Neural Hybrid Differential Equations and Adjoint Sensitivity Analysis

DiffEqSensitivity.jl is a Julia package within the SciML ecosystem for computing (adjoint) sensitivities for various kinds of differential equations in a highly performant manner within a unified user interface. In this project, we aim at implementing continuous adjoint sensitivity methods for hybrid differential equations as well as shadowing methods for chaotic dynamical systems in the DiffEqSensitivity.jl package. Moreover, we will add a symbolic preprocessing option based on the ModelingToolkit.jl package to build highly optimized adjoint differential equation code in DiffEqSensitivity.jl. Finally, we plan to refactor DiffEqSensitivity.jl to make use of a new package, namely AbstractDifferentiation.jl, such that users may straightforwardly select the best performing automatic-differentiation backend in each part of their program without the need to adapt their code substantially.

Possible fields of application for these tools range from model discovery with explicit dosing times in pharmacology, over accurate gradient estimates for chaotic fluid dynamics, to the control of open quantum systems.