How do I find valid points within 7-dim parameter space? Global NuFIT

[u/Inside_Meringue2367]

I don't know where I should ask this, it's related to physical and coding, so I am posting here. I am struggling with this particular problem for a month and still couldn't get to a satisfactory results.

So, I was working on a physics problem, many of you might be familiar or maybe not. I have to find a valid region within a 7-dim parameter space. I have some matrices in hand (Neutrino mass matrices) and 7 free parameters that goes into it i.e. g1,g2,g3,M1,M2, imaginary tau, real tau. I need to build a code that scans the space and finds the values of these free parameters which being inserted into the matrices and upon diagonalization spits out 3 eigenvalues and 3 eigenvalues vectors. From those we then calculate 6 neutrino observables that should be within acceptable range known as Global NuFIT. Any values that comes within the range gets sorted out.

I tried to build the code in python but it seems impossible to search for the whole parameter space! I tried gemini and chat gpt, even they are struggling to satisfy the tight NuFIT bounds. If anyone knows any efficient and fast way for parameter scanning that would atleast give 200 valid points (for scatter plots), please help me.

[u/JustAnotherMortalMan]

There's more elegant solutions, but brute force scanning the parameter space over informed priors is the obvious place to start. It sort of depends on how expensive (in wall clock time) the parameter -> observable map is, how sensitive the observables are to changes in the parameters over the region of space you're sampling, and what compute you have available (are you running on an HPC?).

People have use generative ML models / MCMC to solve these sorts of problems in the past. i.e. train a model to generate a lot of points that satisfy a subset of the constraints, search the generated subset to find points that satisfy a larger subset of the constraints, train a generative model on this data that satisfies a larger subset, etc. and iterate this until you have something that can easily generate points that satisfy all constraints. But it's more trouble than it's worth if brute force search would do and is prone to mode collapse.