Fast and Accurate Numerical Solution of Allen–Cahn Equation

Algorithm 1

Our CNN model for solving AC equation (6).

	class Net (nn.Module):
	def __init__(self, h2, dt, eps, device):
	super (Net, self).__init__()
	# 2^nd order differencing filter
	self.lap = torch.Tensor ([[[[0., 1., 0.], [1., −4., 1], [0., 1., 0.]]]]).to (device)
	self.pad = nn.ReplicationPad2d (1) #Replication pad for boundary condition.
	self.alpha = dt/eps 2
	self.beta = dt/h2
	def forward (self, x):
	u_pad = self.pad (x) #boundary condition
	reaction = F.conv2d (u_pad, self.lap) #reaction term
	x = (1 + self.alpha) x-self.alpha x 3 + self.beta reaction
	return x