# How can I have a computer learn the equation with known dependent variables?

I'm trying to design an orbital rendezvous program for Kerbal Space Program. I'm focusing on when to launch my spacecraft so that I can end up in the general vicinity of the target. If I can control the ascent profile, the remaining dependent variables are the ship's twr and the target's altitude. I want to try a computer learning solution.

What is the best way to formulate the problem of learning the time to launch based on some twr?

How can I make an algorithm to compute the general equation of launch time to a altitude based on my ability to accelerate? What type of learning problem could this be classified as? What are some approaches to solve problems with known dependent variables?

This may be an obvious question, I kind of expect the answer is regression? But it seemed a general enough question to be sure about to get a solid foothold in computer learning with this type of problem, which seems to come up a lot.

• Question is how to calculate the trajectory of an object? – pasaba por aqui Mar 11 '18 at 12:35
• No, powered flight is involved. Also the approach was NOT to calculate the trajectory of ONE (powered)object, but to have a learning algorithm take a good guess at the equation for time as a function of twr for ALL objects. – Oblivion Mar 11 '18 at 17:33
• Meaning of "twr" ? Not in my lost of acronyms – pasaba por aqui Mar 11 '18 at 18:21
• thrust to weight ratio. – Oblivion Mar 11 '18 at 18:27
• What you mean by "learning" is not clear, are you trying to optimize a process or find an optimum point of data which you can reuse? or are you seeking a way to feed data into an AI object (ie NN) which will give more precision based on how much data it is given? – solarflare Mar 12 '18 at 1:15

## 1 Answer

You might want to try symbolic regression. This is a machine learning approach that tries to generate an equation with arbitrary form that best fits a set of examples. I've used it before when working with physicists who wanted an equation in terms of known numeric constants and specific variables, but didn't expect the equation to be linear or one of the other shapes for which we have standard regression models.

Symbolic regression often (usually?) uses genetic programming for the underlying optimization. A decent tool is Eureka. It used to be free, but I think they want a payment now. You can also do it yourself from any genetic programming toolkit with a little know-how.