I am working on parametric studies in physics simulations, i.e. I vary some real input parameters (e.g. x0,x1,x2,x3) and get an output with a larger size (e.g. y0,y1 ... y100). Assuming that I have a database of some thousand different input parameters and corresponding outputs, is there a good way to build a model that can give a prediction for the output at a new position?

I have looked into various techniques, but so far I couldn't find a method that seems promising for this kind of problem. I found a lot of stuff on classification problems and for one output it seems that Gaussian process regression would be suitable. But I am pretty lost when it comes to floating-point input and an output that is larger in dimensions than the input. Any suggestions or references to papers addressing this kind of problem?

Edit: I understand that my description might have been a bit too abstract, so here's the concrete problem: I have a laser physics simulation with a some input parameters that I am changing, e.g. the coefficients of the spatial wavefront and coefficients of the spectral phase. These change the spatio-temporal intensity distribution in focus and I am looking at the resulting dynamics. One observable is the momentum distribution of heated electrons (which is a histogram of ~100 bins). I can run each of these simulations fairly quickly (on a scale of 5 minutes each), but my parameter space is rather large with 5-10 different values to tune. So I am looking for techniques to perform a multi-dimensional regression to see what the influence of each parameter is within the parameter range. Ideally I would like to be able to make a reasonable prediction how the momentum distribution should look like at an unexplored position based on the knowledge of previous simulations ...

  • $\begingroup$ How are the $X$s and $Y$s paired? $\endgroup$ – Dave Aug 11 at 0:52
  • $\begingroup$ Hi @30Femtos, can you please edit your post to include the problem itself you trying to solve, the context behind it? $\endgroup$ – shepan6 Aug 11 at 10:57
  • $\begingroup$ Dear Dave, I am not sure what you mean with "paired", but following also shepan6's request I have described my problem in more detail. $\endgroup$ – 30Femtos Aug 11 at 21:37

It sounds like what you want is Multioutput Regression. Here's an article that might help. Your dataset might not be big enough to use lets say a neural network but some of the algorithms mentioned in the link I sent could work.

| improve this answer | |
  • $\begingroup$ Thanks for the feedback! Seems like "Multioutput Regression" is indeed a good rabbit hole to go down in this context. $\endgroup$ – 30Femtos Aug 11 at 21:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.