Not sure if this belongs in the linear forum, so feel free to move it if need be. I have data representing particle tracks through a volume of air perturbed by the results of a CFD (fluid dynamics) model. I'm attempting to quantitative describe how a volume is deformed as a function of time. Right now, I have two volumes. Volume 1 consists of a collection of particles, each having an x,y,z coordinate. In volume 2, I have the same particles, but in their perturbed state with their new x,y,z coordinate. I'm trying to find a technique to map [x0,y0,z0] to [x1,y1,z1] such that if I were given a perturbed field, I could generate the original particle field. Time can be considered a constant for now, as the background field perturbing the particles is a function of the airspeed, which is the particle release velocity. So I will need to generate a new function for each airspeed anyway. I'm not looking for an answer...more of an approach. I've considered a supervised neural network, but would like to try some other non-black box approaches first. I've also thought about using linear regression to generate slope/intercept pairs for each point combination, and then applying a spline function to generalize it.