Physics-based surrogate modeling of parameterized PDEs for optimization and uncertainty analysis


Nair, P.B. (2002) Physics-based surrogate modeling of parameterized PDEs for optimization and uncertainty analysis In Proceedings of 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. AIAA. 11 pp. (AIAA-2002-1586).

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Description/Abstract

This paper presents physics-based surrogate modeling algorithms for systems governed by parameterized partial differential equations (PDEs) commonly encountered in design optimization and uncertainty analysis. We first outline unsupervised learning approaches that leverage advances in the machine learning literature for a meshfree solution of PDEs. Subsequently, we propose continuum and discrete formulations for systems governed by parameterized steady-state PDEs. We consider the case of both deterministically and randomly parameterized systems. The basic idea is to embody the design variables or uncertain parameters in additional dimensions of the governing PDEs along with the spatial coordinates. We show that the undetermined parameters of the surrogate model can be estimated by minimizing a physics-based objective function derived using a multidimensional least-squares collocation or the Bubnov-Galerkin scheme. This potentially allows us to construct surrogate models without using data from computer experiments on a deterministic analysis code. Finally, we also outline an extension of the present appraoch to directly approximate the density function of random algebraic equations.

Item Type: Conference or Workshop Item (Paper)
Digital Object Identifier (DOI): AIAA-2002-1586
Venue - Dates: 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2002-04-22 - 2002-04-25
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ePrint ID: 21992
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Date Event
2002Published
Date Deposited: 29 Mar 2006
Last Modified: 16 Apr 2017 22:53
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/21992

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