Charging pile load prediction method based on deep learning

Abstract

The invention discloses a charging pile load prediction method based on deep learning. The method comprises the following steps: S1, constructing a regional grid and initializing a cellular basic attribute vector; s2, collecting historical load data and external influence factors, and unifying the historical load data and the external influence factors into an input tensor; s3, generating a time continuous evolution state by using an ordinary differential equation modeling module; s4, constructing a state vector at the current moment; s5, the differentiable cellular automaton module executes primary spatial state propagation; s6, performing multiple rounds of spatial propagation iteration, and outputting enhanced state representation; s7, the load prediction module outputs a future multi-moment prediction value; s8, errors are calculated, and end-to-end training optimization model parameters are executed; and S9, outputting a final optimization model as a load prediction method. According to the method, the response capability of the model to sudden disturbance and the stability of multi-region collaborative prediction are remarkably improved, and the method can be widely applied to multiple application scenes such as smart energy management, electric traffic scheduling and urban public infrastructure intelligent optimization.

Description

Technical Field

[0001] The present invention relates to the field of deep learning technology, and in particular to a charging pile load prediction method based on deep learning. Background Art

[0002] With the continuous growth of new energy vehicle ownership and the continuous advancement of urban intelligent energy management systems, electric vehicle charging piles, as important infrastructure connecting power grids and transportation, have increasingly complex operating load characteristics, showing significant nonlinear, high-frequency fluctuations and regional heterogeneity. In this context, how to perform high-precision, multi-time-scale, and regional-oriented dynamic prediction of charging pile power loads has become a key technical issue in current smart grid load management, transportation energy consumption scheduling, and urban energy system optimization.

[0003] Existing charging pile load forecasting methods can be roughly divided into two categories. One is the load forecasting method based on traditional statistical models, including autoregressive moving average model, exponential smoothing model and rule-based load curve simulation model. This type of method has a simple modeling process and low computational cost, but it shows obvious prediction lag and lack of accuracy when dealing with high-dimensional and dynamically changing data environments, and it is especially difficult to characterize the complex load linkage relationship between urban-level regions. The other is a sequence modeling method based on deep learning, such as using structures such as recurrent neural networks, long short-term memory networks or gated recurrent units for time series modeling. These models can capture the nonlinear pattern of load changes over time to a certain extent and improve the ability to understand historical dependencies, but they still have significant limitations when dealing with electric vehicle charging pile load problems with strong mutation characteristics and environmental impact characteristics.

[0004] First, existing sequence models generally adopt discrete time modeling, encoding each time point as an independent state. This modeling method is difficult to provide a detailed description of state evolution when facing non-stationary factors such as high-speed dynamic scenes, sudden load increases before and after holidays, or sudden weather changes. At the same time, the use of charging piles is often affected by spatial attributes such as geographical location, road layout, traffic density, and regional type. Relying solely on single-point sequence modeling cannot fully reflect the interactivity and dependency between regions. To alleviate this problem, some studies have introduced graph structure modeling methods, taking charging piles as nodes and adjacency relationships as edges, constructing graph neural network models, and encoding spatial relationships. Although the graph structure method can characterize the spatial distribution relationship of the city to a certain extent, its adjacency structure is mostly statically defined and cannot be flexibly adjusted according to environmental changes; and the graph neural network tends to propagate globally and is not easy to control the local response range, so the modeling ability of high-frequency changes and local high-sensitivity areas is still insufficient.

[0005] In addition, traditional deep learning prediction methods usually model the state as a mapping relationship between static inputs and outputs, lacking the ability to model the continuous evolution process of the state. In the scenario of charging pile load prediction, the charging behavior is not only affected by the internal load state, but also by external disturbances such as electricity price policies, weather conditions, and holiday arrangements, and these factors often change continuously. Traditional models are difficult to effectively model this coupled dynamic process of state and environment.

[0006] In terms of model training, existing methods have insufficient design of training strategies for prediction models and lack a systematic optimization mechanism, which often leads to problems such as unstable gradients, overfitting, or weak generalization ability of the model in complex scenarios, restricting its application effect in large-scale, cross-regional, and strongly disturbed environments.

[0007] To address the above problems, the present invention proposes a charging pile load prediction method based on deep learning. By introducing the structure of neural ordinary differential equations to model the continuous evolution process of time states and combining differentiable cellular automata to design a spatial neighborhood propagation mechanism, a set of load prediction methods integrating time continuity, spatial locality, and disturbance responsiveness is constructed. In terms of time modeling, the present invention adopts a neural network modeling method with a differential structure as the core, enabling the state of each cell unit to evolve in a continuous trajectory on the time axis, overcoming the problem of fixed time granularity of traditional sequence models; in terms of spatial modeling, a two-dimensional spatial propagation grid is constructed based on cellular automata, and a differentiable function is used to construct local propagation rules, enabling each cell to perceive neighborhood changes in space and form a spatial perception state expression; in terms of environmental response, a control function is introduced, and external disturbance variables such as weather, electricity price, and holidays are injected into the state derivative function in the form of continuous control terms, enabling the model to have the ability of adaptive adjustment to different situations.

[0008] The present invention further introduces a complete set of optimization strategies for stability and generalization during the model training process, including dynamic learning rate adjustment strategies, early stopping mechanisms, batch normalization mechanisms, data augmentation, and gradient clipping methods, ensuring that the model can still maintain a stable training process, high prediction accuracy, and strong generalization ability in complex and changeable environments.

[0009] Compared with the prior art, the present invention realizes a city charging pile load prediction solution with full-stack modeling capabilities by introducing a time continuous modeling mechanism, a spatial local propagation mechanism, and an external disturbance control mechanism, not only improving the accuracy and stability of prediction, but also providing an intelligent modeling basis that is scalable, interpretable, and deployable for subsequent power grid scheduling, charging guidance, and urban planning.

[0010] Therefore, how to provide a charging pile load prediction method based on deep learning is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0011] An object of the present invention is to propose a charging pile load prediction method based on deep learning. The present invention integrates a neural ordinary differential equation modeling mechanism and a differentiable cellular automaton propagation mechanism, combines the historical load data of charging piles with multi-dimensional external environmental factors, and constructs a load prediction algorithm with the capabilities of time-continuous modeling, spatial local propagation, and perturbation response. The whole process from data input, state evolution, spatial propagation to prediction output and joint training is described in detail, and it has the advantages of high modeling accuracy, sensitive response to load mutations, strong prediction stability, and adaptability to complex urban energy scenarios.

[0012] A charging pile load prediction method based on deep learning according to an embodiment of the present invention includes the following steps:

[0013] S1. Construct a regional grid, divide the area to be predicted into cell units, each unit corresponds to a group of charging piles, and initialize the basic attribute vector of each cell;

[0014] S2. Collect the historical load data and external influencing factors of each cell within the target time window, and unify them into a structured time series input tensor;

[0015] S3. Based on the input tensor, extract the initial state value of each cell, input it into the neural ordinary differential equation modeling module, and generate a time-continuous evolution state;

[0016] S4. Take the evolution state of each cell as its current moment state vector;

[0017] S5. Based on the fixed neighborhood structure, input the current states of all cells into the differentiable cellular automaton module and perform a spatial state propagation;

[0018] S6. Repeat the spatial state propagation operation to obtain an enhanced prediction state representation;

[0019] S7. Input the enhanced prediction state representation into the prediction module and output the load prediction values of each cell at multiple future moments;

[0020] S8. Calculate the error between the prediction value and the real load, perform end-to-end model training, and optimize the parameters of the neural ordinary differential equation module and the cellular automaton module;

[0021] S9. Optimize the model by different strategies to obtain a deep learning model for charging pile network load prediction and output it as the final prediction method.

[0022] Optionally, the S1 specifically includes: dividing the urban area to be predicted into a regular two-dimensional grid structure, with each grid area serving as a cell unit, each cell unit covering a fixed geographical space range, determining the set of electric vehicle charging piles deployed within the coverage range of each cell unit, counting the number of charging piles within the cell unit, constructing a basic attribute vector for each cell unit, where the basic attribute vector includes the number of charging piles within the unit, the average rated power of the charging piles, the geographical coordinates of the cell center, the voltage level of the grid access, and the maximum power supply capacity parameter of the area, and inputting the above basic attribute vector as the initial state of the cell unit.

[0023] Optionally, the S2 specifically includes: collecting basic data based on the basic attribute vector, setting a unified target time window, collecting data for each cell unit within this time window, including the historical load data of all charging piles within the unit, with the recording time granularity being minute-level or hour-level, collecting external influencing factors related to the cell load change, where the external influencing factors include weather conditions, holiday and working day information, road traffic flow conditions, electricity price policy change information, performing time alignment processing on the collected data, filling in the missing time point data, and performing normalization preprocessing on all feature data to unify it into a structured time series format, and combining the processed historical load data and external influencing factors in chronological order into a two-dimensional input tensor.

[0024] Optionally, the S3 specifically includes:

[0025] S31. For each cell unit c i,j , select the historical load data and external influencing factors of this cell for a continuous number of time steps before the current prediction period from the input tensor, including holiday identification, electricity price, meteorological parameters, and traffic status, organize the above data in chronological order into a two-dimensional feature tensor, and input the feature tensor into a multi-layer perceptron encoding network to output a state initial vector h i,j (t0), where t0 represents the starting time of the target prediction period;

[0026] S32. Define the state derivative function as follows:

[0027]

[0028] where h i,j (t) represents the state vector of cell c i,j at any time t, which is a continuous function of time t, and its initial value at t = t0 is h i,j (t0), serving as the starting point for solving this differential equation, f θThe main evolutionary function network constructed by a multi-layer perceptron, including at least two layers of linear transformation and non-linear activation structures, models the time evolution law of the state vector itself, g φ The control function module implemented by a linear neural network is used to receive the external dynamic variable e at the current time t i,j (t) and outputs the environmental regulation increment. θ and φ are the sets of trainable parameters of the main function and the control function respectively;

[0029] S33. Perform numerical solution of the neural ordinary differential system, and input the initial state h i,j (t0) and the derivative function into the ordinary differential equation solver together, and perform integration operations in the time interval [t0, t T , and output the state sequence {h k} at multiple time points {t i,j (t k )};

[0030] S34. Construct a continuous evolution state tensor, select representative time points from the state sequence output by the solver, combine the corresponding state vectors into an evolution state tensor, and use it as the current state input of this cell in the subsequent step S4 for performing spatial propagation modeling operations.

[0031] Optionally, the S33 specifically includes: the ordinary differential equation solver is used to perform numerical integration on the state derivative function, and the constructed initial state vector h i,j (t0) is used as the starting input, and the continuous evolution trajectory of the state variable h T (t) is solved in the time interval [t0, t i,j . The solver is an adaptive step-size integrator with gradient traceability. The step-size adjustment mechanism is based on the dynamic monitoring of the change rate of the derivative function norm, and specifically includes the following operations:

[0032] When the change rate of the state derivative exceeds the preset threshold, the integration step size is automatically reduced to improve the description accuracy of the fast-changing load behavior;

[0033] When the state derivative changes smoothly, the step size is automatically enlarged to improve the calculation efficiency;

[0034] The change rate is defined as the first-order norm form of , where Δt is the micro-element time value in the derivative process;

[0035] The solver generates an intermediate state h i,j (t k ) at each integration time step, supports discrete output sampling based on time nodes, and forms a state tensor sequence for use by the subsequent differentiable cellular automaton module;

[0036] The solver supports integration with deep learning frameworks, is compatible with the automatic differentiation mechanism in PyTorch or TensorFlow, ensures the preservation of the state derivative path during end-to-end training, and allows the backpropagation optimization of all parameters of the differential function f θ and the control function g φ simultaneously. It is compatible with a variety of differentiable numerical methods, including Dormand-Prince, Runge-Kutta, and Adams-Bashforth multi-step methods, adapts to the modeling requirements of different load fluctuation scenarios, and is suitable for dealing with the sudden behavior of electric vehicle charging pile loads during holidays and peak hours.

[0037] Optionally, the S5 specifically includes:

[0038] S51. Establish a grid-type cell structure and a neighborhood mapping function, arrange all cell units c i,j in a fixed-structure grid according to two-dimensional coordinates, and define a Moore neighborhood mapping function for each cell to determine its spatial propagation correlation range;

[0039] S52. Construct a differentiable state propagation function, and define a continuously differentiable state propagation function for each cell unit:

[0040]

[0041] where h i,j (t k ) is the state vector of the cell itself at the current moment, generated by the neural ordinary differential equation solver, and F ωF (·) is a state update function implemented with a convolutional neural network structure, and the parameter ωF is a set of trainable parameters. The propagation function is based on the weighted combination and feature reconstruction of the states within the neighborhood and has end-to-end differentiability;

[0042] S53. Implement a locally updated mechanism with weight sharing. The state propagation function F ω shares the same set of trainable parameters for all cell units. The neural network structure adopted includes: local convolutional kernels, a non-linear activation function σ, and a normalization operation module;

[0043] S54. Integrate the self-state and the neighborhood state for propagation. The updated state of each cell is represented by the following formula:

[0044]

[0045] where W s , W n are trainable transformation matrices acting on the cell itself and the neighboring cells respectively, and αm,n is a learnable adjacency weight parameter, representing the contribution degree of different adjacent cells to the update of the current cell state;

[0046] S55. Output the state tensor after propagation for subsequent steps. Combine the state vectors h′ i,j (t k ) of all cells after the current propagation round into a two-dimensional tensor as the input for the next propagation round.

[0047] Optionally, the S6 specifically includes: performing multiple rounds of spatial propagation iteration on each cell unit, setting a predetermined number of iterations, and updating the state vector of the cell through a weighted combination based on the current cell and its neighborhood state in each round of iteration; in each round of iteration, the updated state is used as the input for the next round, and the process is repeated until the state tensor of the cell after multiple rounds of iteration is finally output for subsequent load prediction.

[0048] Optionally, the S7 specifically includes:

[0049] S71. Use the state tensor {h′ i,j (t k )} of the cells after multiple rounds of spatial propagation as the input and input it into the subsequent load prediction module, which is used to generate the predicted values of the charging pile load at future times;

[0050] S72. For the input state tensor {h′ i,j (t k )}, process it through the trained load prediction model P ω to calculate the predicted values of the load of each cell at future times t k+1 ,t k+2 ,...,t T ; where is the predicted value of the load of cell c i,j at time t, and the load prediction model P ωP is a set of regression prediction modules based on a fully connected neural network, with a trainable parameter set ωP, and is trained through an end-to-end optimization method;

[0051] S73. Combine the predicted values of the load of all cells to form the future load prediction sequence of the entire charging pile network This sequence is used as the input data for the load scheduling of the charging pile network and the grid optimization.

[0052] Optionally, the S8 specifically includes:

[0053] S81. Calculate the prediction error, based on the output predicted load value and the actual load data y i,j(t), calculate the error ∈ of each cell unit c i,j of i,j (t), where y i,j (t) is the true load value of cell c i,j at time t, and the error is defined as:

[0054]

[0055] S82. Calculate the overall error, aggregate the prediction errors of all cells, and calculate the total error ∈ total of the entire network, which is represented by the mean squared error loss function:

[0056]

[0057] where N represents the total number of cell units, T represents the number of prediction time steps, and ∈ i,j (t) is the prediction error of the i,j-th cell at time step t;

[0058] S83. Perform backpropagation optimization. According to the calculated error ∈ total , use the backpropagation algorithm to update the gradients of all trainable parameters of the neural ordinary differential equation module, differentiable cellular automaton module, and load prediction model, and optimize the model parameters θ, φ, ωP, ωF; the specific update process is as follows:

[0059]

[0060] where η is the learning rate, θ old , φ old， ωF old , ωP old are the current parameters of the neural ordinary differential equation module, differentiable cellular automaton module, and load prediction model respectively, are the gradients of the error with respect to the model parameters respectively;

[0061] S84. Termination condition and training iteration. During the training process, repeatedly perform parameter gradient updates until the error converges or reaches the set maximum number of iterations N iter , to obtain the finally optimized model parameters θ final and ω final , and this optimized model can be used for real-time prediction of the charging pile load.

[0062] Optionally, the specific steps of S9 include:

[0063] S91. Adopt a dynamic learning rate strategy. During the training process, dynamically adjust the learning rate η according to the current training round t iter and the change of the error ∈ total , and the specific adjustment includes:

[0064] When the training error converges slowly, use a larger initial learning rate;

[0065] When the training error reaches a small fluctuation, reduce the learning rate to improve the stability of the optimization process;

[0066] The adjustment of the learning rate is updated according to the exponential decay formula:

[0067] η new = η init ·exp(-λ·t iter ) ;

[0068] where exp(·) is the exponential function, η init is the initial learning rate, λ is the learning rate decay factor, and t iter is the current training epoch;

[0069] S92. Adopt an early stopping strategy. During the training process, monitor the validation set error after each training epoch t iter . If the validation error does not decrease significantly within a certain number of consecutive training epochs, stop the training process to prevent overfitting. Specifically, it is defined that if the decrease in the validation error for consecutive epochs is less than a preset threshold, terminate the training; otherwise, continue the training;

[0070] S93. Adopt a batch normalization strategy. When the input data of each training batch passes through each layer of the neural network, use the batch normalization technique to normalize the output of each layer to have a mean of zero and a variance of one, reducing the problem of internal covariate shift. The specific operation is as follows:

[0071]

[0072] where μ B and σ B are the mean and standard deviation of the batch data respectively, and γ and β are trainable scaling and offset parameters;

[0073] S94. Adopt a data augmentation strategy. To enhance the generalization ability of the model, perform data augmentation on the input data. Especially in the case of less charging load data, apply two optional data augmentation methods. One is to perform time series translation on the input load data, and the other is to add a small amount of Gaussian noise to the input data to simulate uncertain environmental changes;

[0074] S95. Adopt a gradient clipping strategy. During the training process, if the norm of the gradient exceeds the preset threshold ∈ clip , then clip the gradient to avoid the phenomenon of gradient explosion. The gradient clipping operation is as follows:

[0075]

[0076] in, is the new gradient norm;

[0077] S96. By introducing the above five strategies, a stable, efficient and generalizable deep model training mechanism for charging pile load prediction for spatiotemporal complex systems is constructed, making the complex model engineering practical and feasible.

[0078] The beneficial effects of the present invention are:

[0079] (1) This invention introduces the Neural Ordinary Differential Equation as the backbone of time modeling, breaking through the limitations of the traditional discrete time modeling method and realizing the dynamic evolution modeling of the charging pile load state in the continuous time domain. By constructing the state derivative function, the coupling relationship between the charging pile state and the external disturbance factors is jointly modeled, and the adaptive step solver is used to improve the response accuracy to high-volatility load changes, so that it still has strong modeling capabilities and prediction accuracy in scenarios such as holidays, electricity price jumps, and sudden weather.

[0080] (2) This paper designs a spatial state propagation module with differentiable cellular automata as the core, divides the urban area into a grid cellular structure, and aggregates and propagates the state of charging piles in each area through sharing trainable local propagation rules. Compared with the traditional graph convolution structure, this mechanism can accurately control the spatial influence range, highlight the local modeling ability, and improve the robustness and generalization ability of the model when dealing with regional mutations, high-density regional load interference and other situations.

[0081] (3) The present invention adopts an end-to-end microarchitecture in the overall structure, jointly trains the time evolution module, the spatial propagation module and the prediction output module, and designs supporting training strategies such as dynamic learning rate adjustment, gradient clipping, early stopping mechanism, batch normalization and data enhancement, constructing a stable, efficient and engineering deployable load prediction deep model training system, which significantly improves the model's convergence efficiency, training stability and prediction reliability, and is suitable for the refined modeling and intelligent scheduling of large-scale urban-level charging pile network loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0083] Figure 1 This is an overall flow chart of a charging pile load prediction method based on deep learning proposed by the present invention;

[0084] Figure 2Structural diagram of the differentiable cellular automaton spatial propagation module for a charging pile load prediction method based on deep learning proposed by the present invention;

[0085] Figure 3 Flowchart of model training and optimization for a charging pile load prediction method based on deep learning proposed by the present invention. Detailed implementation manners

[0086] Now, the present invention will be further described in detail with reference to the accompanying drawings. These drawings are all simplified schematic diagrams, only illustrating the basic structure of the present invention in a schematic manner, so they only show the components related to the present invention.

[0087] Refer to Figures 1-3 , a charging pile load prediction method based on deep learning, comprising the following steps:

[0088] S1. Construct a regional grid, divide the area to be predicted into cell units, each unit corresponding to a group of charging piles, and initialize the basic attribute vectors of each cell;

[0089] S2. Collect the historical load data and external influencing factors of each cell within the target time window, and unify them into a structured time series input tensor;

[0090] S3. Based on the input tensor, extract the initial state values of each cell, input them into the neural ordinary differential equation modeling module, and generate a continuously evolving state over time;

[0091] S4. Take the evolving state of each cell as its current moment state vector;

[0092] S5. Based on the fixed neighborhood structure, input the current states of all cells into the differentiable cellular automaton module, and perform a spatial state propagation;

[0093] S6. Repeat the spatial state propagation operation to obtain an enhanced predicted state representation;

[0094] S7. Input the enhanced predicted state representation into the prediction module, and output the load prediction values of each cell at multiple future moments;

[0095] S8. Calculate the error between the predicted value and the actual load, perform end-to-end model training, and optimize the parameters of the neural ordinary differential equation module and the cellular automaton module;

[0096] S9. Optimize the model by different strategies to obtain a deep learning model for charging pile network load prediction, and output it as the final prediction method.

[0097] The overall method flow provided by the present invention effectively improves the comprehensiveness and response ability of charging pile load prediction by constructing a time - continuous evolution and space - propagation mechanism. Compared with the traditional single - point sequence model, this method introduces a neural ordinary differential structure in the time dimension, enhancing the model's adaptability to dynamic mutations; in the space dimension, it introduces a differentiable cellular automaton to realize the perception and propagation of the behaviors of adjacent charging piles within the region, improving the space generalization ability. The whole set of methods can be jointly trained in an end - to - end framework and is applicable to the intelligent prediction and scheduling optimization of charging loads in complex urban energy networks.

[0098] In this embodiment, S1 specifically includes: dividing the urban area to be predicted into a regular two - dimensional grid structure, with each grid area serving as a cell unit, and each cell unit covering a fixed geographical space range.

[0099] Determine the set of electric vehicle charging piles deployed within the coverage range of each cell unit, count the number of charging piles in this cell unit, and for each cell unit, construct a basic attribute vector. The basic attribute vector includes the number of charging piles in the unit, the average rated power of the charging piles, the geographical coordinates of the cell center, the voltage level of the grid access, and the maximum power supply capacity parameter of this area. Input the above - mentioned basic attribute vector as the initial state of the cell unit.

[0100] The present invention adopts a regular grid modeling method in the regional division stage, constructs a basic cell vector by combining attributes such as spatial coordinates, device density, and electrical characteristics, providing a spatially - input basis with unified structure and comprehensive features for the subsequent deep model. By unifying the expression of cell units, it improves the model's adaptability to regional structure information, helps the model have good migration and deployment capabilities between different urban scales and different - density regions, and enhances the generality and scalability of the prediction system.

[0101] In this embodiment, S2 specifically includes: collecting basic data based on the basic attribute vector, setting a unified target time window, and collecting data for each cell unit within this time window, including the historical load data of all charging piles in the unit, with the recording time granularity being minute - level or hour - level. Collect external influencing factors related to the cell load change, where the external influencing factors include weather conditions, holiday and weekday information, road traffic flow conditions, and electricity price policy change information. Perform time alignment processing on the collected data, fill in the missing time - point data, and perform normalization pre - processing on all feature data to unify it into a structured time - series format. Combine the processed historical load data and external influencing factors in chronological order into a two - dimensional input tensor.

[0102] By uniformly collecting, standardizing, and time-aligning historical load data and external influencing factors, the present invention constructs a complete data input tensor, enabling the model to not only capture time trends but also fuse multi-dimensional external perturbation variables such as weather and electricity prices. In the preprocessing stage, normalization and missing value filling operations are completed, making the model training more stable, effectively reducing the accuracy degradation caused by changes in the input distribution, and enhancing the ability of data quality to guarantee model performance.

[0103] In this embodiment, S3 specifically includes:

[0104] S31. For each cell unit c i,j , select the historical load data and external influencing factors of this cell for several consecutive time steps before the current prediction period from the input tensor, including holiday identification, electricity price, meteorological parameters, and traffic status. Organize the above data into a two-dimensional feature tensor in chronological order, and input the feature tensor into a multi-layer perceptron encoding network to output an initial state vector h i,j (t0), where t0 represents the starting time of the target prediction period;

[0105] S32. Define the state derivative function as follows:

[0106]

[0107] where h i,j (t) represents the state vector of cell c i,j at any time t, which is a continuous function of time t, and its initial value at t = t0 is h i,j (t0), serving as the starting point for solving this differential equation. f θ is the main evolution function network constructed by a multi-layer perceptron, including at least two layers of linear transformation and non-linear activation structures, modeling the time evolution law of the state vector itself. g φ is a control function module implemented by a linear neural network, used to receive the external dynamic variable e i,j (t) at the current time t and output the environmental regulation increment. θ and φ are the trainable parameter sets of the main function and the control function respectively;

[0108] S33. Perform numerical solution of the neural ordinary differential system, and input the initial state h i,j (t0) and the derivative function into the ordinary differential equation solver together, and perform integration operations in the time interval [t0, t T , and output the state sequence {h k} at multiple time points {t i,j (t k )};

[0109] S34. Construct a continuously evolving state tensor. Select representative time points from the state sequence output by the solver, combine the corresponding state vectors into an evolving state tensor, and use it as the current state input for the cell in the subsequent step S4 to perform spatial propagation modeling operations.

[0110] In the present invention, by inputting multi-dimensional historical data into an encoding network to generate an initial state vector and constructing a differential equation system by combining a main function and a control function, continuous evolution modeling of the state in the time domain is achieved, overcoming the problems of fixed granularity and lack of dynamic response in traditional discrete models. At the same time, by injecting an external perturbation variable into the control term, the model has the ability to adapt to changes in situations such as electricity prices and weather, thereby improving the robustness and interpretability of load prediction.

[0111] In this embodiment, the S33 specifically includes: The ordinary differential equation solver is used to numerically integrate the state derivative function, and the constructed initial state vector h i,j (t0) is used as the starting input, and the continuous evolution trajectory of the state variable h T (t) is solved within the time interval [t0, t i,j . The solver is an adaptive step-size integrator with the ability to trace gradients. The step-size adjustment mechanism is based on the dynamic monitoring of the change rate of the norm of the derivative function, and specifically includes the following operations:

[0112] When the change rate of the state derivative exceeds a preset threshold, the integration step size is automatically reduced to improve the characterization accuracy of the rapidly changing load behavior;

[0113] When the change of the state derivative is stable, the step size is automatically enlarged to improve the calculation efficiency;

[0114] The change rate is defined as the first-order norm form of, where Δt is the micro-element time value in the derivative calculation process;

[0115] The solver generates an intermediate state h i,j (t k ) at each integration time step, supports discrete output sampling based on time nodes, and forms a sequence of state tensors for use by the subsequent differentiable cellular automaton module;

[0116] The solver supports integration with deep learning frameworks and is compatible with the automatic differentiation mechanisms in PyTorch or TensorFlow, ensuring that the state derivative path is retained during the end-to-end training process, allowing for the differential function f θ and the control function g φAll parameters are optimized through backpropagation simultaneously, compatible with a variety of differentiable numerical methods, including Dormand-Prince, Runge-Kutta, and Adams-Bashforth multi-step methods, adapting to the modeling requirements of different load fluctuation scenarios, and applicable to dealing with the sudden behaviors of electric vehicle charging piles during holidays and peak hours.

[0117] The ordinary differential equation solver has the ability to trace gradients and a dynamic step size adjustment mechanism, which can adaptively adjust the integration accuracy when the state derivative changes violently or stably, thereby improving the computational efficiency and accuracy stability of the model in different complexity scenarios. This mechanism effectively avoids the problem of misjudging the state due to too large a step size in the high-speed change interval or causing computational redundancy due to too small a step size in the stable interval, which is conducive to achieving efficient and accurate predictive modeling.

[0118] In this embodiment, S5 specifically includes:

[0119] S51. Establish a grid-type cell structure and a neighborhood mapping function, arrange all cell units c i,j in a fixed structure grid according to two-dimensional coordinates, and define a Moore neighborhood mapping function for each cell to determine its spatial propagation correlation range;

[0120] S52. Construct a differentiable state propagation function, and define a continuously differentiable state propagation function for each cell unit:

[0121]

[0122] Among them, h i,j (t k ) is the state vector of the cell itself at the current moment, generated by the neural ordinary differential equation solver, and F ωF (·) is a state update function implemented with a convolutional neural network structure, and the parameter ωF is a set of trainable parameters. The propagation function is based on the weighted combination and feature reconstruction of the states within the neighborhood and has end-to-end differentiability;

[0123] S53. Implement a locally updated mechanism with weight sharing. The state propagation function F ω shares the same set of trainable parameters for all cell units. The neural network structure adopted includes: local convolutional kernels, a non-linear activation function σ, and a normalization operation module;

[0124] S54. Fuse the self-state and the neighborhood state for propagation. The updated state of each cell is represented by the following formula:

[0125]

[0126] Among them, W s 、Wn α is a trainable transformation matrix that acts on the cell itself and its neighboring cells respectively. m,n α is a learnable adjacency weight parameter, indicating the contribution degree of different neighboring cells to the state update of the current cell.

[0127] S55. Output the state tensor after propagation for subsequent steps. Combine the state vectors h′ i,j (t k ) of all cells after the current propagation round into a two-dimensional tensor as the input for the next propagation round.

[0128] The differentiable cellular automaton module takes the local propagation rule as the core, jointly updates the states of the current cell and its neighborhood through a convolutional neural network, and strengthens the model's spatial structure modeling ability. The shared weight mechanism and local perception structure enable the model to have a lightweight and trainable propagation function expression form, which can adapt to different regional densities and connection relationships. Compared with the static graph structure, this mechanism has greater flexibility and generalization ability, especially suitable for scenarios with local heterogeneous charging pile distributions.

[0129] In this embodiment, S6 specifically includes: performing multiple rounds of spatial propagation iterations on each cell unit, setting a predetermined number of iterations, and updating the state vector of the cell through a weighted combination based on the current cell and its neighborhood states in each round of iteration; in each round of iteration, the updated state is used as the input for the next round, and the process is repeated until the state tensor of the cell after multiple rounds of iteration is finally output for subsequent load prediction.

[0130] By setting the number of multiple rounds of spatial propagation iterations in the present invention, the model can transmit state information multiple times within a fixed neighborhood, thereby enhancing the state coupling degree between local regions and effectively capturing the behavior coordination characteristics under spatial high-frequency perturbations. This strategy not only improves the local prediction accuracy but also enhances the model's fitting ability for regional load interaction patterns, contributing to improving the prediction robustness and interpretability in traffic-dense and equipment-dense regions.

[0131] In this embodiment, S7 specifically includes:

[0132] S71. Take the cell state tensor {h′ i,j (t k )} after multiple rounds of spatial propagation as the input and input it into the subsequent load prediction module, which is used to generate the charging pile load prediction values at future times;

[0133] S72. For the input state tensor {h′ i,j (t k )}, process it through the trained load prediction model P ω to calculate the load of each cell at future times t k+1 , t k+2 ,..., tT Load prediction value at a moment wherein is the load prediction value of cell c i,j at time t, and the load prediction model P ωP is a set of regression prediction modules based on a fully connected neural network, with trainable parameter set ωP, and is trained by an end-to-end optimization method;

[0134] S73. Combine the load prediction values of all cells to form a future load prediction sequence of the entire charging pile network This sequence is used as the input data for load scheduling of the charging pile network and power grid optimization.

[0135] The prediction module takes the spatially propagated state tensor as input and combines a deep regression network structure to achieve load predictions at multiple future time points. This module can learn complex spatio-temporal mapping relationships, automatically identify trends and periodic information in the state vector, and achieve high-precision, multi-period rolling prediction outputs. At the same time, the module has trainability and end-to-end optimization capabilities, ensuring that its prediction performance can be continuously improved during training and has engineering deployment value.

[0136] In this embodiment, the specific steps of S8 include:

[0137] S81. Calculate the prediction error. Based on the output load prediction value and the actual load data y i,j (t), calculate the error ∈ i,j of each cell unit c i,j (t), where y i,j (t) is the true load value of cell c i,j at time t, and the error is defined as:

[0138]

[0139] S82. Calculate the overall error. Aggregate the prediction errors of all cells to calculate the total error ∈ total of the entire network, which is represented by the mean square error loss function:

[0140]

[0141] where N represents the total number of cell units, T represents the number of prediction time steps, and ∈ i,j (t) is the prediction error of the i,j-th cell at time step t;

[0142] S83. Perform backpropagation optimization. According to the calculated error ∈ total,The gradient update of all trainable parameters of the neural ordinary differential equation module, the differentiable cellular automaton module and the load prediction model is performed through the back-propagation algorithm to optimize the model parameters θ, φ, ωP, ωF; ,The specific updating process is as follows:

[0143]

[0144] Among them, η is the learning rate, θ old ,φ old， ωF old ,ωP old are the current parameters of the Neural Ordinary Differential Equation module, the Differentiable Cellular Automation module and the load prediction model, respectively. are the gradients of the error with respect to the model parameters;

[0145] S84, termination condition and training iteration. During the training process, the parameter gradient update is repeated until the error converges or the set maximum number of iterations N is reached. iter , and obtain the final optimized model parameter θ final and ω final ,This optimization model can be used for real-time prediction of charging pile load.

[0146] A unified loss function is constructed through error calculation and aggregation function, and end-to-end back-propagation optimization is performed based on the error, realizing the joint update of the parameters of the neural ODE, cellular automaton module and prediction module. This mechanism opens up the gradient path of the entire model, enables the coordinated training of each module, and ensures the optimal overall performance of the final model. At the same time, the model's adaptive ability is improved through multiple rounds of error feedback, effectively alleviating the problem of inconsistent performance between modules.

[0147] In this implementation manner, the S9 specifically includes:

[0148] S91, using a dynamic learning rate strategy, during the training process, according to the current training round t iter And the error ∈ total According to the changes in , the learning rate η is adjusted dynamically, including:

[0149] When the training error converges slowly, use a larger initial learning rate;

[0150] When the training error reaches a small fluctuation, reduce the learning rate to improve the stability of the optimization process;

[0151] The learning rate is updated according to the exponential decay formula:

[0152] η new =η init ·exp(-λ·t iter );

[0153] where exp(·) is the exponential function, and η init is the initial learning rate, λ is the learning rate decay factor, and t iter is the current training epoch;

[0154] S92. Adopt the early stopping strategy. During the training process, monitor the validation set error after each training epoch t iter . If the validation error does not decrease significantly within several consecutive training epochs, stop the training process to prevent overfitting. Specifically, it is defined that if the decrease in the validation error for consecutive epochs is less than a preset threshold, terminate the training; otherwise, continue the training;

[0155] S93. Adopt the batch normalization strategy. When the input data of each training batch passes through each layer of the neural network, use the batch normalization technique to normalize the output of each layer to have a mean of zero and a variance of one, reducing the problem of internal covariate shift. The specific operation is as follows:

[0156]

[0157]

[0158] where μ B and σ B are the mean and standard deviation of the batch data respectively, and γ and β are trainable scaling and offset parameters;

[0159] S94. Adopt the data augmentation strategy. To enhance the generalization ability of the model, perform data augmentation on the input data. Especially in the case of less charging load data, apply two optional data augmentation methods. One is to perform temporal translation on the input load data, and the other is to add a small amount of Gaussian noise to the input data to simulate uncertain environmental changes;

[0160] S95. Adopt the gradient clipping strategy. During the training process, if the norm of the gradient exceeds the preset threshold ∈ clip , then clip the gradient to avoid the phenomenon of gradient explosion. The gradient clipping operation is as follows:

[0161]

[0162] where is the new gradient norm;

[0163] S96. By introducing the above five strategies, a stable, efficient, and generalizable deep model training mechanism for charging pile load prediction facing spatio-temporal complex systems is constructed, making the complex model have engineering practicability and feasibility of implementation.

[0164] The present invention designs a deep model training strategy for complex spatio-temporal systems, covering means such as dynamic learning rate adjustment, early stopping mechanism, batch normalization, data augmentation, and gradient clipping. These strategies effectively improve the convergence speed and stability of the training process and the generalization ability of the final model, avoid common problems such as overfitting and gradient explosion, and significantly enhance the practicality and robustness of the method in diverse actual application scenarios.

[0165] Example 1:

[0166] To verify the feasibility and effectiveness of the charging pile load prediction method based on neural ordinary differential equations and differentiable cellular automata proposed by the present invention in an actual urban environment, we deploy this method in the core area of a large city in East China for field data testing and model comparative analysis. The area of this region is about 20 square kilometers, containing 356 operating electric vehicle charging stations. The stations have a high distribution density, diverse user types, and significant load fluctuations, making it highly representative.

[0167] During the experiment, we select the period from June 1, 2024, to August 31, 2024, as the sample time period. Using the load monitoring module deployed in the platform system, we collect the actual charging load data of each station every 10 minutes. At the same time, we synchronously obtain the weather data, holiday information, urban traffic flow, and electricity price policy in effect at the corresponding moment. After all the data is standardized, normalized, and missing values are filled, it is uniformly input into the tensor structure required by the method of the present invention.

[0168] We divide the entire region into a two-dimensional cell grid. Each cell contains 5 to 8 charging stations, and we calculate its initial attribute vector, including the number of stations, rated total power, geographical location coordinates, etc. Then, according to the steps in the method of the present invention, we perform state initialization, neural ordinary differential equation modeling, cellular automata spatial propagation, state iteration, and prediction output in sequence, and construct an overall end-to-end trainable model. To verify the effect, we select three typical scenarios for testing: ordinary working days, extreme weather days, and peak days before holidays.

[0169] The models compared with the method of the present invention include the traditional long short-term memory network model (LSTM) and a graph convolutional time series model (T-GCN) commonly used in current urban traffic prediction. All models use the same dataset, the same number of training rounds, and the same evaluation metrics. The main measurement metrics are the mean absolute error (MAE) and the mean absolute percentage error (MAPE), and we visually compare their prediction deviations during the load peak period.

[0170] The results show that the proposed method outperformed the comparison model on all three test days, especially on the eve of holidays when external disturbances were severe, showing good early recognition and fine prediction capabilities. The state continuity modeling mechanism introduced by the proposed method makes the model stable in the mutation interval, and the spatial propagation mechanism of cellular automata significantly improves the prediction consistency and local coordination accuracy within the region.

[0171] Here is a brief comparison of the prediction performance of the three models on a typical test day:

[0172] Table 1: Comparison of prediction accuracy of different models on a typical test day

[0173] Date Model MAE (kW) MAPE (%) Weekday (June 20th) The present invention 0.98 4.5 LSTM 1.45 7.2 T-GCN 1.22 6.1 Rainstorm day (July 15th) The present invention 1.12 5.1 LSTM 2.10 9.4 T-GCN 1.65 7.5 Pre-holiday peak (August 9th) The present invention 1.21 5.3 LSTM 2.48 10.0 T-GCN 2.02 8.2

[0174] It can be seen from the results listed in Table 1 that the method of the present invention shows excellent prediction accuracy and stability in different typical scenarios. Taking June 20 as an example, as a regular scenario with relatively stable load fluctuations, the average absolute error of the method of the present invention is 0.98 kilowatts, and the average absolute percentage error is 4.5%, which is significantly lower than the 1.45 kilowatts and 7.2% of the LSTM model, and better than the 1.22 kilowatts and 6.1% of the T-GCN model. This shows that in the basic scenario, the method of the present invention still maintains a high fitting accuracy, indicating that its neural constant differential modeling has good data expression capabilities in daily state evolution.

[0175] During the rainstorm on July 15, the use of charging piles was significantly affected by weather disturbances, resulting in sudden changes in load. Due to the lack of modeling ability for external disturbances, the LSTM model's error soared to 2.10 kilowatts and the MAPE was close to 10%. Although the T-GCN model takes into account spatial topological relationships, it is still difficult to perceive sudden external changes in a timely manner, with an error of 1.65 kilowatts. The method of the present invention dynamically introduces external factors such as weather and electricity prices through the state derivative control function, effectively models the state evolution process under sudden disturbances, and ultimately achieves an average error of 1.12 kilowatts and a relative error of 5.1%, which is the most stable performance.

[0176] In the pre-holiday peak scenario on August 9, the charging load showed a periodic surge due to factors such as a large number of vehicles charging together and urban congestion. The traditional LSTM model had an error of 2.48 kilowatts, with significant prediction lags, and the T-GCN model also had an error of about 2 kilowatts. The method of the present invention combines a multi-round spatial propagation mechanism to effectively identify the linkage effect of charging behaviors within the neighborhood, and improves the ability to perceive changes in regional load peaks. In the end, the method still maintained an average error of 1.21 kilowatts and a MAPE of 5.3% in this complex scenario, with significantly better accuracy than the comparison model.

[0177] In summary, the method of the present invention has good prediction performance in various typical environments. It not only has higher accuracy in stable scenarios, but also maintains strong robustness and the ability to quickly respond to local load peaks in perturbed scenarios. The improvement of this performance mainly comes from the accurate description of the continuous change of time by neural ordinary differential equations and the effective role of differentiable cellular automata in local spatial propagation. The coupling of the two enables the method to have high adaptability under complex spatio-temporal conditions, with obvious engineering practical value and promotion prospects.

[0178] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

Claims

1. A method for predicting the load of a charging pile based on deep learning, characterized in that, It includes the following steps: S1. Construct a regional grid, divide the area to be predicted into cell units, each unit corresponding to a group of charging piles, and initialize the basic attribute vector of each cell; S2. Collect the historical load data and external influencing factors of each cell within the target time window, and unify them into a structured time series input tensor; S3. Based on the input tensor, extract the initial state value of each cell, input it into the neural ordinary differential equation modeling module, and generate a continuously evolving state over time; S4. Take the evolving state of each cell as its current moment state vector; S5. Based on the fixed neighborhood structure, input the current states of all cells into the differentiable cellular automaton module and perform a spatial state propagation once; S6. Repeat the spatial state propagation operation to obtain an enhanced predicted state representation; S7. Input the enhanced predicted state representation into the prediction module and output the load prediction values of each cell at multiple future moments; S8. Calculate the error between the predicted value and the actual load, perform end-to-end model training, and optimize the parameters of the neural ordinary differential equation module and the cellular automaton module; S9. Based on the optimized model, obtain a deep learning model for predicting the load of the charging pile network and output it as the final prediction method.

2. The method for predicting the load of a charging pile based on deep learning according to claim 1, wherein, The specific content of S1 includes: Divide the urban area to be predicted into a regular two-dimensional grid structure, each grid area serving as a cell unit, each cell unit covering a fixed geographical space range, determine the set of electric vehicle charging piles deployed within the coverage range of each cell unit, count the number of charging piles in the cell unit, and for each cell unit, construct a basic attribute vector as the initial state input of the cell unit.

3. A method for predicting the load of a charging pile based on deep learning according to claim 1, characterized in that, The specific content of S2 includes: Collect basic data based on the basic attribute vector, set a unified target time window, collect data for each cell unit within the time window, including the historical load data of all charging piles in the unit, with the time granularity recorded in minutes or hours, collect external influencing factors related to the load change of the cell, where the external influencing factors include weather conditions, holiday and weekday information, road traffic flow conditions, and electricity price policy change information, perform time alignment processing on the collected data, complete the data for missing time points, perform normalization preprocessing on all feature data, unify it into a structured time series format, and combine the processed historical load data and external influencing factors in chronological order into a two-dimensional input tensor.

4. A method for predicting the load of a charging pile based on deep learning according to claim 1, wherein, The specific content of S3 includes: S31. For each cell unit c i,j , select the historical load data and external influencing factors of the cell for several consecutive time steps before the current prediction period from the input tensor, organize the data into a two-dimensional feature tensor in chronological order, and input the feature tensor into the multi-layer perceptron encoding network to output the initial state vector h i,j (t0), where t0 represents the start time of the target prediction period; S32. Define the state derivative function as follows: where h i,j (t) represents the state vector of the cell c i,j at any time t, e i,j (t) is the external control input vector of the current cell c i,j at time t, f θ is the main evolutionary function network constructed by a multi-layer perceptron, g φ is the control function module implemented by a linear neural network, and θ and φ are the sets of trainable parameters of the main function and the control function respectively; S33. Perform numerical solution of the neural ordinary differential system, and input the initial state h i,j (t0) and the derivative function into the ordinary differential equation solver together, and perform integration operations within the time interval [t0, t T , and output the sequence of state vectors {h k} at multiple time points {t i,j (t k )}; S34. Construct a continuously evolving state tensor, select representative time points from the state sequence output by the solver, and combine the corresponding state vectors into an evolving state tensor.

5. The method for predicting the load of a charging pile based on deep learning according to claim 4, wherein The specific steps of S33 include: using an ordinary differential equation solver to construct an initial state vector h i,j (t0) as the starting input, and solving for the state variable h T within the time interval [t0, t i,j (t) of the continuous evolution trajectory. The solver has the ability to trace gradients, and the step size adjustment mechanism is based on the dynamic monitoring of the change rate of the derivative function norm. The specific operations are as follows: When the rate of change of the state derivative exceeds a preset threshold, automatically reduce the integration step size; When the state derivative changes smoothly, automatically increase the step size; The rate of change is defined as in the form of the first-order norm, where Δt is the infinitesimal time value in the derivative process.

6. A method for predicting the load of a charging pile based on deep learning according to claim 1, characterized in that, The specific content of S5 includes: S51. Establish a grid-type cellular structure and a neighborhood mapping function, and arrange all cellular units c i,j in a fixed-structure grid according to two-dimensional coordinates, and define a Moore neighborhood mapping function for each cell S52. Construct a differentiable state propagation function and define a continuously differentiable state propagation function for each cell unit: where h i,j (t k ) is the state vector of the cell itself at the current moment, generated by the neural ordinary differential equation solver, and h m,n (t k ) represents the state vector of the cell c m,n in the neighborhood at time t k . represents the set of current state vectors of all neighboring cells, and F ωF (·) is the state update function implemented by a convolutional neural network structure, and the parameter ωF is the set of trainable parameters; S53. Local update mechanism for implementing weight sharing, state propagation function F ω Share the same set of trainable parameters for all cell units. The neural network structure adopted includes a local convolution kernel, a non-linear activation function σ, and a normalization operation module; S54. Fuse its own state and the neighborhood state for propagation, and the updated state of each cell is represented by the following formula: Among them, W s and W n are trainable transformation matrices respectively acting on the cell itself and its neighboring cells, and α m,n is a learnable adjacency weight parameter, indicating the contribution degree of different neighboring cells to the state update of the current cell; S55. Merge the state vectors h′ i,j (t k ) of all cells after the current propagation round into a two-dimensional tensor.

7. A method for predicting the load of a charging pile based on deep learning according to claim 1, wherein, The specific steps of S6 are as follows: perform multiple rounds of spatial propagation iteration on each cell unit, set a predetermined number of iterations, and update the state vector of the cell in each round of iteration through a weighted combination based on the current cell and the states of its neighborhood. In each round of iteration, the updated state is used as the input for the next round, and this is repeated until the cell state tensor after multiple rounds of iteration is finally output.

8. A method for predicting the load of a charging pile based on deep learning according to claim 1, characterized in that, The specific steps of S7 are as follows: S71. Take the sequence of cell state tensors {h′ i,j (t k )} after multiple rounds of spatial propagation as the input and input it into the load prediction module; S72, for the input state tensor sequence {h′ i,j (t k )}, through the trained load prediction model P ω Processing is performed to calculate each cell at the future time t k+1 ,t k+2 ,...,t T Load forecast value at the moment in For cell c i,j The load forecast value at time t, load forecast model P ωP is a set of regression prediction modules based on fully connected neural networks, with a set of trainable parameters ωP, which are trained through end-to-end optimization; S73. Combine the load prediction values of all cells to form the future load prediction sequence of the entire charging pile network This sequence is used as the input data for load scheduling of the charging pile network and power grid optimization.

9. A method for predicting the load of a charging pile based on deep learning according to claim 1, characterized in that, The specific steps of S8 are as follows: S81. Calculate the prediction error based on the output load prediction value and the actual load data y i,j (t), calculate the error ∈ i,j (t) for each cell unit c i,j , where y i,j (t) is the true load value of cell c i,j at time t, and the error is defined as: S82. Calculate the overall error, aggregate the prediction errors of all cells, and calculate the total error ∈ of the entire network total , which is represented by the mean squared error loss function: where N represents the total number of cell units, T represents the number of predicted time steps, and ∈ i,j (t) is the prediction error of the i,j-th cell at time step t; S83. Perform backpropagation optimization. According to the calculated error ∈ total , use the backpropagation algorithm to perform gradient updates on all trainable parameters of the neural ordinary differential equation module, the differentiable cellular automaton module, and the load prediction model, and optimize the model parameters θ, φ, ωP, ωF; S84: Termination conditions and training iterations. During the training process, repeatedly perform parameter gradient updates until the error converges or the set maximum number of iterations is reached to obtain the finally optimized model parameters.

10. A method for predicting the load of a charging pile based on deep learning according to claim 1, characterized in that, The specific steps of S9 are as follows: S91. Adopt a dynamic learning rate strategy. During the training process, according to the current training epoch t iter and the change of the error ∈ total , dynamically adjust the learning rate η; S92. Adopt an early stopping strategy. During the training process, monitor the validation set error after each training round t. iter If the decrease in the validation error for consecutive rounds is less than a preset threshold, terminate the training; otherwise, continue the training. S93: Adopt the batch normalization strategy. When the input data of each training batch passes through each layer of the neural network, use the batch normalization technique to normalize the output of each layer so that the mean is zero and the variance is one, reducing the problem of internal covariate shift. S94: Adopt the data augmentation strategy. In the case of less charging load data, apply two optional data augmentation methods. One is to perform time series translation on the input load data, and the other is to add a small amount of Gaussian noise to the input data to simulate uncertain environmental changes. S95. Adopt a gradient clipping strategy. During the training process, if the norm of the gradient exceeds a preset threshold ∈ clip , then clip the gradient to avoid the phenomenon of gradient explosion. The gradient clipping operation is as follows: Among them, is the new gradient norm; S96: By introducing the above five strategies, a stable, efficient, and generalizable deep model training mechanism for charging pile load prediction facing spatio-temporal complex systems is constructed.

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