Computational Models

In the nineteenth century, when they came up with the ideal gas laws, computers were not very advanced.
In the intervening 200 years, computers have become able to simulate a vast range of behaviour.
When intuitive analytical solutions are not readily available, computer models can offer good results.
A good example of this is weather models. If you watch the weather on the news, they are really good at predicting what the weather is going to be like tomorrow.
They're pretty good up to a week, and useful up to two weeks. Beyond that, they're not very good.
They take mathematical models of the atmosphere and oceans and weather readings, and simulate the model to predict what is going to happen.
They refine the models all the time improving them.
They also update the state of the model with new weather (atmospheric) readings.
Do note that weather modelling is an active area of research.