3,519 research outputs found
Validating Predictions of Unobserved Quantities
The ultimate purpose of most computational models is to make predictions,
commonly in support of some decision-making process (e.g., for design or
operation of some system). The quantities that need to be predicted (the
quantities of interest or QoIs) are generally not experimentally observable
before the prediction, since otherwise no prediction would be needed. Assessing
the validity of such extrapolative predictions, which is critical to informed
decision-making, is challenging. In classical approaches to validation, model
outputs for observed quantities are compared to observations to determine if
they are consistent. By itself, this consistency only ensures that the model
can predict the observed quantities under the conditions of the observations.
This limitation dramatically reduces the utility of the validation effort for
decision making because it implies nothing about predictions of unobserved QoIs
or for scenarios outside of the range of observations. However, there is no
agreement in the scientific community today regarding best practices for
validation of extrapolative predictions made using computational models. The
purpose of this paper is to propose and explore a validation and predictive
assessment process that supports extrapolative predictions for models with
known sources of error. The process includes stochastic modeling, calibration,
validation, and predictive assessment phases where representations of known
sources of uncertainty and error are built, informed, and tested. The proposed
methodology is applied to an illustrative extrapolation problem involving a
misspecified nonlinear oscillator
Analysis of Dual Consistency for Discontinuous Galerkin Discretizations of Source Terms
The effects of dual consistency on discontinuous Galerkin (DG) discretizations of solution
and solution gradient dependent source terms are examined. Two common discretizations are
analyzed: the standard weighting technique for source terms and the mixed formulation. It
is shown that if the source term depends on the first derivative of the solution, the standard
weighting technique leads to a dual inconsistent scheme. A straightforward procedure for correcting
this dual inconsistency and arriving at a dual consistent discretization is demonstrated.
The mixed formulation, where the solution gradient in the source term is replaced by an additional
variable that is solved for simultaneously with the state, leads to an asymptotically
dual consistent discretization. A priori error estimates are derived to reveal the effect of dual
inconsistent discretization on computed functional outputs. Combined with bounds on the dual
consistency error, these estimates show that for a dual consistent discretization or the asymptotically
dual consistent discretization resulting from the mixed formulation, O(h2p) convergence
can be shown for linear problems and linear outputs. For similar but dual inconsistent schemes,
only O(hp) can be shown. Numerical results for a one-dimensional test problem confirm that
the dual consistent and asymptotically dual consistent schemes achieve higher asymptotic convergence
rates with grid refinement than a similar dual inconsistent scheme for both the primal
and adjoint solutions as well as a simple functional output.This work was supported by the U. S. Air Force Research Laboratory (USAF-3306-03-SC-0001) and The Boeing
Company
Automated Estimation of Plasma Temperature and Density from Emission Spectroscopy
This paper introduces a novel approach for automated estimation of plasma
temperature and density using emission spectroscopy, integrating Bayesian
inference with sophisticated physical models. We provide an in-depth
examination of Bayesian methods applied to the complexities of plasma
diagnostics, supported by a robust framework of physical and measurement
models. Our methodology is validated through experimental observations,
focusing on individual and sequential shot analyses. The results demonstrate
the effectiveness of our approach in enhancing the accuracy and reliability of
plasma parameter estimation, marking a significant advancement in the field of
emission spectroscopy for plasma diagnostics. This study not only offers a new
perspective in plasma analysis but also paves the way for further research and
applications in nuclear instrumentation and related domains.Comment: 25 pages, 8 figure
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