How to build a simulator for a physical machine given a set of datapoints of its behaviour?

I have a database with millions of datapoints describing the behaviour of a heat pump. For every second, I know various temperature, pressure, mass flow and power measurements as a response to the signals sent by a controller. In other words, I have records of what the machine is being told to do and what actually does.

I would like to build a simulator that, given a set of artificial inputs (e.g. coming from a web page) attempts to simulate the behaviour of the machinery.

I have no expertise in machine learning, so I am wondering what are the best/most common approaches to takle this kind of situation?