First- and second-order parameter sensitivities of a metabolically and isotopically non-stationary biochemical network model

Abstract

The Jülich-Aachen Dynamic optimization Environment (JADE) is employed for computing first-and second-order parameter sensitivities of a metabolically and isotopically non-stationary biochemical network model. Based on a Modelica representation of the model, code generation, algorithmic differentiation and first-and second-order adjoint sensitivity analysis are employed for computing the gradient and the Hessian of a parameter estimation objective function.In particular, we use composite adjoints, an extension of the classical adjoint sensitivity analysis, and a numerical integrator based a modification of secondorder discrete adjoints of the extrapolated linearlyimplicit Euler method. Therewith, the 116 × 116-Hessian of the objective function with respect to 116 model parameters can be computed at the cost equivalent to only 18 objective function evaluations, while computing the same Hessian with the cheapest finitedifference formula would require 6845 evaluations of the objective function.

Dynamic Parameter Sensitivities: Summary of Computation Methods for Continuous-time Modelica Models

“…In the case of n p n x , excessive computational efforts can be avoided by following a backward AD approach as demonstrated in (Braun et al, 2017). (Hannemann-Tamas et al, 2012) shows another approach for computing first and secondorder DPS using adjoint sensitivity analysis applied to a flattened Modelica model.…”