  Differentiable programming has recently received much interest as a paradigm
that facilitates taking gradients of computer programs. While the corresponding
flexible gradient-based optimization approaches so far have been used
predominantly for deep learning or enriching the latter with modeling
components, we want to demonstrate that they can also be useful for statistical
modeling per se, e.g., for quick prototyping when classical maximum likelihood
approaches are challenging or not feasible. In an application from a COVID-19
setting, we utilize differentiable programming to quickly build and optimize a
flexible prediction model adapted to the data quality challenges at hand.
Specifically, we develop a regression model, inspired by delay differential
equations, that can bridge temporal gaps of observations in the central German
registry of COVID-19 intensive care cases for predicting future demand. With
this exemplary modeling challenge, we illustrate how differentiable programming
can enable simple gradient-based optimization of the model by automatic
differentiation. This allowed us to quickly prototype a model under time
pressure that outperforms simpler benchmark models. We thus exemplify the
potential of differentiable programming also outside deep learning
applications, to provide more options for flexible applied statistical
modeling.
