Date of Award

2026-08-01

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Advisor(s)

Xiaogang Su

Abstract

Physics based computational simulators encode the governing equations of complex physical phenomena through parameters that must be inferred from empirical observations, and the observational record in modern experimental campaigns is increasingly a high dimensional functional response rather than a scalar summary. The canonical treatment of this calibration problem through the additive discrepancy decomposition of Kennedy and O'Hagan incurs O(N^3obs) Gaussian process inversion costs at functional resolution, sensitivity to discrepancy prior specification, and the confounding identifiability between the calibration parameter and the discrepancy function; scalar reduction strategies bypass the cost but discard the morphological information that the functional response carries about the parameters. We develop calibration via functional kernel regression, a non parametric inverse mapping that recovers the multivariate calibration parameter vector directly from the observed functional response through kernel regression in the finite dimensional coefficient space induced by a penalized basis expansion of the response. The framework operates with no prior elicitation on the calibration parameters, no joint discrepancy modeling, and no Markov chain machinery; conditions under which the estimator is consistent are identified, stated in the intrinsic dimension of the calibration parameter space rather than the ambient coefficient dimension, and the kernel weights over the candidate library furnish a discrete posterior approximation together with intrinsic identifiability diagnostics as byproducts of the calibration step. The framework is exercised on two physics model calibration benchmarks drawn from structurally distinct regimes of high energy density physics and laminar hypersonic aerothermodynamics, recovering the calibration parameters to within instrumentation uncertainty of the stated experimental values and the published reference estimates while reproducing the established identifiability structure of the underlying inverse problems, with empirical predictive coverage coinciding with the nominal 95% level in both applications. Functional kernel regression provides a scalable, prior-free, and externally validated approach to physics model calibration with functional observations and multivariate calibration parameters.

Language

en

Provenance

Received from ProQuest

File Size

195 p.

File Format

application/pdf

Rights Holder

Kwesi Appau Ohene-Obeng

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