I am seeking knowledge from the community. I am solving a transport PDE (conservation of solute mass) using COMSOL. At each Newton-Raphson iteration, I need to update a constant called $Kd$ for some of the chemical species that are being transported (maybe I will update the $Kd$ at each time step depends on the convergence).
This Kd is obtained from 5 parameters. Hence, $Kd = f(X_1, X_2, X_3, X_4, X_5)$. I have a multidimensional array (or table, or whatever you prefer to called it), where from different combinations of $X_1$, $X_2$, $X_3$, $X_4$, and $X_5$ I obtain a $Kd$. The number of combinations is $61440$, hence the size of $X_1$, $X_2$, $X_3$, $X_4$, $X_5$ and $Kd$ is also $61440$ (Not sure if that is considered a big amount or no, for me it is).
At some point in the simulation, I will have to interpolate, I have tried in Matlab by using the griddatan function, but it took too much time and I got
NaN as an answer. So, I am looking for alternatives. I have read that it should be possible to do a "prediction" (what for me would be an interpolation) using neuronal networks, but I wonder:
1) What are the algorithms in multivariate interpolation and neural networks field? (I am not too familiar with these fields)
2) Which one could be better or faster?
3) Where would be the difference in my case of using interpolation algorithms or neural network algorithms? (I do not have noise, although I have a big data).
Note: The grids of the combination $X_1$, $X_2$, $X_3$, $X_4$, $X_5$ are supposed to be equidistant.