Hamiltonian Neural Networks

Background - Physics-Informed Machine Learning (PIML)

Suppose you have a dynamic / physical system to be analyzed / predicted. Several cases:

1. If you don't know the physics -> You cannot use physics much - this may be the scope of Machine Learning - e.g., finding patterns from data, etc.

2. If you know the physics and you can solve the physics equation (e.g., PDE) analytically -> You are good. Analytic math does the job.

3. If you know the physics and you cannot solve the physics equation numerically because of computation limits (e.g., complicated non-linear system) -> Physics-Informed ML (PIML) comes in to play. How? Get the data from the system dynamics -> Train the neural networks, but passing it some hints that are based on known physics.

Even a more funny (shocking) thing is that the neural networks can learn the physics itself - for example, it can learn the conservation law of energy purely from data - Hamiltonian Neural Networks (HNN) was born from this context.

Hamiltonian Neural Networks - Time-series predictions for pendulum dynamics.

This work demonstrates Hamiltonian Neural Networks (HNN) - to predict (non-linear) pendulum dynamics.

Demo: https://github.com/uriyeobi/hamlitonian_neural_networks/blob/main/notebooks/pendulum_hnn.ipynb

Blog posts: Part 1 | Part 2