https://www.youtube.com/watch?v=AxC770lpSLw shows one of the old tide prediction mechanical computers briefly mentioned in this article. It is effectively doing an inverse Fourier Transform, summing all the various 30+ sinusoids that affect the tides.

Relevant xkcd: https://xkcd.com/3135

> Kelvin’s machine automates the second half of that task. As the pulleys spin, they pull on a common chain by the correct amount for each of the calculated components. A year’s worth of tidal tables can be put together in half an hour, if you know the components. Even better, you can “guess and check” the components by comparing your machine’s output to past records, and adjusting the pulleys until you get something that works correctly.

I didn't know they already had machine learning and model fitting algorithms in the 1800s, but here we are...