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This paper proposes a novel computationally efficient dynamicbi-orthogonality based approach for calibration of a computer simulator withhigh dimensional parametric and model structure uncertainty. The proposedmethod is based on a decomposition of the solution into mean and a random fieldusing a generic Karhunnen-Loeve expansion. The random field is represented as aconvolution of separable Hilbert spaces in stochastic and spacial dimensionsthat are spectrally represented using respective orthogonal bases. Inparticular, the present paper investigates generalized polynomial chaos basesfor stochastic dimension and eigenfunction bases for spacial dimension. Dynamicorthogonality is used to derive closed form equations for the time evolution ofmean, spacial and the stochastic fields. The resultant system of equationsconsists of a partial differential equation (PDE) that define dynamic evolutionof the mean, a set of PDEs to define the time evolution of eigenfunction bases,while a set of ordinary differential equations (ODEs) define dynamics of thestochastic field. This system of dynamic evolution equations efficientlypropagates the prior parametric uncertainty to the system response. Theresulting bi-orthogonal expansion of the system response is used to reformulatethe Bayesian inference for efficient exploration of the posterior distribution.Efficacy of the proposed method is investigated for calibration of a 2Dtransient diffusion simulator with uncertain source location and diffusivity.Computational efficiency of the method is demonstrated against a Monte Carlomethod and a generalized polynomial chaos approach.

A Dynamic Bi-orthogonal Field Equation Approach for Efficient Bayesian Calibration of Large-Scale Systems