Dear community,
I am trying to make a Physics Informed Neural Network for the heat equation in 1D:
I tried the following code to make a loss function for PDE residual:
def lossPDE(self,x_PDE):
g = x_PDE.clone()
g.requires_grad = True # Enable differentiation
f = self.forward(g)
f_x_t = torch.autograd.grad(f,g,torch.ones([g.shape[0],1]).to(device),retain_graph=True, create_graph=True)[0] # first derivative of time
f_xx_tt = torch.autograd.grad(f_x_t,g,torch.ones(g.shape).to(device), create_graph=True)[0]#second derivative of x
f_t = f_x_t[:,[1]]
f_xx = f_xx_tt[:,[0]]
f = f_t - alpha * f_xx
return self.loss_function(f,f_hat) # f_hat is a tensor of zeros and it minimizes the f value
In the simulation I am making a one day simulation (86400 seconds) for a bar with the length of 1 meters. Now, I want to make my PDE dimensionless. How can I do it in pytorch? Which part of my code should be changed? The unit of alpha is already in m2/s. I can share my whole code but it would be hundreds lines of code.
I very much appreciate any help in advance.