Interpolation between 3D data sets. Neural Networks or Other Methods?

I am looking for guidance on best approaches and recommendation to interpolate data between 3-Dimensional data sets. Is a neural network the best method of data analysis for this sort of use case? Possible other interpolate methods I should be looking into? I am really just looking for some guidance on where I should begin to look for a use case of building 3D data sets by interpolating between 3D data sets I have using MatLAB.

For Example. I Have many 3D Plots where I have the following 4 parameters. Fixed X1, and varying X2, and Y1 with a calculated Z1 Solution from a finite element simulation.

I have an algorithm that provides multiple 3D response surfaces using scatter interpolate function. Obtaining multiple 3D plots/datasets of X2,Y1, vs Z1 for a given fixed X1 parameter.

I would like to develop some interpolate methods between these 3D data sets. That is predict what Z1 would be if I wanted to interpolate some 3D data sets between some of these fixed X1 parameters.

Answer 1

[Matt J]

Some of the routine interpolation functions to consider would be: griddedInterpolant, scatteredInterpolant, interp3, griddata,griddatan.

[Lloyd Utt]

Thanks, Matt. I will look into these. I have been using scatteredInterpolant to develop the 3D response surface plots. Maybe I can further use the same function with the derived datasets. I will look into these routines.

Answer 2

[John D'Errico]

What is the "best" method? Impossible to say.

To know what defines best, we would need to know EXACTLY what your requirements are, and EXACTLY what your data looks like, and what issues you can tolerate. Every interpolant will have its own specific issues. Do you need a differentiable result, or can you tolerate a piecewise linear interpolant? Is your data noisy? Some interpolants will amplify any noise. Will you need to extrapolate? I can probably list many other factors given some time.

Even if we compare different interpolants that are "linear" in some respect, they can vary significantly. Linear in multiple dimensions is not as trivial a thing as you might think.

Are any of the methods you might consider better than a neural network? Um, first of all, a neural net will not even be an exact interpolant in general, so it is a very different thing.

Essentially, you need to learn about the different methods available. You need to understand your data, and your requirements, and you need to decide for yourself which method is best for your purposes.