A continuation method for the efficient solution of parametric optimization problems in kinetic model reduction

TL;DR

This paper introduces a predictor-corrector method combining Euler prediction and interior point or Gauss-Newton correctors to efficiently solve optimization problems approximating slow invariant manifolds in dynamical systems.

Contribution

It presents a novel predictor-corrector approach for fast solution of parametric optimization problems in kinetic model reduction, enhancing efficiency in identifying slow invariant manifolds.

Findings

The method improves solution speed for kinetic model reduction problems.

A step size strategy enhances the predictor-corrector scheme.

Demonstrated effectiveness on a representative example.

Abstract

Model reduction methods often aim at an identification of slow invariant manifolds in the state space of dynamical systems modeled by ordinary differential equations. We present a predictor corrector method for a fast solution of an optimization problem the solution of which is supposed to approximate points on slow invariant manifolds. The corrector method is either an interior point method or a generalized Gauss--Newton method. The predictor is an Euler prediction based on the parameter sensitivities of the optimization problem. The benefit of a step size strategy in the predictor corrector scheme is shown for an example.