Building a surrogate for discontinuous fields

[RemDelaporteMathurin]

Hi Team!

I would like to look into the dimensionality reduction features of autoemulate to build an emulator for a simulator producing a discontinuous field.

Here's an example of the type of problem we are interested in. I assume the sharp discontinuity should be handled with care. My initial thought was to use two separate emulators for each subdomain but they are not physically independent so that may not be a very good idea!

Any pointers?

[radka-j]

Hi @RemDelaporteMathurin!

I had a chat with @sgreenbury about this and we think there are 3 approaches you could try:

1. We agreed that since the discontinuity is fixed and both the fields are smooth, your idea to split the problem into two and fit an emulator for each should perform well even if you lose the ability to share information between them. That's probably the most straightforward.
2. You could also compare this to modelling the whole field with a single emulator. In that case, VAE as the dimensionality reduction technique should outperform PCA because it is more flexible so we'd recommend trying that.
3. It might still be interesting to also try PCA applied to the whole field for comparison with the VAE approach but maybe try varying the number of components (you might need more to capture the discontinuity).

I hope this helps :)