18,180 research outputs found
The ROMES method for statistical modeling of reduced-order-model error
This work presents a technique for statistically modeling errors introduced
by reduced-order models. The method employs Gaussian-process regression to
construct a mapping from a small number of computationally inexpensive `error
indicators' to a distribution over the true error. The variance of this
distribution can be interpreted as the (epistemic) uncertainty introduced by
the reduced-order model. To model normed errors, the method employs existing
rigorous error bounds and residual norms as indicators; numerical experiments
show that the method leads to a near-optimal expected effectivity in contrast
to typical error bounds. To model errors in general outputs, the method uses
dual-weighted residuals---which are amenable to uncertainty control---as
indicators. Experiments illustrate that correcting the reduced-order-model
output with this surrogate can improve prediction accuracy by an order of
magnitude; this contrasts with existing `multifidelity correction' approaches,
which often fail for reduced-order models and suffer from the curse of
dimensionality. The proposed error surrogates also lead to a notion of
`probabilistic rigor', i.e., the surrogate bounds the error with specified
probability
Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 2: Application to TRACE
Inverse Uncertainty Quantification (UQ) is a process to quantify the
uncertainties in random input parameters while achieving consistency between
code simulations and physical observations. In this paper, we performed inverse
UQ using an improved modular Bayesian approach based on Gaussian Process (GP)
for TRACE physical model parameters using the BWR Full-size Fine-Mesh Bundle
Tests (BFBT) benchmark steady-state void fraction data. The model discrepancy
is described with a GP emulator. Numerical tests have demonstrated that such
treatment of model discrepancy can avoid over-fitting. Furthermore, we
constructed a fast-running and accurate GP emulator to replace TRACE full model
during Markov Chain Monte Carlo (MCMC) sampling. The computational cost was
demonstrated to be reduced by several orders of magnitude.
A sequential approach was also developed for efficient test source allocation
(TSA) for inverse UQ and validation. This sequential TSA methodology first
selects experimental tests for validation that has a full coverage of the test
domain to avoid extrapolation of model discrepancy term when evaluated at input
setting of tests for inverse UQ. Then it selects tests that tend to reside in
the unfilled zones of the test domain for inverse UQ, so that one can extract
the most information for posterior probability distributions of calibration
parameters using only a relatively small number of tests. This research
addresses the "lack of input uncertainty information" issue for TRACE physical
input parameters, which was usually ignored or described using expert opinion
or user self-assessment in previous work. The resulting posterior probability
distributions of TRACE parameters can be used in future uncertainty,
sensitivity and validation studies of TRACE code for nuclear reactor system
design and safety analysis
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