One reason I believe that log-linear dynamical systems have so much potential as a modeling tool is that they measure the relative change in quantities rather than the absolute change. For example, suppose we’re tracking the heat of a system \(h_t\). The absolute change from time \(t\) to \(t+1\) is given by \(h_{t+1} - h_t\). The relative change is given by \(h_{t+1}/h_t\). I also call the relative change the geometric change, since it is based on ratios.

I realize that most people have never learned about linear dynamical systems. It’s a pity, because it’s a very beautiful and useful area of applied math. In the next few posts I’m going to give a crash course on linear dynamical systems, which I hope will convey some sense of why they’re important. For more information check out my advisor’s class. I’ll start here with the most fundamental of the fundamentals.

In my PhD, I studied convex optimization, which is a sub-field of numerical optimization. The essence of convex optimization is restricting what’s allowed in an optimization model, in return for getting an optimization problem that can be solved quickly and reliably, with generic frameworks like CVXPY.