为什么我非常简单的神经网络没有产生正确的结果？

Question

我创建了一个非常简单的神经网络来求解以下ode：

我的代码似乎不正常，这很奇怪，因为颂歌很简单。以下是我的评论代码。我相信这个问题来自torch.gradient（preds），但我无法弄清楚。任何帮助将不胜感激！

inputs = np.linspace(0,2,50,dtype='float32')
inputs = torch.from_numpy(inputs)
inputs.requires_grad = True
inputs.float()

# Initial Condition
A = 0.0


# Known trial solution for general ODE 
trial_solution = lambda I: A + I * NN(I)


ODE = lambda x: x


# Numbers of neurons from layers 1 to 3 
neuron_1 = 9
neuron_2 = 12
neuron_3 = 8

# Initializing the weights and biases 
W1 = torch.randn(len(inputs), neuron_1, requires_grad=True).float()
B1 = torch.randn(neuron_1, requires_grad=True).float()

W2 = torch.randn(neuron_1, neuron_2, requires_grad=True)
B2 = torch.randn(neuron_2, requires_grad=True)

W3 = torch.randn(neuron_2, neuron_3, requires_grad=True)
B3 = torch.randn(neuron_3, requires_grad=True)

W4 = torch.randn(neuron_3, len(inputs), requires_grad=True)
B4 = torch.randn(len(inputs), requires_grad=True)

# General sigmoid function used for neurons inside hidden layers
def Sigmoid(z):
    return 1/(1+torch.exp(-z))


# Defining the structure of my Neural Network
def NN(x):
    z1 = W1.t() @ x  + B1
    z2 = Sigmoid(z1)
    z3 = W2.t() @ z2 + B2
    z4 = Sigmoid(z3)
    z5 = W3.t() @ z4 + B3
    z6 = Sigmoid(z5)
    return W4.t() @ z6 + B4

# Defining the mean squared error to be my loss function
def mse(t1,t2):
    diff = t1-t2
    return torch.sum(diff*diff)/diff.numel()

# Iterating over number of epochs for backprop. 
for i in range(10000):
    preds = trial_solution(inputs)
    preds_gradient = torch.gradient(preds) # Possible problem!! 
    preds_gradient =preds_gradient[0]
    target_gradient = ODE(inputs)
    loss = mse(preds_gradient,target_gradient)
    loss.backward()
    #print(loss)
    with torch.no_grad():
        W1 -= W1.grad*1e-2
        B1 -= B1.grad*1e-2
        W1.grad.zero_()
        B1.grad.zero_()
        
        W2 -= W2.grad*1e-2
        B2 -= B2.grad*1e-2
        W2.grad.zero_()
        B2.grad.zero_()
        
        W3 -= W3.grad*1e-2
        B3 -= B3.grad*1e-2
        W3.grad.zero_()
        B3.grad.zero_()
        
        W4 -= W4.grad*1e-2
        B4 -= B4.grad*1e-2
        W4.grad.zero_()
        B4.grad.zero_()
        
        



numpy_tensors = np.linspace(0,2,50,dtype='float32')
numpy_tensors = torch.from_numpy(numpy_tensors)


final_pred = trial_solution(inputs).detach().numpy()


xx = np.linspace(0,2,50)
yt = xx*xx * 0.5
plt.plot(numpy_tensors,final_pred, label='Prediction from NN')
plt.plot(xx,yt,label = 'True Solution')
plt.legend()