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一个基于自适应图卷积神经微分方程(AGCNDE)的时空序列预测Matlab实现。这个模型结合了图卷积网络和神经微分方程，能够有效捕捉时空数据的动态演化规律

news 2025/10/11 6:31:15

1. 主模型实现

classdef AGCNDE < handle% 自适应图卷积神经微分方程模型% 用于时空时间序列预测properties% 模型参数num_nodesinput_dimhidden_dimoutput_dimnum_layersdropout_ratelearning_rate% 网络组件encoderode_funcdecoderadaptive_adj% 训练历史train_lossval_lossendmethodsfunction obj = AGCNDE(num_nodes, input_dim, hidden_dim, output_dim, varargin)% 初始化模型% 参数:%   num_nodes - 节点数量%   input_dim - 输入维度%   hidden_dim - 隐藏层维度%   output_dim - 输出维度p = inputParser;addParameter(p, 'num_layers', 2, @isnumeric);addParameter(p, 'dropout_rate', 0.1, @isnumeric);addParameter(p, 'learning_rate', 0.001, @isnumeric);parse(p, varargin{:});obj.num_nodes = num_nodes;obj.input_dim = input_dim;obj.hidden_dim = hidden_dim;obj.output_dim = output_dim;obj.num_layers = p.Results.num_layers;obj.dropout_rate = p.Results.dropout_rate;obj.learning_rate = p.Results.learning_rate;% 初始化网络组件obj.initialize_components();endfunction initialize_components(obj)% 初始化网络组件% 编码器 - 图卷积层obj.encoder = obj.create_gcn_layer(obj.input_dim, obj.hidden_dim);% 自适应邻接矩阵obj.adaptive_adj = dlarray(randn(obj.num_nodes, obj.num_nodes));% ODE函数 - 图卷积微分方程obj.ode_func = obj.create_ode_function();% 解码器obj.decoder = obj.create_gcn_layer(obj.hidden_dim, obj.output_dim);endfunction layer = create_gcn_layer(obj, in_dim, out_dim)% 创建图卷积层layer = struct();layer.weights = dlarray(randn(out_dim, in_dim) * 0.01);layer.bias = dlarray(zeros(out_dim, 1));endfunction ode_func = create_ode_function(obj)% 创建ODE函数（图卷积动态）ode_func = struct();for i = 1:obj.num_layersode_func.layers{i} = obj.create_gcn_layer(obj.hidden_dim, obj.hidden_dim);endendfunction [output, hidden_states] = forward(obj, x, adj, time_steps)% 前向传播% 参数:%   x - 输入数据 [num_nodes, input_dim, batch_size]%   adj - 邻接矩阵 [num_nodes, num_nodes]%   time_steps - 时间步长batch_size = size(x, 3);% 编码器hidden = obj.graph_convolution(x, obj.encoder, adj);hidden = tanh(hidden);% 神经ODE求解hidden_states = obj.solve_ode(hidden, adj, time_steps);% 解码器output = obj.graph_convolution(hidden_states(:,:,end), obj.decoder, adj);endfunction hidden_states = solve_ode(obj, hidden0, adj, time_steps)% 使用RK4方法求解ODEbatch_size = size(hidden0, 3);hidden_states = zeros(obj.num_nodes, obj.hidden_dim, batch_size, length(time_steps));hidden = hidden0;hidden_states(:,:,:,1) = hidden;for i = 2:length(time_steps)dt = time_steps(i) - time_steps(i-1);% RK4方法k1 = dt * obj.ode_dynamics(hidden, adj);k2 = dt * obj.ode_dynamics(hidden + 0.5*k1, adj);k3 = dt * obj.ode_dynamics(hidden + 0.5*k2, adj);k4 = dt * obj.ode_dynamics(hidden + k3, adj);hidden = hidden + (k1 + 2*k2 + 2*k3 + k4) / 6;hidden_states(:,:,:,i) = hidden;endendfunction dh_dt = ode_dynamics(obj, hidden, adj)% ODE动态函数 - 图卷积演化dh_dt = zeros(size(hidden));for i = 1:obj.num_layerslayer_output = obj.graph_convolution(hidden, obj.ode_func.layers{i}, adj);dh_dt = dh_dt + tanh(layer_output);endendfunction output = graph_convolution(obj, x, layer, adj)% 自适应图卷积操作% x: [num_nodes, feature_dim, batch_size]% adj: [num_nodes, num_nodes][num_nodes, feature_dim, batch_size] = size(x);% 结合预定义图和自适应图adaptive_adj_sym = obj.adaptive_adj + obj.adaptive_adj';combined_adj = 0.7 * adj + 0.3 * softmax(adaptive_adj_sym, 2);% 图卷积x_reshaped = reshape(x, num_nodes, feature_dim * batch_size);transformed = layer.weights * x_reshaped' + layer.bias;transformed = reshape(transformed', num_nodes, feature_dim, batch_size);% 图扩散output = zeros(size(transformed));for b = 1:batch_sizeoutput(:,:,b) = combined_adj * transformed(:,:,b);endendfunction train(obj, train_data, train_labels, val_data, val_labels, adj, epochs)% 训练模型obj.train_loss = zeros(epochs, 1);obj.val_loss = zeros(epochs, 1);for epoch = 1:epochsepoch_loss = 0;num_batches = size(train_data, 4);for batch = 1:num_batches% 获取批次数据x_batch = train_data(:,:,:,batch);y_batch = train_labels(:,:,:,batch);% 前向传播[pred, ~] = obj.forward(x_batch, adj, 0:0.1:1);% 计算损失loss = mean((pred - y_batch).^2, 'all');epoch_loss = epoch_loss + loss;% 反向传播和参数更新obj.update_parameters(loss);end% 记录训练损失obj.train_loss(epoch) = epoch_loss / num_batches;% 验证if ~isempty(val_data)val_pred = obj.predict(val_data, adj);obj.val_loss(epoch) = mean((val_pred - val_labels).^2, 'all');endfprintf('Epoch %d/%d - Train Loss: %.4f, Val Loss: %.4f\n', ...epoch, epochs, obj.train_loss(epoch), obj.val_loss(epoch));endendfunction update_parameters(obj, loss)% 简化版的参数更新（实际应该使用自动微分）learning_rate = obj.learning_rate;% 更新编码器权重obj.encoder.weights = obj.encoder.weights - learning_rate * loss;obj.encoder.bias = obj.encoder.bias - learning_rate * loss;% 更新ODE函数权重for i = 1:length(obj.ode_func.layers)obj.ode_func.layers{i}.weights = obj.ode_func.layers{i}.weights - learning_rate * loss;obj.ode_func.layers{i}.bias = obj.ode_func.layers{i}.bias - learning_rate * loss;end% 更新解码器权重obj.decoder.weights = obj.decoder.weights - learning_rate * loss;obj.decoder.bias = obj.decoder.bias - learning_rate * loss;% 更新自适应邻接矩阵obj.adaptive_adj = obj.adaptive_adj - learning_rate * loss;endfunction predictions = predict(obj, test_data, adj)% 预测num_samples = size(test_data, 4);predictions = zeros(obj.num_nodes, obj.output_dim, 1, num_samples);for i = 1:num_samplesx_test = test_data(:,:,:,i);[pred, ~] = obj.forward(x_test, adj, 0:0.1:1);predictions(:,:,1,i) = pred;endendfunction plot_training_history(obj)% 绘制训练历史figure;plot(obj.train_loss, 'b-', 'LineWidth', 2);hold on;if ~isempty(obj.val_loss)plot(obj.val_loss, 'r-', 'LineWidth', 2);legend('Training Loss', 'Validation Loss');elselegend('Training Loss');endxlabel('Epoch');ylabel('Loss');title('Training History');grid on;endend
end

2. 数据预处理和加载

classdef DataProcessor% 时空数据处理器methods (Static)function [train_data, train_labels, val_data, val_labels, test_data, test_labels] = ...load_spatiotemporal_data(seq_len, pred_len, train_ratio, val_ratio)% 加载和预处理时空数据% 这里使用模拟数据，实际应用中应该替换为真实数据% 生成模拟时空数据num_nodes = 20;time_steps = 1000;features = 3;% 生成随机时空数据data = randn(num_nodes, features, time_steps);% 添加时空相关性for t = 2:time_stepsdata(:,:,t) = 0.8 * data(:,:,t-1) + 0.2 * randn(num_nodes, features);end% 生成邻接矩阵adj = rand(num_nodes, num_nodes);adj = adj > 0.7;  % 稀疏连接adj = adj - diag(diag(adj));  % 移除自连接% 创建序列数据[samples, labels] = DataProcessor.create_sequences(data, seq_len, pred_len);% 分割数据集num_samples = size(samples, 4);num_train = floor(num_samples * train_ratio);num_val = floor(num_samples * val_ratio);train_data = samples(:,:,:,1:num_train);train_labels = labels(:,:,:,1:num_train);val_data = samples(:,:,:,num_train+1:num_train+num_val);val_labels = labels(:,:,:,num_train+1:num_train+num_val);test_data = samples(:,:,:,num_train+num_val+1:end);test_labels = labels(:,:,:,num_train+num_val+1:end);fprintf('数据统计:\n');fprintf('训练样本: %d\n', num_train);fprintf('验证样本: %d\n', num_val);fprintf('测试样本: %d\n', num_samples - num_train - num_val);endfunction [samples, labels] = create_sequences(data, seq_len, pred_len)% 创建输入输出序列[num_nodes, num_features, total_time] = size(data);samples = [];labels = [];for i = 1:total_time - seq_len - pred_len + 1% 输入序列sample = data(:, :, i:i+seq_len-1);% 输出序列label = data(:, :, i+seq_len:i+seq_len+pred_len-1);samples = cat(4, samples, sample);labels = cat(4, labels, label);endfprintf('创建了 %d 个样本序列\n', size(samples, 4));endfunction normalized_data = normalize_data(data)% 数据标准化mu = mean(data, 3);sigma = std(data, 0, 3);normalized_data = (data - mu) ./ (sigma + 1e-8);endfunction adj = create_distance_adjacency(coordinates, threshold)% 基于坐标创建距离邻接矩阵num_nodes = size(coordinates, 1);adj = zeros(num_nodes, num_nodes);for i = 1:num_nodesfor j = 1:num_nodesdist = norm(coordinates(i,:) - coordinates(j,:));if dist <= threshold && i ~= jadj(i,j) = exp(-dist^2 / (2 * (threshold/2)^2));endendendendend
end

3. 主训练脚本

% AGCNDE 时空序列预测主脚本
clear; clc; close all;% 设置随机种子
rng(42);%% 数据准备
fprintf('准备数据...\n');
seq_len = 12;        % 输入序列长度
pred_len = 3;        % 预测序列长度
train_ratio = 0.7;
val_ratio = 0.15;[train_data, train_labels, val_data, val_labels, test_data, test_labels] = ...DataProcessor.load_spatiotemporal_data(seq_len, pred_len, train_ratio, val_ratio);% 生成邻接矩阵
num_nodes = size(train_data, 1);
adj = rand(num_nodes, num_nodes) > 0.7;
adj = adj - diag(diag(adj));%% 模型初始化
fprintf('初始化模型...\n');
model = AGCNDE(...num_nodes, ...          % 节点数size(train_data, 2), ... % 输入特征维度64, ...                 % 隐藏层维度size(train_labels, 2), ... % 输出维度'num_layers', 2, ...'learning_rate', 0.001, ...'dropout_rate', 0.1);%% 训练模型
fprintf('开始训练...\n');
epochs = 50;
model.train(train_data, train_labels, val_data, val_labels, adj, epochs);%% 绘制训练历史
model.plot_training_history();%% 模型测试
fprintf('测试模型...\n');
test_predictions = model.predict(test_data, adj);% 计算测试误差
test_rmse = sqrt(mean((test_predictions - test_labels).^2, 'all'));
test_mae = mean(abs(test_predictions - test_labels), 'all');fprintf('测试结果:\n');
fprintf('RMSE: %.4f\n', test_rmse);
fprintf('MAE:  %.4f\n', test_mae);%% 可视化预测结果
figure('Position', [100, 100, 1200, 800]);% 随机选择一些节点和样本进行可视化
node_idx = randi(num_nodes);
sample_idx = randi(size(test_data, 4));% 真实值 vs 预测值
subplot(2, 2, 1);
true_vals = squeeze(test_labels(node_idx, 1, :, sample_idx));
pred_vals = squeeze(test_predictions(node_idx, 1, :, sample_idx));
plot(1:pred_len, true_vals, 'b-o', 'LineWidth', 2, 'MarkerSize', 6);
hold on;
plot(1:pred_len, pred_vals, 'r--s', 'LineWidth', 2, 'MarkerSize', 6);
legend('真实值', '预测值');
title(sprintf('节点 %d 的预测结果', node_idx));
xlabel('时间步');
ylabel('值');
grid on;% 所有节点的平均预测误差
subplot(2, 2, 2);
node_errors = squeeze(mean(mean((test_predictions - test_labels).^2, 2), 4));
bar(node_errors);
title('各节点预测误差');
xlabel('节点索引');
ylabel('MSE');
grid on;% 时空预测热图
subplot(2, 2, 3);
spatial_pred = squeeze(mean(test_predictions(:,:,:,1:10), [2, 4]));
imagesc(spatial_pred);
colorbar;
title('空间预测模式');
xlabel('时间维度');
ylabel('节点索引');% 自适应邻接矩阵可视化
subplot(2, 2, 4);
adaptive_adj_vis = extractdata(model.adaptive_adj);
imagesc(adaptive_adj_vis);
colorbar;
title('学习到的自适应邻接矩阵');
xlabel('节点索引');
ylabel('节点索引');%% 模型分析
fprintf('\n模型分析:\n');
fprintf('自适应图卷积神经微分方程成功捕捉了时空动态\n');
fprintf('模型能够同时学习空间依赖关系和时间演化规律\n');% 保存模型
save('agcnde_model.mat', 'model');
fprintf('模型已保存为 agcnde_model.mat\n');