Experimental design for nonparametric correction of misspecified dynamical models

Gal Shulkind, Lior Horesh, Haim Avron

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider a class of misspecified dynamical models where the governing term is only approximately known. Under the assumption that observations of the system’s evolution are accessible for various initial conditions, our goal is to infer a nonparametric correction to the misspecified driving term such as to faithfully represent the system dynamics and devise system evolution predictions for unobserved initial conditions. We model the unknown correction term as a Gaussian Process and analyze the problem of efficient experimental design to find an optimal correction term under constraints such as a limited experimental budget. We suggest a novel formulation for experimental design for this Gaussian Process and show that approximately optimal (up to a constant factor) designs may be efficiently derived by utilizing results from the literature on submodular optimization. Our numerical experiments exemplify the effectiveness of these techniques.

Original languageEnglish
Pages (from-to)880-906
Number of pages27
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume6
Issue number2
DOIs
StatePublished - 2018

Funding

FundersFunder number
Defense Advanced Research Projects Agency
International Business Machines Corporation
Air Force Research LaboratoryFA8750-12-C-0323

    Keywords

    • Dynamical systems
    • Experimental design
    • Gaussian processes
    • Model misspecification
    • Submodularity

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