Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review. (English) Zbl 1461.62129
Summary: We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the placement of measurement points, at which data are collected, such that the uncertainty in the estimated parameters is minimized. We present the mathematical foundations of OED in this context and survey the computational methods for the class of OED problems under study. We also outline some directions for future research in this area.
MSC:
| 62K05 | Optimal statistical designs |
| 62F15 | Bayesian inference |
| 46N10 | Applications of functional analysis in optimization, convex analysis, mathematical programming, economics |
| 35Q62 | PDEs in connection with statistics |
| 62-08 | Computational methods for problems pertaining to statistics |
Keywords:
optimal experimental design; inverse problem; Bayesian inference in Hilbert space; sensor placementSoftware:
VPLANReferences:
| [1] | Agapiou S, Larsson S and Stuart A M 2013 Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems Stoch. Process. Appl.123 3828-60 · Zbl 1284.62289 · doi:10.1016/j.spa.2013.05.001 |
| [2] | Alexanderian A, Gloor P J and Ghattas O 2016 On Bayesian A-and D-optimal experimental designs in infinite dimensions Bayesian Anal.11 671-95 · Zbl 1359.62315 · doi:10.1214/15-ba969 |
| [3] | Alexanderian A, Petra N, Stadler G and Ghattas O 2014 A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized ℓ0-sparsification SIAM J. Sci. Comput.36 A2122-48 · Zbl 1314.62163 · doi:10.1137/130933381 |
| [4] | Alexanderian A, Petra N, Stadler G and Ghattas O 2016 A fast and scalable method for A-optimal design of experiments for infinite-dimensional Bayesian nonlinear inverse problems SIAM J. Sci. Comput.38 A243-72 · Zbl 06536072 · doi:10.1137/140992564 |
| [5] | Alexanderian A, Petra N, Stadler G and Sunseri I 2021 Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don’t know SIAM/ASA J. Uncertain. Quantification9 163-84 · Zbl 1460.62120 · doi:10.1137/20m1347292 |
| [6] | Alexanderian A and Saibaba A 2018 Efficient D-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems SIAM J. Sci. Comput.40 A2956-85 · Zbl 1401.62123 · doi:10.1137/17m115712x |
| [7] | Atkinson A C 1996 The usefulness of optimum experimental designs J. R. Stat. Soc. B 58 59-76 · Zbl 0850.62602 · doi:10.1111/j.2517-6161.1996.tb02067.x |
| [8] | Atkinson A C and Donev A N 1992 Optimum Experimental Designs ((Oxford: Oxford University Press)) · Zbl 0829.62070 |
| [9] | Attia A, Alexanderian A and Saibaba A K 2018 Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems Inverse Problems34 895009 · Zbl 1475.65037 · doi:10.1088/1361-6420/aad210 |
| [10] | Avron H and Toledo S 2011 Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix J. ACM58 17 · Zbl 1327.68331 · doi:10.1145/1944345.1944349 |
| [11] | Bandara S, Schlöder J P, Eils R, Bock H G and Meyer T 2009 Optimal experimental design for parameter estimation of a cell signaling model PLoS Comput. Biol.5 e1000558 · doi:10.1371/journal.pcbi.1000558 |
| [12] | Bardsley J M, Cui T, Marzouk Y M and Wang Z 2020 Scalable optimization-based sampling on function space SIAM J. Sci. Comput.42 A1317-47 · Zbl 1471.62023 · doi:10.1137/19m1245220 |
| [13] | Bauer I, Bock H G, Körkel S and Schlöder J P 2000 Numerical methods for optimum experimental design in DAE systems J. Comput. Appl. Math.120 1-25 · Zbl 0998.65083 · doi:10.1016/s0377-0427(00)00300-9 |
| [14] | Beck J, Dia B M, Espath L F, Long Q and Tempone R 2018 Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain Comput. Methods Appl. Mech. Eng.334 523-53 · Zbl 1440.62293 · doi:10.1016/j.cma.2018.01.053 |
| [15] | Beskos A, Girolami M, Lan S, Farrell P E and Stuart A M 2017 Geometric MCMC for infinite-dimensional inverse problems J. Comput. Phys.335 327-51 · Zbl 1375.35627 · doi:10.1016/j.jcp.2016.12.041 |
| [16] | Beskos A, Pinski F J, Sanz-Serna J M and Stuart A M 2011 Hybrid Monte Carlo on Hilbert spaces Stoch. Process. Appl.121 2201-30 · Zbl 1235.60091 · doi:10.1016/j.spa.2011.06.003 |
| [17] | Bock H G, Körkel S and Schlöder J P 2013 Parameter estimation and optimum experimental design for differential equation models Model Based Parameter Estimation(Contributions in Mathematical and Computational Sciences vol 4) ed H G Bock, T Carraro, W Jäger, S Körkel, R Rannacher and J P Schlöder (Berlin: Springer) pp 1-30 · Zbl 1269.65014 · doi:10.1007/978-3-642-30367-8_1 |
| [18] | Bogachev V I 1998 Gaussian Measures(Mathematical Surveys and Monographs) (Providence, RI: Americal Mathematical Society) · Zbl 0913.60035 · doi:10.1090/surv/062 |
| [19] | Boyd S and Vandenberghe L 2004 Convex Optimization (Cambridge: Cambridge University Press) · Zbl 1058.90049 · doi:10.1017/CBO9780511804441 |
| [20] | Brauer F, Castillo-Chavez C and Feng Z 2019 Mathematical Models in Epidemiology (Berlin: Springer) · Zbl 1433.92001 · doi:10.1007/978-1-4939-9828-9 |
| [21] | Bui-Thanh T, Ghattas O, Martin J and Stadler G 2013 A computational framework for infinite-dimensional Bayesian inverse problems part I: the linearized case, with application to global seismic inversion SIAM J. Sci. Comput.35 A2494-523 · Zbl 1287.35087 · doi:10.1137/12089586x |
| [22] | Bui-Thanh T and Nguyen Q P 2016 FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems Inverse Problems Imaging10 943 · Zbl 1348.65013 · doi:10.3934/ipi.2016028 |
| [23] | Butler T, Jakeman J and Wildey T 2018 Combining push-forward measures and Bayes’ rule to construct consistent solutions to stochastic inverse problems SIAM J. Sci. Comput.40 A984-A1011 · Zbl 1390.60255 · doi:10.1137/16m1087229 |
| [24] | Butler T, Jakeman J and Wildey T 2020 Optimal experimental design for prediction based on push-forward probability measures J. Comput. Phys.416 109518 · Zbl 1437.62297 · doi:10.1016/j.jcp.2020.109518 |
| [25] | Castro P and De los Reyes J C 2020 A bilevel learning approach for optimal observation placement in variational data assimilation Inverse Problems36 035020 · Zbl 1473.35608 · doi:10.1088/1361-6420/ab4bfa |
| [26] | Chaloner K and Verdinelli I 1995 Bayesian experimental design: a review Stat. Sci.10 273-304 · Zbl 0617.60015 · doi:10.1214/ss/1177009939 |
| [27] | Chamon L and Ribeiro A 2017 Approximate supermodularity bounds for experimental design arXiv:1711.01501 |
| [28] | Chung M and Haber E 2012 Experimental design for biological systems SIAM J. Control Optim.50 471-89 · Zbl 1243.93130 · doi:10.1137/100791063 |
| [29] | Clyde M A 2001 Experimental design: a Bayesian perspective International Encyclopedia of the Social & Behavioral Sciences 5075-81 ed N J Smelser and P B Baltes · doi:10.1016/b0-08-043076-7/00421-6 |
| [30] | Conway J B 2000 A Course in Operator Theory (Providence, RI: American Mathematical Society) · Zbl 0936.47001 |
| [31] | Cotter S L, Roberts G O, Stuart A M and White D 2013 MCMC methods for functions: modifying old algorithms to make them faster Stat. Sci.28 424-46 · Zbl 1331.62132 · doi:10.1214/13-sts421 |
| [32] | Cui T, Law K J H and Marzouk Y M 2016 Dimension-independent likelihood-informed MCMC J. Comput. Phys.304 109-37 · Zbl 1349.65009 · doi:10.1016/j.jcp.2015.10.008 |
| [33] | Da Prato G 2006 An Introduction to Infinite-Dimensional Analysis (Berlin: Springer) · Zbl 1109.46001 · doi:10.1007/3-540-29021-4 |
| [34] | Da Prato G and Zabczyk J 2002 Second-Order Partial Differential Equations in Hilbert Spaces (Cambridge: Cambridge University Press) · Zbl 1012.35001 · doi:10.1017/CBO9780511543210 |
| [35] | Da Prato G and Zabczyk J 2014 Stochastic Equations in Infinite Dimensions vol 152 (Cambridge: Cambridge University Press) · Zbl 1317.60077 · doi:10.1017/CBO9781107295513 |
| [36] | Dashti M, Harris S and Stuart A 2012 Besov priors for Bayesian inverse problems Inverse Problems Imaging6 183-200 · Zbl 1243.62032 · doi:10.3934/ipi.2012.6.183 |
| [37] | Dashti M, Law K J, Stuart A M and Voss J 2013 MAP estimators and their consistency in Bayesian nonparametric inverse problems Inverse Problems29 095017 · Zbl 1281.62089 · doi:10.1088/0266-5611/29/9/095017 |
| [38] | Dashti M and Stuart A M 2017 The Bayesian approach to inverse problems Handbook of Uncertainty Quantification ed R Ghanem, D Higdon and H Owhadi (Berlin: Springer) · doi:10.1007/978-3-319-12385-1_7 |
| [39] | Djikpesse H A, Khodja M R, Prange M D, Duchenne S and Menkiti H 2012 Bayesian survey design to optimize resolution in waveform inversion Geophysics77 R81-93 · doi:10.1190/geo2011-0143.1 |
| [40] | Einsiedler M and Ward T 2017 Functional Analysis, Spectral Theory, and Applications(Graduate Texts in Mathematics vol 276) (Berlin: Springer) · Zbl 1387.46001 · doi:10.1007/978-3-319-58540-6 |
| [41] | Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Berlin: Springer) · Zbl 0859.65054 · doi:10.1007/978-94-009-1740-8 |
| [42] | Etling T and Herzog R 2018 Optimum experimental design by shape optimization of specimens in linear elasticity SIAM J. Appl. Math.78 1553-76 · Zbl 1394.35579 · doi:10.1137/17m1147743 |
| [43] | Fedorov V V and Leonov S L 2013 Optimal Design for Nonlinear Response Models (Boca Raton, FL: CRC Press) · Zbl 1373.62001 · doi:10.1201/b15054 |
| [44] | Feng C and Marzouk Y M 2019 A layered multiple importance sampling scheme for focused optimal Bayesian experimental design (arXiv:1903.11187) |
| [45] | Fitzpatrick B G 1991 Bayesian analysis in inverse problems Inverse Problems7 675 · Zbl 0743.35084 · doi:10.1088/0266-5611/7/5/003 |
| [46] | Franklin J N 1970 Well-posed stochastic extensions of ill-posed linear problems J. Math. Anal. Appl.31 682-716 · Zbl 0198.20601 · doi:10.1016/0022-247x(70)90017-x |
| [47] | Haber E, Horesh L and Tenorio L 2008 Numerical methods for experimental design of large-scale linear ill-posed inverse problems Inverse Problems24 125-37 · Zbl 1153.65062 · doi:10.1088/0266-5611/24/5/055012 |
| [48] | Haber E, Horesh L and Tenorio L 2010 Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems Inverse Problems26 025002 · Zbl 1189.65073 · doi:10.1088/0266-5611/26/2/025002 |
| [49] | Haber E, Magnant Z, Lucero C and Tenorio L 2012 Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems Comput. Optim. Appl.52 293-314 · Zbl 1259.90135 · doi:10.1007/s10589-011-9404-4 |
| [50] | Hairer M, Stuart A M and Vollmer S J 2014 Spectral gaps for a metropolis—hastings algorithm in infinite dimensions Ann. Appl. Probab.24 2455-90 · Zbl 1307.65002 · doi:10.1214/13-aap982 |
| [51] | Hannukainen A, Hyvönen N and Perkkiö L 2020 Inverse heat source problem and experimental design for determining iron loss distribution (arXiv:2003.10395) |
| [52] | Helin T and Burger M 2015 Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems Inverse Problems31 085009 · Zbl 1325.62058 · doi:10.1088/0266-5611/31/8/085009 |
| [53] | Herman E 2020 Design of inverse problems and reduced order modeling in complex physical systems PhD Dissertation North Carolina State University |
| [54] | Herman E, Alexanderian A and Saibaba A K 2020 Randomization and reweighted ℓ1-minimization for A-optimal design of linear inverse problems SIAM J. Sci. Comput.42 A1714-40 · Zbl 1442.62175 · doi:10.1137/19m1267362 |
| [55] | Herzog R, Riedel I and Uciński D 2018 Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics Optim. Eng.19 591-627 · Zbl 1507.93226 · doi:10.1007/s11081-018-9391-8 |
| [56] | Hoang V H, Quek J H and Schwab C 2019 Analysis of multilevel MCMC-FEM for Bayesian inversion of log-normal diffusions p 2019 SAM Research Report |
| [57] | Horesh L, Haber E and Tenorio L 2010 Optimal experimental design for the large-scale nonlinear ill-posed problem of impedance imaging Large-Scale Inverse Problems and Quantification of Uncertainty (New York: Wiley) pp 273-90 ch 13 · doi:10.1002/9780470685853.ch13 |
| [58] | Huan X and Marzouk Y M 2013 Simulation-based optimal Bayesian experimental design for nonlinear systems J. Comput. Phys.232 288-317 · doi:10.1016/j.jcp.2012.08.013 |
| [59] | Huan X and Marzouk Y 2014 Gradient-based stochastic optimization methods in Bayesian experimental design SIAM/ASA J. Uncertain. Quantification4 479-510 · Zbl 1497.62069 · doi:10.1615/int.j.uncertaintyquantification.2014006730 |
| [60] | Hutchinson M F 1990 A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines Commun. Stat. Simulat. Comput.19 433-50 · Zbl 0718.62058 · doi:10.1080/03610919008812866 |
| [61] | Hyvönen N, Seppänen A and Staboulis S 2014 Optimizing electrode positions in electrical impedance tomography SIAM J. Appl. Math.74 1831-51 · Zbl 1457.65168 · doi:10.1137/140966174 |
| [62] | Isaac T, Petra N, Stadler G and Ghattas O 2015 Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet J. Comput. Phys.296 348-68 · Zbl 1352.86017 · doi:10.1016/j.jcp.2015.04.047 |
| [63] | Jagalur-Mohan J and Marzouk Y 2020 Batch greedy maximization of non-submodular functions: guarantees and applications to experimental design (arXiv:2006.04554) |
| [64] | Kaipio J and Somersalo E 2006 Statistical and Computational Inverse Problems vol 160 (Berlin: Springer) |
| [65] | Kiefer J and Wolfowitz J 1959 Optimum designs in regression problems Ann. Math. Stat.30 271-94 · Zbl 0090.11404 · doi:10.1214/aoms/1177706252 |
| [66] | Körkel S, Bauer I, Bock H G and Schlöder J 1999 A sequential approach for nonlinear optimum experimental design in DAE systems Sci. Comput. Chem. Eng. II2 338-45 |
| [67] | Körkel S, Kostina E, Bock H G and Schlöder J P 2004 Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes Optim. Methods Softw.19 327-38 · Zbl 1060.49025 · doi:10.1080/10556780410001683078 |
| [68] | Koval K, Alexanderian A and Stadler G 2020 Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs Inverse Problems36 075007 · Zbl 1443.62213 · doi:10.1088/1361-6420/ab89c5 |
| [69] | Krause A, Singh A and Guestrin C 2008 Near-optimal sensor placements in Gaussian processes: theory, efficient algorithms and empirical studies J. Mach. Learn. Res.9 235-84 · Zbl 1225.68192 |
| [70] | Kullback S and Leibler R A 1951 On information and sufficiency Ann. Math. Stat.22 79-86 · Zbl 0042.38403 · doi:10.1214/aoms/1177729694 |
| [71] | Lassas M, Saksman E, Saksman E and Siltanen S 2009 Discretization-invariant Bayesian inversion and Besov space priors Inverse Problems Imaging3 87-122 · Zbl 1191.62046 · doi:10.3934/ipi.2009.3.87 |
| [72] | Lassas M and Siltanen S 2004 Can one use total variation prior for edge-preserving bayesian inversion? Inverse Problems20 1537-63 · Zbl 1062.62260 · doi:10.1088/0266-5611/20/5/013 |
| [73] | Lehtinen M S, Päivärinta L and Somersalo E 1989 Linear inverse problems for generalized random variables Inverse Problems5 599-612 · Zbl 0681.60015 · doi:10.1088/0266-5611/5/4/011 |
| [74] | Li F et al 2019 A combinatorial approach to goal-oriented optimal Bayesian experimental design Master’s Thesis Massachusetts Institute of Technology |
| [75] | Liu S, Chepuri S P, Fardad M, Masazade E, Leus G and Varshney P K 2016 Sensor selection for estimation with correlated measurement noise IEEE Trans. Signal Process.64 3509-22 · Zbl 1414.94372 · doi:10.1109/tsp.2016.2550005 |
| [76] | Long Q, Motamed M and Tempone R 2015 Fast Bayesian optimal experimental design for seismic source inversion Comput. Methods Appl. Mech. Eng.291 123-45 · Zbl 1423.74006 · doi:10.1016/j.cma.2015.03.021 |
| [77] | Long Q, Scavino M, Tempone R and Wang S 2013 Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations Comput. Methods Appl. Mech. Eng.259 24-39 · Zbl 1286.62068 · doi:10.1016/j.cma.2013.02.017 |
| [78] | Mandelbaum A 1984 Linear estimators and measurable linear transformations on a Hilbert space Z. Wahrscheinlichkeitstheor. Verwandte Geb.65 385-97 · Zbl 0506.60004 · doi:10.1007/bf00533743 |
| [79] | McCormack K A et al 2018 Earthquakes, groundwater and surface deformation: exploring the poroelastic response to megathrust earthquakes PhD Dissertation The University of Texas at Austin |
| [80] | Müller P 2005 Simulation based optimal design Handb. Stat.25 509-18 · doi:10.1016/s0169-7161(05)25017-4 |
| [81] | Müller W G 2007 Collecting Spatial Data: Optimum Design of Experiments for Random Fields (Berlin: Springer) · Zbl 1266.62048 |
| [82] | Neitzel I, Pieper K, Vexler B and Walter D 2019 A sparse control approach to optimal sensor placement in PDE-constrained parameter estimation problems Numer. Math.143 943-84 · Zbl 1423.35452 · doi:10.1007/s00211-019-01073-3 |
| [83] | Nemhauser G L, Wolsey L A and Fisher M L 1978 An analysis of approximations for maximizing submodular set functions-I Math. Program.14 265-94 · Zbl 0374.90045 · doi:10.1007/bf01588971 |
| [84] | Pázman A 1986 Foundations of Optimum Experimental Design · Zbl 0588.62117 |
| [85] | Petra N, Martin J, Stadler G and Ghattas O 2014 A computational framework for infinite-dimensional Bayesian inverse problems, part II: stochastic Newton MCMC with application to ice sheet flow inverse problems SIAM J. Sci. Comput.36 A1525-55 · Zbl 1303.35110 · doi:10.1137/130934805 |
| [86] | Pinski F J, Simpson G, Stuart A M and Weber H 2015 Kullback-Leibler approximation for probability measures on infinite dimensional spaces SIAM J. Math. Anal.47 4091-122 · Zbl 1342.60049 · doi:10.1137/140962802 |
| [87] | Prato G D and Zabczyk J 1992 Stochastic Equations in Infinite Dimensions (Cambridge: Cambridge University Press) · Zbl 1140.60034 · doi:10.1017/CBO9780511666223 |
| [88] | Prenter P M and Vogel C R 1985 Stochastic inversion of linear first kind integral equations I. Continuous theory and the stochastic generalized inverse J. Math. Anal. Appl.106 202-18 · Zbl 0602.60052 · doi:10.1016/0022-247x(85)90144-1 |
| [89] | Pronzato L and Pázmanj A 2013 Design of Experiments in Nonlinear Models. Asymptotic Normality, Optimality Criteria and Small-Sample Properties (Berlin: Springer) · Zbl 1275.62026 |
| [90] | Pukelsheim F 1993 Optimal Design of Experiments (New York: Wiley) · Zbl 0834.62068 |
| [91] | Reed M and Simon B 1972 Methods of Modern Mathematical Physics. I. Functional Analysis (New York: Academic) p xvii+325 · Zbl 0242.46001 |
| [92] | Roberts G O and Rosenthal J S 2001 Optimal scaling for various metropolis-hastings algorithms Stat. Sci.16 351-67 · Zbl 1127.65305 · doi:10.1214/ss/1015346320 |
| [93] | Rudolf D and Sprungk B 2018 On a generalization of the preconditioned Crank-Nicolson metropolis algorithm Found. Comput. Math.18 309-43 · Zbl 1391.60169 · doi:10.1007/s10208-016-9340-x |
| [94] | Ruthotto L, Chung J and Chung M 2018 Optimal experimental design for inverse problems with state constraints SIAM J. Sci. Comput.40 B1080-100 · Zbl 1392.62232 · doi:10.1137/17m1143733 |
| [95] | Ryan E G, Drovandi C C, McGree J M and Pettitt A N 2016 A review of modern computational algorithms for Bayesian optimal design Int. Stat. Rev.84 128-54 · Zbl 07763475 · doi:10.1111/insr.12107 |
| [96] | Ryan K J 2003 Estimating expected information gains for experimental designs with application to the random fatigue-limit model J. Comput. Graph. Stat.12 585-603 · doi:10.1198/1061860032012 |
| [97] | Saibaba A K, Alexanderian A and Ipsen I C F 2017 Randomized matrix-free trace and log-determinant estimators Numer. Math.137 353-95 · Zbl 1378.65094 · doi:10.1007/s00211-017-0880-z |
| [98] | Saibaba A K, Bardsley J, Brown D A and Alexanderian A 2019 Efficient marginalization-based MCMC methods for hierarchical bayesian inverse problems SIAM/ASA J. Uncertain. Quantification7 1105-31 · Zbl 07118424 · doi:10.1137/18m1220625 |
| [99] | Shulkind G, Horesh L and Avron H 2018 Experimental design for nonparametric correction of misspecified dynamical models SIAM/ASA J. Uncertain. Quantification6 880-906 · Zbl 1403.62140 · doi:10.1137/17m1128435 |
| [100] | Sprungk B 2020 On the local Lipschitz stability of Bayesian inverse problems Inverse Problems36 055015 · Zbl 1469.62216 · doi:10.1088/1361-6420/ab6f43 |
| [101] | Stuart A M 2010 Inverse problems: a Bayesian perspective Acta Numer.19 451-559 · Zbl 1242.65142 · doi:10.1017/s0962492910000061 |
| [102] | Sunseri I, Hart J, van Bloemen Waanders B and Alexanderian A 2020 Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations Inverse Problems36 125001 · Zbl 1453.35197 · doi:10.1088/1361-6420/abaf63 |
| [103] | Tarantola A 2005 Inverse Problem Theory and Methods for Model Parameter Estimation (Philadelphia, PA: SIAM) · Zbl 1074.65013 · doi:10.1137/1.9780898717921 |
| [104] | Uciński D 2005 Optimal Measurement Methods for Distributed Parameter System Identification (Boca Raton, FL: CRC Press) · Zbl 1155.93003 |
| [105] | Uciński D 2020 D-optimal sensor selection in the presence of correlated measurement noise Measurement164 107873 · doi:10.1016/j.measurement.2020.107873 |
| [106] | Vogel C R 2002 Computational Methods for Inverse Problems(Frontiers in Applied Mathematics) (Philadelphia, PA: SIAM) · Zbl 1008.65103 · doi:10.1137/1.9780898717570 |
| [107] | Walsh S, Wildey T and Jakeman J D 2017 Optimal experimental design using a consistent Bayesian approach ASCE-ASME J. Risk Uncertain. Eng. Syst. B 4 011005 · doi:10.1115/1.4037457 |
| [108] | Walter D 2019 On sparse sensor placement for parameter identification problems with partial differential equations PhD Thesis Technische Universität München |
| [109] | Weiser M, Freytag Y, Erdmann B, Hubig M and Mall G 2018 Optimal design of experiments for estimating the time of death in forensic medicine Inverse Problems34 125005 · Zbl 1408.62186 · doi:10.1088/1361-6420/aae7a5 |
| [110] | Williams D 1991 Probability with Martingales (Cambridge: Cambridge University Press) · Zbl 0722.60001 · doi:10.1017/CBO9780511813658 |
| [111] | Wu K, Chen P and Ghattas O 2020 A fast and scalable computational framework for large-scale and high-dimensional Bayesian optimal experimental design (arXiv:2010.15196) |
| [112] | Yu J, Zavala V M and Anitescu M 2017 A scalable design of experiments framework for optimal sensor placement J. Process Control67 44-55 · doi:10.1016/j.jprocont.2017.03.011 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
