I have modified my training scripts as follows, adding the torch.nn.utils.clip_grad_norm_  just after  loss.backward, but the issue still remains:
class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv1d(1, 6, 5)
        self.bn1 = nn.BatchNorm1d(6)
        self.conv2 = nn.Conv1d(6, 16, 1)
        self.bn2 = nn.BatchNorm1d(16)
        self.fc1 = nn.Linear(16 * 996, 120)
        self.bn3 = nn.BatchNorm1d(120)
        self.fc2 = nn.Linear(120, 84)
        self.bn4 = nn.BatchNorm1d(84)
        self.fc3 = nn.Linear(84, 4)

    def forward(self, x):
        x = F.relu(self.bn1(self.conv1(x)))
        x = F.relu(self.bn2(self.conv2(x)))
        x = torch.flatten(x, 1)
        x = F.relu(self.bn3(self.fc1(x)))
        x = F.relu(self.bn4(self.fc2(x)))
        x = F.log_softmax(self.fc3(x))
        return x

net = Net()
net.to(device)

epsilon = 1e-6
# criterion = nn.CrossEntropyLoss()
criterion = nn.NLLLoss()
# optimizer = optim.SGD(net.parameters(), lr=1e-10, momentum=0.9)
# optimizer = optim.Adagrad(net.parameters(), lr=1e-5)
optimizer = optim.Adam(net.parameters(), lr=1e-10)

epochs = 100
for epoch in range(epochs):
    running_loss = 0.0
    for i, data in enumerate(data_loader, 0):
        input, label = data
        input, label = input.unsqueeze(1).float().to(device), label.to(device)

        # zero the parameter gradients
        optimizer.zero_grad()

        # forward + backward + optimize
        outputs = net(input)
        outputs = outputs.add(epsilon)
        loss = criterion(outputs, label)
        print(loss.item())
        loss.backward()
        torch.nn.utils.clip_grad_norm_(net.parameters(), 0.5)
        print(loss.item())
        optimizer.step()

        # print statistics
        running_loss += loss.item()
        if i % 100 == 0:
            print('[%d, %5d] loss: %.3f' %
                  (epoch + 1, i + 1, running_loss / 2000))
            running_loss = 0.0

print('Finished Training')

1.5973020792007446
1.5973020792007446
[1,     1] loss: 0.001
1.4559650421142578
1.4559650421142578
1.5160048007965088
1.5160048007965088
1.5282397270202637
1.5282397270202637
1.4953101873397827
1.4953101873397827
1.4367845058441162
1.4367845058441162
1.48429274559021
1.48429274559021
1.5157661437988281
1.5157661437988281
1.4474157094955444
1.4474157094955444
1.4853960275650024
1.4853960275650024
nan
nan
nan
nan
nan
nan
nan

What am I doing wrong here? Desperately need some help here.