用pytorch拟合一个圆

Question

如何构建一个网络，输入为横截面圆上的坐标，输出为该坐标的平方和。输入=[x,y,1]，输出=[square(x)+平方(y)]

import torch 
import torch.nn as nn
import numpy as np
from torch.utils.data import TensorDataset, DataLoader
import torch.optim 
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
features = torch.tensor([[8.3572,-11.3008,1],[6.2795,-12.5886,1],[4.0056,-13.4958,1]
                         ,[1.6219,-13.9933,1],[-0.8157,-14.0706,1],[-3.2280,-13.7250,1]
                         ,[-5.5392,-12.9598,1],[-7.6952,-11.8073,1],[-9.6076,-10.3035,1],
                         [-11.2532,-8.4668,1],[-12.5568,-6.3425,1],[-13.4558,-4.0691,1],
                         [-13.9484,-1.7293,1],[-14.0218,0.7224,1],[-13.6791,3.1211,1],
                         [-12.9064,5.4561,1],[-11.7489,7.6081,1],[-10.2251,9.5447,1],
                         [5.4804,12.8044,1],[7.6332,11.6543,1],[9.5543,10.1454,1],
                         [11.1890,8.3117,1],[12.4705,6.2460,1],[13.3815,3.9556,1],
                         [13.8733,1.5884,1],[13.9509,-0.8663,1],[13.6014,-3.2793,1],
                         [12.8572,-5.5526,1],[11.7042,-7.7191,1],[10.1761,-9.6745,1],
                         [-8.4301,11.1605,1],[-6.3228,12.4433,1],[-4.0701,13.3401,1],
                         [-1.6816,13.8352,1],[0.7599,13.9117,1],[3.1672,13.5653,1]]).to(device)
labels = []
for i in range(features.shape[0]):
    label=(features[i][0])**2+(features[i][1])**2
    labels.append(label)
labels = torch.tensor(labels).to(device)
num_input ,num_hidden,num_output = 3,64,1
net = nn.Sequential(
    nn.Linear(num_input,num_hidden),
    nn.Linear(num_hidden,num_output)
).to(device)

def init_weights(m):
    if type(m) == nn.Linear:
        nn.init.xavier_normal_(m.weight)

net.apply(init_weights)

def init_bias(m):
    if type(m) == nn.Linear:
        nn.init.xavier_normal_(m.bias)

loss = nn.MSELoss()


num_epochs = 10
batch_size = 6
lr=0.001
trainer = torch.optim.RAdam(net.parameters(),lr=lr)
dataset = TensorDataset(features,labels)
data_loader = DataLoader(dataset,batch_size=batch_size,shuffle=True)

for i in range (num_epochs):
    for X,y in data_loader:
        y_hat = net(X)
        l = loss(y_hat,y.reshape(y_hat.shape))
        trainer.zero_grad()
        l.backward()
        trainer.step()
    with torch.no_grad():
        print(l.item())

我制作了一个只有一个隐藏层的网络，但它的损失非常高，几乎不可能拟合。

Answer 1

为了提高代码的收敛性，您可以执行以下建议：

• 使用最小-最大缩放或标准化将输入数据缩放到类似范围：

mean = features[:,:2].mean(dim=0)
std = features[:,:2].std(dim=0)
features[:,:2] = (features[:,:2] - mean) / std

• 增加

  num_epochs

  ：

num_epochs = 100

• 改变

  batch_size

  ：

batch_size = 2

我使用上述更改运行您的代码，它收敛了。

希望这有帮助。