Train aerodynamic analysis method, device and equipment based on double-branch dynamic neural operator and medium

Abstract

The application discloses a train aerodynamic analysis method and device based on a double-branch dynamic neural operator, equipment and medium, and relates to the technical field of computers, which comprises the following steps: performing pulse coding on initial space data of a target train and using an input layer of an LSM branch in a target neural operator, converting the obtained coded pulse sequence into an input current, updating the neuron state of a liquid layer of the LSM branch, averaging and linearly mapping the obtained pulse response sequence to obtain a first target feature; obtaining a second target feature based on the initial space data and using an LSTM branch; splicing intensity indicators and quality indicators corresponding to each target feature, adjusting the first target feature and the second target feature by using a multilayer perceptron, and generating a train aerodynamic analysis result corresponding to the target train by using the obtained target fusion feature. The operator avoids high training cost and high energy consumption in a high-resolution scenario.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a method, apparatus, equipment and medium for train aerodynamics analysis based on a dual-branch dynamic neural operator. Background Technology

[0002] Current neural operator methods, such as DeepONet (Deep Operator Network), Fourier Neural Operator (FNO), and Wavelet Neural Operator (WNO), have achieved high accuracy in solving partial differential equations. However, for high-resolution problems, these operators typically require a large amount of high-fidelity training data and a significant amount of computational resources. This results in large-scale models and significant energy consumption, posing a key bottleneck to their deployment in large-scale scientific computing, resource-constrained edge devices, and energy-limited environments.

[0003] As can be seen from the above, how to avoid high training costs and high energy consumption of operators in high-resolution scenarios is an urgent problem to be solved. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a train aerodynamics analysis method, apparatus, device, and medium based on a dual-branch dynamic neural operator, which can avoid the high training cost and high energy consumption of the operator in high-resolution scenarios. The specific solution is as follows: In a first aspect, this application provides a train aerodynamics analysis method based on a dual-branch dynamic neural operator, including: Based on the initial spatial data corresponding to the target train, pulse coding is performed using the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence; the initial spatial data is the flow field spacetime tensor of the partial differential equation of train aerodynamics collected by the on-board edge device. The encoded pulse sequence is converted into an input current using a preset weight matrix. The neuron state of the liquid layer of the LSM branch is updated based on the input current to obtain the corresponding pulse response sequence. The pulse response sequence is averaged and linearly mapped to obtain the first target feature. The initial spatial data is subjected to dimensional transformation, and the transformed spatial data is input into the LSTM branch of the target neural operator to obtain the second target feature; The intensity index and quality index corresponding to the first target feature and the second target feature are determined respectively, and the first target feature and the second target feature are concatenated to obtain an analysis vector. Based on the analysis vector, a fusion weight is generated using a multilayer perceptron. The fusion weight is used to adjust the first target feature and the second target feature to obtain the query, key, and value in the attention mechanism. The intensity index is an indicator that reflects the degree of feature activation. The quality index is an indicator that reflects the credibility of the feature. Based on the query, the key, and the value, and using a cross-attention mechanism and a feature enhancer, the target fusion feature is determined, and the target neural operator is used to solve the train aerodynamic partial differential equation. Based on the obtained train aerodynamic partial differential equation solution, the train aerodynamic analysis result corresponding to the target train is generated.

[0005] Optionally, the step of performing pulse coding based on the initial spatial data corresponding to the target train and utilizing the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence includes: The initial spatial data corresponding to the target train is downsampled and flattened to obtain processed spatial data, and the processed spatial data is normalized to obtain normalized spatial data. The normalized spatial data is sequentially input into the input layer of the LSM branch in the target neural operator, so as to convert the normalized spatial data into a pulse sequence based on the input layer and using rate coding to obtain the encoded pulse sequence.

[0006] Optionally, the step of converting the encoded pulse sequence into an input current using a preset weight matrix, and updating the neuron state of the liquid layer of the LSM branch based on the input current to obtain a corresponding pulse response sequence, includes: The encoded pulse sequence is converted into an input current using a preset weight matrix. The target synaptic current for the next time step is determined based on the current input current at the current time step, the current synaptic current at the current time step, and a first preset attenuation coefficient. The target membrane potential for the next time step is determined based on the target synaptic current, the current membrane potential at the current time step, the second preset attenuation coefficient, and the recursive feedback input data inside the liquid layer; the recursive feedback input data is a signal obtained by feedback based on the current pulse situation at the current time step and using a preset recursive connection weight matrix. Determine whether the target membrane potential is greater than the target threshold; If it is greater than the target threshold, then the target pulse condition for the next time step is to generate a pulse; If it is not greater than the target threshold, then the target pulse condition for the next time step is no pulse generated; The next input current corresponding to the next time step in the input current is determined as the new current input current, the target synaptic current is determined as the new current synaptic current, the target membrane potential is determined as the new current membrane potential, and the target pulse condition is determined as the new current pulse condition. Then, the process jumps to the step of determining the target synaptic current of the next time step based on the current input current of the current time step, the current synaptic current of the current time step, and the first preset attenuation coefficient, until all time steps in the input current are updated to obtain each target pulse condition. The pulse conditions are then spliced ​​together in chronological order to obtain the corresponding pulse response sequence.

[0007] Optionally, the step of performing a dimensionality transformation on the initial spatial data and inputting the resulting transformed spatial data into the LSTM branch of the target neural operator to obtain the second target feature includes: The initial spatial data is flattened to obtain flattened spatial data, and the flattened spatial data is then subjected to dimensional transformation to obtain transformed spatial data. The transformed spatial data is input into the LSTM branch of the target neural operator to obtain the output result of the last time step; The output is linearly mapped to obtain the second target feature.

[0008] Optionally, the step of determining the intensity index and quality index corresponding to the first target feature and the second target feature respectively, concatenating the first target feature and the second target feature to obtain an analysis vector, generating fusion weights based on the analysis vector using a multilayer perceptron, and adjusting the first target feature and the second target feature using the fusion weights to obtain the query, key, and value in the attention mechanism includes: Determine the first intensity index and the first quality index corresponding to the first target feature, and determine the second intensity index and the second quality index corresponding to the second target feature; The characteristics, intensity indicators, and quality indicators of each target are concatenated to obtain the analysis vector; The analysis vector is input into a multilayer perceptron to obtain the first weight corresponding to the LSM branch, the second weight corresponding to the LSTM branch, and the attention weight; The first target feature and the second target feature are adjusted using the first weight and the second weight respectively to obtain the first adjusted feature and the second adjusted feature; The first adjusted feature is converted into a query in the attention mechanism based on the first preset linear layer, and the second adjusted feature is converted into a key and a value using the second preset linear layer and the third preset linear layer.

[0009] Optionally, determining the target fusion feature of the output based on the query, the key, and the value, and utilizing a cross-attention mechanism and a feature enhancer, includes: Determine the similarity score between the query and the key, and normalize the similarity score to obtain a normalized score; Based on the normalized score and the value, attention enhancement features are determined, and the attention enhancement features are mapped to the target dimension to obtain the target attention features; Based on the target attention features and using a feature enhancer to determine the enhanced features, the enhanced features, the attention weights, the first adjusted features, and the second adjusted features are used to determine the fused features; Based on the fused features, the target attention features are mapped using the output mapping layer of the target neural operator. The obtained mapping results are then used to perform residual connections and layer normalization with the fused features to obtain the target fused features.

[0010] Optionally, the training process of the target neural operator includes: The target loss function is determined based on the average relative error between the target fusion features and the target true features; The target neural operator is obtained by training and optimization based on the target loss function and by using backpropagation and gradient pruning.

[0011] Secondly, this application provides a train aerodynamics analysis device based on a dual-branch dynamic neural operator, comprising: The pulse coding module is used to perform pulse coding based on the initial spatial data corresponding to the target train and using the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence; the initial spatial data is the flow field spacetime tensor of the partial differential equation of train aerodynamics collected by the on-board edge device; The response sequence mapping module is used to convert the encoded pulse sequence into an input current using a preset weight matrix, update the neuron state of the liquid layer of the LSM branch based on the input current to obtain the corresponding pulse response sequence, and perform averaging and linear mapping on the pulse response sequence to obtain the first target feature. The spatial data transformation module is used to perform dimensional transformation on the initial spatial data and input the transformed spatial data into the LSTM branch in the target neural operator to obtain the second target feature; The feature adjustment module is used to determine the intensity index and quality index corresponding to the first target feature and the second target feature, respectively, and to concatenate the first target feature and the second target feature to obtain an analysis vector. Based on the analysis vector, a fusion weight is generated using a multilayer perceptron. The fusion weight is used to adjust the first target feature and the second target feature to obtain the query, key, and value in the attention mechanism. The intensity index is an indicator reflecting the degree of feature activation; the quality index is an indicator reflecting the credibility of the feature. The target feature determination module is used to determine the output target fusion features based on the query, the key, and the value, using a cross-attention mechanism and a feature enhancer, and to use the target fusion features to complete the solution of the train aerodynamic partial differential equation by the target neural operator, so as to generate the train aerodynamic analysis result corresponding to the target train based on the obtained solution result of the train aerodynamic partial differential equation.

[0012] Thirdly, this application provides an electronic device, comprising: Memory, used to store computer programs; A processor is used to execute the computer program to implement the aforementioned train aerodynamics analysis method based on a dual-branch dynamic neural operator.

[0013] Fourthly, this application provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned train aerodynamics analysis method based on a dual-branch dynamic neural operator.

[0014] This application uses initial spatial data corresponding to the target train and performs pulse coding on the input layer of the LSM branch in the target neural operator to obtain a coded pulse sequence. The initial spatial data is the flow field spatiotemporal tensor of the partial differential equation of train aerodynamics acquired by an onboard edge device. The coded pulse sequence is converted into an input current using a preset weight matrix. The neuron state of the liquid layer of the LSM branch is updated based on the input current to obtain a corresponding pulse response sequence. The pulse response sequence is averaged and linearly mapped to obtain a first target feature. The initial spatial data is dimensionally transformed, and the transformed spatial data is input into the LSTM branch in the target neural operator to obtain a second target feature. The intensity index and quality index corresponding to the first target feature and the second target feature are determined respectively, and the first target feature and the second target feature are concatenated to obtain an analysis vector. Based on the analysis vector, a fusion weight is generated using a multilayer perceptron. The fusion weight is used to adjust the first target feature and the second target feature to obtain the query, key, and value in the attention mechanism. The intensity index is an indicator reflecting the degree of feature activation. The quality index is an indicator reflecting the credibility of the feature. Based on the query, the key, and the value, the target fusion feature is determined using a cross-attention mechanism and a feature enhancer. The target fusion feature is then used to complete the solution of the train aerodynamic partial differential equation by the target neural operator.

[0015] As shown above, this application utilizes the input layer of the LSM branch in the target neural operator for pulse coding, and uses a weight matrix to convert the encoded sequence into an input current to update the neuron state of the liquid layer of the LSM branch frame by frame, thereby obtaining the first target feature. Then, the LSTM branch is used to capture long-term dependencies to obtain the second target feature. By calculating the intensity and quality indices of the two branch features, the analysis vector is concatenated and then a multilayer perceptron is used to generate fusion weights. In this way, the target features are adjusted using the fusion weights, and the target fusion features are generated through an attention mechanism and a feature enhancer. The target fusion features are then used to solve the partial differential equations of train aerodynamics, resulting in high-precision, low-latency flow field prediction results. Furthermore, adaptive and stable training is performed for various complex working conditions, reducing training costs and energy consumption. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 This is a flowchart of a train aerodynamics analysis method based on a dual-branch dynamic neural operator disclosed in this application; Figure 2 This is a schematic diagram of a target neural operator structure disclosed in this application; Figure 3 This is a schematic diagram of an LSM branch structure disclosed in this application; Figure 4 This is a schematic diagram of an LSTM branch structure disclosed in this application; Figure 5 This is a schematic diagram of a train aerodynamics analysis device based on a dual-branch dynamic neural operator disclosed in this application. Figure 6 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Currently, neural operator methods for high-resolution problems typically require large amounts of high-fidelity training data and significant computational resources, resulting in large model sizes and substantial energy consumption. This poses a critical bottleneck to their deployment in large-scale scientific computing, resource-constrained edge devices, and energy-limited environments. To address this, this application presents a train aerodynamics analysis method based on a bi-branch dynamic neural operator. It adjusts target features using fusion weights and generates target fusion features through an attention mechanism and feature enhancer. These fusion features are then used to solve the partial differential equations of train aerodynamics, yielding highly accurate and low-latency flow field prediction results. Furthermore, adaptive and stable training is performed for various complex operating conditions, reducing training costs and energy consumption.

[0020] See Figure 1 As shown, this invention discloses a train aerodynamics analysis method based on a dual-branch dynamic neural operator, comprising: Step S11: Based on the initial spatial data corresponding to the target train, pulse coding is performed using the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence; the initial spatial data is the flow field spatiotemporal tensor of the partial differential equation of train aerodynamics collected by the on-board edge device.

[0021] The partial differential equation used in this embodiment is the Burgers equation, and the data dimensions involved are also based on the dataset of this equation. Figure 2 This is a schematic diagram of a target neural operator structure, including an LSM (Liquid State Machine) branch and an LSTM (Long Short-Term Memory) branch. Figure 3 LSM branch structure diagram and Figure 4 A schematic diagram of the LSTM branch structure is shown. The initial spatial data is a spatiotemporal sampling tensor characterizing the physical scene corresponding to the partial differential equation. In the train scenario, the initial spatial data is the flow field distribution data of the train aerodynamic partial differential equation collected by the onboard edge device, i.e., a three-dimensional flow field spatiotemporal tensor, and the corresponding data shape is as follows. ,in, Indicates the batch size; This represents the spatial dimension, i.e., the number of spatial sampling points; This represents the historical time step. To reduce data volume and computational energy consumption, the initial spatial data corresponding to the target train is downsampled and flattened to obtain processed spatial data. Flattening is used to convert the multidimensional initial spatial data into a one-dimensional sequence. Based on the time order, the processed spatial data is input frame by frame into the LSM branch of the target neural operator. LSM is a special type of spiking neural network (SNN), whose basic structure consists of an input layer, a liquid layer, and a readout layer, as shown below. Figure 3 As shown, red dots in the liquid layer represent neurons that fired pulses at the current time step, while blue dots represent neurons that did not fire pulses at the current time step.

[0022] It is understandable that for each time step of the processed spatial data, the input frame... ,in, , Indicates the historical time step; each input frame is denoted as... ,and , Indicates the batch size; Indicates spatial dimension; The input frame is normalized, and rate coding is used to convert the normalized continuous values ​​into a pulse sequence to obtain the encoded pulse sequence. ,in, The pulse coding time step is the number of steps, and each element in the encoded pulse sequence is... This indicates whether the j-th input channel of the b-th sample generates a pulse at time s. This encoding process can be modeled as a homogeneous Poisson process.

[0023] In one specific implementation, the pulse coding process is as follows: For the input value 12.26, it is normalized to the interval [0,1]. Assuming the original range of the input value is [0,20], the pulse generation probability is (12.26-0) / (20-0) = 0.613. Pulse generation is usually modeled as a homogeneous Poisson process, and its probability mass function is: ; in, This represents the number of pulses generated by a neuron at this spatial point within a time length t. This refers to the specific number of pulses; The average distribution rate is positively correlated with the normalized input value. The time window length; within a fixed time window containing 10 time steps. Within this range, the number of pulses follows this Poisson distribution. On average, approximately 6 pulses are expected to be generated because... The generated pulse sequence is a binary array of length 10. Due to the randomness of the Poisson process, the specific pulse sequence obtained each time may be slightly different, but the total number of pulses will fluctuate around the theoretical mean.

[0024] Specifically, the step of performing pulse coding based on the initial spatial data corresponding to the target train and using the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence includes: downsampling and flattening the initial spatial data corresponding to the target train to obtain processed spatial data, and normalizing the processed spatial data to obtain normalized spatial data; inputting the normalized spatial data sequentially into the input layer of the LSM branch in the target neural operator, and converting the normalized spatial data into a pulse sequence based on the input layer and using rate coding to obtain the encoded pulse sequence.

[0025] Step S12: Convert the encoded pulse sequence into an input current using a preset weight matrix, update the neuron state of the liquid layer of the LSM branch based on the input current to obtain a corresponding pulse response sequence, and perform averaging and linear mapping on the pulse response sequence to obtain the first target feature.

[0026] In this embodiment, after obtaining the encoded pulse sequence, the encoded pulse sequence is mapped to the neurons of the liquid layer of the LSM branch via a preset weight matrix to obtain the instantaneous input current, and the corresponding formula is as follows: ; in, is the preset weight matrix of the input layer, and N is the total number of neurons in the liquid layer; Indicates spatial dimension; The encoded pulse sequence at the s-th encoding time step; This is a bias term. The neuronal state of the liquid layer in the LSM branch is dynamically updated over time. The neuronal state includes synaptic current, membrane potential, and impulse firing; the update formula for the synaptic current is as follows: ; in, The synaptic current at the current time step s; The first preset attenuation coefficient; This represents the synaptic current at the previous time step s-1; The input current is given. The update formula for the membrane potential is as follows: ; in, This represents the membrane potential at the current time step s; This is the second preset attenuation coefficient; This represents the membrane potential at the previous time step s-1; is the preset recursive connection weight matrix inside the liquid layer; N is the total number of neurons in the liquid layer; This refers to the pulse delivery at the previous time step s-1. The update formula corresponding to the pulse delivery is as follows: ; in, The pulse is emitted at the current time step s; It is a step function; This represents the membrane potential at the current time step s; The target threshold is the membrane potential. When the membrane potential exceeds the target threshold, the neuron will fire a pulse.

[0027] Understandably, if the membrane potential exceeds the target threshold, the neuron will fire a pulse and perform a potential reset. The accumulation of the membrane potential follows an exponential decay accumulation rule in discrete time. Specifically, at each time step s, the synaptic current at the current time step is generated by the synaptic current at the previous time step through a decay factor. After attenuation, the input current from the input layer is superimposed to form the membrane potential; while the membrane potential at the current time step is based on the membrane potential of the previous time step after attenuation factor. After attenuation, the recursive input is obtained by superimposing the synaptic current of the current time step and the pulse emission of the previous time step through a preset recursive connection weight matrix inside the liquid layer. , The pre-defined recursive connection weight matrix; This refers to the pulse firing status at the previous time step s-1. When the membrane potential exceeds the target threshold, the neuron generates a pulse and resets according to the rules. It is worth noting that the target threshold can be set according to actual conditions.

[0028] Specifically, the step of converting the encoded pulse sequence into an input current using a preset weight matrix, and updating the neuron state of the liquid layer of the LSM branch based on the input current to obtain a corresponding pulse response sequence, includes: converting the encoded pulse sequence into an input current using a preset weight matrix; determining the target synaptic current for the next time step based on the current input current at the current time step, the current synaptic current at the current time step, and a first preset attenuation coefficient; determining the target membrane potential for the next time step based on the target synaptic current, the current membrane potential at the current time step, a second preset attenuation coefficient, and recursive feedback input data within the liquid layer; the recursive feedback input data being a signal obtained by feedback based on the current pulse situation at the current time step and using a preset recursive connection weight matrix; and determining whether the target membrane potential is greater than a target threshold. If the value is greater than the target threshold, the target pulse condition for the next time step is that a pulse is generated; if the value is not greater than the target threshold, the target pulse condition for the next time step is that no pulse is generated. The next input current corresponding to the next time step in the input current is determined as the new current input current, the target synaptic current is determined as the new current synaptic current, the target membrane potential is determined as the new current membrane potential, and the target pulse condition is determined as the new current pulse condition. Then, the process jumps to the step of determining the target synaptic current for the next time step based on the current input current of the current time step, the current synaptic current of the current time step, and the first preset attenuation coefficient, until all time steps in the input current are updated to obtain each target pulse condition. The pulse conditions are then spliced ​​together in chronological order to obtain the corresponding pulse response sequence.

[0029] In this embodiment, the neuron outputs a pulse response sequence. ; Indicates the batch size; Indicates the time step in history; Where is the pulse coding time step; N is the total number of neurons in the liquid layer. The pulse response sequence is averaged over time to obtain the average firing rate of the neurons, and the corresponding formula is as follows: ; in, The average discharge rate; Indicates the time step in history; This represents the number of pulse encoding time steps. The pulse response sequence is given. After obtaining the average discharge rate, it is compressed to the target dimension through a linear projection layer to obtain the first target feature, and the corresponding formula is as follows: ; in, This refers to the first target feature; For linear projection layers, Mapping the N-dimensional average discharge rate feature to dimension; The average discharge rate is denoted as .

[0030] Step S13: Perform dimensional transformation on the initial spatial data, and input the transformed spatial data into the LSTM branch of the target neural operator to obtain the second target feature.

[0031] In this embodiment, after obtaining the first target feature corresponding to the LSM branch, the memory network unit in the LSTM branch includes an input gate, a forget gate, candidate cell states, and an output gate, such as... Figure 4 As shown, The input vector at the current time step. This is the hidden state from the previous time step. The weight matrix is ​​input to the corresponding gated / candidate state. This is the weight matrix from the hidden state to the corresponding gated / candidate state. For the corresponding gating / candidate state bias terms, f is the forget gate, i is the input gate, g is the candidate cell state, o is the output gate, Sigmoid is the Sigmoid function, and Tanh is the Tanh function (i.e., the hyperbolic tangent function). The output of the forget gate, The output of the input gate, The output of the candidate cell state, The output of the output gate. This represents the cell state at the current time step. Then, the initial spatial data... Convert to the format required for LSTM The LSTM branch expands the initial spatial data along the time dimension and encodes it step by step, outputting a hidden state at each time step to obtain the shape of the output tensor. ,in, This represents the hidden layer dimension. To obtain a global representation of the time series, the output of the last time step is taken. And projected to the target dimension through a linear layer. In order to obtain the second target features ; Indicates the batch size.

[0032] Specifically, the step of performing dimensional transformation on the initial spatial data and inputting the transformed spatial data into the LSTM branch of the target neural operator to obtain the second target feature includes: flattening the initial spatial data to obtain flattened spatial data, performing dimensional transformation on the flattened spatial data to obtain transformed spatial data; inputting the transformed spatial data into the LSTM branch of the target neural operator to obtain the output result of the last time step; and performing linear mapping on the output result to obtain the second target feature.

[0033] Step S14: Determine the intensity index and quality index corresponding to the first target feature and the second target feature respectively, and concatenate the first target feature and the second target feature to obtain an analysis vector. Based on the analysis vector, generate fusion weights using a multilayer perceptron, and adjust the first target feature and the second target feature using the fusion weights to obtain the query, key, and value in the attention mechanism. The intensity index is an indicator that reflects the degree of feature activation; the quality index is an indicator that reflects the credibility of the feature.

[0034] In this embodiment, after obtaining the second target feature, each target feature is evaluated in terms of both intensity and quality, and the corresponding formulas are as follows: ; ; in, The first intensity index corresponds to the first target feature; The first quality index corresponds to the first target feature; The second intensity index corresponds to the second target feature; The second quality index corresponding to the second target feature; The preset evaluation analyzer; the shape of each indicator is as follows: , The batch size is represented by the formula. The analysis vector is obtained by concatenating the target features, intensity indices, and quality indices. The formula corresponding to the analysis vector is as follows: ; in, The analysis vector; A function used to concatenate two or more arrays or strings; This is the second target feature; This refers to the first target feature; This refers to the first strength index; This refers to the first quality indicator; This is the second strength index; This is the second quality indicator.

[0035] Understandably, after obtaining the analysis vector, three weights are output using a multilayer perceptron (MLP) and a softmax function (i.e., a normalized exponential function), with the corresponding formulas as follows: ; in, The first weight corresponding to the output LSM branch; The second weight corresponding to the output LSTM branch; Attention weights; The Softmax function; For the multilayer sensor; Let be the analysis vector. Furthermore, the sum of the three weights mentioned above is 1, and each weight is between 0 and 1.

[0036] It should be explained that the structure of the preset evaluation analyzer includes a hidden width, an intensity branch, and a quality branch, wherein the hidden width is... Where 8 represents 8 neurons, The target dimension is defined as follows: the strength branch and the quality branch have the same structure, including a first linear layer, a ReLU (Rectified Linear Unit) activation function, a second linear layer, and a Sigmoid activation function (a type of sigmoid function). The structure of the multilayer perceptron is a first linear layer, a ReLU activation function, a Dropout layer (a random deactivation layer), a second linear layer, and a Softmax function.

[0037] Furthermore, the target features are adjusted using the obtained weights to obtain the adjusted features, as shown in the following formula: ; ; in, The first adjusted feature is the feature corresponding to the first target feature; This refers to the first target feature; This is the first weight; This refers to the second adjusted feature corresponding to the second target feature; This is the second target feature; This is the second weight. After obtaining the adjusted features, the adjusted features are mapped into the three key vectors required by the attention mechanism through three independent linear layers, as shown in the following formula: ; ; ; in, For queries in the attention mechanism; As a key in the attention mechanism; This is the value in the attention mechanism; , , It consists of three independent linear layers; This is the first adjusted feature; This is the second adjusted feature. Then, the query, the key, and the value are split into a multi-head form to enhance learning ability, with the corresponding formula as follows: ; in, Indicates the batch size; For the number of heads; For each dimension of the head, the corresponding formula is as follows: ; in, The target dimension; The number of attention heads.

[0038] Specifically, the steps of determining the intensity index and quality index corresponding to the first target feature and the second target feature, respectively, concatenating the first target feature and the second target feature to obtain an analysis vector, generating fusion weights based on the analysis vector using a multilayer perceptron, and adjusting the first target feature and the second target feature using the fusion weights to obtain the query, key, and value in the attention mechanism include: determining the first intensity index and the first quality index corresponding to the first target feature, and determining the second intensity index and the second quality index corresponding to the second target feature; concatenating each target feature, each intensity index, and each quality index to obtain an analysis vector; inputting the analysis vector into a multilayer perceptron to obtain a first weight corresponding to the LSM branch, a second weight corresponding to the LSTM branch, and an attention weight; adjusting the first target feature and the second target feature using the first weight and the second weight respectively to obtain a first adjusted feature and a second adjusted feature; converting the first adjusted feature into a query in the attention mechanism based on a first preset linear layer, and converting the second adjusted feature into a key and value using a second preset linear layer and a third preset linear layer.

[0039] Step S15: Based on the query, the key, and the value, and using a cross-attention mechanism and a feature enhancer, determine the output target fusion feature, and use the target fusion feature to complete the solution of the train aerodynamic partial differential equation by the target neural operator, and generate the train aerodynamic analysis result corresponding to the target train based on the obtained solution result of the train aerodynamic partial differential equation.

[0040] In this embodiment, the LSM branch is used as the query, and the LSTM branch is used as the key and value to determine the attention score of each head. First, the similarity score between the query and the key is determined, and the corresponding formula is as follows: ; in, The similarity score is given; For the query; For the key; Let T be the dimension of the attention head; T is the transpose. Then, the similarity score is normalized using the following formula: ; in, The normalized score; It is a normalized exponential function; The similarity score is used to determine the attention enhancement features based on the normalized score and the value, using the following formula: ; in, For the attention enhancement feature; The normalized score; Let the value be denoted as ; then the attention enhancement feature is mapped to the target dimension to obtain the target attention feature, and the corresponding formula is as follows: ; in, The target attention features; The `reshape` function is used to adjust the dimensions of an array or matrix. Indicates the batch size; The target dimension; This refers to the attention enhancement feature.

[0041] It is understandable that after obtaining the target attention features, a feature enhancer is used to determine the enhanced features, and the corresponding formula is as follows: ; in, The enhanced feature; The feature enhancer is described above; the structure of the feature enhancer includes a first linear layer, layer normalization, ReLU activation function, Dropout layer, and a second linear layer. The target attention features are defined as follows. The enhanced features are then weighted and fused to obtain the fused features, as shown in the following formula: ; in, The fused features; The enhanced feature; Attention weights; This is the first adjusted feature; This is the second adjusted feature. The fused feature is then output-mapped and normalized to obtain the target fused feature, as shown in the following formula: ; in, The target fusion feature has the following shape: , Indicates the batch size. The target dimension; The fused features; This is the output mapping layer of the target neural operator; The target attention feature is defined as follows.

[0042] Specifically, the step of determining the target fusion feature based on the query, the key, and the value using a cross-attention mechanism and a feature enhancer includes: determining the similarity score between the query and the key, and normalizing the similarity score to obtain a normalized score; determining an attention enhancement feature based on the normalized score and the value, and mapping the attention enhancement feature to the target dimension to obtain a target attention feature; determining an enhanced feature based on the target attention feature and using a feature enhancer, and determining a fusion feature using the enhanced feature, the attention weight, the first adjusted feature, and the second adjusted feature; mapping the target attention feature based on the fusion feature and using the output mapping layer of the target neural operator, and performing residual connections and layer normalization with the obtained mapping result and the fusion feature to obtain the target fusion feature.

[0043] In this embodiment, after obtaining the target fusion features, the loss value is determined based on the average relative error between the target fusion features and the target true features. Backpropagation `loss.backward()` is called to determine the gradient of the trainable parameters in the target neural operator, and the gradient is limited to `max_norm=1.0`. If the gradient is too large, it will lead to training instability. Then, `optimizer.step()` is called to update the trainable parameters, and the learning rate is adjusted by the learning rate scheduler `scheduler.step()`. Due to the structural characteristics of the LSM, the weights inside the LSM and the weights input to the liquid layer do not participate in gradient descent and are not updated. Furthermore, during testing, the target neural operator is switched to evaluation mode `model.eval()`. The Dropout layer randomly deactivates neurons, and the normalization layer uses batch statistics. In evaluation mode, these layers disable random behavior and use fixed statistics to ensure stable and reproducible prediction results. During testing, no parameter updates are needed, therefore gradient calculation is disabled. The testing process is as follows: input data and ground truth labels are extracted from the test dataset in batches; prediction is performed for each batch using the same strategy as during training; the immediate loss is calculated for each batch, and the test metrics are accumulated using the target loss function; finally, the average loss of the test set is obtained by averaging across all batches. Specifically, the training process of the target neural operator includes: determining the target loss function based on the average relative error between the target fused features and the target ground truth features; training and optimization are performed based on the target loss function using backpropagation and gradient clipping to obtain the target neural operator. Further, after obtaining the target fused features, the partial differential equations of train aerodynamics can be solved to obtain the corresponding equation solution results. The equation solution results can be train aerodynamic drag, aerodynamic lift, lateral force, etc., and then the equation solution results are summarized to obtain the train aerodynamic analysis results corresponding to the target train.

[0044] As shown above, this application utilizes the input layer of the LSM branch in the target neural operator for pulse coding, and uses a weight matrix to convert the encoded sequence into an input current to update the neuron state of the liquid layer of the LSM branch frame by frame, thereby obtaining the first target feature. Then, the LSTM branch is used to capture long-term dependencies to obtain the second target feature. By calculating the intensity and quality indices of the two branch features, the analysis vector is concatenated and then a multilayer perceptron is used to generate fusion weights. In this way, the target features are adjusted using the fusion weights, and the target fusion features are generated through an attention mechanism and a feature enhancer. The target fusion features are then used to solve the partial differential equations of train aerodynamics, resulting in high-precision, low-latency flow field prediction results. Furthermore, adaptive and stable training is performed for various complex working conditions, reducing training costs and energy consumption.

[0045] Accordingly, see Figure 5 As shown, this application also provides a train aerodynamics analysis device based on a dual-branch dynamic neural operator, comprising: The pulse coding module 11 is used to perform pulse coding based on the initial spatial data corresponding to the target train and using the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence; the initial spatial data is the flow field spacetime tensor of the partial differential equation of train aerodynamics collected by the on-board edge device. The response sequence mapping module 12 is used to convert the encoded pulse sequence into an input current using a preset weight matrix, update the neuron state of the liquid layer of the LSM branch based on the input current to obtain the corresponding pulse response sequence, and perform averaging and linear mapping on the pulse response sequence to obtain the first target feature. The spatial data transformation module 13 is used to perform dimensional transformation on the initial spatial data and input the transformed spatial data into the LSTM branch in the target neural operator to obtain the second target feature; The feature adjustment module 14 is used to determine the intensity index and quality index corresponding to the first target feature and the second target feature, respectively, and to concatenate the first target feature and the second target feature to obtain an analysis vector. Based on the analysis vector, a fusion weight is generated using a multilayer perceptron. The fusion weight is used to adjust the first target feature and the second target feature to obtain the query, key, and value in the attention mechanism. The intensity index is an indicator reflecting the degree of feature activation; the quality index is an indicator reflecting the credibility of the feature. The target feature determination module 15 is used to determine the output target fusion features based on the query, the key, and the value, using a cross-attention mechanism and a feature enhancer, and to use the target fusion features to complete the solution of the train aerodynamic partial differential equation by the target neural operator, so as to generate the train aerodynamic analysis result corresponding to the target train based on the obtained solution result of the train aerodynamic partial differential equation.

[0046] In some specific embodiments, the pulse coding module 11 may specifically include: The data normalization unit is used to downsample and flatten the initial spatial data corresponding to the target train to obtain processed spatial data, and to normalize the processed spatial data to obtain normalized spatial data. The spatial data conversion unit is used to sequentially input the normalized spatial data into the input layer of the LSM branch in the target neural operator, so as to convert the normalized spatial data into a pulse sequence based on the input layer and using rate coding to obtain the encoded pulse sequence.

[0047] In some specific embodiments, the response sequence mapping module 12 may specifically include: The target current determination unit is used to convert the encoded pulse sequence into an input current using a preset weight matrix, and to determine the target synaptic current for the next time step based on the current input current at the current time step, the current synaptic current at the current time step, and a first preset attenuation coefficient in the input current. The target membrane potential determination unit is used to determine the target membrane potential of the next time step based on the target synaptic current, the current membrane potential of the current time step, the second preset attenuation coefficient, and the recursive feedback input data inside the liquid layer; the recursive feedback input data is a signal obtained by feedback based on the current pulse situation of the current time step and using a preset recursive connection weight matrix. A target membrane potential determination unit is used to determine whether the target membrane potential is greater than a target threshold. A pulse generation unit is used to characterize the target pulse situation in the next time step as generating a pulse if the pulse value is greater than the target threshold. A pulse-not-generating unit is used to characterize the target pulse condition for the next time step as "no pulse is generated" if the pulse value is not greater than the target threshold. The pulse situation splicing unit is used to determine the next input current corresponding to the next time step in the input current as the new current input current, the target synaptic current as the new current synaptic current, the target membrane potential as the new current membrane potential, and the target pulse situation as the new current pulse situation. Then, it jumps to the step of determining the target synaptic current of the next time step based on the current input current of the current time step, the current synaptic current of the current time step, and the first preset attenuation coefficient, until all time steps in the input current are updated to obtain each target pulse situation. The pulse situations are then spliced ​​in chronological order to obtain the corresponding pulse response sequence.

[0048] In some specific embodiments, the spatial data transformation module 13 may specifically include: A spatial data transformation unit is used to flatten the initial spatial data to obtain flattened spatial data, and to perform dimensional transformation on the flattened spatial data to obtain transformed spatial data. The spatial data input unit is used to input the transformed spatial data into the LSTM branch of the target neural operator to obtain the output result of the last time step; The output result mapping unit is used to perform a linear mapping on the output result to obtain the second target feature.

[0049] In some specific embodiments, the feature adjustment module 14 may specifically include: The indicator determination unit is used to determine the first intensity indicator and the first quality indicator corresponding to the first target feature, and to determine the second intensity indicator and the second quality indicator corresponding to the second target feature. The index splicing unit is used to splice together the target features, intensity indices and quality indices to obtain the analysis vector; A vector input unit is used to input the analysis vector into a multilayer perceptron to obtain a first weight corresponding to the LSM branch, a second weight corresponding to the LSTM branch, and an attention weight. The feature adjustment unit is used to adjust the first target feature and the second target feature using the first weight and the second weight respectively, so as to obtain the first adjusted feature and the second adjusted feature. The feature transformation unit is used to transform the first adjusted feature into a query in the attention mechanism based on the first preset linear layer, and to transform the second adjusted feature into a key and a value using the second preset linear layer and the third preset linear layer.

[0050] In some specific embodiments, the target feature determination module 15 may specifically include: A score normalization unit is used to determine the similarity score between the query and the key, and to normalize the similarity score to obtain a normalized score. An enhanced feature mapping unit is used to determine attention enhancement features based on the normalized score and the value, and map the attention enhancement features to the target dimension to obtain the target attention features; The feature fusion unit is used to determine enhanced features based on the target attention features and using a feature enhancer, and to determine fused features using the enhanced features, the attention weights, the first adjusted features, and the second adjusted features; The target feature determination unit is used to map the target attention features based on the fused features and using the output mapping layer of the target neural operator, and to perform residual connection and layer normalization with the fused features using the obtained mapping result to obtain the target fused features.

[0051] In some specific embodiments, the training process of the target neural operator may specifically include: The loss function determination unit is used to determine the target loss function based on the average relative error between the target fused features and the target true features; The target operator optimization unit is used to train and optimize based on the target loss function and using backpropagation and gradient pruning to obtain the target neural operator.

[0052] Furthermore, embodiments of this application also disclose an electronic device, Figure 6 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application. The electronic device 20 may specifically include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the train aerodynamics analysis method based on a dual-branch dynamic neural operator disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0053] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0054] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0055] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the train aerodynamics analysis method based on a dual-branch dynamic neural operator disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0056] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned train aerodynamics analysis method based on a dual-branch dynamic neural operator. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0057] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0058] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0059] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0060] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0061] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A train aerodynamics analysis method based on a dual-branch dynamic neural operator, characterized in that, include: Based on the initial spatial data corresponding to the target train, pulse coding is performed using the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence; The initial spatial data is the flow field spacetime tensor of the partial differential equation of train aerodynamics, collected using onboard edge devices; The encoded pulse sequence is converted into an input current using a preset weight matrix. The neuron state of the liquid layer of the LSM branch is updated based on the input current to obtain the corresponding pulse response sequence. The pulse response sequence is averaged and linearly mapped to obtain the first target feature. The initial spatial data is subjected to dimensional transformation, and the transformed spatial data is input into the LSTM branch of the target neural operator to obtain the second target feature; The intensity index and quality index corresponding to the first target feature and the second target feature are determined respectively, and the first target feature and the second target feature are concatenated to obtain an analysis vector. Based on the analysis vector, a fusion weight is generated using a multilayer perceptron. The fusion weight is used to adjust the first target feature and the second target feature to obtain the query, key, and value in the attention mechanism. The intensity index is an indicator that reflects the degree of feature activation. The quality index is an indicator that reflects the credibility of the feature. Based on the query, the key, and the value, and using a cross-attention mechanism and a feature enhancer, the target fusion feature is determined, and the target neural operator is used to solve the train aerodynamic partial differential equation. Based on the obtained train aerodynamic partial differential equation solution, the train aerodynamic analysis result corresponding to the target train is generated.

2. The train aerodynamics analysis method based on a dual-branch dynamic neural operator according to claim 1, characterized in that, The step of performing pulse coding based on the initial spatial data corresponding to the target train and utilizing the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence includes: The initial spatial data corresponding to the target train is downsampled and flattened to obtain processed spatial data, and the processed spatial data is normalized to obtain normalized spatial data. The normalized spatial data is sequentially input into the input layer of the LSM branch in the target neural operator, so as to convert the normalized spatial data into a pulse sequence based on the input layer and using rate coding to obtain the encoded pulse sequence.

3. The train aerodynamics analysis method based on a dual-branch dynamic neural operator according to claim 1, characterized in that, The step of converting the encoded pulse sequence into an input current using a preset weight matrix, and updating the neuron state of the liquid layer of the LSM branch based on the input current to obtain a corresponding pulse response sequence includes: The encoded pulse sequence is converted into an input current using a preset weight matrix. The target synaptic current for the next time step is determined based on the current input current at the current time step, the current synaptic current at the current time step, and a first preset attenuation coefficient. The target membrane potential for the next time step is determined based on the target synaptic current, the current membrane potential at the current time step, the second preset attenuation coefficient, and the recursive feedback input data inside the liquid layer; the recursive feedback input data is a signal obtained by feedback based on the current pulse situation at the current time step and using a preset recursive connection weight matrix. Determine whether the target membrane potential is greater than the target threshold; If it is greater than the target threshold, then the target pulse condition for the next time step is to generate a pulse; If it is not greater than the target threshold, then the target pulse condition for the next time step is no pulse generated; The next input current corresponding to the next time step in the input current is determined as the new current input current, the target synaptic current is determined as the new current synaptic current, the target membrane potential is determined as the new current membrane potential, and the target pulse condition is determined as the new current pulse condition. Then, the process jumps to the step of determining the target synaptic current of the next time step based on the current input current of the current time step, the current synaptic current of the current time step, and the first preset attenuation coefficient, until all time steps in the input current are updated to obtain each target pulse condition. The pulse conditions are then spliced ​​together in chronological order to obtain the corresponding pulse response sequence.

4. The train aerodynamics analysis method based on a dual-branch dynamic neural operator according to claim 1, characterized in that, The step of performing a dimensionality transformation on the initial spatial data and inputting the transformed spatial data into the LSTM branch of the target neural operator to obtain the second target feature includes: The initial spatial data is flattened to obtain flattened spatial data, and the flattened spatial data is then subjected to dimensional transformation to obtain transformed spatial data. The transformed spatial data is input into the LSTM branch of the target neural operator to obtain the output result of the last time step; The output is linearly mapped to obtain the second target feature.

5. The train aerodynamics analysis method based on a dual-branch dynamic neural operator according to claim 1, characterized in that, The process involves determining the intensity and quality indices corresponding to the first and second target features, concatenating them to obtain an analysis vector, generating fusion weights based on the analysis vector using a multilayer perceptron, and adjusting the first and second target features using these fusion weights to obtain the query, key, and value in the attention mechanism. Determine the first intensity index and the first quality index corresponding to the first target feature, and determine the second intensity index and the second quality index corresponding to the second target feature; The characteristics, intensity indicators, and quality indicators of each target are concatenated to obtain the analysis vector; The analysis vector is input into a multilayer perceptron to obtain the first weight corresponding to the LSM branch, the second weight corresponding to the LSTM branch, and the attention weight; The first target feature and the second target feature are adjusted using the first weight and the second weight respectively to obtain the first adjusted feature and the second adjusted feature; The first adjusted feature is converted into a query in the attention mechanism based on the first preset linear layer, and the second adjusted feature is converted into a key and a value using the second preset linear layer and the third preset linear layer.

6. The train aerodynamics analysis method based on a dual-branch dynamic neural operator according to claim 5, characterized in that, The process of determining the target fusion feature of the output based on the query, the key, and the value, and utilizing a cross-attention mechanism and a feature enhancer, includes: Determine the similarity score between the query and the key, and normalize the similarity score to obtain a normalized score; Based on the normalized score and the value, attention enhancement features are determined, and the attention enhancement features are mapped to the target dimension to obtain the target attention features; Based on the target attention features and using a feature enhancer to determine the enhanced features, the enhanced features, the attention weights, the first adjusted features, and the second adjusted features are used to determine the fused features; Based on the fused features, the target attention features are mapped using the output mapping layer of the target neural operator. The obtained mapping results are then used to perform residual connections and layer normalization with the fused features to obtain the target fused features.

7. The train aerodynamics analysis method based on a dual-branch dynamic neural operator according to any one of claims 1 to 6, characterized in that, The training process of the target neural operator includes: The target loss function is determined based on the average relative error between the target fusion features and the target true features; The target neural operator is obtained by training and optimization based on the target loss function and by using backpropagation and gradient pruning.

8. A train aerodynamics analysis device based on a dual-branch dynamic neural operator, characterized in that, include: The pulse coding module is used to perform pulse coding based on the initial spatial data corresponding to the target train and using the input layer of the LSM branch in the target neural operator to obtain the encoded pulse sequence. The initial spatial data is the flow field spacetime tensor of the partial differential equation of train aerodynamics, collected using onboard edge devices; The response sequence mapping module is used to convert the encoded pulse sequence into an input current using a preset weight matrix, update the neuron state of the liquid layer of the LSM branch based on the input current to obtain the corresponding pulse response sequence, and perform averaging and linear mapping on the pulse response sequence to obtain the first target feature. The spatial data transformation module is used to perform dimensional transformation on the initial spatial data and input the transformed spatial data into the LSTM branch in the target neural operator to obtain the second target feature; The feature adjustment module is used to determine the intensity index and quality index corresponding to the first target feature and the second target feature, respectively, and to concatenate the first target feature and the second target feature to obtain an analysis vector. Based on the analysis vector, a fusion weight is generated using a multilayer perceptron. The fusion weight is used to adjust the first target feature and the second target feature to obtain the query, key, and value in the attention mechanism. The intensity index is an indicator reflecting the degree of feature activation; the quality index is an indicator reflecting the credibility of the feature. The target feature determination module is used to determine the output target fusion features based on the query, the key, and the value, using a cross-attention mechanism and a feature enhancer, and to use the target fusion features to complete the solution of the train aerodynamic partial differential equation by the target neural operator, so as to generate the train aerodynamic analysis result corresponding to the target train based on the obtained solution result of the train aerodynamic partial differential equation.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the train aerodynamics analysis method based on a dual-branch dynamic neural operator as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the train aerodynamics analysis method based on a dual-branch dynamic neural operator as described in any one of claims 1 to 7.

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