PINN - Heat Equation

Physics-Informed Neural Network (PINN) model for simulating the dissipation of a heat source in time and space according to the Fourier equation.

The file HE_PINN is organized into the following sections:

• Training dataset creation
• Neural network (NN) architecture definition
• NN training using ADAM optimizer
• Trining plots
• Validation plots
• Error analysis

Implemented Functions

The file modelLoss includes the following main functions:

• model_loss: main function for computing the total loss
• pinn_loss: PDE-based loss function
• lossIC: loss for initial condition enforcement

     alpha = 5^2;
  T0 =exp(-alpha*x.^2);

• lossBC: loss for boundary condition enforcement (Dirichlet conditions)

The function heat_solution calculates the numerical solution of the partial differential equation with the command pdepe that needs the following main functions:

• pde_function: defines the partial differential equation (PDE).
• initial_condition: defines the initial condition

     alpha = 5^2;
  T0 =exp(-alpha*x.^2);

• boundary_condition: defines the boundary condition

  %Dirichlet conditions
   pl = Tl; ql = 0;  % Left condition: T(-1,t) = 0
    pr = Tr; qr = 0;  % Right condition: T(1,t) = 0