Higher-order Discrete Adjoint ODE Solver in C++ for Dynamic Optimization

Parametric ordinary differential equations (ODE) arise in many engineering applications. We consider ODE solutions to be embedded in an overall objective function which is to be minimized, e.g. for parameter estimation. For derivative-based optimization algorithms adjoint methods should be used. In this article, we present a discrete adjoint ODE integration framework written in C++ (NIXE 2.0) combined with Algorithmic Differentiation by overloading (dco/c++). All required derivatives, i.e. Jacobians for the integration as well as gradients and Hessians for the optimization, are generated automatically. With this framework, derivatives of arbitrary order can be implemented with minimal programming effort. The practicability of this approach is demonstrated in a dynamic parameter estimation case study for a batch fermentation process using sequential method of dynamic optimization. Ipopt is used as the optimizer which requires second derivatives.