Simple answer is past-times. For example, I have a side interest in ODEs and PDEs, which I basically never get to apply for work. So I'm working on 3 problems

Simple answer is past-times. For example, I have a side interest in ODEs and PDEs, which I basically never get to apply for work. So I'm working on 3 problems from orbital mechanics, control theory and investment science respectively, each which is interesting in itself but each which flexes my ODE and PDE muscles. In short, just invent problems you find engaging and then scratch away at them on planes and trains, and in all those in-between times.