PyTorch使用Torchdyn实现连续时间神经网络的代码示例

 from torchdyn.datasets import ToyDataset  
 import matplotlib.pyplot as plt  
   
 # 生成示例数据
 d = ToyDataset()  
 X, yn = d.generate(n_samples=512, noise=1e-1, dataset_type='moons')  
 # 可视化数据集
 colors = ['orange', 'blue']  
 fig, ax = plt.subplots(figsize=(3, 3))  
 for i in range(len(X)):  
     ax.scatter(X[i, 0], X[i, 1], s=1, color=colors[yn[i].int()])  
 plt.show()

 import torch  
 import torch.utils.data as data  
   
 device = torch.device("cpu")  # 如果使用GPU则改为'cuda'
 X_train = torch.Tensor(X).to(device)  
 y_train = torch.LongTensor(yn.long()).to(device)  
 train = data.TensorDataset(X_train, y_train)  
 trainloader = data.DataLoader(train, batch_size=len(X), shuffle=True)

 import torch.nn as nn  
   
 # 定义向量场f
 f = nn.Sequential(  
     nn.Linear(2, 16),  
     nn.Tanh(),  
     nn.Linear(16, 2)  
 )

NeuralODE

 from torchdyn.core import NeuralODE  
   
 t_span = torch.linspace(0, 1, 5)  # 时间跨度
 model = NeuralODE(f, sensitivity='adjoint', solver='dopri5').to(device)

 import pytorch_lightning as pl  
   
 class Learner(pl.LightningModule):  
     def __init__(self, t_span: torch.Tensor, model: nn.Module):  
         super().__init__()  
         self.model, self.t_span = model, t_span  
     def forward(self, x):  
         return self.model(x)  
     def training_step(self, batch, batch_idx):  
         x, y = batch  
         t_eval, y_hat = self.model(x, self.t_span)  
         y_hat = y_hat[-1]  # 选择轨迹的最后一个点
         loss = nn.CrossEntropyLoss()(y_hat, y)  
         return {'loss': loss}  
     def configure_optimizers(self):  
         return torch.optim.Adam(self.model.parameters(), lr=0.01)  
     def train_dataloader(self):  
         return trainloader

 learn = Learner(t_span, model)  
 trainer = pl.Trainer(max_epochs=200)  
 trainer.fit(learn)

 t_eval, trajectory = model(X_train, t_span)  
 trajectory = trajectory.detach().cpu()  
   
 fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(10, 2))  
 for i in range(500):  
     ax0.plot(t_span, trajectory[:, i, 0], alpha=0.1, color=colors[int(yn[i])])  
     ax1.plot(t_span, trajectory[:, i, 1], alpha=0.1, color=colors[int(yn[i])])  
 ax0.set_title("维度 0")  
 ax1.set_title("维度 1")  
 plt.show()

 x = torch.linspace(trajectory[:, :, 0].min(), trajectory[:, :, 0].max(), 50)  
 y = torch.linspace(trajectory[:, :, 1].min(), trajectory[:, :, 1].max(), 50)  
 X, Y = torch.meshgrid(x, y)  
 z = torch.cat([X.reshape(-1, 1), Y.reshape(-1, 1)], 1)  
 f_eval = model.vf(0, z.to(device)).cpu().detach()  
   
 fx, fy = f_eval[:, 0], f_eval[:, 1]  
 fx, fy = fx.reshape(50, 50), fy.reshape(50, 50)  
 fig, ax = plt.subplots(figsize=(4, 4))  
 ax.streamplot(X.numpy(), Y.numpy(), fx.numpy(), fy.numpy(), color='black')  
 plt.show()