Differential Equations in Data Science

Several things about this just seem odd:

- the second example given of an ODE is Black-Scholes (which is a PDE)

- ODE's are said to be missing from the "top 10 data science algorithms", but the actual title of the linked paper is "Top 10 algorithms in data mining". Clearly, ODEs are not data mining algorithms and would not belong on such a list.

- it repeatedly refers to the "derivate of a function", instead of "derivative of a function"

- it introduces the matrix exponential without giving a definition or link to wikipedia (it's important to at least mention in passing that it is not formed by taking the exponential of each matrix element)

- it says that "They're common constructs used in physics (Newton's law is a second-order ODE), chemistry and biology where it's often easier to measure the derivate of a function (e.g., velocity) than the function itself (e.g., position)". I'd have said that differential equations are ubiquitous in science and engineering because they can be used to describe how quantities change over (continuous) time.

etc.

I recently finished my masters in environmental science, which was diffeq heavy, and got a position working with energy data and doing some economic modeling and operations research. I was a bit surprised that the project I came into doesn't seem to use any diffeq in its broad pieces, although it's possible I just haven't come across it yet.

We're doing most of our analysis in python with the scipy stack, so maybe I'll try a couple ODE-based projections this afternoon.

It's exciting to see under-appreciated math techniques in use for modern-day data science!