# Given enough graphical data, could you train an AI to plot a polynomial graph based on the input conditions?

Good day everyone.

I am curious if it is possible for an AI to plot a time-series graph based on a single input. Using free fall impact as an example.

Assuming we drop a ball from height 100m and record the force it receives relative to time. We will get a graph that looks something like below.

Now we drop the ball from a height of 120m, record the forces, and we get another graph in addition to our original.

What I am wondering is: If we have a large set of data on 60m to 140m (20m interval) height drops, would we be able to generate a regression model that plots the responses when given an arbitrary drop height? (i.e plot force response when dropped from 105m)

Thank you all very much for your time and attention.

• Input $$h$$ the height of the drop, multiple outputs, one per time offset that you want to plot. Each individual output calculates the predicted force at a specific offset time.
• Inputs $$h$$ the height of the drop and $$t$$ a time offset, one output. The single output calculates the predicted force due to given height and at given time.