# Good 3D surface fits for multiscale oscillatory surfaces

I have a 3D surface in $$x$$, $$y$$, and $$z$$. where $$z$$ is a function of $$x$$ and $$y$$ and my points are on a structured grid in $$x$$ and $$y$$. My function $$z$$ is highly oscillatory and irregular with multiscale phenomena. I'd like a fitting tool that will capture the large scale phenomena and provide a differentiable closed function without getting derailed by the small scale phenomena. Are there any good 3D data fitting toolboxes or methods?

• Do you accept black box fitting tools? Such as support vector machine or gradient boosting? My only doubt is that they may not be easily differentiable. Other than that, to capture something funky that oscillates crazy in small scales, I don't think you have a chance to get a good result with fitting method other than black boxes. Cause, as far as I know more fancier black boxes such as neural network did a good job even to capture crazy turbulent structures, so they should be OK with your data. Jan 28 '20 at 19:24
• I'll accept any tool that returns a closed form C1 differentiable function. I'm not familiar with what you mentioned, but if they return a continuously differentiable function I'm game. I'd even be okay with something that damps out the small scale phenomena as those are not too important.
– EMP
Jan 28 '20 at 23:03
• OK, I'll elaborate my comment in an answer, which might work your dataset. Jan 28 '20 at 23:19
• Probably a standard 2D FFT transform is all what's needed here. Jan 29 '20 at 6:45