| 1. |
- Tabiri, S, et al.
(författare)
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- 2021
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swepub:Mat__t
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| 2. |
- Bravo, L, et al.
(författare)
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- 2021
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swepub:Mat__t
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| 3. |
- Glasbey, JC, et al.
(författare)
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- 2021
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swepub:Mat__t
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| 4. |
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| 5. |
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| 6. |
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| 7. |
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| 8. |
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- 2019
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Tidskriftsartikel (refereegranskat)
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| 9. |
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| 10. |
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| 11. |
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| 12. |
- Babuska, I., et al.
(författare)
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A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria
- 2008
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 197:29-32, s. 2517-2539
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Tidskriftsartikel (refereegranskat)abstract
- This work describes a solution to the validation challenge problem posed at the SANDIA Validation Challenge Workshop, May 21-23, 2006, NM. It presents and applies a general methodology to it. The solution entails several standard steps, namely selecting and fitting several models to the available prior information and then sequentially rejecting those which do not perform satisfactorily in the validation and accreditation experiments. The rejection procedures are based on Bayesian updates, where the prior density is related to the current candidate model and the posterior density is obtained by conditioning on the validation and accreditation experiments. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data.
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| 13. |
- Babuska, I., et al.
(författare)
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Formulation of the static frame problem
- 2008
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 197:29-32, s. 2496-2499
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Tidskriftsartikel (refereegranskat)abstract
- This report describes a static framework validation challenge problem used in the SANDIA Validation Challenge Workshop, May 21-23, 2006. The challenge problem has clear engineering character, is simple to state and allows many different approaches to solve it. The regulatory assessment problem is to estimate the probability of a given vertical displacement to exceed a prescribed threshold.
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| 14. |
- Babuska, I., et al.
(författare)
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Reliability of computational science
- 2007
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Ingår i: Numerical Methods for Partial Differential Equations. - : Wiley. - 0749-159X .- 1098-2426. ; 23:4, s. 753-784
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Tidskriftsartikel (refereegranskat)abstract
- Today's computers allow us to simulate large, complex physical problems. Many times the mathematical models describing such problems are based on a relatively small amount of available information such as experimental measurements. The question arises whether the computed data could be used as the basis for decision in critical engineering, economic, and medicine applications. The representative list of engineering accidents occurred in the past years and their reasons illustrate the question. The paper describes a general framework for verification and validation (V&V) which deals with this question. The framework is then applied to an illustrative engineering problem, in which the basis for decision is a specific quantity of interest, namely the probability that the quantity does not exceed a given value. The V&V framework is applied and explained in detail. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data.
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| 15. |
- Babuska, I., et al.
(författare)
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Worst case scenario analysis for elliptic problems with uncertainty
- 2005
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Ingår i: Numerische Mathematik. - : Springer Science and Business Media LLC. - 0029-599X .- 0945-3245. ; 101:2, s. 185-219
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Tidskriftsartikel (refereegranskat)abstract
- This work studies linear elliptic problems under uncertainty. The major emphasis is on the deterministic treatment of such uncertainty. In particular, this work uses the Worst Scenario approach for the characterization of uncertainty on functional outputs (quantities of physical interest). Assuming that the input data belong to a given functional set, eventually infinitely dimensional, this work proposes numerical methods to approximate the corresponding uncertainty intervals for the quantities of interest. Numerical experiments illustrate the performance of the proposed methodology.
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| 16. |
- Fisser, C, et al.
(författare)
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Validation of Prognostic Scores in Extracorporeal Life Support: A Multi-Centric Retrospective Study
- 2021
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Ingår i: Membranes. - : MDPI AG. - 2077-0375. ; 11:2
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Tidskriftsartikel (refereegranskat)abstract
- Multiple prognostic scores have been developed for both veno-arterial (VA) and veno-venous (VV) extracorporeal membrane oxygenation (ECMO), mostly in single-center cohorts. The aim of this study was to compare and validate different prediction scores in a large multicenter ECMO-population. Methods: Data from five ECMO centers included 300 patients on VA and 329 on VV ECMO support (March 2008 to November 2016). Different prognostic scores were compared between survivors and non-survivors: APACHE II, SOFA, SAPS II in all patients; SAVE, modified SAVE and MELD-XI in VA ECMO; RESP, PRESET, ROCH and PRESERVE in VV ECMO. Model performance was compared using receiver-operating-curve analysis and assessment of model calibration. Survival was assessed at intensive care unit discharge. Results: The main indication for VA ECMO was cardiogenic shock; overall survival was 51%. ICU survivors had higher Glasgow Coma Scale scores and pH, required cardiopulmonary resuscitation (CPR) less frequently, had lower lactate levels and shorter ventilation time pre-ECMO at baseline. The best discrimination between survivors and non-survivors was observed with the SAPS II score (area under the curve [AUC] of 0.73 (95% CI 0.67–0.78)). The main indication for VV ECMO was pneumonia; overall survival was 60%. Lower PaCO2, higher pH, lower lactate and lesser need for CPR were observed among survivors. The best discrimination between survivors and non-survivors was observed with the PRESET score (AUC 0.66 (95% CI 0.60–0.72)). Conclusion: The prognostic performance of most scores was moderate in ECMO patients. The use of such scores to decide about ECMO implementation in potential candidates should be discouraged.
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| 17. |
- Nobile, F., et al.
(författare)
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A sparse grid stochastic collocation method for partial differential equations with random input data
- 2008
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 46:5, s. 2309-2345
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Tidskriftsartikel (refereegranskat)abstract
- This work proposes and analyzes a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coeffcients and forcing terms ( input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems as in the Monte Carlo method. If the number of random variables needed to describe the input data is moderately large, full tensor product spaces are computationally expensive to use due to the curse of dimensionality. In this case the sparse grid approach is still expected to be competitive with the classical Monte Carlo method. Therefore, it is of major practical relevance to understand in which situations the sparse grid stochastic collocation method is more efficient than Monte Carlo. This work provides error estimates for the fully discrete solution using L-q norms and analyzes the computational efficiency of the proposed method. In particular, it demonstrates algebraic convergence with respect to the total number of collocation points and quantifies the effect of the dimension of the problem ( number of input random variables) in the final estimates. The derived estimates are then used to compare the method with Monte Carlo, indicating for which problems the former is more efficient than the latter. Computational evidence complements the present theory and shows the effectiveness of the sparse grid stochastic collocation method compared to full tensor and Monte Carlo approaches.
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| 18. |
- Nobile, F., et al.
(författare)
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An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data
- 2008
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 46:5, s. 2411-2442
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Tidskriftsartikel (refereegranskat)abstract
- This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving partial differential equations with random coefficients and forcing terms ( input data of the model). The method consists of a Galerkin approximation in the space variables and a collocation, in probability space, on sparse tensor product grids utilizing either Clenshaw-Curtis or Gaussian knots. Even in the presence of nonlinearities, the collocation approach leads to the solution of uncoupled deterministic problems, just as in the Monte Carlo method. This work includes a priori and a posteriori procedures to adapt the anisotropy of the sparse grids to each given problem. These procedures seem to be very effective for the problems under study. The proposed method combines the advantages of isotropic sparse collocation with those of anisotropic full tensor product collocation: the first approach is effective for problems depending on random variables which weigh approximately equally in the solution, while the benefits of the latter approach become apparent when solving highly anisotropic problems depending on a relatively small number of random variables, as in the case where input random variables are Karhunen-Loeve truncations of "smooth" random fields. This work also provides a rigorous convergence analysis of the fully discrete problem and demonstrates ( sub) exponential convergence in the asymptotic regime and algebraic convergence in the preasymptotic regime, with respect to the total number of collocation points. It also shows that the anisotropic approximation breaks the curse of dimensionality for a wide set of problems. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo. In particular, for moderately large-dimensional problems, the sparse grid approach with a properly chosen anisotropy seems to be very efficient and superior to all examined methods.
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| 19. |
- Nobile, F., et al.
(författare)
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Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients
- 2009
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 80:6-7, s. 979-1006
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of numerically approximating statistical moments of the solution of a time-dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forzing terms are Spatially correlated random fields The stochastic coefficients of the PDE are approximated by truncated Karhunen-Loeve expansions driven by a finite number of uncorrelated random variables. After approximating the stochastic coefficients, the original stochastic PDE turns into a new deterministic parametric PDE; of the same type, the dimension of the parameter set being equal to the number of random variables Introduced. After proving that the. solution of the parametric PDE problem is analytic with respect to the parameters, we consider global polynomial approximations based oil tensor product. total degree or sparse polynomial Spaces and constructed by either a Stochastic Galerkin or I Stochastic Collocation approach. We derive convergence rates for the different Cases and present numerical results that show how these approaches are a valid 'alternative to the more traditional Monte Carlo Method for this class of problems.
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| 20. |
- Oden, J. T., et al.
(författare)
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Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty
- 2005
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 194:05-feb, s. 195-204
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Tidskriftsartikel (refereegranskat)abstract
- The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented.
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| 21. |
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| 22. |
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