https://github.com/kach/lagrange-climbs-a-hill

Interpolating Lagrangian mechanics by AD and gradient descent
https://github.com/kach/lagrange-climbs-a-hill

Last synced: about 1 month ago
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Interpolating Lagrangian mechanics by AD and gradient descent

• Host: GitHub
• URL: https://github.com/kach/lagrange-climbs-a-hill
• Owner: kach
• Created: 2019-10-28T20:22:28.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2019-10-28T20:22:41.000Z (over 6 years ago)
• Last Synced: 2025-03-23T14:36:59.853Z (about 1 year ago)
• Language: Python
• Size: 2.14 MB
• Stars: 1
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
I'm a CS major in a physics class, which means that all optimization problems

just look like opportunities for gradient descent... here I use PyTorch's

automatic differentiation tools to try and optimize the "action" of a physical

system (in the Lagrangian sense) in order to "learn" its true trajectory -- a

visual display of the Principle of Stationary Action!

## Some demos

All of these are seeded with random trajectories and left to tune for a few

thousand steps of gradient descent, just a few minutes of total computation

time.

### Trajectory of a projectile

![a parabola](trajectory.gif)

### Keplerian Orbit

![an ellipse](orbit.gif)

### Spherical Cart-Pole

![who knows](cart-pole.gif)