https://github.com/jqhoogland/pytransfer

Library for implementing the transfer operator method
https://github.com/jqhoogland/pytransfer

Last synced: 10 days ago
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Library for implementing the transfer operator method

• Host: GitHub
• URL: https://github.com/jqhoogland/pytransfer
• Owner: jqhoogland
• Created: 2021-01-26T14:47:07.000Z (about 4 years ago)
• Default Branch: master
• Last Pushed: 2021-03-10T11:57:41.000Z (almost 4 years ago)
• Last Synced: 2024-11-19T18:55:08.941Z (2 months ago)
• Language: Python
• Size: 17.6 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# pytransfer

Library for implementing the transfer operator approach.

### The approach

Consider a discrete (or discretized) dynamical system:

```math

x(t+\Delta t) = f(x(t)),

```

where $`x\in\mathbb R^n`$ and $`f`$ is the iterated map $`f:\mathbb R^n \to \mathbb R^n`$.

Then, the transfer operator $`\mathcal T`$ is the corresponding map over probability measures, $`u\in\mathcal M`$:

```math

u(t+\Delta t) = \mathcal T u(t)

```

We get to exchange possibly horribly non-linear intractable (but finite dimensional) dynamics for well-behaving linear (but infinite dimensional) dynamics.

But we can usually get by with a finite rank approximation, which we can compute directly from data.