This repository contains my notebooks for my diffusion models for my master's project, see below...
To test the physics of different theories of the universe, we need simulations. To get simulations, we need supercomputers... Or do we? Generative AI is incredibly powerful and we're going to use diffusion to speed up the theoretical testing of physics!
This project uses the CAMELs CMD dataset which includes over 150,000 2D simulations of universe. Each image is an universe which has different starting parameters which determine how the universe evolves. Determining how the universe evolves can be done in two ways:
- N-body
- Hydrodynamical (
$M_{gas}$ ,$V_{gas}$ ,$T$ ...)
Hydrodynamical simulations are more physically realistic than N-body simulations but are much more computationally complex to simulate, typically requiring supercomputers.
Perhaps there's a way to convert the simple N-body simulations to realistic Hydrodynamical maps? 🤔
A Diffusion model starts with a image of random noise and the model learns from the training dataset to slowly remove sections of the noise in the image until a clear denoised image is generated.
The way the diffusion model denoises the image depends on the particular pixel values of the starting image. Since the starting image is random, it acts as a 'seed' and generates a new random and slightly different image for every output.
This is where the magic happens...
By adding the pixel values of the N-body (training dataset)image to the starting image, and setting the hydrodynamical image as the truth, we can guide the model to 'denoise' the N-body into a hydrodynamical one.
Of course this is harder said than done and the model takes around 45 mins just to train on 10% of the training dataset. But the results below are remarkably similar.
The technical details can get very overwhelming so I made sure avoid them here and instead provide a summary here. The full details and report are provided here: Simulating the Universe Report
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Eariler I simplified the concept of the generating a image of random image. In reality, the truth hydrodynamical map is 'noised' up by the model in the forward process and then model learns to remove the noise that was added.
The diffusion model also uses a U-net which is a image to image neural network bulit with convolution layers.
The hydrodynamical simulations shown above normally requires supercomputers processing over days and weeks to produce but this diffusion model can cut that down to a matter of hours. Analysing the generated results and comparing their physical significance, we can see that the model outputs are similar and physically correct! Perhaps we can improve the generation time but this is a new era of universe simulations.