How to know when a Environment will yield a deterministic model

Given enough experiment data on time taken for objects to fall to earth from different heights, one can create various models that will accurately predict the time it will take for an object falling at any height (in the inner the atmosphere, this is a toy example).

In this simple example the model is deterministic, it will always produce an output given an input regardless of the amount of data over a small threshold—something akin to Newton’s gravity equation.

Try modelling something like the stock-market (the other extreme end of the scale) and the predictions will never reliably converge on a predictable accurate model.

Is there any way of knowing whether your domain will yield a deterministic or non-deterministic model or not?

• Deterministic is a slippery term. Newton's laws although deterministic are just approximations for large bodies, the real laws yield solutions which are not deterministic (atleast at molecular level, and probably for bigger bodies too). Also, to predict a bodies descent you need a lot of information like temperature, viscosity, gravitational variations, etc (if you want absolutely deterministic solution). So you must define what you mean by deterministic.
– user9947
May 26 '19 at 19:24
• I guess I want to know two things: is there ever a way to reduce a complex model into a quick equation given my example above where within a tolerance it can be reduced to an equation. And two whether there are ever deterministic models and how to know: e.g. if I had a load of data for the Fibonacci sequence, would there be a way of knowing that there is a simply representation rather than the complex model I could have produced? May 27 '19 at 8:35
• Just wonder if there if you are expecting a determinsitic outcome (e.g. like a squence on numbers with an underlying pattern) whether there would be a good enough method of reducing the problem to a simplified equation using a ML method, or whether this is not really a thing? Jul 17 '19 at 8:52