Adjoint-based optimization of experimental designs with many control variables

• Verfasst von: Walter, Sebastian F. [VerfasserIn]
• Verfasst von: Schmidt, Andreas [VerfasserIn]
• Verfasst von: Körkel, Stefan [VerfasserIn]
• Titel: Adjoint-based optimization of experimental designs with many control variables
• Verf.angabe: Sebastian F. Walter, Andreas Schmidt, Stefan Körkel
• E-Jahr: 2014
• Jahr: 4 September 2014
• Umfang: 12 S.
• Fussnoten: Gesehen am 16.07.2020
• Titel Quelle: Enthalten in: Journal of process control
• Ort Quelle: Amsterdam [u.a.] : Elsevier Science, 1991
• Jahr Quelle: 2014
• Band/Heft Quelle: 24(2014), 10, Seite 1504-1515
• ISSN Quelle: 0959-1524
• DOI: doi:10.1016/j.jprocont.2014.06.019
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Automatic differentiation
• Sach-SW: Constrained least-squares
• Sach-SW: Differential algebraic equation
• Sach-SW: Optimum experimental design
• Sach-SW: Reverse mode
• K10plus-PPN: 1724953389

Abstract

We propose a method for an efficient optimization of experimental designs, using a combination of discrete adjoint computations, Taylor arithmetic and matrix calculus. Compared to the state of the art of using finite differences or the forward mode of automatic differentiation, our proposed approach leads to a reduction of the relative temporal complexity from linear to constant time in the number of control variables and measurement weights. We demonstrate that the advantageous complexity results are not only of theoretical nature, but lead to significant speedups in practice as well. With our implementation we are very close to the theoretical bound of the cheap gradient principle. We present one academic (spatially discretized heat equation) and two industrial application examples (biochemical process/Diesel-oxidation catalysis process) where we achieve speedups that range between 10 and 100. In addition to our core results, we also describe an efficient adjoint approach for the treatment of differential algebraic equations and present adjoint formulas for constrained least-squares problems.