LSTM model, a Transformer model, and a CNN model.

[0024] The step S3 specifically includes the following steps:

[0025] Select a 2-layer fully connected layer model to construct an initial model for chaotic sequence prediction;

[0026] The 2-layer fully connected layer model includes an input layer, a first fully connected layer, a second fully connected layer, and an output layer connected in series in sequence; among them, the first fully connected layer includes a first linear transformation layer and a first activation function layer; the second fully connected layer includes a second linear transformation layer and a second activation function layer;

[0027] The input layer is used to receive an input of n x elements;

[0028] The first linear transformation layer is used to perform a linear transformation on the data of the input layer to learn the linear combination features of the input data; the first linear transformation layer includes n h neurons, which are used to map the input n x elements to an n h -dimensional feature space;

[0029] The first activation function layer uses the hyperbolic tangent function tanh as the activation function, so as to perform a non-linear transformation on the output of the first linear transformation layer and map it to the interval (-1, 1); the first activation function layer is used to introduce non-linearity into the model, so that the model can learn more complex non-linear features;

[0030] The second linear transformation is used to perform a linear transformation on the data output by the first activation function layer to extract higher-level feature representations; the second linear transformation layer includes n h neurons, which are used to transform the data output by the first activation function layer in the n h -dimensional feature space;

[0031] The second activation function layer uses the hyperbolic tangent function tanh as the activation function, so as to perform a non-linear transformation on the output of the second linear transformation layer and enhance the non-linear features of the model;

[0032] The output layer adopts a fully connected layer structure and is used to output n y derivative values.

[0033] The training described in step S4 specifically includes the following steps:

[0034] Use the following formula as the loss function:

[0035]

[0036] where L is the value of the loss function; m is the dimension of the output layer; is the output value of the model output layer; y i is the learning target value of the training set (the fractional derivative value of the data set);

[0037] During training, the forward propagation process is expressed as

[0038] First fully connected layer: where z1 is the output value of the linear transformation of the first fully connected layer, W1 is the weight of the linear transformation process of the first fully connected layer, b1 is the bias of the linear transformation of the first fully connected layer, a1 is the output value of the first activation layer, and σ() is the tanh() function;

[0039] Second fully connected layer: where z2 is the output value of the linear transformation of the second fully connected layer, W2 is the weight of the linear transformation process of the second fully connected layer, b2 is the bias of the linear transformation of the second fully connected layer, and a2 is the output value of the second activation layer;

[0040] Output layer: where z3 is the output value of the linear transformation of the output layer, W3 is the weight of the output layer, b3 is the bias of the output layer, σ2() is the straight-through process, expressed as σ2(z3) = z3, and a3 is the output value of the output layer;

[0041] Then calculate the loss function value L, and perform L2 regularization to prevent overfitting. At the same time, use the backpropagation algorithm to calculate the gradient of the loss function with respect to each weight and bias and

[0042] Update parameters:

[0043] Update the weights and biases using the following equations:

[0044]

[0045] where W i ' is all the weights of the updated model; W i is all the weights of the model before update; γ is the learning rate; b i ' is the updated bias; b i is the bias before update; i is the index of all weights and biases;

[0046] Repeat the training process until the set stop condition is met; finally, obtain the trained weights and biases to complete the training of the model.

[0047] Using the chaotic sequence prediction model obtained in step S4 as described in step S5, perform continuous chaotic sequence prediction, specifically including the following steps:

[0048] Select the initial value as the input of the chaotic sequence prediction model obtained in step S4;

[0049] Input the initial value into the chaotic sequence prediction model, and through forward processing, obtain the output of the corresponding chaotic sequence prediction model;

[0050] Adopt the output of the chaotic sequence prediction model to further obtain the evolution value of the next sequence;

[0051] Take the obtained evolution value as the input of the new chaotic sequence prediction model and continuously iterate to realize the prediction of continuous chaotic sequences.

[0052] The present invention also provides a weather prediction method including the chaotic sequence prediction method based on the fractional-order ordinary differential neural network, which includes the following steps:

[0053] A. Obtain the historical weather data information of the target location;

[0054] B. Perform data cleaning and feature extraction on the weather data information obtained in step A to obtain the evolution value of the system state sequence and the corresponding derivative value, and form the training set of the model;

[0055] C. Use the training set obtained in step B to train the chaotic sequence prediction model in the chaotic sequence prediction method based on the fractional-order ordinary differential neural network to obtain a weather prediction model;

[0056] D. Use the weather prediction model obtained in step C to predict the weather state;

[0057] E. Take the prediction result obtained in step D as the final weather prediction result of the target location.

[0058] The chaotic sequence prediction method and weather prediction method based on the fractional-order ordinary differential neural network provided by the present invention, through the design, implementation and training of the neural network, not only realize the prediction of chaotic sequences and weather prediction, but also have higher reliability, better accuracy and better interpretability. Brief Description of the Drawings

[0059] Figure 1 It is a schematic diagram of the method flow of the prediction method of the present invention.

[0060] Figure 2 It is a schematic diagram of the phase diagram of the 2-scroll attractor of the fractional-order Chua chaotic system of the prediction method of the present invention.

[0061] Figure 3 It is a schematic diagram of the prediction effect of the prediction method of the present invention.

[0062] Figure 4 It is a schematic diagram of the method flow of the weather prediction method of the present invention. Specific implementation manner

[0063] As Figure 1 shown in the schematic diagram of the method flow of the prediction method of the present invention: This chaotic sequence prediction method based on a fractional-order ordinary differential neural network disclosed by the present invention includes the following steps:

[0064] S1. Select a fractional-order chaotic system; including the following steps:

[0065] The selected fractional-order chaotic systems include a 2-scroll fractional-order Chua chaotic system, a fractional-order Lorenz system, a fractional-order JerK system, a fractional-order Chen system, etc.;

[0066] In specific implementation, the selected fractional-order chaotic system is a 2-scroll fractional-order Chua chaotic system;

[0067] The 2-scroll fractional-order Chua chaotic system is expressed as

[0068]

[0069] In the formula is the fractional-order first differential operator; α is the first parameter (preferably 10); y is the second state variable that changes with time t; h(x) is a non-linear function, and h(x)=k·p·tanh(n·x), k is the third parameter (preferably 0.4), p is the fourth parameter (preferably 25), n is the fifth parameter (preferably 5), and x is the first state variable that changes with time t; is the fractional-order second differential operator; z is the third state variable that changes with time t; is the fractional-order third differential operator; β is the second parameter (preferably -16);

[0070] The attractor phase diagram of the 2-scroll fractional-order Chua chaotic system is as Figure 2 shown;

[0071] S2. According to the fractional-order chaotic system selected in step S1, obtain the corresponding input-output data and construct a training data set; specifically including the following steps:

[0072] Based on the Adomian algorithm, solve the fractional-order chaotic system selected in step S1 to obtain the continuous evolution state (x, y, z) of the target value corresponding chaotic sequence and the derivative value of the corresponding continuous fractional-order differential operator at the corresponding state (x, y, z) to form the corresponding training data set; where The mapping behavior of characterizes the dynamic equation of the corresponding fractional-order chaotic system;

[0073] S3. Select a neural network to construct an initial model for chaotic sequence prediction; the steps are as follows:

[0074] The selected neural network includes an N-layer fully connected layer model, an LSTM model, a Transformer model, a CNN model, etc.;

[0075] Specifically, when implementing, select a 2-layer fully connected layer model to construct an initial model for chaotic sequence prediction;

[0076] The 2-layer fully connected layer model includes an input layer, a first fully connected layer, a second fully connected layer, and an output layer connected in series in sequence; among them, the first fully connected layer includes a first linear transformation layer and a first activation function layer; the second fully connected layer includes a second linear transformation layer and a second activation function layer;

[0077] The input layer is used to receive an input of n x elements;

[0078] The first linear transformation layer is used to perform a linear transformation on the data of the input layer to learn the linear combination features of the input data; the first linear transformation layer includes n h (preferably 4096) neurons, which are used to map the input of n x (preferably 3) elements to an n h -dimensional feature space;

[0079] The first activation function layer uses the hyperbolic tangent function tanh as the activation function, so as to perform a non-linear transformation on the output of the first linear transformation layer and map it to the interval (-1, 1); the first activation function layer is used to introduce non-linearity into the model, enabling the model to learn more complex non-linear features;

[0080] The second linear transformation is used to perform a linear transformation on the data output by the first activation function layer to extract higher-level feature representations; the second linear transformation layer includes n h (preferably 4096) neurons, which are used to transform the data output by the first activation function layer in the n h -dimensional feature space;

[0081] The second activation function layer uses the hyperbolic tangent function tanh as the activation function, so as to perform a non-linear transformation on the output of the second linear transformation layer and enhance the non-linear features of the model;

[0082] The output layer adopts a fully connected layer structure and is used to output n y derivative values;

[0083] S4. Use the training data set obtained in step S2 to train the initial model for chaotic sequence prediction constructed in step S3 to obtain a chaotic sequence prediction model;

[0084] The training process specifically includes the following steps:

[0085] The following formula is used as the loss function:

[0086]

[0087] In the formula, L is the value of the loss function; m is the dimension of the output layer; is the output value of the model's output layer; y i is the learning target value of the training set (the fractional derivative value of the data set);

[0088] During training, the forward propagation process is expressed as

[0089] The first fully connected layer: where z1 is the output value of the linear transformation of the first fully connected layer, W1 is the weight for the linear transformation process of the first fully connected layer, b1 is the bias of the linear transformation of the first fully connected layer, a1 is the output value of the first activation layer, and σ() is the tanh() function;

[0090] The second fully connected layer: where z2 is the output value of the linear transformation of the second fully connected layer, W2 is the weight for the linear transformation process of the second fully connected layer, b2 is the bias of the linear transformation of the second fully connected layer, and a2 is the output value of the second activation layer;

[0091] The output layer: where z3 is the output value of the linear transformation of the output layer, W3 is the weight of the output layer, b3 is the bias of the output layer, σ2() is the straight-through process, expressed as σ2(z3) = z3, and a3 is the output value of the output layer;

[0092] Then calculate the loss function value L, and perform L2 regularization (the regularization coefficient is 0.05) to prevent overfitting. At the same time, use the backpropagation algorithm to calculate the gradients of the loss function with respect to each weight and bias and

[0093] Update the parameters:

[0094] The following formula is used to update the weights and biases:

[0095]

[0096] In the formula, W i ' is all the weights of the updated model; W i is all the weights of the model before update; γ is the learning rate; b i ' is the updated bias; b i is the bias before update; i is the index of all weights and biases;

[0097] Repeat the training process until the set stop condition is met; finally, obtain the trained weights and biases to complete the training of the model;

[0098] S5. Use the chaotic sequence prediction model obtained in step S4 to predict continuous chaotic sequences; specifically, it includes the following steps:

[0099] Select the initial value (preferably (0.3, 0.5, 0.05)) as the input of the chaotic sequence prediction model obtained in step S4;

[0100] Input the initial value into the chaotic sequence prediction model, and through forward processing, obtain the output of the corresponding chaotic sequence prediction model;

[0101] Use the output of the chaotic sequence prediction model to obtain the evolution value of the next sequence;

[0102] Take the obtained evolution value as the input of the new chaotic sequence prediction model and continuously iterate to achieve the prediction of continuous chaotic sequences.

[0103] The following combines an embodiment to illustrate the prediction method of the present invention:

[0104] Existing solutions, such as the solution proposed by researchers such as Inoue H in the paper "Efficient hybrid neural network for chaotic time series prediction", can only predict chaotic sequences for more than 2200 time steps;

[0105] And the prediction effect of the solution of the present invention is as Figure 3 shown; through Figure 3 It can be seen that the method of the present invention can accurately predict chaotic sequences for at least about more than 12000 time steps. Therefore, the prediction effect of the present invention is better, and both the accuracy and reliability are higher.

[0106] As Figure 4 shown is the schematic flow chart of the method of the meteorological prediction method of the present invention: The meteorological prediction method including the chaotic sequence prediction method based on the fractional-order ordinary differential neural network disclosed by the present invention includes the following steps:

[0107] A. Obtain the historical meteorological data information of the target location;

[0108] B. Perform data cleaning and feature extraction on the meteorological data information obtained in step A to obtain the state sequence evolution value and the corresponding derivative value of the system, and form the training set of the model; the specific processing method is: where α is a scaling factor related to the differential order;

[0109] C. Using the training set obtained in step B, train the chaotic sequence prediction model in the chaotic sequence prediction method based on the fractional-order ordinary differential neural network to obtain a weather prediction model;

[0110] D. Using the weather prediction model obtained in step C, predict the weather state;

[0111] E. Take the prediction result obtained in step D as the weather prediction result of the final destination.

[0112] The meteorological data information described in step A includes His = (x, y, z), where x is the convection intensity, representing the movement speed of the fluid in the vertical direction, reflecting the strength of atmospheric convection. When x > 0, it represents an updraft; when x < 0, it represents a downdraft. The larger the absolute value of x, the more intense the convective movement (such as the intense vertical airflow in a severe storm). y is the horizontal temperature difference, representing the temperature difference between the updraft and the downdraft, reflecting the temperature inhomogeneity in the horizontal direction. When y > 0, it means the updraft (warm air) is warmer than the downdraft (cold air) (positive temperature difference); when y < 0, it means the updraft (warm air) is colder than the downdraft (cold air) (negative temperature difference). z is the vertical temperature gradient, representing the change in the temperature gradient in the vertical direction, reflecting the atmospheric stability. If the temperature in the lower layer of the atmosphere is higher than that in the upper layer (large lapse rate), the vertical gradient z decreases, and the atmosphere tends to be unstable and is prone to form convection.

[0113] In addition, the chaotic sequence prediction method based on the fractional-order ordinary differential neural network provided by the present invention can also be applied to power system load prediction, financial market evolution prediction, traffic system flow state prediction, etc.

Claims

1. A method for predicting chaotic sequences based on a fractional-order ordinary differential neural network, comprising the following steps: S1. Select a fractional-order chaotic system; S2. According to the fractional-order chaotic system selected in step S1, obtain the corresponding input-output data and construct a training data set; S3. Select a neural network to construct an initial chaotic sequence prediction model; S4. Use the training data set obtained in step S2 to train the initial chaotic sequence prediction model constructed in step S3 to obtain a chaotic sequence prediction model; S5. Use the chaotic sequence prediction model obtained in step S4 to perform continuous chaotic sequence prediction.

2. The chaotic sequence prediction method based on a fractional-order ordinary differential neural network according to claim 1, wherein The step of selecting a fractional-order chaotic system in step S1 includes the following steps: The selected fractional-order chaotic systems include a 2-scroll fractional-order Chua chaotic system, a fractional-order Lorenz system, a fractional-order JerK system, and a fractional-order Chen system.

3. The chaotic sequence prediction method based on a fractional-order ordinary differential neural network according to claim 2, wherein The step S1 specifically includes the following steps: Select the 2-scroll fractional-order Chua chaotic system as the fractional-order chaotic system; The 2-scroll fractional-order Chua chaotic system is expressed as In the formula is the fractional-order first differential operator; α is the first parameter; y is the second state variable varying with time t; h(x) is a non-linear function, and h(x) = k·p·tanh(n·x), where k is the third parameter, p is the fourth parameter, n is the fifth parameter, and x is the first state variable varying with time t; is the fractional-order second differential operator; z is the third state variable varying with time t; is the fractional-order third differential operator; β is the second parameter.

4. The chaotic sequence prediction method based on the fractional-order ordinary differential neural network according to claim 3, characterized in that The step of obtaining the corresponding input-output data and constructing a training data set according to the fractional-order chaotic system selected in step S1 in step S2 specifically includes the following steps: Based on the Adomian algorithm, solve the fractional-order chaotic system selected in step S1 to obtain the continuous evolution state (x, y, z) of the chaotic sequence corresponding to the target value and the derivative value of the corresponding continuous fractional-order differential operator at the corresponding state (x, y, z). Form the corresponding training data set; among them The mapping behavior characterizes the dynamic equation of the corresponding fractional-order chaotic system.

5. The chaotic sequence prediction method based on the fractional order ordinary differential neural network according to claim 4, wherein The step of selecting a neural network to construct an initial chaotic sequence prediction model in step S3 includes the following steps: The selected neural networks include an N-layer fully connected layer model, an LSTM model, a Transformer model, and a CNN model.

6. The chaotic sequence prediction method based on a fractional-order ordinary differential neural network according to claim 5, wherein The step S3 specifically includes the following steps: Select a 2-layer fully connected layer model to construct an initial chaotic sequence prediction model; The 2-layer fully connected layer model includes an input layer, a first fully connected layer, a second fully connected layer, and an output layer connected in series in sequence; among them, the first fully connected layer includes a first linear transformation layer and a first activation function layer; the second fully connected layer includes a second linear transformation layer and a second activation function layer; The input layer is used to receive the input of n x elements; The first linear transformation layer is used to perform a linear transformation on the data of the input layer to learn the linear combination features of the input data; the first linear transformation layer includes n h neurons, which are used to map the input n x elements to an n h -dimensional feature space; The first activation function layer uses the hyperbolic tangent function tanh as the activation function to perform a non-linear transformation on the output of the first linear transformation layer and map it to the interval (-1, 1); the first activation function layer is used to introduce non-linearity into the model, enabling the model to learn more complex non-linear features; The second linear transformation is used to perform a linear transformation on the data output by the first activation function layer to extract higher-level feature representations; the second linear transformation layer includes n h neurons, which are used to transform the data output by the first activation function layer in an n h -dimensional feature space; The second activation function layer uses the hyperbolic tangent function tanh as the activation function to perform a non-linear transformation on the output of the second linear transformation layer to enhance the non-linear features of the model; The output layer adopts a fully connected layer structure and is used to output n y derivative values.

7. The chaotic sequence prediction method based on the fractional-order ordinary differential neural network according to claim 6, characterized in that The training in step S4 specifically includes the following steps: Use the following formula as the loss function: Where L is the value of the loss function; m is the dimension of the output layer; is the output value of the model's output layer; y i is the learning target value of the training set; During training, the forward propagation process is expressed as The first fully connected layer: Where z1 is the output value of the linear transformation of the first fully connected layer, W1 is the weight for the linear transformation process of the first fully connected layer, b1 is the bias of the linear transformation of the first fully connected layer, a1 is the output value of the first activation layer, and σ() is the tanh() function; Second fully connected layer: where z2 is the output value of the linear transformation of the second fully connected layer, W2 is the weight for the linear transformation processing of the second fully connected layer, b2 is the bias of the linear transformation of the second fully connected layer, and a2 is the output value of the second activation layer; Output layer: Among them, z3 is the output value of the linear transformation of the output layer, W3 is the weight of the output layer, b3 is the bias of the output layer, and σ2() is the straight-through processing, expressed as σ2(z3)=z3, and a3 is the output value of the output layer; Then calculate the loss function value L, and perform L2 regularization to prevent overfitting. At the same time, use the backpropagation algorithm to calculate the gradients of the loss function with respect to each weight and bias and Update the parameters: Update the weights and biases using the following formula: where \(W\) i ' are all the weights of the updated model; \(W\) i are all the weights of the model before the update; γ is the learning rate; b i ' is the updated bias; b i is the bias before update; i is the index of all weights and biases; Repeat the training process until the set stop condition is met; finally, obtain the trained weights and biases to complete the training of the model.

8. The chaotic sequence prediction method based on a fractional-order ordinary differential neural network according to claim 7, wherein The step of using the chaotic sequence prediction model obtained in step S4 to perform continuous chaotic sequence prediction in step S5 specifically includes the following steps: Select an initial value as the input of the chaotic sequence prediction model obtained in step S4; Input the initial value into the chaotic sequence prediction model, and through forward processing, obtain the output of the corresponding chaotic sequence prediction model; Adopt the output of the chaotic sequence prediction model to obtain the evolution value of the next sequence; Use the obtained evolution value as the input of the new chaotic sequence prediction model and continuously iterate to achieve the prediction of continuous chaotic sequences.

9. A weather prediction method comprising the chaotic sequence prediction method based on a fractional-order ordinary differential neural network according to any one of claims 1 to 8, characterized in that It includes the following steps: A. Obtain the historical meteorological data information of the target location; B. Clean and extract features from the meteorological data information obtained in step A to obtain the evolution value of the system state sequence and the corresponding derivative value, and form the training set of the model; C. Use the training set obtained in step B to train the chaotic sequence prediction model in the chaotic sequence prediction method based on the fractional-order ordinary differential neural network described in any one of claims 1 to 8 to obtain a meteorological prediction model; D. Use the meteorological prediction model obtained in step C to predict the meteorological state; E. Use the prediction result obtained in step D as the final meteorological prediction result of the target location.

Images