From a STEM problem, I vary a variable x within a range and calculate quantities $U(x)$, $V(x)$ and $W(x)$. I want to figure out an analytical relationship between unknown $U(x)$ and the other two quantities.

However, in my setup, I have 3 vectors: $A(x), B(x)$ and $C(x)$. Each vector results in a value of $V(x)$ and $W(x)$. This means that my $V(x)$ and $W(x)$ are in fact: $V_A(x),V_B(x),V_C(x),W_A(x),W_B(x)$ and $W_C(x)$ (where the subscripts indicate the vector used to calculate the quantity). However, to calculate $U(x)$, I must choose a pair of distinct vectors. So, my $U(x)$ are in fact $U_{AB}(x), U_{AB}(x)$ and $U_{BC}(x)$ (where the subscripts indicate the chosen pair of vectors).

I have reason to believe that each of my 3 $U(x)$ can be expressed entirely in terms of the 6 $V(x)$ and $W(x)$ terms. However, I am having trouble finding this relationship.

On top of that, $U(x)$ takes on integer values while $V(x)$ and $W(x)$ are smooth functions with only a few discontinuities. So, I tried various combinations of derivatives, sigmum functions, etc to try and recover $U(x)$ without explicitly calculating it. However, I am now out of ideas.

I am not too familiar with data science methods, and so wanted advice on how I could go about finding an analytic relationship between my quantities. I figured I should try to use machine learning (where the software could try various relationships until a match is found), but I haven't done that before. So, I was hoping for advice on a path to take to try and figure my problem out. I have access to supercomputing nodes, if it's anything.


Your Answer

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

Browse other questions tagged or ask your own question.