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An adaptive sampling approach for solving PDEs with uncertain inputs and evaluating risk

19th AIAA Non-Deterministic Approaches Conference, 2017

Kouri, Drew P.; Zou, Zilong; Aquino, Wilkins A.

When solving partial differential equations (PDEs) with random inputs, it is often computationally inefficient to merely propagate samples of the input probability law (or an approximation thereof) because the input law may not accurately capture the behavior of critical system responses that depend on the PDE solution. To further complicate matters, in many applications it is critical to accurately approximate the “risk” associated with the statistical tails of the system responses, not just the statistical moments. In this paper, we develop an adaptive sampling and local reduced basis method for approximately solving PDEs with random inputs. Our method determines a set of parameter atoms and an associated (implicit) Voronoi partition of the parameter domain on which we build local reduced basis approximations of the PDE solution. In addition, we extend our adaptive sampling approach to accurately compute measures of risk evaluated at quantities of interest that depend on the PDE solution.

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TYPE Conference Poster YEAR 2017
OSTIScopus

Data-Driven Optimization for the Design and Control of Large-Scale Systems (LDRD Final Report)

Kouri, Drew P.

Engineering decisions are often formulated as optimization problems such as the optimal design or control of physical systems. In these applications, the resulting optimization problems are constrained by large-scale simulations involving systems of partial differential equations (PDEs), ordinary differential equations (ODEs), and differential algebraic equations (DAEs). In addition, critical components of these systems are fraught with uncertainty, including unverifiable modeling assumptions, unknown boundary and initial conditions, and uncertain coefficients. Typically, these components are estimated using noisy and incomplete data from a variety of sources (e.g., physical experiments). The lack of knowledge of the true underlying probabilistic characterization of model inputs motivates the need for optimal solutions that are robust to this uncertainty. In this report, we introduce a framework for handling "distributional" uncertainties in the context of simulation-based optimization. This includes a novel measure discretization technique that will lead to an adaptive optimization algorithm tailored to exploit the structures inherent to simulation- based optimization.

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TYPE SAND Report YEAR 2016
DOIOSTI

Inversion for Eigenvalues and Modes Using Sierra-SD and ROL

Walsh, Timothy W.; Aquino, Wilkins A.; Ridzal, Denis R.; Kouri, Drew P.

In this report we formulate eigenvalue-based methods for model calibration using a PDE-constrained optimization framework. We derive the abstract optimization operators from first principles and implement these methods using Sierra-SD and the Rapid Optimization Library (ROL). To demon- strate this approach, we use experimental measurements and an inverse solution to compute the joint and elastic foam properties of a low-fidelity unit (LFU) model.

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TYPE SAND Report YEAR 2015
DOIOSTI
Results 51–75 of 89
Results 51–75 of 89