Abonnement à la biblothèque: Guest
International Journal for Uncertainty Quantification

Publication de 6  numéros par an

ISSN Imprimer: 2152-5080

ISSN En ligne: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

Indexed in

AN ADAPTIVE MULTIFIDELITY PC-BASED ENSEMBLE KALMAN INVERSION FOR INVERSE PROBLEMS

Volume 9, Numéro 3, 2019, pp. 205-220
DOI: 10.1615/Int.J.UncertaintyQuantification.2019029059
Get accessGet access

RÉSUMÉ

The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by highdimensional nonlinear PDEs, as EKI requires a relatively large ensemble size to guarantee its performance. In this paper, we propose an adaptive multifidelity polynomial chaos (PC) based EKI technique to address this challenge. Our new strategy combines a large number of low-order PC surrogate model evaluations and a small number of high-fidelity forward model evaluations, yielding a multifidelity approach. Specifically, we present a new approach that adaptively constructs and refines a local multifidelity PC surrogate during the EKI simulation. Since the forward model evaluations are only required for updating the low-order local multifidelity PC model, whose number can be much smaller than the total ensemble size of the classic EKI, the entire computational costs are thus significantly reduced. The new algorithm was tested through the two-dimensional time fractional inverse diffusion problems and demonstrated great effectiveness in comparison with PC-based EKI and classic EKI.

RÉFÉRENCES
  1. Tarantola, A., Inverse Problem Theory and Methods for Model Parameter Estimation, Applied Mathematics, vol. 89, Philadelphia: SIAM, 2005.

  2. Kaipio, J.P. and Somersalo, E., Statistical and Computational Inverse Problems, vol. 160, Berlin: Springer, 2005.

  3. Stuart, A.M., Inverse Problems: A Bayesian Perspective, Acta Numer, 19(1):451-559, 2010.

  4. Evensen, G., Sequential Data Assimilation with a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics, J. Geophys. Res.: Oceans, 99(C5):10143-10162, 1994.

  5. Kalman, R.E., A New Approach to Linear Filtering and Prediction Problems, J. Basic Eng., 82(1):35-45, 1960.

  6. Bertino, L., Evensen, G., and Wackernagel, H., Sequential Data Assimilation Techniques in Oceanography, Int. Stat. Rev, 71(2):223-241,2003.

  7. Aanonsen, S.I., Nsvdal, G., Oliver, D.S., Reynolds, A.C., and Valles, B., The Ensemble Kalman Filter in Reservoir Engineering-A Review, SPEJ., 14(3):393-412, 2009.

  8. Emerick, A.A. and Reynolds, A.C., Ensemble Smoother with Multiple Data Assimilation, Comput. Geosci., 55:3-15,2013.

  9. Evensen, G., Data Assimilation: The Ensemble Kalman Filter, Berlin: Springer Science & Business Media, 2009.

  10. van Leeuwen, P. J. and Evensen, G., Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation, Monthly Weather Rev, 124(12):2898-2913,1996.

  11. Skjervheim, J. and Evensen, G., An Ensemble Smoother for Assisted History Matching, in Proc. of SPEReservoir Simulation Symposium, New York: Society of Petroleum Engineers, 2011.

  12. Emerick, A.A. and Reynolds, A.C., History Matching Time-Lapse Seismic Data Using the Ensemble Kalman Filter with Multiple Data Assimilations, Comput. Geosci., 16(3):639-659, 2012.

  13. Gu, Y. and Oliver, D., An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation, SPEJ., 12(4):438-446, 2007.

  14. Lorentzen, R.J. and Nsvdal, G., An Iterative Ensemble Kalman Filter, IEEE Trans. Automat. Control, 56(8):1990-1995,2011.

  15. Chen, Y. and Oliver, D.S., Ensemble Randomized Maximum Likelihood Method as an Iterative Ensemble Smoother, Math. Geosci, 44(1):1-26,2012.

  16. Chen, Y. and Oliver, D.S., Levenberg-Marquardt Forms of the Iterative Ensemble Smoother for Efficient History Matching and Uncertainty Quantification, Comput. Geosci., 17(4):689-703, 2013.

  17. Evensen, G., Analysis of Iterative Ensemble Smoothers for Solving Inverse Problems, Comput. Geosci., 22(3):885-908,2018.

  18. Iglesias, M.A., Law, K.J., and Stuart, A.M., Ensemble Kalman Methods for Inverse Problems, Inverse Problems, 29(4):045001, 2013.

  19. Asch, M., Bocquet, M., and Nodet, M., Data Assimilation: Methods, Algorithms, and Applications, Fundamentals of Algorithms, vol. 11, Philadelphia: SIAM, 2016.

  20. Law, K., Stuart, A., and Zygalakis, K., Data Assimilation: A Mathematical Introduction, Texts in Applied Mathematics, vol. 62, Berlin: Springer, 2015.

  21. Iglesias, M.A., A Regularizing Iterative Ensemble Kalman Method for PDE-Constrained Inverse Problems, Inverse Probl., 32(2):025002, 2016.

  22. Asher, M., Croke, B., Jakeman, A., and Peeters, L., A Review of Surrogate Models and Their Application to Groundwater Modeling, Water Resour. Res, 51(8):5957-5973,2015.

  23. Li, J. and Xiu, D., A Generalized Polynomial Chaos based Ensemble Kalman Filter with High Accuracy, J. Comput. Phys., 228(15):5454-5469,2009.

  24. Li, W., Lin, G., and Zhang, D., An Adaptive Anova-Based PCKF for High-Dimensional Nonlinear Inverse Modeling, J. Comput. Phys, 258:752-772, 2014.

  25. Li, W., Zhang, D., and Lin, G., A Surrogate-Based Adaptive Sampling Approach for History Matching and Uncertainty Quantification, in Proc. of SPE Reservoir Simulation Symposium, New York: Society of Petroleum Engineers, 2015.

  26. Ju, L., Zhang, J., Meng, L., Wu, L., and Zeng, L., An Adaptive Gaussian Process-Based Iterative Ensemble Smoother for Data Assimilation, Adv. Water Resour., 115:125-135, 2018.

  27. Saad, G. and Ghanem, R., Characterization of Reservoir Simulation Models Using a Polynomial Chaos-Based Ensemble Kalman Filter, Water Resour. Res., 45(4), 2009.

  28. Xiu, D., Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton, NJ: Princeton University Press, 2010.

  29. Lu, F., Morzfeld, M., Tu, X., and Chorin, A.J., Limitations of Polynomial Chaos Expansions in the Bayesian Solution of Inverse Problems, J. Comput. Phys., 282:138-147, 2015.

  30. Yan, L. and Zhang, Y., Convergence Analysis of Surrogate-Based Methods for Bayesian Inverse Problems, Inverse Probl., 33(12):125001,2017.

  31. Yan, L. and Zhou, T., Adaptive Multi-Fidelity Polynomial Chaos Approach to Bayesian Inference in Inverse Problems, J. Comput. Phys.,381:110-128,2019.

  32. Iglesias, M.A., Iterative Regularization for Ensemble Data Assimilation in Reservoir Models, Comput. Geosci., 19(1):177-212,2015.

  33. Ghanem, R.G. and Spanos, P.D., Stochastic Finite Elements: A Spectral Approach, New York: Springer-Verlag, 1991.

  34. Zhou, T., Narayan, A., and Xiu, D., Weighted Discrete Least-Squares Polynomial Approximation Using Randomized Quadratures, J. Comput. Phys, 298:787-800, 2015.

  35. Narayan, A., Jakeman, J.D., and Zhou, T., A Christoffel Function Weighted Least Squares Algorithm for Collocation Approx-imations, Math. Comput, 86(306):1913-1947,2017.

  36. Peherstorfer, B., Willcox, K., and Gunzburger, M., Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization, SIAMRev., 60(3):550-591,2018.

  37. Hampton, J., Fairbanks, H., Narayan, A., and Doostan, A., Practical Error Bounds for a Non-Intrusive Bi-Fidelity Approach to Parametric/Stochastic Model Reduction, J. Comput. Phys, 386:315-332, 2018.

  38. Eldred, M.S., Ng, L.W., Barone, M.F., and Domino, S.P., Multifidelity Uncertainty Quantification Using Spectral Stochastic Discrepancy Models, in Handbook of Uncertainty Quantification, R. Ghanem, D. Higdon, and H. Owhadi, Eds., Berlin: Springer, pp. 991-1036, 2017.

  39. Narayan, A., Gittelson, C., and Xiu, D., A Stochastic Collocation Algorithm with Multifidelity Models, SIAMJ. Sci. Comput., 36(2):A495-A521, 2014.

  40. Peherstorfer, B., Cui, T., Marzouk, Y., and Willcox, K., Multifidelity Importance Sampling, Comput. Methods Appl. Mech. Eng., 300:490-509,2016.

  41. Perdikaris, P., Venturi, D., Royset, J., and Karniadakis, G., Multi-Fidelity Modelling via Recursive Co-Kriging and Gaussian- Markov Random Fields, Proc. R. Soc. A, 471(2179):20150018, 2015.

  42. Zhu, X., Narayan, A., and Xiu, D., Computational Aspects of Stochastic Collocation with Multifidelity Models, SIAM/ASA J. Uncertainty Quantif, 2(1):444-463,2014.

  43. Ng, L.W.T. and Eldred, M., Multifidelity Uncertainty Quantification Using Non-Intrusive Poly-Nomial Chaos and Stochastic Collocation, in Proc. of 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, p. 1852, 2012.

  44. Palar, P.S., Tsuchiya, T., and Parks, G.T., Multi-Fidelity Non-Intrusive Polynomial Chaos based on Regression, Comput. Methods Appl. Mech. Eng., 305:579-606, 2016.

  45. Lin, Y. and Xu, C., Finite Difference/Spectral Approximations for the Time-Fractional Diffusion Equation, J. Comput. Phys, 225(2):1533-1552, 2007.

CITÉ PAR
  1. Yang Feng-lian, Yan Liang, A Non-Intrusive Reduced Basis EKI for Time Fractional Diffusion Inverse Problems, Acta Mathematicae Applicatae Sinica, English Series, 36, 1, 2020. Crossref

  2. Liao Qifeng, Li Jinglai, An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems, Journal of Computational Physics, 396, 2019. Crossref

  3. Calvetti Daniela, Cosmo Anna, Perotto Simona, Somersalo Erkki, Bayesian Mesh Adaptation for Estimating Distributed Parameters, SIAM Journal on Scientific Computing, 42, 6, 2020. Crossref

  4. Yan Liang, Zhou Tao, Stein variational gradient descent with local approximations, Computer Methods in Applied Mechanics and Engineering, 386, 2021. Crossref

  5. Yan X.B., Zhang Y.X., Wei T., Identify the fractional order and diffusion coefficient in a fractional diffusion wave equation, Journal of Computational and Applied Mathematics, 393, 2021. Crossref

  6. Cleary Emmet, Garbuno-Inigo Alfredo, Lan Shiwei, Schneider Tapio, Stuart Andrew M., Calibrate, emulate, sample, Journal of Computational Physics, 424, 2021. Crossref

  7. Liu Liu, Zhu Xueyu, A bi-fidelity method for the multiscale Boltzmann equation with random parameters, Journal of Computational Physics, 402, 2020. Crossref

  8. Weissmann Simon, Chada Neil K, Schillings Claudia, Tong Xin T, Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion, Inverse Problems, 38, 4, 2022. Crossref

Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections Prix et politiques d'abonnement Begell House Contactez-nous Language English 中文 Русский Português German French Spain