# zbMATH — the first resource for mathematics

## SIAM/ASA Journal on Uncertainty Quantification

 Short Title: SIAM/ASA J. Uncertain. Quantif. Publisher: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; American Statistical Association (ASA), Alexandria, VA ISSN: 2166-2525/e Online: http://epubs.siam.org/loi/sjuqa3 Comments: Indexed cover-to-cover; Published electronic only as of Vol. 1 (2013).
 Documents Indexed: 408 Publications (since 2013) References Indexed: 343 Publications with 14,190 References.
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#### Latest Issues

 9 (2021) 8 (2020) 7 (2019) 6 (2018) 5 (2017) 4 (2016) 3 (2015) 2 (2014) 1 (2013)
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#### Authors

 7 Ullmann, Elisabeth 6 Giles, Michael B. 6 Marzouk, Youssef M. 6 Schwab, Christoph 6 Soize, Christian 6 Tartakovsky, Alexandre M. 6 Teckentrup, Aretha L. 5 Estep, Donald J. 5 Gunzburger, Max D. 5 Narayan, Akil C. 5 Nobile, Fabio 5 Owen, Art B. 5 Roustant, Olivier 5 Scheichl, Robert 5 Stuart, Andrew M. 4 Bardsley, Johnathan M. 4 Elman, Howard C. 4 Ginsbourger, David 4 Rahman, Sharif 3 Abdulle, Assyr 3 Alexanderian, Alen 3 Bachoc, François 3 Banks, Harvey Thomas 3 Barajas-Solano, David A. 3 Berger, James Orvis 3 Bocquet, Marc 3 Carlberg, Kevin T. 3 Chen, Nan 3 Constantinescu, Emil M. 3 Eigel, Martin 3 Frenklach, Michael 3 Gamboa, Fabrice 3 Gratton, Serge 3 Grigoriu, Mircea D. 3 Heitzinger, Clemens 3 Hosseini, Bamdad 3 Jasra, Ajay 3 Klein, Thierry E. 3 Kouri, Drew P. 3 Krämer, Boris 3 Lee, Kookjin 3 Morris, Max D. 3 Packard, Andrew K. 3 Peherstorfer, Benjamin 3 Petra, Noemi 3 Powell, Catherine Elizabeth 3 Quarteroni, Alfio M. 3 Sanz-Alonso, Daniel 3 Sinsbeck, Michael 3 Smith, Ralph C. 3 Sousedík, Bedřich 3 Sudret, Bruno 3 Tan, Matthias Hwai Yong 3 Tartakovsky, Daniel M. 3 Tavener, Simon J. 3 Tuo, Rui 3 Webster, Clayton G. 3 Willcox, Karen E. 3 Wolpert, Robert L. 2 Arnst, Maarten 2 Baccou, Jean 2 Baker, Ruth Elizabeth 2 Bao, Feng 2 Bect, Julien 2 Belomestny, Denis 2 Ben Salem, Malek 2 Benner, Peter 2 Berry, Tyrus 2 Beskos, Alexandros 2 Bessac, Julie 2 Binev, Peter G. 2 Borgonovo, Emanuele 2 Braverman, Amy J. 2 Brown, D. Andrew 2 Cao, Yanzhao 2 Carrassi, Alberto 2 Chaudhry, Jehanzeb Hameed 2 Chen, Peng 2 Chevalier, Clément 2 Cohen, Albert 2 Cotter, Colin John 2 Cotter, Simon L. 2 Crisan, Dan O. 2 De Lozzo, Matthias 2 Djurdjevac, Ana 2 Dodwell, Timothy J. 2 Dolgov, Sergey V. 2 Dupuis, Paul G. 2 Elfverson, Daniel 2 Ghanem, Roger G. 2 Ghattas, Omar N. 2 Gobet, Emmanuel 2 Gramacy, Robert B. 2 Grudzien, Colin J. 2 Guillas, Serge 2 Gunson, Michael 2 Haaland, Benjamin 2 Harlim, John 2 Hart, Joseph L. 2 Hegde, Arun ...and 732 more Authors
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#### Fields

 276 Numerical analysis (65-XX) 216 Statistics (62-XX) 168 Probability theory and stochastic processes (60-XX) 106 Partial differential equations (35-XX) 30 Systems theory; control (93-XX) 23 Fluid mechanics (76-XX) 21 Geophysics (86-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 19 Computer science (68-XX) 18 Operations research, mathematical programming (90-XX) 12 Approximations and expansions (41-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Information and communication theory, circuits (94-XX) 10 Ordinary differential equations (34-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Operator theory (47-XX) 8 Functional analysis (46-XX) 8 Biology and other natural sciences (92-XX) 7 Mechanics of deformable solids (74-XX) 6 Mechanics of particles and systems (70-XX) 5 Optics, electromagnetic theory (78-XX) 3 Integral equations (45-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mathematics education (97-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX)

#### Citations contained in zbMATH Open

292 Publications have been cited 1,704 times in 1,183 Documents Cited by Year
A multilevel stochastic collocation method for partial differential equations with random input data. Zbl 1327.65014
Teckentrup, A. L.; Jantsch, P.; Webster, C. G.; Gunzburger, M.
2015
A hierarchical multilevel Markov chain Monte Carlo algorithm with applications to uncertainty quantification in subsurface flow. Zbl 1330.65007
Dodwell, T. J.; Ketelsen, C.; Scheichl, R.; Teckentrup, A. L.
2015
Weighted reduced basis method for stochastic optimal control problems with elliptic PDE constraint. Zbl 1309.35182
Chen, Peng; Quarteroni, Alfio
2014
Sequential Monte Carlo methods for high-dimensional inverse problems: a case study for the Navier-Stokes equations. Zbl 1308.65010
Kantas, Nikolas; Beskos, Alexandros; Jasra, Ajay
2014
Polynomial chaos expansion of random coefficients and the solution of stochastic partial differential equations in the tensor train format. Zbl 1329.65271
Dolgov, Sergey; Khoromskij, Boris N.; Litvinenko, Alexander; Matthies, Hermann G.
2015
Reduced basis collocation methods for partial differential equations with random coefficients. Zbl 1282.35424
Elman, Howard C.; Liao, Qifeng
2013
The ROMES method for statistical modeling of reduced-order-model error. Zbl 1322.65029
Drohmann, Martin; Carlberg, Kevin
2015
Analysis of the ensemble and polynomial chaos Kalman filters in Bayesian inverse problems. Zbl 1339.60041
Ernst, Oliver G.; Sprungk, Björn; Starkloff, Hans-Jörg
2015
Data assimilation in reduced modeling. Zbl 06736493
Binev, Peter; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald; Petrova, Guergana; Wojtaszczyk, Przemyslaw
2017
Inverse random source scattering problems in several dimensions. Zbl 1355.78025
Bao, Gang; Chen, Chuchu; Li, Peijun
2016
Variance components and generalized Sobol’ indices. Zbl 1459.62144
Owen, Art B.
2013
Hierarchical tensor approximation of output quantities of parameter-dependent PDEs. Zbl 1327.65010
Ballani, Jonas; Grasedyck, Lars
2015
(Sub-)gradient formulae for probability functions of random inequality systems under Gaussian distribution. Zbl 1434.90111
van Ackooij, Wim; Henrion, R.
2017
A least-squares method for sparse low rank approximation of multivariate functions. Zbl 1327.65029
Chevreuil, M.; Lebrun, R.; Nouy, A.; Rai, P.
2015
An analysis of infinite dimensional Bayesian inverse shape acoustic scattering and its numerical approximation. Zbl 1306.65270
Bui-Thanh, Tan; Ghattas, Omar
2014
Computational aspects of stochastic collocation with multifidelity models. Zbl 1306.65010
Zhu, Xueyu; Narayan, Akil; Xiu, Dongbin
2014
Reduced basis methods for parameterized partial differential equations with stochastic influences using the Karhunen-Loève expansion. Zbl 1281.35100
Haasdonk, Bernard; Urban, Karsten; Wieland, Bernhard
2013
Uniform regularity for linear kinetic equations with random input based on hypocoercivity. Zbl 1398.65257
Li, Qin; Wang, Li
2017
Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031
Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph
2016
Analysis of the Gibbs sampler for hierarchical inverse problems. Zbl 1308.62097
Agapiou, Sergios; Bardsley, Johnathan M.; Papaspiliopoulos, Omiros; Stuart, Andrew M.
2014
Multilevel estimation of rare events. Zbl 1327.65246
Ullmann, Elisabeth; Papaioannou, Iason
2015
Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations. Zbl 1391.93289
Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Ghattas, Omar
2017
Reduced basis methods for uncertainty quantification. Zbl 1400.65010
Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi
2017
Quasi-Monte Carlo and multilevel Monte Carlo methods for computing posterior expectations in elliptic inverse problems. Zbl 06736512
Scheichl, R.; Stuart, A. M.; Teckentrup, A. L.
2017
Multilevel accelerated quadrature for PDEs with log-normally distributed diffusion coefficient. Zbl 1343.65006
Harbrecht, Helmut; Peters, Michael; Siebenmorgen, Markus
2016
Sequential design with mutual information for computer experiments (MICE): emulation of a tsunami model. Zbl 1349.62364
Beck, Joakim; Guillas, Serge
2016
Uncertainty quantification in graph-based classification of high dimensional data. Zbl 1394.62083
Bertozzi, Andrea L.; Luo, Xiyang; Stuart, Andrew M.; Zygalakis, Konstantinos C.
2018
Convergence of the square root ensemble Kalman filter in the large ensemble limit. Zbl 1329.60083
Kwiatkowski, Evan; Mandel, Jan
2015
Subsampled Gauss quadrature nodes for estimating polynomial chaos expansions. Zbl 1308.41005
Tang, Gary; Iaccarino, Gianluca
2014
Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models. Zbl 1383.35251
Manzoni, A.; Pagani, S.; Lassila, T.
2016
Transport map accelerated Markov chain Monte Carlo. Zbl 1394.65004
Parno, Matthew D.; Marzouk, Youssef M.
2018
Existence and optimality conditions for risk-averse PDE-constrained optimization. Zbl 1393.49002
Kouri, D. P.; Surowiec, T. M.
2018
Numerical solution of scalar conservation laws with random flux functions. Zbl 1343.65007
Mishra, Siddhartha; Risebro, Nils Henrik; Schwab, Christoph; Tokareva, Svetlana
2016
A Bayesian approach for global sensitivity analysis of (multifidelity) computer codes. Zbl 1308.62107
Le Gratiet, Loic; Cannamela, Claire; Iooss, Bertrand
2014
Local equilibration error estimators for guaranteed error control in adaptive stochastic higher-order Galerkin finite element methods. Zbl 1398.65297
Eigel, Martin; Merdon, Christian
2016
Mean exit times and the multilevel Monte Carlo method. Zbl 1282.65020
Higham, Desmond J.; Mao, Xuerong; Roj, Mikolaj; Song, Qingshuo; Yin, George
2013
Path-space information bounds for uncertainty quantification and sensitivity analysis of stochastic dynamics. Zbl 1371.65004
Dupuis, Paul; Katsoulakis, Markos A.; Pantazis, Yannis; Plecháč, Petr
2016
A multilevel stochastic collocation algorithm for optimization of PDEs with uncertain coefficients. Zbl 1307.49026
Kouri, D. P.
2014
Shapley effects for global sensitivity analysis: theory and computation. Zbl 1403.62226
Song, Eunhye; Nelson, Barry L.; Staum, Jeremy
2016
An adaptive multilevel Monte Carlo method with stochastic bounds for quantities of interest with uncertain data. Zbl 1398.35306
Eigel, Martin; Merdon, Christian; Neumann, Johannes
2016
Higher-order quasi-Monte Carlo for Bayesian shape inversion. Zbl 1402.65141
Gantner, Robert N.; Peters, Michael D.
2018
Multilevel Monte Carlo approximation of distribution functions and densities. Zbl 1322.65014
Giles, Michael B.; Nagapetyan, Tigran; Ritter, Klaus
2015
Low-rank solution of unsteady diffusion equations with stochastic coefficients. Zbl 1325.65016
Benner, Peter; Onwunta, Akwum; Stoll, Martin
2015
An efficient numerical method for acoustic wave scattering in random media. Zbl 1327.65213
Feng, Xiaobing; Lin, Junshan; Lorton, Cody
2015
A multilevel Monte Carlo method for computing failure probabilities. Zbl 1343.65004
Elfverson, Daniel; Hellman, Fredrik; Målqvist, Axel
2016
A theoretical framework for calibration in computer models: parametrization, estimation and convergence properties. Zbl 1383.62354
Tuo, Rui; Jeff Wu, C. F.
2016
A generalized ANOVA dimensional decomposition for dependent probability measures. Zbl 1311.62106
Rahman, Sharif
2014
Uncertainty propagation; intrusive kinetic formulations of scalar conservation laws. Zbl 1362.35342
Despres, Bruno; Perthame, Benoit
2016
Fast sampling in a linear-Gaussian inverse problem. Zbl 1398.94081
Fox, Colin; Norton, Richard A.
2016
A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068
Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen
2013
Monotone emulation of computer experiments. Zbl 1327.62146
Golchi, S.; Bingham, D. R.; Chipman, H.; Campbell, D. A.
2015
Polynomial chaos expansion of a multimodal random vector. Zbl 1327.62332
Soize, C.
2015
Efficient Bayesian experimentation using an expected information gain lower bound. Zbl 1370.62019
Tsilifis, Panagiotis; Ghanem, Roger G.; Hajali, Paris
2017
Well-posed Bayesian inverse problems: priors with exponential tails. Zbl 1371.35349
2017
Mixed finite elements for spatial regression with PDE penalization. Zbl 1306.65275
Azzimonti, Laura; Nobile, Fabio; Sangalli, Laura M.; Secchi, Piercesare
2014
Optimal adaptation for early stopping in statistical inverse problems. Zbl 1401.65058
Blanchard, Gilles; Hoffmann, Marc; Reiß, Markus
2018
Greedy algorithms for optimal measurements selection in state estimation using reduced models. Zbl 1407.65256
Binev, Peter; Cohen, Albert; Mula, Olga; Nichols, James
2018
Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation. Zbl 1394.35493
Peherstorfer, Benjamin; Kramer, Boris; Willcox, Karen
2018
Robust bounds on risk-sensitive functionals via Rényi divergence. Zbl 1341.60008
Atar, Rami; Chowdhary, Kenny; Dupuis, Paul
2015
A posteriori error estimates for the solution of variational inverse problems. Zbl 1327.65135
2015
On Shapley value for measuring importance of dependent inputs. Zbl 1386.65064
Owen, Art B.; Prieur, Clémentine
2017
Metropolized randomized maximum likelihood for improved sampling from multimodal distributions. Zbl 1370.62018
Oliver, Dean S.
2017
Multilevel Monte Carlo analysis for optimal control of elliptic PDEs with random coefficients. Zbl 1371.35371
2017
Efficient white noise sampling and coupling for multilevel Monte Carlo with nonnested meshes. Zbl 07003649
Croci, Matteo; Giles, Mike B.; Rognes, M. E.; Farrell, Patrick E.
2018
Multilevel sequential Monte Carlo with dimension-independent likelihood-informed proposals. Zbl 1395.82229
Beskos, Alexandros; Jasra, Ajay; Law, Kody; Marzouk, Youssef; Zhou, Yan
2018
Probabilistic description of extreme events in intermittently unstable dynamical systems excited by correlated stochastic processes. Zbl 1327.62324
Mohamad, Mustafa A.; Sapsis, Themistoklis P.
2015
Numerical continuation and SPDE stability for the 2D cubic-quintic Allen-Cahn equation. Zbl 1339.60096
Kuehn, Christian
2015
Sequential Monte Carlo with highly informative observations. Zbl 1327.65004
Del Moral, Pierre; Murray, Lawrence M.
2015
Transport reversal for model reduction of hyperbolic partial differential equations. Zbl 1398.65084
Rim, Donsub; Moe, Scott; LeVeque, Randall J.
2018
Efficient history matching of a high dimensional individual-based HIV transmission model. Zbl 1387.62111
Andrianakis, Ioannis; McCreesh, Nicky; Vernon, Ian; McKinley, Trevelyan J.; Oakley, Jeremy E.; Nsubuga, Rebecca N.; Goldstein, Michael; White, Richard G.
2017
Sobol’ indices and Shapley value. Zbl 1308.91129
Owen, Art B.
2014
A multiscale strategy for Bayesian inference using transport maps. Zbl 1356.62038
Parno, Matthew; Moselhy, Tarek; Marzouk, Youssef
2016
Analysis of boundary effects on PDE-based sampling of Whittle-Matérn random fields. Zbl 07118418
Khristenko, U.; Scarabosio, L.; Swierczynski, P.; Ullmann, E.; Wohlmuth, B.
2019
Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs. Zbl 1408.35021
Torlo, Davide; Ballarin, Francesco; Rozza, Gianluigi
2018
Random forward models and log-likelihoods in Bayesian inverse problems. Zbl 1409.62062
Lie, H. C.; Sullivan, T. J.; Teckentrup, A. L.
2018
Multifidelity Monte Carlo estimation of variance and sensitivity indices. Zbl 1394.62175
Qian, Elizabeth; Peherstorfer, Benjamin; O’Malley, Daniel; Vesselinov, Velimir V.; Willcox, Karen
2018
Bayesian analysis of hierarchical multifidelity codes. Zbl 1280.62033
Le Gratiet, Loic
2013
Optimal learning in experimental design using the knowledge gradient policy with application to characterizing nanoemulsion stability. Zbl 1327.62098
Chen, Si; Reyes, Kristofer-Roy G.; Gupta, Maneesh K.; McAlpine, Michael C.; Powell, Warren B.
2015
Dimension-independent MCMC sampling for inverse problems with non-Gaussian priors. Zbl 1322.65008
Vollmer, Sebastian J.
2015
Error decomposition and adaptivity for response surface approximations from PDEs with parametric uncertainty. Zbl 1327.65011
Bryant, C. M.; Prudhomme, S.; Wildey, T.
2015
Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data. Zbl 1384.35146
Nane, Erkan; Tuan, Nguyen Huy
2018
Dimension reduction for Gaussian process emulation: an application to the influence of bathymetry on tsunami heights. Zbl 1403.62217
Liu, Xiaoyu; Guillas, Serge
2017
Optimal design for estimation in diffusion processes from first hitting times. Zbl 1365.62305
Iolov, Alexandre; Ditlevsen, Susanne; Longtin, André
2017
Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems. Zbl 1337.93094
Sanz-Alonso, Daniel; Stuart, Andrew M.
2015
The $$f$$-sensitivity index. Zbl 1348.62015
Rahman, Sharif
2016
When is a model good enough? Deriving the expected value of model improvement via specifying internal model discrepancies. Zbl 1351.60133
Strong, Mark; Oakley, Jeremy E.
2014
A measure-theoretic computational method for inverse sensitivity problems. III: multiple quantities of interest. Zbl 1351.60084
Butler, T.; Estep, D.; Tavener, S.; Dawson, C.; Westerink, J. J.
2014
Response statistics for random heterogeneous microstructures. Zbl 1348.60099
Grigoriu, M.
2014
Bayesian adaptive reconstruction of profile optima and optimizers. Zbl 1308.62157
Ginsbourger, David; Baccou, Jean; Chevalier, Clément; Perales, Frédéric; Garland, Nicolas; Monerie, Yann
2014
Spectral approximation of the IMSE criterion for optimal designs in kernel-based interpolation models. Zbl 1308.62158
Gauthier, Bertrand; Pronzato, Luc
2014
Sparse adaptive tensor Galerkin approximations of stochastic PDE-constrained control problems. Zbl 1398.65252
Kunoth, Angela; Schwab, Christoph
2016
Robust optimization of PDEs with random coefficients using a multilevel Monte Carlo method. Zbl 1421.35396
Van Barel, Andreas; Vandewalle, Stefan
2019
Bayesian model and dimension reduction for uncertainty propagation: applications in random media. Zbl 1422.62377
Grigo, Constantin; Koutsourelakis, Phaedon-Stelios
2019
Rigorous analysis for efficient statistically accurate algorithms for solving Fokker-Planck equations in large dimensions. Zbl 1410.35244
Chen, Nan; Majda, Andrew J.; Tong, Xin T.
2018
Finite-dimensional Gaussian approximation with linear inequality constraints. Zbl 1405.60047
López-Lopera, Andrés F.; Bachoc, François; Durrande, Nicolas; Roustant, Olivier
2018
Displacement interpolation using monotone rearrangement. Zbl 07003644
Rim, Donsub; Mandli, Kyle T.
2018
A nonstationary space-time Gaussian process model for partially converged simulations. Zbl 1291.60075
Picheny, Victor; Ginsbourger, David
2013
A posteriori error estimates for mixed finite element and finite volume methods for parabolic problems coupled through a boundary. Zbl 1322.65093
Arbogast, T.; Estep, D.; Sheehan, B.; Tavener, S.
2015
Stochastic Galerkin finite element method with local conductivity basis for electrical impedance tomography. Zbl 1327.65224
Hyvönen, N.; Leinonen, M.
2015
Sequential design of experiment for sparse polynomial chaos expansions. Zbl 06861783
Fajraoui, Noura; Marelli, Stefano; Sudret, Bruno
2017
A quasi-Monte Carlo method for optimal control under uncertainty. Zbl 07332584
Guth, Philipp A.; Kaarnioja, Vesa; Kuo, Frances Y.; Schillings, Claudia; Sloan, Ian H.
2021
Multilevel Monte Carlo finite difference methods for fractional conservation laws with random data. Zbl 07307678
Koley, Ujjwal; Ray, Deep; Sarkar, Tanmay
2021
Using coupling methods to estimate sample quality of stochastic differential equations. Zbl 1459.65009
Dobson, Matthew; Li, Yao; Zhai, Jiayu
2021
Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don’t know. Zbl 1460.62120
Alexanderian, Alen; Petra, Noemi; Stadler, Georg; Sunseri, Isaac
2021
Convergence rates for penalized least squares estimators in PDE constrained regression problems. Zbl 1436.62163
Nickl, Richard; van de Geer, Sara; Wang, Sven
2020
A spline chaos expansion. Zbl 1436.41009
Rahman, Sharif
2020
Domain uncertainty quantification in computational electromagnetics. Zbl 07193414
Aylwin, Ruben; Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob
2020
A Bayesian approach to estimating background flows from a passive scalar. Zbl 1455.65205
Borggaard, Jeff; Glatt-Holtz, Nathan; Krometis, Justin
2020
A particle filter for stochastic advection by Lie transport: a case study for the damped and forced incompressible two-dimensional Euler equation. Zbl 1454.62528
Cotter, Colin; Crisan, Dan; Holm, Darryl D.; Pan, Wei; Shevchenko, Igor
2020
The Helmholtz equation in random media: well-posedness and a priori bounds. Zbl 1436.35085
Pembery, O. R.; Spence, E. A.
2020
Generating nested quadrature rules with positive weights based on arbitrary sample sets. Zbl 07193409
van den Bos, Laurent; Sanderse, Benjamin; Bierbooms, Wim; van Bussel, Gerard
2020
Uncertainty quantification for Markov processes via variational principles and functional inequalities. Zbl 07193421
Birrell, Jeremiah; Rey-Bellet, Luc
2020
Convergence of Gaussian process regression with estimated hyper-parameters and applications in Bayesian inverse problems. Zbl 1461.60022
Teckentrup, Aretha L.
2020
Kernel methods for Bayesian elliptic inverse problems on manifolds. Zbl 1448.65205
Harlim, John; Sanz-Alonso, Daniel; Yang, Ruiyi
2020
Diagnostics-driven nonstationary emulators using kernel mixtures. Zbl 1436.62365
Volodina, Victoria; Williamson, Daniel
2020
Block preconditioning of stochastic Galerkin problems: new two-sided guaranteed spectral bounds. Zbl 1447.65151
Kubínová, Marie; Pultarová, Ivana
2020
Multifidelity approximate Bayesian computation. Zbl 1436.62097
Prescott, Thomas P.; Baker, Ruth E.
2020
Statistical treatment of inverse problems constrained by differential equations-based models with stochastic terms. Zbl 1439.35466
Constantinescu, Emil M.; Petra, Noémi; Bessac, Julie; Petra, Cosmin G.
2020
Density estimation in uncertainty propagation problems using a surrogate model. Zbl 07193413
2020
Bernstein-von Mises theorems and uncertainty quantification for linear inverse problems. Zbl 1436.62161
Giordano, Matteo; Kekkonen, Hanne
2020
A Bayesian numerical homogenization method for elliptic multiscale inverse problems. Zbl 1436.62089
Abdulle, Assyr; Blasio, Andrea Di
2020
On the well-posedness of Bayesian inverse problems. Zbl 1437.49050
Latz, Jonas
2020
Stable approximation schemes for optimal filters. Zbl 1441.93310
Crisan, Dan; López-Yela, Alberto; Miguez, Joaquin
2020
On multilevel best linear unbiased estimators. Zbl 1439.35591
2020
Adaptive reduced-order model construction for conditional value-at-risk estimation. Zbl 1443.62152
Heinkenschloss, Matthias; Kramer, Boris; Takhtaganov, Timur
2020
Group kernels for Gaussian process metamodels with categorical inputs. Zbl 1443.60040
Roustant, Olivier; Padonou, Espéran; Deville, Yves; Clément, Aloïs; Perrin, Guillaume; Giorla, Jean; Wynn, Henry
2020
Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions. Zbl 1461.60020
Karvonen, Toni; Wynne, George; Tronarp, Filip; Oates, Chris; Särkkä, Simo
2020
Stratification as a general variance reduction method for Markov chain Monte Carlo. Zbl 07242148
Dinner, Aaron R.; Thiede, Erik H.; Koten, Brian Van; Weare, Jonathan
2020
An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains. Zbl 1447.65137
Eigel, Martin; Marschall, Manuel; Multerer, Michael
2020
Analysis of boundary effects on PDE-based sampling of Whittle-Matérn random fields. Zbl 07118418
Khristenko, U.; Scarabosio, L.; Swierczynski, P.; Ullmann, E.; Wohlmuth, B.
2019
Robust optimization of PDEs with random coefficients using a multilevel Monte Carlo method. Zbl 1421.35396
Van Barel, Andreas; Vandewalle, Stefan
2019
Bayesian model and dimension reduction for uncertainty propagation: applications in random media. Zbl 1422.62377
Grigo, Constantin; Koutsourelakis, Phaedon-Stelios
2019
An efficient, globally convergent method for optimization under uncertainty using adaptive model reduction and sparse grids. Zbl 1448.65057
Zahr, Matthew J.; Carlberg, Kevin T.; Kouri, Drew P.
2019
Bayesian parameter identification in Cahn-Hilliard models for biological growth. Zbl 1422.65239
Kahle, Christian; Lam, Kei Fong; Latz, Jonas; Ullmann, Elisabeth
2019
On the asymptotic normality of adaptive multilevel splitting. Zbl 1412.82029
Cérou, Frédéric; Delyon, Bernard; Guyader, Arnaud; Rousset, Mathias
2019
Stability preservation in stochastic Galerkin projections of dynamical systems. Zbl 1440.65275
Pulch, Roland; Augustin, Florian
2019
Second order discretization of Bismut-Elworthy-Li formula: application to sensitivity analysis. Zbl 1454.60073
2019
A hybrid alternating least squares-TT-cross algorithm for parametric PDEs. Zbl 1418.65170
Dolgov, Sergey; Scheichl, Robert
2019
Generalized modes in Bayesian inverse problems. Zbl 1430.62053
Clason, Christian; Helin, Tapio; Kretschmann, Remo; Piiroinen, Petteri
2019
Robustness of the Sobol’ indices to marginal distribution uncertainty. Zbl 07118428
Hart, Joseph L.; Gremaud, Pierre A.
2019
Multilevel nested simulation for efficient risk estimation. Zbl 1457.91416
Giles, Michael B.; Haji-Ali, Abdul-Lateef
2019
Continuous level Monte Carlo and sample-adaptive model hierarchies. Zbl 07003658
Detommaso, Gianluca; Dodwell, Tim; Scheichl, Rob
2019
Adjustments to computer models via projected kernel calibration. Zbl 1430.62261
Tuo, Rui
2019
Multifidelity Monte Carlo estimation with adaptive low-fidelity models. Zbl 1428.35570
Peherstorfer, Benjamin
2019
Extreme event quantification in dynamical systems with random components. Zbl 1448.60063
Dematteis, Giovanni; Grafke, Tobias; Vanden-Eijnden, Eric
2019
Efficient marginalization-based MCMC methods for hierarchical Bayesian inverse problems. Zbl 07118424
Saibaba, Arvind K.; Bardsley, Johnathan; Brown, D. Andrew; Alexanderian, Alen
2019
Global sensitivity analysis for optimization with variable selection. Zbl 1421.49032
Spagnol, Adrien; Riche, Rodolphe Le; Da Veiga, Sébastien
2019
Prediction uncertainties beyond the range of experience: a case study in inertial confinement fusion implosion experiments. Zbl 1430.62263
Osthus, Dave; Vander Wiel, Scott A.; Hoffman, Nelson M.; Wysocki, Frederick J.
2019
Emulating satellite drag from large simulation experiments. Zbl 1430.62085
Sun, Furong; Gramacy, Robert B.; Haaland, Benjamin; Lawrence, Earl; Walker, Andrew
2019
Analysis of an asymptotic preserving scheme for stochastic linear kinetic equations in the diffusion limit. Zbl 07118412
Ayi, Nathalie; Faou, Erwan
2019
A Bramble-Pasciak conjugate gradient method for discrete Stokes equations with random viscosity. Zbl 1425.65018
Müller, Christopher; Ullmann, Sebastian; Lang, Jens
2019
Uncertainty quantification for spectral fractional diffusion: sparsity analysis of parametric solutions. Zbl 07118417
Herrmann, Lukas; Schwab, Christoph; Zech, Jakob
2019
A Shapley-Owen index for interaction quantification. Zbl 1426.91022
Rabitti, Giovanni; Borgonovo, Emanuele
2019
Two Metropolis-Hastings algorithms for posterior measures with non-Gaussian priors in infinite dimensions. Zbl 07118427
2019
Gradient-free construction of active subspaces for dimension reduction in complex models with applications to neutronics. Zbl 1453.62561
Coleman, Kayla D.; Lewis, Allison; Smith, Ralph C.; Williams, Brian; Morris, Max; Khuwaileh, Bassam
2019
Allocation strategies for high fidelity models in the multifidelity regime. Zbl 1418.65059
Perry, Daniel J.; Kirby, Robert M.; Narayan, Akil; Whitaker, Ross T.
2019
Constructing sampling schemes via coupling: Markov semigroups and optimal transport. Zbl 1454.60118
Nüsken, N.; Pavliotis, G. A.
2019
Ensemble transport adaptive importance sampling. Zbl 1422.62104
Cotter, Colin; Cotter, Simon; Russell, Paul
2019
Global sensitivity analysis for statistical model parameters. Zbl 1409.62113
Hart, Joseph L.; Bessac, Julie; Constantinescu, Emil M.
2019
Dimension reduction via Gaussian ridge functions. Zbl 1436.60038
Seshadri, Pranay; Yuchi, Shaowu; Parks, Geoffrey T.
2019
Uncertainty quantification in graph-based classification of high dimensional data. Zbl 1394.62083
Bertozzi, Andrea L.; Luo, Xiyang; Stuart, Andrew M.; Zygalakis, Konstantinos C.
2018
Transport map accelerated Markov chain Monte Carlo. Zbl 1394.65004
Parno, Matthew D.; Marzouk, Youssef M.
2018
Existence and optimality conditions for risk-averse PDE-constrained optimization. Zbl 1393.49002
Kouri, D. P.; Surowiec, T. M.
2018
Higher-order quasi-Monte Carlo for Bayesian shape inversion. Zbl 1402.65141
Gantner, Robert N.; Peters, Michael D.
2018
Optimal adaptation for early stopping in statistical inverse problems. Zbl 1401.65058
Blanchard, Gilles; Hoffmann, Marc; Reiß, Markus
2018
Greedy algorithms for optimal measurements selection in state estimation using reduced models. Zbl 1407.65256
Binev, Peter; Cohen, Albert; Mula, Olga; Nichols, James
2018
Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation. Zbl 1394.35493
Peherstorfer, Benjamin; Kramer, Boris; Willcox, Karen
2018
Efficient white noise sampling and coupling for multilevel Monte Carlo with nonnested meshes. Zbl 07003649
Croci, Matteo; Giles, Mike B.; Rognes, M. E.; Farrell, Patrick E.
2018
Multilevel sequential Monte Carlo with dimension-independent likelihood-informed proposals. Zbl 1395.82229
Beskos, Alexandros; Jasra, Ajay; Law, Kody; Marzouk, Youssef; Zhou, Yan
2018
Transport reversal for model reduction of hyperbolic partial differential equations. Zbl 1398.65084
Rim, Donsub; Moe, Scott; LeVeque, Randall J.
2018
Stabilized weighted reduced basis methods for parametrized advection dominated problems with random inputs. Zbl 1408.35021
Torlo, Davide; Ballarin, Francesco; Rozza, Gianluigi
2018
Random forward models and log-likelihoods in Bayesian inverse problems. Zbl 1409.62062
Lie, H. C.; Sullivan, T. J.; Teckentrup, A. L.
2018
Multifidelity Monte Carlo estimation of variance and sensitivity indices. Zbl 1394.62175
Qian, Elizabeth; Peherstorfer, Benjamin; O&rsquo;Malley, Daniel; Vesselinov, Velimir V.; Willcox, Karen
2018
Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data. Zbl 1384.35146
Nane, Erkan; Tuan, Nguyen Huy
2018
Rigorous analysis for efficient statistically accurate algorithms for solving Fokker-Planck equations in large dimensions. Zbl 1410.35244
Chen, Nan; Majda, Andrew J.; Tong, Xin T.
2018
Finite-dimensional Gaussian approximation with linear inequality constraints. Zbl 1405.60047
López-Lopera, Andrés F.; Bachoc, François; Durrande, Nicolas; Roustant, Olivier
2018
Displacement interpolation using monotone rearrangement. Zbl 07003644
Rim, Donsub; Mandli, Kyle T.
2018
Efficient adaptive algorithms for elliptic PDEs with random data. Zbl 1398.65289
Bespalov, Alex; Rocchi, Leonardo
2018
Conditional-value-at-risk estimation via reduced-order models. Zbl 1405.35263
Heinkenschloss, Matthias; Kramer, Boris; Takhtaganov, Timur; Willcox, Karen
2018
Sensitivity analysis based on Cramér-von Mises distance. Zbl 1392.62091
Gamboa, Fabrice; Klein, Thierry; Lagnoux, Agnès
2018
Importance sampling and necessary sample size: an information theory approach. Zbl 1396.65016
Sanz-Alonso, Daniel
2018
Parallel local approximation MCMC for expensive models. Zbl 1398.65017
Conrad, Patrick R.; Davis, Andrew D.; Marzouk, Youssef M.; Pillai, Natesh S.; Smith, Aaron
2018
Multilevel estimation of expected exit times and other functionals of stopped diffusions. Zbl 1405.60076
Giles, Michael B.; Bernal, Francisco
2018
Representing model inadequacy: a stochastic operator approach. Zbl 1396.65014
Morrison, Rebecca E.; Oliver, Todd A.; Moser, Robert D.
2018
Experimental design for partially observed Markov decision processes. Zbl 1391.90634
Thorbergsson, Leifur; Hooker, Giles
2018
Mathematical properties of polynomial dimensional decomposition. Zbl 06908463
Rahman, Sharif
2018
Experimental design for nonparametric correction of misspecified dynamical models. Zbl 1403.62140
Shulkind, Gal; Horesh, Lior; Avron, Haim
2018
Compressive sensing with cross-validation and stop-sampling for sparse polynomial chaos expansions. Zbl 1403.62133
Huan, Xun; Safta, Cosmin; Sargsyan, Khachik; Vane, Zachary P.; Lacaze, Guilhem; Oefelein, Joseph C.; Najm, Habib N.
2018
Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013
Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles
2018
Efficient distribution estimation and uncertainty quantification for elliptic problems on domains with stochastic boundaries. Zbl 1400.35239
Chaudhry, Jehanzeb H.; Burch, Nathanial; Estep, Donald
2018
Compressed sensing with sparse corruptions: fault-tolerant sparse collocation approximations. Zbl 1405.42001
Adcock, Ben; Bao, Anyi; Jakeman, John D.; Narayan, Akil
2018
Scaled Gaussian stochastic process for computer model calibration and prediction. Zbl 1409.62185
Gu, Mengyang; Wang, Long
2018
Low-rank eigenvector compression of posterior covariance matrices for linear Gaussian inverse problems. Zbl 1398.65057
Benner, Peter; Qiu, Yue; Stoll, Martin
2018
Bayesian inference via filtering equations for ultrahigh frequency data. I: Model and estimation. Zbl 1390.60259
Hu, Grace X.; Kuipers, David R.; Zeng, Yong
2018
Probability and cumulative density function methods for the stochastic advection-reaction equation. Zbl 1390.60225
Barajas-Solano, David A.; Tartakovsky, Alexandre M.
2018
Multilevel Monte Carlo approximation of functions. Zbl 07003636
Krumscheid, Sebastian; Nobile, Fabio
2018
Asymptotic forecast uncertainty and the unstable subspace in the presence of additive model error. Zbl 1405.93212
Grudzien, Colin; Carrassi, Alberto; Bocquet, Marc
2018
Evolving surface finite element methods for random advection-diffusion equations. Zbl 1407.65258
Djurdjevac, Ana; Elliott, Charles M.; Kornhuber, Ralf; Ranner, Thomas
2018
A study of elliptic partial differential equations with jump diffusion coefficients. Zbl 1405.60104
Barth, Andrea; Stein, Andreas
2018
Bayesian inference via filtering equations for ultrahigh frequency data. II: Model selection. Zbl 1390.60260
Hu, Grace X.; Kuipers, David R.; Zeng, Yong
2018
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#### Cited by 1,969 Authors

 26 Schwab, Christoph 20 Narayan, Akil C. 19 Stuart, Andrew M. 15 Marzouk, Youssef M. 14 Jasra, Ajay 14 Nobile, Fabio 14 Tempone, Raúl F. 13 Ullmann, Elisabeth 12 Bachoc, François 11 Peherstorfer, Benjamin 11 Soize, Christian 11 Willcox, Karen E. 10 Alexanderian, Alen 10 Chen, Peng 10 Scheichl, Robert 9 Giles, Michael B. 9 Jin, Shi 9 Kouri, Drew P. 9 Schillings, Claudia 9 Van Ackooij, Wim 8 Bardsley, Johnathan M. 8 Beskos, Alexandros 8 Borgonovo, Emanuele 8 Ghanem, Roger G. 8 Grigoriu, Mircea D. 8 Jiang, Lijian 8 Katsoulakis, Markos A. 8 Kühn, Christian 8 Latz, Jonas 8 Law, Kody J. H. 8 Papaioannou, Iason 8 Pulch, Roland 8 Rozza, Gianluigi 8 Tong, Xin Thomson 8 Wohlmuth, Barbara I. 7 Chaudhry, Jehanzeb Hameed 7 Cui, Tiangang 7 Eigel, Martin 7 Girolami, Mark A. 7 Goda, Takashi 7 Gunzburger, Max D. 7 Helin, Tapio 7 Henrion, René 7 Jakeman, John Davis 7 Li, Qin 7 Majda, Andrew J. 7 Quarteroni, Alfio M. 7 Reich, Sebastian 7 Sandu, Adrian 7 Teckentrup, Aretha L. 6 Bespalov, Alexei 6 Chen, Nan 6 Crisan, Dan O. 6 Dolgov, Sergey V. 6 Elman, Howard C. 6 Griebel, Michael 6 Heitsch, Holger 6 Iglesias, Marco A. 6 Kressner, Daniel 6 Lin, Guang 6 Manzoni, Andrea 6 Matthies, Hermann Georg 6 Mula, Olga 6 Powell, Warren Buckler 6 Rahman, Sharif 6 Sangalli, Laura Maria 6 Sprungk, Björn 6 Sudret, Bruno 6 Zhu, Xueyu 5 Bernal, Francisco 5 Doostan, Alireza 5 Ganesh, Mahadevan 5 Gramacy, Robert B. 5 Haji-Ali, Abdul-Lateef 5 Harbrecht, Helmut 5 Helbert, Céline 5 Herrmann, Lukas 5 Hesthaven, Jan S. 5 Hosseini, Bamdad 5 Hou, Thomas Yizhao 5 Klein, Thierry E. 5 Krämer, Boris 5 Kuo, Frances Y. 5 Lagnoux, Agnès 5 Li, Qiuqi 5 Litvinenko, Alexander 5 Liu, Liu 5 Mattis, Steven A. 5 Nguyen Huy Tuan 5 Oates, Chris J. 5 Owen, Art B. 5 Pérez-Aros, Pedro 5 Prieur, Clémentine 5 Rey-Bellet, Luc 5 Roustant, Olivier 5 Saibaba, Arvind Krishna 5 Sanz-Alonso, Daniel 5 Schneider, Reinhold 5 Surowiec, Thomas 5 Tsilifis, Panagiotis A. ...and 1,869 more Authors
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#### Cited in 201 Journals

 179 SIAM/ASA Journal on Uncertainty Quantification 96 SIAM Journal on Scientific Computing 93 Journal of Computational Physics 65 Computer Methods in Applied Mechanics and Engineering 35 Inverse Problems 24 SIAM Journal on Numerical Analysis 22 Journal of Computational and Applied Mathematics 20 Journal of Scientific Computing 19 Computational Geosciences 18 Numerische Mathematik 16 Computers & Mathematics with Applications 16 Statistics and Computing 13 Multiscale Modeling & Simulation 13 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 Electronic Journal of Statistics 11 Advances in Computational Mathematics 11 Chaos 10 Mathematics of Computation 10 Journal of the American Statistical Association 10 European Journal of Operational Research 10 Computational Statistics and Data Analysis 9 Journal of Differential Equations 9 SIAM Journal on Optimization 8 International Journal for Numerical Methods in Engineering 8 Monte Carlo Methods and Applications 8 SIAM Journal on Applied Dynamical Systems 8 The Annals of Applied Statistics 7 SIAM Journal on Control and Optimization 7 The Annals of Applied Probability 7 Applied Mathematical Modelling 7 Inverse Problems and Imaging 6 Computers and Fluids 6 Applied Mathematics and Computation 6 Mathematics and Computers in Simulation 6 Journal of Complexity 6 Statistical Science 6 SIAM Journal on Applied Mathematics 6 Foundations of Computational Mathematics 5 Journal of Mathematical Analysis and Applications 5 Nonlinearity 5 BIT 5 Applied Numerical Mathematics 5 SIAM Journal on Matrix Analysis and Applications 5 SIAM Journal on Mathematical Analysis 5 Mathematical Programming. Series A. Series B 5 Journal of Nonlinear Science 5 Journal of Machine Learning Research (JMLR) 4 Advances in Applied Probability 4 Journal of Fluid Mechanics 4 Journal of Statistical Physics 4 Journal of Multivariate Analysis 4 Physica D 4 Computational Mechanics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Numerical Algorithms 4 Journal of Statistical Computation and Simulation 4 SIAM Review 4 Inverse Problems in Science and Engineering 4 SIAM Journal on Imaging Sciences 4 Mathematical Geosciences 4 Journal of Mathematics in Industry 4 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Bulletin of Mathematical Biology 3 The Annals of Statistics 3 Calcolo 3 Operations Research 3 Chinese Annals of Mathematics. Series B 3 Stochastic Analysis and Applications 3 Optimization 3 Constructive Approximation 3 European Journal of Applied Mathematics 3 Journal of Global Optimization 3 Stochastic Processes and their Applications 3 Applied and Computational Harmonic Analysis 3 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 3 Methodology and Computing in Applied Probability 3 Computational Methods in Applied Mathematics 3 Analysis and Applications (Singapore) 3 Acta Numerica 3 Mathematical Biosciences and Engineering 3 Kinetic and Related Models 3 Set-Valued and Variational Analysis 3 Journal of Agricultural, Biological, and Environmental Statistics 3 Bayesian Analysis 3 Stochastic and Partial Differential Equations. Analysis and Computations 3 Research in the Mathematical Sciences 3 SMAI Journal of Computational Mathematics 3 Electronic Research Archive 2 Applicable Analysis 2 International Journal of Engineering Science 2 Journal of Mathematical Biology 2 Applied Mathematics and Optimization 2 Journal of Approximation Theory 2 Journal of Econometrics 2 Journal of Optimization Theory and Applications 2 Journal of Statistical Planning and Inference 2 Mathematics of Operations Research 2 Quarterly of Applied Mathematics 2 Statistics & Probability Letters ...and 101 more Journals
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#### Cited in 44 Fields

 703 Numerical analysis (65-XX) 468 Statistics (62-XX) 320 Probability theory and stochastic processes (60-XX) 302 Partial differential equations (35-XX) 100 Fluid mechanics (76-XX) 80 Operations research, mathematical programming (90-XX) 77 Computer science (68-XX) 67 Calculus of variations and optimal control; optimization (49-XX) 62 Systems theory; control (93-XX) 50 Biology and other natural sciences (92-XX) 47 Approximations and expansions (41-XX) 46 Mechanics of deformable solids (74-XX) 44 Geophysics (86-XX) 43 Dynamical systems and ergodic theory (37-XX) 42 Statistical mechanics, structure of matter (82-XX) 30 Linear and multilinear algebra; matrix theory (15-XX) 29 Information and communication theory, circuits (94-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 27 Optics, electromagnetic theory (78-XX) 19 Operator theory (47-XX) 18 Ordinary differential equations (34-XX) 16 Functional analysis (46-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Classical thermodynamics, heat transfer (80-XX) 8 Integral equations (45-XX) 8 Mechanics of particles and systems (70-XX) 7 Measure and integration (28-XX) 7 Global analysis, analysis on manifolds (58-XX) 5 Combinatorics (05-XX) 5 Real functions (26-XX) 5 Potential theory (31-XX) 5 Special functions (33-XX) 4 Quantum theory (81-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Difference and functional equations (39-XX) 2 Number theory (11-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Astronomy and astrophysics (85-XX)