Multi-variable interpolation (modeling?)

[#1]

Suppose I have a big table of simulation output with 5 input variables (i1, i2, i3, i4, i5) and 2 output variables (o1, o2).

Now suppose I have a pair of output numbers, e.g. (5,17) and I want to find pretty good values for i1 thru i5, such that if I put them back into the simulation, I'd get something close to (5,17) as output.

Does JMP do anything like this?

[#2]

There are basically two steps you'll need to go through:

1. Build a model that works for your data and practical problem using one of the multiple JMP modeling methods...there are scores of them.

2. Each of these modeling platforms has a capability called the Prediction Profiler which has the ability to 'find' input variable levels that will provide values of the output variables.

Or if you have a model already, just use the standalone JMP Prediction Profiler.

[#3]

What is considered a "modeling method"?  Is that things like Standard Least Squares, Stepwise, Manova, etc.?  Or am I looking in the wrong place?  I'm hoping for something that acts like linear interpolation.

I just did a least-squares fit, but I don't see a Prediction Profiler under any of the red triangles.

[#4]

If you run Analyze>Fit Model Enter the model and the response variables.  Click on the red triangle next to each response Factor Profiling>Profiler

[#5]

By modeling method, yes, Standard Least Squares, Stepwise, or even the non linear methods such as Partition, and if you have JMP Pro, Bootstrap Forest, or the any of the penalized regression methods in the Generalized Regression platform. Each of these pathways will have as part of the workflow the option to go from model selection to evaluation to prediction using the Profiler right in the same workflow.

When you say 'linear interpolation' I'm not 100% sure what you are getting at, but, what the profiler does conceptually is treat your n dimensional factor space as an n dimensional surface and allows for the optimizing algorithm to stop at any point in the factor space which meets the maximum desirability for the response you've specified within the Profiler set up. You can also include surface plots to visualize the response surface around the optimal factor settings. There is also a built in simulation capability. Lots of options within the Profiler for exploration and visualization.

I was a JMP user since version 1...and I think it's safe to say...at least for many, JMP's Prediction Profiler capabilities to this day are one of, if not the, defining 'killer app' in the entire JMP ecosystem.

[#6]

I may be trying to do something that I'm not mentally/intellectually qualified to do.

Suppose I have data that looks like the blue points on this image (that I found on Google):

https://www.researchgate.net/profile/Michel-Bercovier/publication/280567956/figure/fig2/AS:640636273...

... and I want to be able to interpolate a bunch of z-values of new points in the yellow region.  It's linear because the sections between the points could be created as planes (with triangulation).  

Fundamentally what is this process called?  Modeling?  I'm happy to go learn about how to do it, I just don't even know where to start.  

(Note, I'd like to eventually do this in more than 2 dimensions.)

[#7]

It is all modeling, but you may call it interpolation. A particular flexible and power interpolator is a Gaussian Process. You can read about it and how to use it with JMP and your data in the help.

[#8]

Modeling is what one uses to create the surface you showed in the picture. Then other techniques not technically 'modeling' are used to create the predictions. These can be as simple as creating a visualization like the picture and picking points off the graph visually. In multiple dimensions wrt to x's this becomes an untenable solution, so you use something like the JMP Prediction Profiler to help with the predictions. Granted at the heart of the Prediction Profiler is the model you are using to create the surface. As @Mark_Bailey suggests, especially for a surface like the one shown in your picture a Gaussian Process model might work very well. But the specific model you end up with is up to you...

If you know nothing about modeling, I have two thoughts:

1. Do you want to solve this problem once and never again expect to use these methods? If yes, my suggestion is hire a consultant to do the work. By the time you invest your time and energy to go from ground zero to solution, you'll spend the equivalent in your time vs. paying a consultant...and you'll probably make some mistakes along the way without even knowing it. That's how learning occurs. If no, and you want to build your own personal capability in this space, read on.

2. I'm presuming you know very little about statistical methods and JMP. If that's the case a great place to start is the free SAS course "Statistical Thinking for Industrial Problem Solving". Start at the beginning and complete the entire course. THEN work on solving your problem. Here's a link to the course: Statistical Thinking for Industrial Problem Solving