What's meant by "regularization" of ODEs?
Such as, "in order to be solved by conventional ODE solvers such as ode45"?
The context where I encountered this was related to discontinuities of ODEs. And there it seemed that by adding some term or function, one may fix the discontinuous behavior.
To encourage simple solutions and avoid overly complicated solutions.
To make the problem more well posed and robust to noise in the data or instabilities caused by properties in the numerical solver.
You can read more here Regularization (Wikipedia)