Stuart, Andrew

Article from CaltechAUTHORS

• Batlle, Pau and Chen, Yifan, el al. (2025) Error analysis of kernel/GP methods for nonlinear and parametric PDEs; Journal of Computational Physics; Vol. 520; 113488; 10.1016/j.jcp.2024.113488
• Pradhan, Anshuman and Adams, Kyra H., el al. (2024) Modeling Groundwater Levels in California's Central Valley by Hierarchical Gaussian Process and Neural Network Regression; Journal of Geophysical Research: Machine Learning and Computation; Vol. 1; No. 4; e2024JH000322; 10.1029/2024jh000322
• Carrillo, J. A. and Hoffmann, F., el al. (2024) The Mean-Field Ensemble Kalman Filter: Near-Gaussian Setting; SIAM Journal on Numerical Analysis; Vol. 62; No. 6; 2549-2587; 10.1137/24m1628207
• Wu, Jin-Long and Levine, Matthew E., el al. (2024) Learning about structural errors in models of complex dynamical systems; Journal of Computational Physics; Vol. 513; 113157; 10.1016/j.jcp.2024.113157
• Bach, Eviatar and Colonius, Tim, el al. (2024) Filtering dynamical systems using observations of statistics; Chaos: An Interdisciplinary Journal of Nonlinear Science; Vol. 34; No. 3; 033119; 10.1063/5.0171827
• Schneider, Tapio and Behera, Swadhin, el al. (2023) Harnessing AI and computing to advance climate modelling and prediction; Nature Climate Change; Vol. 13; No. 9; 887-889; 10.1038/s41558-023-01769-3
• Sirlanci, Melike and Levine, Matthew E., el al. (2023) A simple modeling framework for prediction in the human glucose–insulin system; Chaos: An Interdisciplinary Journal of Nonlinear Science; Vol. 33; No. 7; 073150; PMCID PMC10368459; 10.1063/5.0146808
• de Hoop, Maarten V. and Kovachki, Nikola B., el al. (2023) Convergence Rates for Learning Linear Operators from Noisy Data; SIAM/ASA Journal on Uncertainty Quantification; Vol. 11; No. 2; 480-513; 10.1137/21m1442942
• Bhattacharya, Kaushik and Liu, Burigede, el al. (2023) Learning Markovian Homogenized Models in Viscoelasticity; Multiscale Modeling & Simulation; Vol. 21; No. 2; 641-679; 10.1137/22M1499200
• Schneider, Tapio and Stuart, Andrew M., el al. (2022) Ensemble Kalman inversion for sparse learning of dynamical systems from time-averaged data; Journal of Computational Physics; Vol. 470; Art. No. 111559; 10.1016/j.jcp.2022.111559
• Dunbar, Oliver R. A. and Howland, Michael F., el al. (2022) Ensemble-Based Experimental Design for Targeting Data Acquisition to Inform Climate Models; Journal of Advances in Modeling Earth Systems; Vol. 14; No. 9; Art. No. e2022MS002997; 10.1029/2022ms002997
• Huang, Daniel Zhengyu and Schneider, Tapio, el al. (2022) Iterated Kalman methodology for inverse problems; Journal of Computational Physics; Vol. 463; Art. No. 111262; 10.1016/j.jcp.2022.111262
• Dunbar, Oliver R. A. and Duncan, Andrew B., el al. (2022) Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods; SIAM Journal on Applied Dynamical Systems; Vol. 21; No. 2; 1539-1572; 10.1137/21M1410853
• Carrillo, J. A. and Hoffmann, F., el al. (2022) Consensus-based sampling; Studies in Applied Mathematics; Vol. 148; No. 3; 1069-1140; 10.1111/sapm.12470
• Kovachki, Nikola and Liu, Burigede, el al. (2022) Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization; Mechanics of Materials; Vol. 165; Art. No. 104156; 10.1016/j.mechmat.2021.104156
• Pavliotis, G. A. and Stuart, A. M., el al. (2022) Derivative-Free Bayesian Inversion Using Multiscale Dynamics; SIAM Journal on Applied Dynamical Systems; Vol. 21; No. 1; 284-326; 10.1137/21M1397416
• Liu, Burigede and Kovachki, Nikola, el al. (2022) A learning-based multiscale method and its application to inelastic impact problems; Journal of the Mechanics and Physics of Solids; Vol. 158; Art. No. 104668; 10.1016/j.jmps.2021.104668
• Hoffmann, Franca and Hosseini, Bamdad, el al. (2022) Spectral analysis of weighted Laplacians arising in data clustering; Applied and Computational Harmonic Analysis; Vol. 56; 189-249; 10.1016/j.acha.2021.07.004
• Chen, Yifan and Hosseini, Bamdad, el al. (2021) Solving and learning nonlinear PDEs with Gaussian processes; Journal of Computational Physics; Vol. 447; Art. No. 110668; 10.1016/j.jcp.2021.110668
• Bertozzi, Andrea L. and Hosseini, Bamdad, el al. (2021) Posterior consistency of semi-supervised regression on graphs; Inverse Problems; Vol. 37; No. 10; Art. No. 105011; 10.1088/1361-6420/ac1e80
• Nelsen, Nicholas H. and Stuart, Andrew M. (2021) The Random Feature Model for Input-Output Maps between Banach Spaces; SIAM Journal on Scientific Computing; Vol. 43; No. 5; A3212-A3243; 10.1137/20M133957X
• Dunbar, Oliver R. A. and Garbuno-Inigo, Alfredo, el al. (2021) Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM; Journal of Advances in Modelling Earth Systems; Vol. 13; No. 9; Art. No. e2020MS002454; 10.1029/2020MS002454
• Burov, Dmitry and Giannakis, Dimitrios, el al. (2021) Kernel Analog Forecasting: Multiscale Test Problems; Multiscale Modeling and Simulation; Vol. 19; No. 2; 1011-1040; 10.1137/20M1338289
• Chen, Yifang and Owhadi, Houman, el al. (2021) Consistency of empirical Bayes and kernel flow for hierarchical parameter estimation; Mathematics of Computation; Vol. 90; 2527-2578; 10.1090/mcom/3649
• Cleary, Emmet and Garbuno-Inigo, Alfredo, el al. (2021) Calibrate, emulate, sample; Journal of Computational Physics; Vol. 424; Art. No. 109716; 10.1016/j.jcp.2020.109716
• Kovachki, Nikola B. and Stuart, Andrew M. (2021) Continuous Time Analysis of Momentum Methods; Journal of Machine Learning Research; Vol. 22; No. 17; 1-40
• Abdulle, Assyr and Garegnani, Giacomo, el al. (2020) Drift Estimation of Multiscale Diffusions Based on Filtered Data; Foundations of Computational Mathematics; 10.1007/s10208-021-09541-9
• Dunlop, Matthew M. and Slepčev, Dejan, el al. (2020) Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms; Applied and Computational Harmonic Analysis; Vol. 49; No. 2; 655-697; 10.1016/j.acha.2019.03.005
• Dunbar, Oliver R. A. and Dunlop, Matthew M., el al. (2020) Reconciling Bayesian and Perimeter Regularization for Binary Inversion; SIAM Journal on Scientific Computing; Vol. 42; No. 4; A1984-A2013; 10.1137/18M1179559
• Hoffmann, Franca and Hosseini, Bamdad, el al. (2020) Consistency of Semi-Supervised Learning Algorithms on Graphs: Probit and One-Hot Methods; Journal of Machine Learning Research; Vol. 21; 1-55; 10.48550/arXiv.1906.07658
• Seylabi, Elnaz and Stuart, Andrew M., el al. (2020) Site Characterization at Downhole Arrays by Joint Inversion of Dispersion Data and Acceleration Time Series; Bulletin of the Seismological Society of America; Vol. 110; No. 3; 1323-1337; 10.1785/0120190256
• Newton, Kit and Li, Qin, el al. (2020) Diffusive optical tomography in the Bayesian framework; Multiscale Modeling and Simulation; Vol. 18; No. 2; 589-611; 10.1137/19M1247346
• Chada, Neil K. and Stuart, Andrew M., el al. (2020) Tikhonov Regularization Within Ensemble Kalman Inversion; SIAM Journal on Numerical Analysis; Vol. 58; No. 2; 1263-1294; 10.1137/19M1242331
• Stuart, Andrew M. and Wolfram, Marie-Therese (2020) Inverse optimal transport; SIAM Journal on Applied Mathematics; Vol. 80; No. 1; 599-619; 10.1137/19M1261122
• Garbuno-Inigo, Alfredo and Hoffmann, Franca, el al. (2020) Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler; SIAM Journal on Applied Dynamical Systems; Vol. 19; No. 1; 412-441; 10.1137/19M1251655
• Lie, Han Cheng and Stuart, A. M., el al. (2019) Strong convergence rates of probabilistic integrators for ordinary differential equations; Statistics and Computing; Vol. 29; No. 6; 1265-1283; 10.1007/s11222-019-09898-6
• Kuntz, Juan and Ottobre, Michela, el al. (2019) Diffusion Limit For The Random Walk Metropolis Algorithm Out Of stationarity; Annales De l'Institut Henri Poincaré - Probabilitiés et Statistiques; Vol. 55; No. 3; 1599-1648; 10.1214/18-AIHP929
• Kovachki, Nikola B. and Stuart, Andrew M. (2019) Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks; Inverse Problems; Vol. 35; No. 9; Art. No. 095005; 10.1088/1361-6420/ab1c3a
• Kelly, David and Stuart, Andrew M. (2019) Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation; Chinese Annals of Mathematics, Series B; Vol. 40; No. 5; 811-842; 10.1007/s11401-019-0161-5
• Albers, David J. and Blancquart, Paul-Adrien, el al. (2019) Ensemble Kalman Methods With Constraints; Inverse Problems; Vol. 35; No. 9; Art. No. 095007; PMCID PMC7677878; 10.1088/1361-6420/ab1c09
• Gomes, Susana N. and Stuart, Andrew M., el al. (2019) Parameter estimation for macroscopic pedestrian dynamics models from microscopic data; SIAM Journal on Applied Mathematics; Vol. 79; No. 4; 1475-1500; 10.1137/18M1215980
• Qiao, Yiling and Shi, Chang, el al. (2019) Uncertainty quantification for semi-supervised multi-class classification in image processing and ego-motion analysis of body-worn videos; Electronic Imaging; Vol. 2019; Art. No. 264; 10.2352/ISSN.2470-1173.2019.11.IPAS-264
• Albers, David J. and Levine, Matthew E., el al. (2018) Mechanistic machine learning: how data assimilation leverages physiologic knowledge using Bayesian inference to forecast the future, infer the present, and phenotype; Journal of the American Medical Informatics Association; Vol. 25; No. 10; 1392-1401; PMCID PMC6188514; 10.1093/jamia/ocy106
• Dunlop, Matthew M. and Girolami, Mark A., el al. (2018) How Deep Are Deep Gaussian Processes?; Journal of Machine Learning Research; Vol. 19; No. 54; 1-46; 10.48550/arXiv.1711.11280
• Kuntz, Juan and Ottobre, Michela, el al. (2018) Non-stationary phase of the MALA algorithm; Stochastics and Partial Differential Equations: Analysis and Computations; Vol. 6; No. 3; 446-499; PMCID PMC6411168; 10.1007/s40072-018-0113-1
• Chada, Neil K. and Iglesias, Marco A., el al. (2018) Parameterizations for ensemble Kalman inversion; Inverse Problems; Vol. 34; No. 5; Art. No. 055009; 10.1088/1361-6420/aab6d9
• Bertozzi, Andrea L. and Luo, Xiyang, el al. (2018) Uncertainty Quantification in Graph-Based Classification of High Dimensional Data; SIAM/ASA Journal on Uncertainty Quantification; Vol. 6; No. 2; 568-595; 10.1137/17M1134214
• Bréhier, Charles-Edouard and Hairer, Martin, el al. (2018) Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization; Journal of Computational Mathematics; Vol. 36; No. 2; 159-182; 10.4208/jcm.1607-m2016-0539
• Stuart, Andrew M. and Teckentrup, Aretha L. (2018) Posterior consistency for Gaussian process approximations of Bayesian posterior distributions; Mathematics of Computation; Vol. 87; No. 310; 721-753; 10.1090/mcom/3244
• Calvetti, Daniela and Dunlop, Matthew, el al. (2018) Iterative Updating of Model Error for Bayesian Inversion; Inverse Problems; Vol. 34; No. 2; Art. No. 025008; 10.1088/1361-6420/aaa34d
• Schillings, C. and Stuart, A. M. (2018) Convergence analysis of ensemble Kalman inversion: the linear, noisy case; Applicable Analysis: An International Journal; Vol. 97; No. 1; 107-123; 10.1080/00036811.2017.1386784
• Schneider, Tapio and Lan, Shiwei, el al. (2017) Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations; Geophysical Research Letters; Vol. 44; No. 24; 12396-12417; 10.1002/2017GL076101
• Lu, Yulong and Stuart, Andrew, el al. (2017) Gaussian Approximations for Probability Measures on R^d; SIAM/ASA Journal on Uncertainty Quantification; Vol. 5; No. 1; 1136-1165; 10.1137/16M1105384
• Dunlop, Matthew M. and Iglesias, Marco A., el al. (2017) Hierarchical Bayesian level set inversion; Statistics and Computing; Vol. 27; No. 6; 1555-1584; 10.1007/s11222-016-9704-8
• Sanz-Alonso, Daniel and Stuart, Andrew M. (2017) Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence; Communications in Mathematical Sciences; Vol. 15; No. 7; 2087-2097; 10.4310/CMS.2017.v15.n7.a13
• Agapiou, S. and Papaspiliopoulos, O., el al. (2017) Importance Sampling: Intrinsic Dimension and Computational Cost; Statistical Science; Vol. 32; No. 3; 405-431; 10.1214/17-STS611
• Lu, Yulong and Stuart, Andrew, el al. (2017) Gaussian Approximations for Transition Paths in Brownian Dynamics; SIAM Journal on Mathematical Analysis; Vol. 49; No. 4; 3005-3047; 10.1137/16M1071845
• Conrad, Patrick R. and Girolami, Mark, el al. (2017) Statistical analysis of differential equations: introducing probability measures on numerical solutions; Statistics and Computing; Vol. 27; No. 4; 1065-1082; 10.1007/s11222-016-9671-0
• Schillings, Claudia and Stuart, Andrew M. (2017) Analysis of the ensemble Kalman filter for inverse problems; SIAM Journal on Numerical Analysis; Vol. 55; No. 3; 1264-1290; 10.1137/16M105959X
• Scheichl, R. and Stuart, A. M., el al. (2017) Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems; SIAM/ASA Journal on Uncertainty Quantification; Vol. 5; No. 1; 493-518; 10.1137/16M1061692
• Beskos, Alexandros and Girolami, Mark, el al. (2017) Geometric MCMC for Infinite-Dimensional Inverse Problems; Journal of Computational Physics; Vol. 335; 327-351; 10.1016/j.jcp.2016.12.041
• Lee, Wongjung and Stuart, Andrew (2017) Derivation and analysis of simplified filters; Communications in Mathematical Sciences; Vol. 15; No. 2; 413-450; 10.4310/CMS.2017.v15.n2.a6
• Iglesias, Marco A. and Lin, Kui, el al. (2017) Filter Based Methods For Statistical Linear Inverse Problems; Communications in Mathematical Sciences; Vol. 15; No. 7; 1867-1896; 10.4310/CMS.2017.v15.n7.a4
• Dunlop, Matthew M. and Stuart, Andrew M. (2016) The Bayesian formulation of EIT: Analysis and algorithms; Inverse Problems and Imaging; Vol. 10; No. 4; 1007-1036; 10.3934/ipi.2016030
• Dunlop, M. M. and Stuart, A. M. (2016) MAP estimators for piecewise continuous inversion; Inverse Problems; Vol. 32; No. 10; Art. No. 105003; 10.1088/0266-5611/32/10/105003
• Law, K. J. H. and Sanz-Alonso, D., el al. (2016) Filter accuracy for the Lorenz 96 model: fixed versus adaptive observation operators; Physica D: Nonlinear Phenomena; Vol. 325; 1-13; 10.1016/j.physd.2015.12.008
• Bühlmann, Peter and Stuart, A. M. (2016) Mathematics, Statistics and Data Science; EMS Newsletter; Vol. 100; 28-30
• Ottobre, Michela and Pillai, Natesh S., el al. (2016) A Function Space HMC Algorithm With Second Order Langevin Diffusion Limit; Bernoulli; Vol. 22; No. 1; 60-106; 10.3150/14-BEJ621
• Iglesias, Marco A. and Lu, Yulong, el al. (2016) A Bayesian Level Set Method for Geometric Inverse Problems; Interfaces and Free Boundaries; Vol. 18; No. 2; 181-217; 10.4171/IFB/362
• Sanz-Alonso, Daniel and Stuart, Andrew M. (2015) Long-Time Asymptotics of the Filtering Distribution for Partially Observed Chaotic Dynamical Systems; SIAM/ASA Journal on Uncertainty Quantification; Vol. 3; No. 1; 1200-1220; 10.1137/140997336
• Beskos, Alexandros and Jasra, Ajay, el al. (2015) Sequential Monte Carlo methods for Bayesian elliptic inverse problems; Statistics and Computing; Vol. 25; No. 4; 727-737; 10.1007/s11222-015-9556-7
• Duncan, A. B. and Elliott, C. M., el al. (2015) A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces; Journal of Nonlinear Science; Vol. 25; No. 2; 389-449; 10.1007/s00332-015-9237-x
• Pinski, F. J. and Simpson, G., el al. (2015) Algorithms for Kullback--Leibler Approximation of Probability Measures in Infinite Dimensions; SIAM Journal on Scientific Computing; Vol. 37; No. 6; A2733-A2757; 10.1137/14098171X
• Pinski, F. J. and Simpson, G., el al. (2015) Kullback-Leibler approximation for probability measures on infinite dimensional spaces; SIAM Journal on Mathematical Analysis; Vol. 47; No. 6; 4091-4122; 10.1137/140962802
• Reich, Sebastian and Stuart, Andrew M. (2015) Data Assimilation: New Challenges in Random and Stochastic Dynamical Systems; SIAM News; Vol. 48; No. 8 & 9
• Hairer, Martin and Stuart, Andrew M., el al. (2014) Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions; Annals of Applied Probability; Vol. 24; No. 6; 2455-2490; 10.1214/13-AAP982
• Iglesias, Marco A. and Lin, Kui, el al. (2014) Well-posed Bayesian geometric inverse problems arising in subsurface flow; Inverse Problems; Vol. 30; No. 11; Art. No. 114001; 10.1088/0266-5611/30/11/114001
• Kelly, D. B. T. and Law, K. J. H., el al. (2014) Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time; Nonlinearity; Vol. 27; No. 10; 2579-2603; 10.1088/0951-7715/27/10/2579
• Agapiou, Sergios and Bardsley, Jonathan M., el al. (2014) Analysis of the Gibbs Sampler for Hierarchical Inverse Problems; SIAM/ASA Journal on Uncertainty Quantification; Vol. 2; No. 1; 511-544; 10.1137/130944229
• Pillai, Natesh S. and Stuart, Andrew M., el al. (2014) Noisy gradient flow from a random walk in Hilbert space; Stochastic Partial Differential Equations: Analysis and Computations; Vol. 2; No. 2; 196-232; 10.1007/s40072-014-0029-3
• Hoang, Viet Ha and Law, Kody J. H., el al. (2014) Determining white noise forcing from Eulerian observations in the Navier-Stokes equation; Stochastic Partial Differential Equations: Analysis and Computations; Vol. 2; No. 2; 233-261; 10.1007/s40072-014-0028-4
• Agapiou, Sergios and Stuart, Andrew M., el al. (2014) Bayesian posterior contraction rates for linear severely ill-posed inverse problems; Journal of Inverse and Ill-posed Problems; Vol. 22; No. 3; 297-321; 10.1515/jip-2012-0071
• Law, Kody and Shukla, Abishek, el al. (2014) Analysis of the 3DVAR filter for the partially observed Lorenz'63 model; Discrete and Continuous Dynamical Systems A; Vol. 34; No. 3; 1061-1078; 10.3934/dcds.2014.34.1061
• Iglesias, Marco and Stuart, Andrew M. (2014) Inverse Problems and Uncertainty Quantification; SIAM News; 2-3
• Beskos, Alexandros and Pillai, Natesh, el al. (2013) Optimal tuning of the hybrid Monte Carlo algorithm; Bernoulli; Vol. 19; No. 5A; 1501-1534; 10.3150/12-BEJ414
• Agapiou, Sergios and Larsson, Stig, el al. (2013) Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems; Stochastic Processes and their Applications; Vol. 123; No. 10; 3828-3860; 10.1016/j.spa.2013.05.001
• Dashti, M. and Law, K. J. H., el al. (2013) MAP estimators and their consistency in Bayesian nonparametric inverse problems; Inverse Problems; Vol. 29; No. 9; Art. No. 095017; 10.1088/0266-5611/29/9/095017
• Cotter, S. L. and Roberts, G. O., el al. (2013) MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster; Statistical Science; Vol. 28; No. 3; 424-446; 10.1214/13-STS421
• Hoang, Viet Ha and Schwab, Christoph, el al. (2013) Complexity analysis of accelerated MCMC methods for Bayesian inversion; Inverse Problems; Vol. 29; No. 8; Art No. 085010; 10.1088/0266-5611/29/8/085010
• Blömker, D. and Law, K., el al. (2013) Accuracy and stability of the continuous-time 3DVAR filter for the Navier–Stokes equation; Nonlinearity; Vol. 26; No. 8; 2193-2219; 10.1088/0951-7715/26/8/2193
• Iglesias, Marco A. and Law, Kody, el al. (2013) Evaluation of Gaussian approximations for data assimilation in reservoir models; Computational Geosciences; Vol. 17; No. 5; 851-885; 10.1007/s10596-013-9359-x
• Iglesias, Marco A. and Law, Kody J. H., el al. (2013) Ensemble Kalman methods for inverse problems; Inverse Problems; Vol. 29; No. 4; Art. No. 045001; 10.1088/0266-5611/29/4/045001
• Brett, C. E. A. and Lam, K. F., el al. (2013) Accuracy and stability of filters for dissipative PDEs; Physica D: Nonlinear Phenomena; Vol. 245; No. 1; 34-35; 10.1016/j.physd.2012.11.005
• Pokern, Y. and Stuart, A. M., el al. (2013) Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs; Stochastic Processes and their Applications; Vol. 123; No. 2; 603-628; 10.1016/j.spa.2012.08.010
• Pillai, Natesh S. and Stuart, Andrew M., el al. (2012) Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions; Annals of Applied Probability; Vol. 22; No. 6; 2320-2356; 10.1214/11-AAP828
• Law, K. J. H. and Stuart, A. M. (2012) Evaluating Data Assimilation Algorithms; Monthly Weather Review; Vol. 140; 3757-3782; 10.1175/MWR-D-11-00257.1
• Papaspiliopoulos, Omiros and Pokern, Yvo, el al. (2012) Nonparametric estimation of diffusions: a differential equations approach; Biometrika; Vol. 99; No. 3; 511-531; 10.1093/biomet/ass034
• Mattingly, Jonathan C. and Pillai, Natesh S., el al. (2012) Diffusion limits of the random walk Metropolis algorithm in high dimensions; Annals of Applied Probability; Vol. 22; No. 3; 881-930; 10.1214/10-AAP754
• Dashti, Masoumeh and Harris, Stephen J., el al. (2012) Besov priors for Bayesian inverse problems; Inverse Problems and Imaging; Vol. 6; No. 2; 183-200; 10.3934/ipi.2012.6.183
• Schwab, C. and Stuart, A. M. (2012) Sparse determinisitc approximation of Bayesian inverse problems; Inverse Problems; Vol. 28; No. 4; Art. No. 045003; 10.1088/0266-5611/28/4/045003
• Pinski, F. J. and Stuart, A. M., el al. (2012) Γ-Limit for Transition Paths of Maximal Probability; Journal of Statistical Physics; Vol. 146; No. 5; 955-974; 10.1007/s10955-012-0443-8
• Cotter, S. L. and Dashti, M., el al. (2012) Variational data assimilation using targetted random walks; International Journal for Numerical Methods in Fluids; Vol. 68; No. 4; 403-421; 10.1002/fld.2510
• Dashti, M. and Stuart, A. M. (2011) Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem; SIAM Journal on Numerical Analysis; Vol. 49; No. 6; 2524-2542; 10.1137/100814664
• Beskos, A. and Pinski, F. J., el al. (2011) Hybrid Monte Carlo on Hilbert spaces; Stochastic Processes and their Applications; Vol. 121; No. 10; 2201-2230; 10.1016/j.spa.2011.06.003
• Lee, Wonjung and McDougall, D., el al. (2011) Kalman filtering and smoothing for linear wave equations with model error; Inverse Problems; Vol. 27; No. 9; Art. No. 095008; 10.1088/0266-5611/27/9/095008
• Melbourne, I. and Stuart, A. M. (2011) A note on diffusion limits of chaotic skew-product flows; Nonlinearity; Vol. 24; No. 4; 1361-1367; 10.1088/0951-7715/24/4/018
• Hairer, Martin and Stuart, Andrew M., el al. (2011) Sampling conditioned hypoelliptic diffusions; Annals of Applied Probability; Vol. 21; No. 2; 669-698; 10.1214/10-AAP708
• Fearnhead, Paul and Papaspiliopoulos, Omiros, el al. (2010) Random-weight particle filtering of continuous time processes; Journal of the Royal Statistical Society: Series B; Vol. 72; No. 4; 497-512; 10.1111/j.1467-9868.2010.00744.x
• Fearnhead, Paul and Papaspiliopoulos, Omiros, el al. (2010) Random-weight particle filtering of continuous time processes; Statistical Methodology; Vol. 72; No. 4; 497-512; 10.1111/j.1467-9868.2010.00744.x
• Pinski, F. J. and Stuart, A. M. (2010) Transition paths in molecules at finite temperature; Journal of Chemical Physics; Vol. 132; No. 18; Art. No. 184104; 10.1063/1.3391160
• Mattingly, J. C. and Stuart, A. M., el al. (2010) Convergence of numerical time-averaging and stationary measures via Poisson equations; SIAM Journal of Numerical Analysis; Vol. 48; No. 2; 552-577; 10.1137/090770527
• Stuart, A. M. (2010) Inverse problems: A Bayesian perspective; Acta Numerica; Vol. 19; 451-559; 10.1017/S0962492910000061
• Cotter, S. L. and Dashti, M., el al. (2010) Approximation of Bayesian Inverse Problems for PDEs; SIAM Journal on Numerical Analysis; Vol. 48; No. 1; 322-345; 10.1137/090770734
• Cotter, S. L. and Dashti, M., el al. (2009) Bayesian inverse problems for functions and applications to fluid mechanics; Inverse Problems; Vol. 25; No. 11; Art. No 115008; 10.1088/0266-5611/25/11/115008
• Pokern, Yvo and Stuart, Andrew M., el al. (2009) Remarks on Drift Estimation for Diffusion Processes; Multiscale Modeling and Simulation; Vol. 8; No. 1; 69-95; 10.1137/070694806
• Papavasiliou, A. and Pavliotis, G. A., el al. (2009) Maximum likelihood drift estimation for multiscale diffusions; Stochastic Processes and their Applications; Vol. 119; No. 10; 3173-3210; 10.1016/j.spa.2009.05.003
• Beskos, Alexandros and Roberts, Gareth, el al. (2009) Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions; Annals of Applied Probability; Vol. 19; No. 3; 863-898; 10.1214/08-AAP563
• Pavliotis, G. A. and Stuart, A. M., el al. (2009) Calculating effective diffusivities in the limit of vanishing molecular diffusion; Journal of Computational Physics; Vol. 288; No. 4; 1030-1055; 10.1016/j.jcp.2008.10.014
• Pokern, Yvo and Stuart, Andrew M., el al. (2009) Parameter estimation for partially observed hypoelliptic diffusions; Statistical Methodology; Vol. 71; No. 1; 49-73; 10.1111/j.1467-9868.2008.00689.x
• Pokern, Yvo and Stuart, Andrew M., el al. (2009) Parameter estimation for partially observed hypo-elliptic diffusions; Journal of the Royal Society: Series B (Statistical Methodology); Vol. 71; No. 1; 49-73; 10.1111/j.1467-9868.2008.00689.x
• Beskos, Alexandros and Roberts, Gareth, el al. (2008) MCMC Methods for Diffusion Bridges; Stochastics and Dynamics; Vol. 8; No. 3; 319-350; 10.1142/S0219493708002378
• Apte, A. and Jones, C. K. R. T., el al. (2008) Data assimilation: Mathematical and statistical perspectives; International Journal for Numerical Methods in Fluids; Vol. 56; No. 8; 1033-1046; 10.1002/fld.1698
• Apte, A. and Jones, C. K. R. T., el al. (2008) A Bayesian approach to Lagrangian data assimilation; Tellus A; Vol. 60; No. 2; 336-347; 10.1111/j.1600-0870.2007.00295.x
• Lamba, H. and Mattingly, J. C., el al. (2007) An adaptive Euler-Maruyama scheme for SDEs: convergence and stability; IMA Journal of Numerical Analysis; Vol. 27; No. 3; 479-506; 10.1093/imanum/drl032
• Apte, A. and Hairer, M., el al. (2007) Sampling the posterior: An approach to non-Gaussian data assimilation; Physica D; Vol. 230; No. 1-2; 50-64; 10.1016/j.physd.2006.06.009
• Pavliotis, G. A. and Stuart, A. M. (2007) Parameter Estimation for Multiscale Diffusions; Journal of Statistical Physics; Vol. 127; No. 4; 741-781; 10.1007/s10955-007-9300-6
• Pavliotis, G. A. and Stuart, A. M., el al. (2007) Homogenization for inertial particles in a random flow; Communications in Mathematical Sciences; Vol. 5; No. 3; 507-531; 10.4310/CMS.2007.v5.n3.a1
• Hairer, M. and Stuart, A. M., el al. (2007) Analysis of SPDEs arising in path sampling part II: The nonlinear case; Annals of Applied Probability; Vol. 17; No. 5/6; 1657-1706; 10.1214/07-AAP441
• Barkley, D. and Kevrekidis, I. G., el al. (2006) The Moment Map: Nonlinear Dynamics of Density Evolution via a Few Moments; SIAM Journal on Applied Dynamical Systems; Vol. 5; No. 3; 403-434; 10.1137/050638667
• Pavliotis, G. A. and Stuart, A. M. (2005) Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation Times; Multiscale Modeling and Simulation; Vol. 4; No. 1; 1-35; 10.1137/040610507
• Pavliotis, G. A. and Stuart, A. M. (2005) Periodic homogenization for inertial particles; Physica D; Vol. 204; No. 3-4; 161-187; 10.1016/j.physd.2005.04.011
• Hairer, M. and Stuart, A. M., el al. (2005) Analysis of SPDEs arising in path sampling. Part I: The Gaussian case; Communications in Mathematical Sciences; Vol. 3; No. 4; 587-603; 10.4310/CMS.2005.v3.n4.a8
• Kupferman, R. and Stuart, A. M. (2004) Fitting SDE models to nonlinear Kac–Zwanzig heat bath models; Physica D; Vol. 199; No. 3-4; 279-316; 10.1016/j.physd.2004.04.011
• Stuart, Andrew M. and Voss, Jochen, el al. (2004) Conditional Path Sampling of SDEs and the Langevin MCMC Method; Communications in Mathematical Sciences; Vol. 2; No. 4; 685-697; 10.4310/CMS.2004.v2.n4.a7
• Givon, Dror and Kupferman, Raz, el al. (2004) Extracting macroscopic dynamics: model problems and algorithms; Nonlinearity; Vol. 17; No. 6; R55-R127; 10.1088/0951-7715/17/6/R01
• Kupferman, R. and Pavliotis, G. A., el al. (2004) Itô versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise; Physical Review E; Vol. 70; No. 3; Art. No. 036120; 10.1103/PhysRevE.70.036120
• Pavliotis, G. A. and Stuart, A. M. (2003) White Noise Limits for Inertial Particles in a Random Field; Multiscale Modeling and Simulation; Vol. 1; No. 4; 527-553; 10.1137/S1540345903421076
• Huisinga, Wilhelm and Schütte, Christof, el al. (2003) Extracting macroscopic stochastic dynamics: Model problems; Communications on Pure and Applied Mathematics; Vol. 56; No. 2; 234-269; 10.1002/cpa.10057
• Higham, Desmond J. and Mao, Xuerong, el al. (2003) Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations; LMS Journal of Computation and Mathematics; Vol. 6; 297-313; 10.1112/S1461157000000462
• Kupferman, R. and Stuart, A. M., el al. (2002) Long-Term Behavior of Large Mechanical Systems with Random Initial Data; Stochastics and Dynamics; Vol. 02; No. 04; 533-562; 10.1142/S0219493702000571
• Sigurgeirsson, H. and Stuart, A. M. (2002) A model for preferential concentration; Physics of Fluids; Vol. 14; No. 12; 4352-4361; 10.1063/1.1517603
• Mattingly, J. C. and Stuart, A. M., el al. (2002) Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise; Stochastic Processes and their Applications; Vol. 101; No. 2; 185-232; 10.1016/S0304-4149(02)00150-3
• Higham, Desmond J. and Mao, Xuerong, el al. (2002) Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations; SIAM Journal on Numerical Analysis; Vol. 40; No. 3; 1041-1063; 10.1137/S0036142901389530
• Estep, Donald J. and Stuart, Andrew M. (2002) The dynamical behavior of the discontinuous Galerkin method and related difference schemes; Mathematics of Computation; Vol. 71; No. 239; 1075-1103; 10.1090/S0025-5718-01-01364-3
• Sigurgeirsson, H. and Stuart, A. M. (2002) Inertial Particles in a Random Field; Stochastics and Dynamics; Vol. 02; No. 02; 295-310; 10.1142/S021949370200042X
• Mattingly, J. C. and Stuart, A. M. (2002) Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions; Markov Processes And Related Fields; Vol. 8; No. 2; 199-214
• Sigurgeirsson, Hersir and Stuart, Andrew, el al. (2001) Algorithms for Particle-Field Simulations with Collisions; Journal of Computational Physics; Vol. 172; No. 2; 766-807; 10.1006/jcph.2001.6858
• Cano, B. and Stuart, A. M. (2001) Underresolved Simulations of Heat Baths; Journal of Computational Physics; Vol. 169; No. 1; 193-214; 10.1006/jcph.2001.6722
• Cano, B. and Stuart, A. M., el al. (2001) Stiff Oscillatory Systems, Delta Jumps and White Noise; Foundations of Computational Mathematics; Vol. 1; No. 1; 69-100; 10.1007/s10208001002
• Shardlow, T. and Stuart, A. M. (2000) A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations; SIAM Journal on Numerical Analysis; Vol. 37; No. 4; 1120-1137; 10.1137/S0036142998337235
• Stuart, A. M. and Warren, J. O. (1999) Analysis and Experiments for a Computational Model of a Heat Bath; Journal of Statistical Physics; Vol. 97; No. 3/4; 687-723; 10.1023/A:1004667325896
• Sanz-Serna, J. M. and Stuart, A. M. (1999) Ergodicity of Dissipative Differential Equations Subject to Random Impulses; Journal of Differential Equations; Vol. 155; No. 2; 262-284; 10.1006/jdeq.1998.3594
• Gonzalez, O. and Higham, D. J., el al. (1999) Qualitative properties of modified equations; IMA Journal of Numerical Analysis; Vol. 19; No. 2; 169-190; 10.1093/imanum/19.2.169
• Lamba, H. and Stuart, A. M. (1998) Convergence results for the MATLAB ODE23 routine; BIT Numerical Mathematics; Vol. 38; No. 4; 751-780; 10.1007/BF02510413
• Gander, Martin J. and Stuart, Andrew M. (1998) Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation; SIAM Journal on Scientific Computing; Vol. 19; No. 6; 2014-2031; 10.1137/S1064827596305337
• Budd, C. J. and Koomullil, G. P., el al. (1998) On the Solution of Convection-Diffusion Boundary Value Problems Using Equidistributed Grids; SIAM Journal on Scientific Computing; Vol. 20; No. 2; 591-618; 10.1137/S1064827595280454
• Jones, Don A. and Stuart, Andrew M., el al. (1998) Persistence of Invariant Sets for Dissipative Evolution Equations; Journal of Mathematical Analysis and Applictions; Vol. 219; No. 2; 479-502; 10.1006/jmaa.1997.5847
• Higham, D. J. and Stuart, A. M. (1998) Analysis of the dynamics of local error control via a piecewise continuous residual; BIT Numerical Mathematics; Vol. 38; No. 1; 44-57; 10.1007/BF02510916
• Bjørhus, Morten and Stuart, Andrew M. (1997) Waveform relaxation as a dynamical system; Mathematics of Computation; Vol. 66; No. 219; 1101-1118; 10.1090/S0025-5718-97-00847-8
• Stuart, A. M. (1997) Probabilistic and deterministic convergence proofs for software for initial value problems; Numerical Algorithms; Vol. 14; No. 1/3; 227-260; 10.1023/A:1019169114976
• Elliott, C. M. and Stuart, A. M. (1996) Viscous Cahn–Hilliard Equation II. Analysis; Journal of Differential Equations; Vol. 128; No. 2; 387-414; 10.1006/jdeq.1996.0101
• Stuart, A. M. and Humphries, A. R. (1995) The Essential Stability of Local Error Control for Dynamical Systems; SIAM Journal on Numerical Analysis; Vol. 32; No. 6; 1940-1971; 10.1137/0732087
• Jones, D. A. and Stuart, A. M. (1995) Attractive Invariant Manifolds under Approximation. Inertial Manifolds; Journal of Differential Equations; Vol. 123; No. 2; 588-637; 10.1006/jdeq.1995.1174
• Estep, Donald J. and Stuart, Andrew M. (1995) The rate of error growth in Hamiltonian-conserving integrators; Zeitschrift für Angewandte Mathematik und Physik; Vol. 46; No. 3; 407-418; 10.1007/BF01003559
• Lord, Gabriel J. and Stuart, Andrew M. (1995) Discrete Gevrey regularity attractors and uppers–semicontinuity for a finite difference approximation to the Ginzburg–Landau equation; Numerical Functional Analysis and Optimization; Vol. 16; No. 7-8; 1003-1047; 10.1080/01630569508816658
• Bai, F. and Elliott, C. M., el al. (1995) The viscous Cahn-Hilliard equation. I. Computations; Nonlinearity; Vol. 8; No. 2; 131-160; 10.1088/0951-7715/8/2/002
• Bai, Fengshan and Spence, Alastair, el al. (1994) Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation; Physica D; Vol. 78; No. 3-4; 155-165; 10.1016/0167-2789(94)90112-0
• Humphries, A. R. and Stuart, A. M. (1994) Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems; SIAM Journal on Numerical Analysis; Vol. 31; No. 5; 1452-1485; 10.1137/0731075
• Budd, C. J. and Dold, J. W., el al. (1994) Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part II: Problems with Convection; SIAM Journal on Applied Mathematics; Vol. 54; No. 3; 610-640; 10.1137/S0036139992232131
• Stuart, A. M. and Humphries, A. R. (1994) Model Problems in Numerical Stability Theory for Initial Value Problems; SIAM Review; Vol. 36; No. 2; 226-257; 10.1137/1036054
• Stuart, Andrew M. (1994) Numerical analysis of dynamical systems; Acta Numerica; Vol. 3; 467-572; 10.1017/S0962492900002488
• Elliott, C. M. and Stuart, A. M. (1993) The Global Dynamics of Discrete Semilinear Parabolic Equations; SIAM Journal on Numerical Analysis; Vol. 30; No. 6; 1622-1663; 10.1137/0730084
• Chaplain, M. A. J. and Stuart, A. M. (1993) A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor; Mathematical Medicine and Biology; Vol. 10; No. 3; 149-168; 10.1093/imammb/10.3.149
• Bai, Fengshan and Spence, Alastair, el al. (1993) The Numerical Computation of Heteroclinic Connections in Systems of Gradient Partial Differential Equations; SIAM Journal on Applied Mathematics; Vol. 53; No. 3; 743-769; 10.1137/0153037
• Budd, Chris and Dold, Bill, el al. (1993) Blowup in a Partial Differential Equation with Conserved First Integral; SIAM Journal on Applied Mathematics; Vol. 53; No. 3; 718-742; 10.1137/0153036
• Iserles, A. and Stuart, A. M. (1992) Unified approach to spurious solutions introduced by time discretization Part II: BDF-like methods; IMA Journal of Numerical Analysis; Vol. 12; No. 4; 487-502; 10.1093/imanum/12.4.487
• Griffiths, D. F. and Stuart, A. M., el al. (1992) Numerical Wave Propagation in an Advection Equation with a Nonlinear Source Term; SIAM Journal on Numerical Analysis; Vol. 29; No. 5; 1244-1260; 10.1137/0729074
• Sanz-Serna, J. M. and Stuart, A. M. (1992) A note on uniform in time error estimates for approximations to reaction-diffusion equations; IMA Journal of Numerical Analysis; Vol. 12; No. 3; 457-462; 10.1093/imanum/12.3.457
• Iserles, A. and Peplow, A. T., el al. (1991) A Unified Approach to Spurious Solutions Introduced by Time Discretisation. Part I: Basic Theory; SIAM Journal on Numerical Analysis; Vol. 28; No. 6; 1723-1751; 10.1137/0728086
• Stuart, A. M. and Peplow, A. T. (1991) The Dynamics of the Theta Method; SIAM Journal on Scientific and Statistical Computing; Vol. 12; No. 6; 1351-1372; 10.1137/0912074
• Chaplain, M. A. J. and Stuart, A. M. (1991) A Mathematical Model for the Diffusion of Tumour Angiogenesis Factor into the Surrounding Host Tissue; Mathematical Medicine and Biology; Vol. 8; No. 3; 191-220; 10.1093/imammb/8.3.191
• Stuart, Andrew M. (1991) Singular Limits in Free Boundary Problems; Rocky Mountain Journal of Mathematics; Vol. 21; No. 2; 809-811; 10.1216/rmjm/1181072969
• Stuart, A. M. and Floater, M. S. (1990) On the computation of blow-up; European Journal of Applied Mathematics; Vol. 1; No. 01; 47-71; 10.1017/S095679250000005X
• Stuart, Andrew (1989) Linear Instability Implies Spurious Periodic Solutions; IMA Journal of Numerical Analysis; Vol. 9; No. 4; 465-486; 10.1093/imanum/9.4.465
• Stuart, Andrew (1989) Nonlinear Instability in Dissipative Finite Difference Schemes; SIAM Review; Vol. 31; No. 2; 191-220; 10.1137/1031048
• Norbury, J. and Stuart, A. M. (1989) A Model for Porous-Medium Combustion; Quarterly Journal of Mechanics and Applied Mathematics; Vol. 42; No. 1; 159-178; 10.1093/qjmam/42.1.159
• Stuart, A. M. (1989) Singular Free Boundary Problems and Local Bifurcation Theory; SIAM Journal on Applied Mathematics; Vol. 49; No. 1; 72-85; 10.1137/0149004
• Stuart, Andrew (1989) A Note on High/Low-Wave-Number Interactions in Spatially Discrete Parabolic Equations; IMA Journal of Applied Mathematics; Vol. 42; No. 1; 27-42; 10.1093/imamat/42.1.27
• Stuart, Andrew (1988) Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity; IMA Journal of Applied Mathematics; Vol. 40; No. 3; 217-234; 10.1093/imamat/40.3.217
• Norbury, J. and Stuart, A. M. (1988) Travelling Combustion Waves in a Porous Medium. Part II—Stability; SIAM Journal on Applied Mathematics; Vol. 48; No. 2; 374-392; 10.1137/0148019
• Norbury, J. and Stuart, A. M. (1988) Travelling Combustion Waves in a Porous Medium. Part I—Existence; SIAM Journal on Applied Mathematics; Vol. 48; No. 1; 155-169; 10.1137/0148007
• Norbury, J. and Stuart, A. M. (1987) Parabolic Free Boundary Problems Arising in Porous Medium Combustion; IMA Journal of Applied Mathematics; Vol. 39; No. 3; 241-257; 10.1093/imamat/39.3.241
• Stuart, A. M. (1987) Existence of Solutions of a Two-Point Free-Boundary Problem Arising in the Theory of Porous Medium Combustion; IMA Journal of Applied Mathematics; Vol. 38; No. 1; 23-34; 10.1093/imamat/38.1.23
• Norbury, J. and Stuart, A. M. (1987) Volterra integral equations and a new Gronwall inequality (Part II: The nonlinear case); Proceedings of the Royal Society of Edinburgh: Section A Mathematics; Vol. 106; No. 3-4; 375-384; 10.1017/S0308210500018485
• Norbury, J. and Stuart, A. M. (1987) Volterra integral equations and a new Gronwall inequality (Part I: The linear case); Proceedings of the Royal Society of Edinburgh: Section A Mathematics; Vol. 106; No. 3-4; 361-373; 10.1017/S0308210500018473