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

Robotic Surgery may Not “Make the Cut” in Pediatrics

Since the introduction of robotic surgery in children in 2001, it has been employed by select pediatric laparoscopic surgeons but not to the degree of adult surgical specialists. It has been suggested that the technical capabilities of the robot may be ideal for complex pediatric surgical cases that require intricate dissection. However, due to the size constraints of the robot for small pediatric patients, the tight financial margins that pediatric hospitals face, and the lack of high level data displaying patient benefit when compared to conventional laparoscopic surgery, it may be some time before the robotic surgical platform is widely embraced in pediatric surgical practice