GNN预测多步长时间步预测

### 使用图神经网络 (GNN) 进行多步长时间序列预测 #### 数据准备与预处理 为了使用图神经网络进行多步长时间序列预测，首先需要准备好输入数据并将其转换成适合模型的形式。对于时间序列数据而言，通常会将历史观测值作为节点特征，并构建合适的邻接矩阵来表示不同时间节点之间的关系。 ```python import torch from torch_geometric.data import Data def prepare_data(time_series, window_size=24): """Prepare time series data into graph format.""" num_nodes = len(time_series) - window_size edge_index = [] # Create edges between consecutive timesteps within the sliding window for i in range(num_nodes): for j in range(window_size-1): edge_index.append([i+j, i+j+1]) x = torch.tensor(time_series[:-window_size], dtype=torch.float).view(-1, 1) y = torch.tensor(time_series[window_size:], dtype=torch.float) return Data(x=x, edge_index=torch.LongTensor(edge_index).t().contiguous(), y=y) ``` 此函数创建了一个滑动窗口内的边连接相邻的时间戳，并返回一个`torch_geometric.Data`对象用于后续建模[^3]。 #### 构建基于GNN的预测模型 接下来定义一个简单的图卷积层堆叠结构来进行回归任务： ```python import torch.nn.functional as F from torch_geometric.nn import GCNConv class TimeSeriesPredictor(torch.nn.Module): def __init__(self, input_dim, hidden_dims=[64]): super(TimeSeriesPredictor, self).__init__() layers = [] prev_dim = input_dim for dim in hidden_dims: conv_layer = GCNConv(prev_dim, dim) layers += [conv_layer] prev_dim = dim self.layers = torch.nn.ModuleList(layers) self.regressor = torch.nn.Linear(hidden_dims[-1], 1) def forward(self, data): h = data.x for layer in self.layers: h = F.relu(layer(h, data.edge_index)) out = self.regressor(h.mean(dim=-2)) # Average pooling over all nodes/timestamps return out.squeeze() ``` 这里采用平均池化操作汇总整个图的信息以得到最终输出向量[^4]。 #### 训练过程 最后编写一段代码片段展示如何训练上述定义好的模型: ```python device = 'cuda' if torch.cuda.is_available() else 'cpu' model = TimeSeriesPredictor(input_dim=1).to(device) optimizer = torch.optim.Adam(model.parameters(), lr=0.01) criterion = torch.nn.MSELoss() data = prepare_data(your_time_series_here).to(device) for epoch in range(epochs): model.train() optimizer.zero_grad() output = model(data) loss = criterion(output[data.train_mask], data.y[data.train_mask]) loss.backward() optimizer.step() print(f'Training Loss: {loss.item():.4f}') ``` 通过这种方式可以有效地利用图神经网络捕捉到时间序列中的复杂模式从而完成对未来多个时间点上的预测[^5]。