PINN Initialization: Setting Up the Neural Network for PDE Solving

The code snippet represents the initialization function for the physics-informed neural network (PINN) class. This class is utilized to solve partial differential equations (PDEs) using neural networks.

The parameters of the initialization function are:

• 'x0': Initial condition for the PDE.
• 'u0': Initial value of the solution.
• 'x1': Final condition for the PDE.
• 'layers': List containing the number of neurons in each hidden layer of the neural network.
• 'dt': Time step size.
• 'lb': Lower bound of the domain.
• 'ub': Upper bound of the domain.
• 'q': Number of stages in the IRK method used for time integration.

The initialization function initializes the necessary variables and placeholders for the PINN, including the neural network weights and biases, the IRK weights and times, and the TensorFlow session. It also defines the computational graph for the PINN, encompassing the forward pass through the network and the loss function. Finally, it initializes the TensorFlow session and the optimizer for training the PINN.