Constructing a Simulation Surrogate with Partially Observed Output

Abstract

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these surrogates. However, surrogate methods with dimension reduction generally rely on complete output training data. This article proposes a new Gaussian process surrogate method that permits the use of partially observed output while remaining computationally efficient. The new method involves the imputation of missing values and the adjustment of the covariance matrix used for Gaussian process inference. The resulting surrogate represents the available responses, disregards the missing responses, and provides meaningful uncertainty quantification. The proposed approach is shown to offer sharper inference than alternatives in a simulation study and a case study where an energy density functional model that frequently returns incomplete output is calibrated.

Keywords:

• Calibration
• Gaussian process
• High-dimensional output
• Missing data
• Statistical emulation

Supplementary Materials

The supplementary materials contain (i) proofs for Theorems 1 and 2, (ii) technical details for computation, (iii) descriptions of test functions, (iv) full results from the numerical experiments, (v) the original scaling of the Fayans EDF parameter space, and (vi) the code and data for the Fayans EDF case study.

Acknowledgments

We thank the editor, AE, two anonymous referees, Earl Lawrence and Kelly Moran for their valuable feedback for improving this article’s exposition. We are grateful to Jared O’Neal and Paul-Gerhard Reinhard for developing the Fayans EDF model employed here. We gratefully acknowledge the computing resources provided on Bebop, a high-performance computing cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory. This research was supported in part through the computational resources and staff contributions provided for the Quest high-performance computing facility at Northwestern University, which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This material is based upon work supported by NSF grants OAC 2004601, DMS 1953111, 1952897. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research SciDAC and applied mathematics programs under contract DE-AC02-05CH11231, and by NSF grants OAC 2004601 and DMS 1952897.