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Drag Parameter Estimation Using Gradients and Hessian from a Polynomial Chaos Model Surrogate

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  • 1 Duke University, Durham, North Carolina
  • 2 University of Miami, Miami, Florida
  • 3 University of Miami, and Atlantic Oceanographic and Meteorological Laboratory, Miami, Florida
  • 4 University of Miami, Miami, Florida
  • 5 Duke University, Durham, North Carolina
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Abstract

A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model’s (HYCOM’s) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian’s inverse yields an estimate of the uncertainty in the solution when the latter’s probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed.

Corresponding author address: Omar Knio, Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708. E-mail: omar.knio@duke.edu

Abstract

A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model’s (HYCOM’s) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian’s inverse yields an estimate of the uncertainty in the solution when the latter’s probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed.

Corresponding author address: Omar Knio, Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708. E-mail: omar.knio@duke.edu
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