Short introduction to Physics Informed Neural Networks (PINN)

Lecture 1:

• Plan of the course, goals
• Bayesian approach to linear regression
• Likelihood analysis
• Linear regression from scratch
• Bias-Variance trade off

Lecture 2

• Basics of PyTorch
  • tensors
  • Autograd
  • Optimizers
  • Data
  • Simple implementations

Lecture 3

• Some PyTorch functionalities: datasets, dataloader
• Radial basis functions
• Basics of Neural Networks (NNs)
• Implementation of various models, including NN, in the PyTroch

Lecture 4

• Ordinary differential equations (ODE)
  • General Solvability Theory
  • Stability of the initial value problem
• Numerical approch to ODE
  • Forward Euler Method
  • Backward Euler Method
  • Higher order ODE
  • System of the first order ODE
  • Solving ODE with Neural Networks by Lagaris et al.

Lecture 5

• Partial differential equations (PDE)
  • Burgers’ equation
  • Laplace equation
• Physics Informed Neural Network (PINN)
  • Runge–Kutta method
  • PINN: a discrate time model
• How to estimate uncertainties in the predictions of the networks?
  • Monte Carlo Dropout
  • Bootstrap
• Outlook: Differentiable Physics