How to describe a graph with an equation?

Question

Mathematics

There are instrument readings: <depth> <value>. There is a huge amount of data, 18 billion key-value pairs.
The task is to transfer all the data to the database to speed up access. If we transfer everything “on the forehead” and wind up the index, we will get an 800 gigabyte dump.
There are several alternative solutions, one of them is converting the graph into a vector.
On average, there are ~2500 key-value pairs per chart.
I would like to hear the opinion of experts. How to implement it? Are there ready-made solutions?

Chart example:

Answer 1

This is called Curve Fitting . Polynomial interpolation is a special case.
Through the links I got to the page Compression_using_wavelet and realized that what you are trying to do is the same compression of an audio (for example) stream. Perhaps the study of multimedia data encoding algorithms will lead to good ideas.

Answer 2

That is, you need to reduce the amount of data by replacing part of the data with approximate functions?

Answer 3

Isn't this the problem of the discrete Fourier transform?

Answer 4

Weird question. As far as I remember the theory of communication, the information flow is therefore considered as stochastic (random) because it cannot be described by any law (equation), otherwise it becomes deterministic (given) and the amount of information contained becomes equal to the description of the law. Another thing is if you need to save the picture very roughly, then yes, you can approximate. And if it's still accurate, then see sebres