Differentiation of discontinuities in ODEs arising from dosing

In this talk, we present continuous-adjoint sensitivity methods for hybrid differential equations (i.e., ordinary or stochastic differential equations with callbacks) modeling explicit and implicit events. The methods are implemented in the SciMLSensitivity.jl package. As a concrete example, we consider the sensitivity analysis of dosing times in pharmacokinetic models. We discuss different options for the automatic differentiation backend.

Sensitivity analysis, uncertainty quantification, and inverse design tasks typically involve computing a gradient with respect to a loss function modeling the objective in a computer program. Handling objectives that require the numerical simulation of a differential equation with discontinuities, such as in pharmacology applications involving drug dosing, is of great interest. In the forward simulation of an (ordinary or stochastic) differential equation, discontinuities can be implemented using callbacks. However, the computation of the derivatives can be challenging: Discrete sensitivity analysis techniques based on automatic differentiation (AD) packages may scale poorly with the number of parameters (in the case of forward-mode AD) or have a large memory footprint due to the caching of intermediate values (in the case of reverse-mode AD). Therefore, it is highly desirable to make continuous adjoints compatible with callbacks as well. In this talk, we present continuous-adjoint sensitivity methods for hybrid differential equations that model explicit and implicit events and are available within the SciMLSensitivity.jl package.