Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation
Tài liệu tham khảo
Allen, 1979, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metall., 27, 1085, 10.1016/0001-6160(79)90196-2
Alnæs, 2015, The fenics project version 1.5, Arch. Numer. Softw., 3
Alsayed, 2022, Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs, Discrete Contin. Dyn. Syst., Ser. S, 10.3934/dcdss.2022003
Bangerth, 2013
Becker, 2001, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numer., 10, 1, 10.1017/S0962492901000010
Biros, 2011
Conrad, 2016, Accelerating asymptotically exact MCMC for computationally intensive models via local approximations, J. Am. Stat. Assoc., 111, 1591, 10.1080/01621459.2015.1096787
Frangos, 2010, 123
Fritz, 2021, Modeling and simulation of vascular tumors embedded in evolving capillary networks, Comput. Methods Appl. Mech. Eng., 384, 10.1016/j.cma.2021.113975
Fritz, 2021, Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network, Nonlinear Anal., Real World Appl., 61, 10.1016/j.nonrwa.2021.103331
Galbally, 2010, Non-linear model reduction for uncertainty quantification in large-scale inverse problems, Int. J. Numer. Methods Eng., 81, 1581, 10.1002/nme.2746
Hawkins-Daarud, 2012, Numerical simulation of a thermodynamically consistent four-species tumor growth model, Int. J. Numer. Methods Biomed. Eng., 28, 3, 10.1002/cnm.1467
Lassila, 2013, A reduced computational and geometrical framework for inverse problems in hemodynamics, Int. J. Numer. Methods Biomed. Eng., 29, 741, 10.1002/cnm.2559
Li, 2018, Model adaptivity for goal-oriented inference using adjoints, Comput. Methods Appl. Mech. Eng., 331, 1, 10.1016/j.cma.2017.11.018
Lima, 2017, Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data, Comput. Methods Appl. Mech. Eng., 327, 277, 10.1016/j.cma.2017.08.009
Lima, 2016, Selection, calibration, and validation of models of tumor growth, Math. Models Methods Appl. Sci., 26, 2341, 10.1142/S021820251650055X
Logg, 2012
Lorenzo, 2016, Tissue-scale, personalized modeling and simulation of prostate cancer growth, Proc. Natl. Acad. Sci., 113, E7663, 10.1073/pnas.1615791113
Manzoni, 2016, Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models, SIAM/ASA J. Uncertain. Quantificat., 4, 380, 10.1137/140995817
Marzouk, 2009, Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems, J. Comput. Phys., 228, 1862, 10.1016/j.jcp.2008.11.024
Oden, 2017
Oden, 2018, Adaptive multiscale predictive modelling, Acta Numer., 27, 353, 10.1017/S096249291800003X
Oden, 2017, Predictive computational science: computer predictions in the presence of uncertainty, 1
Oden, 2010, General diffuse-interface theories and an approach to predictive tumor growth modeling, Math. Models Methods Appl. Sci., 20, 477, 10.1142/S0218202510004313
Oden, 2001, Goal-oriented error estimation and adaptivity for the finite element method, Comput. Math. Appl., 41, 735, 10.1016/S0898-1221(00)00317-5
Oden, 2002, Estimation of modeling error in computational mechanics, J. Comput. Phys., 182, 496, 10.1006/jcph.2002.7183
Prudhomme, 1999, On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors, Comput. Methods Appl. Mech. Eng., 176, 313, 10.1016/S0045-7825(98)00343-0
Prudhomme, 2003, 207
Rannacher, 1997, A feed-back approach to error control in finite element methods: application to linear elasticity, Comput. Mech., 19, 434, 10.1007/s004660050191
Roderick, 2014, Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models, Int. J. Comput. Math., 91, 748, 10.1080/00207160.2013.844431
van der Zee, 2011, Goal-oriented error estimation for Cahn–Hilliard models of binary phase transition, Numer. Methods Partial Differ. Equ., 27, 160, 10.1002/num.20638
Villa, 2018, hiPPYlib: an extensible software framework for large-scale inverse problems, J. Open Sour. Softw., 3, 940, 10.21105/joss.00940
Villa, 2021, hiPPYlib: an extensible software framework for large-scale inverse problems governed by PDEs: part I: deterministic inversion and linearized Bayesian inference, ACM Trans. Math. Softw., 47, 1, 10.1145/3428447
Yan, 2019, Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems, J. Comput. Phys., 381, 110, 10.1016/j.jcp.2018.12.025
Yan, 2020, An adaptive surrogate modeling based on deep neural networks for large-scale Bayesian inverse problems, Commun. Comput. Phys., 28, 2180, 10.4208/cicp.OA-2020-0186