Koopman operator method for solution of generalized aggregate data inverse problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:428

Article

Meyers, Joseph¹  Rogers, Jonathan²  Gerlach, Adam³ 

[1] Georgia Inst Technol, Woodruff Sch Mech Engn, Atlanta, GA 30332 USA

[2] Georgia Inst Technol, Guggenheim Sch Aerosp Engn, Atlanta, GA 30332 USA

[3] Air Force Res Lab, Dayton, OH 45325 USA

关键词: Inverse problems;    Koopman operator;    Uncertainty quantification;   

DOI  :  10.1016/j.jcp.2020.110082

来源: Elsevier

【 摘 要 】

Probabilistic inverse problems arise in a variety of scientific and engineering applications. A particular type of probabilistic inverse problem, termed a generalized aggregate data inverse problem, involves the specification of expected value targets and/or probabilistic constraints at discrete times or in a discrete set of transformed domains. Because the transformed distributions themselves are not specified, these problems cannot be readily solved by typical Bayesian solution techniques. In this work, a novel solution technique using the Koopman operator is proposed. The Koopman operator is used to pull-back the cost and constraint functions acting on the transformed probability densities to the initial domain, forming a set of integral equations and integral inequalities over a common integration domain. A quadrature technique is employed to approximate this system of equations and inequalities, leading to the formulation of a linearly-constrained convex quadratic program that can be solved using a variety of well-known techniques. Results show that the method can be feasibly applied to solve several practical engineering problems of interest, illustrating tradeoffs in various aspects of the solution process. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free