Burgers equation solved by PINN in PyTorch

• PyTorch
• Numpy
• SciPy
• Matplotlib

• Boundary train data collected in a [100, 2] numpy array: pairs of (x, t)
• Boundary solution data collected in a [100, 2] numpy array
• Collocation points come in a [10100, 2] numpy array: paris of (x, t)
• These arrays are passed to the PINN
• These arrays are transformed into torch tensors
• The net is created manualy, although you should better inherit from torch.nn.Module
• The net takes a two-input vector and returns a one-output vector
• LBFGS is used to update the net's gradients (this is a full-batch prodecure)
• Xavier initialization didn't work out for me, so I left it alone
• The net represents the u function, f is a function of the net
• f is the differential equation equaled to zero
• Both the boundary conditions and the PDE losses (u_loss and f_loss) are added together
• The sum of these two losses is the minimized using the torch.optimizer

• Just run the module
• Type pinn.plot() in the console to check the plot