This is my NN :
class torchNET(torch.nn.Module):
    
    def __init__(self, D_in, H1, H2, H3, D_out):
        """
        In the constructor we instantiate four nn.Linear modules and assign them as
        member variables.
        """
        super(torchNET, self).__init__()
        self.linear1 = torch.nn.Linear(D_in, H1)
        self.linear2 = torch.nn.Linear(H1, H2)
        self.linear3 = torch.nn.Linear(H2, H3)
        self.linear4 = torch.nn.Linear(H3, D_out)

    def forward(self, x):
        """
        In the forward function we accept a Tensor of input data and we must return
        a Tensor of output data. We can use Modules defined in the constructor as
        well as arbitrary operators on Tensors.
        """
        r1 = torch.nn.ReLU()
        t1 = torch.nn.Tanh()
        g1 = torch.nn.GLU
        m1 = torch.nn.Dropout(p=0.1)
        m2 = torch.nn.Dropout(p=0.1)
        m3 = torch.nn.Dropout(p=0.1)
        h1 = m1(t1(self.linear1(x)))#.clamp(min=0)))
        h2 = m2(t1(self.linear2(h1)))
        h3 = m3(t1(self.linear3(h2)))
        y_pred = self.linear4(h3)
        return y_pred

This is my evaluation loop :
losss_tn  = []
losss_tt  = []
losss_vl  = []

model     = torchNET(32, H1, H2, H3, D_out)

criterion = torch.nn.MSELoss(reduction='sum')
optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)
# print("It has started!")
# print("Epoch                Training     Testing     Validation")
# print("--------------------------------------------------------")
s = np.arange(10,15,1)
print("It has started!")
for num in s:
    print(num)
    print("Epoch                Training     Testing     Validation")
    print("--------------------------------------------------------")
    #for 60 20 20 splitting
    X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=num)
    X_train, X_val, y_train, y_val = train_test_split(X_train, y_train, test_size=0.25, random_state=num)
    for t in range(5000):
        optimizer.zero_grad()
        # Forward pass: Compute predicted y by passing x to the model
        y_pred    = model(X_train)
        r2        = r2_score(y_train.detach().numpy(),y_pred.detach().numpy())
        loss_tn   = criterion(y_pred, y_train)
        losss_tn.append(loss_tn.item())
        loss_tn.backward()
        optimizer.step()
        #setting model to prediction/evaluation mode
        mod_chk   = model.eval()

        #making predictions on the test dataset 20%
        y_pred_tt = mod_chk(X_test)
        r2_test   = r2_score(y_test.detach().numpy(),y_pred_tt.detach().numpy())        
        loss_tt   = criterion(y_pred_tt, y_test)
        losss_tt.append(loss_tt.item())

        #making predictions on the validation dataset 20%       
        y_pred_vl = mod_chk(X_val)
        r2_vali   = r2_score(y_val.detach().numpy(),y_pred_vl.detach().numpy())        
        loss_vl   = criterion(y_pred_vl, y_val)
        losss_vl.append(loss_vl.item())

        if t % 1000 == 999:
    #         print("Epoch = ",t)
    #         print("Epoch    Losses:     Training     Testing     Validation")
    #         print("--------------------------------------------------------")
            if t==999:
                print("%d         Losses:   %0.3f        %0.3f        %0.3f "%(t,loss_tn.item(),loss_tt.item(),loss_vl.item()))
                print("            R2_sc :   %0.3f        %0.3f        %0.3f "%(r2,r2_test,r2_vali))
            else:
                print("%d        Losses:   %0.3f        %0.3f        %0.3f "%(t,loss_tn.item(),loss_tt.item(),loss_vl.item()))
                print("            R2_sc :   %0.3f        %0.3f        %0.3f "%(r2,r2_test,r2_vali))
        # Zero gradients, perform a backward pass, and update the weights.
#         optimizer.zero_grad()
#         loss_tn.backward()
#         loss_tt.backward()
#         loss_vl.backward()
#         optimizer.step()
    plt.plot(losss_tn,label='Training Loss')
    plt.plot(losss_tt,label='Testing Loss')
    plt.plot(losss_vl,label='Validation Loss')
    plt.ylim([0,5])
    plt.xlabel('Epochs')
    plt.ylabel('Loss, MSE')
    plt.title('Visualising Losses')
    plt.legend(loc='upper right')
    plt.show()
    losss_tn  = []
    losss_tt  = []
    losss_vl  = []

This is the snippet of the output :

Screenshot 2020-03-24 at 12.51.19 AM822×834 119 KB

My issue is my training loss is higher than testing and validation loss. Let me know where I am making the mistake.