Publications
Journal Publications
2024
[191] E. Bach, T. Colonius, I. Scherl, A. Stuart; Filtering Dynamical Systems Using Observations of Statistics; Chaos, Vol. 34, Issue 3, March 2024.
[Online Publication] [pdf]
2023
[190] T. Schneider, S. Behera, G. Boccaletti, C. Deser, K. Emanuel, R. Ferrari, L. R. Leung, N. Lin, T. Müller, A. Navarra, O. Ndiaye, A. Stuart, J. Tribbia & T. Yamagata; Harnessing AI and computing to advance climate modelling and prediction, Nature Climate Change, Volume 13, September 2023, 887–889, 887.
[Read]
[189] M. Sirlanci, M. E. Levine, C. C. L. Wang, D. J. Albers, A. M. Stuart; A Simple Modeling Framework For Prediction In The Human Glucose-Insulin System, Chaos, Vol. 33, Issue 7, July 2023.
[Online Publication] [pdf]
[188] B. Liu, E. Ocegueda, M. Trautner, A. M. Stuart, K. Bhattacharya; Learning Macroscopic Internal Variables and History Dependence From Microscopic Models, J. Mech. Phys. Solids, Vol. 178 (2023) 105329
[Online Publication] [pdf]
[187] K. Bhattacharya, B. Liu, A. Stuart, M. Trautner; Learning Markovian Homogenized Models in Viscoelasticity, Society for Industrial and Applied Mathematics, (2023) Vol. 21, No. 2, 641-679.
[Online Publication] [pdf]
[186] M. V. de Hoop, N. B. Kovachki, N. H. Nelsen, and A. M. Stuart; Convergence Rates for Learning Linear Operators from Noisy Data, SIAM/ASA Journal on Uncertainty Quantification, (2023) Vol. 11, No. 2, 480-513.
[Online Publication] [pdf]
[185] N. Kovachki, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, A. Anandkumar; Neural Operator: Learning Maps Between Function Spaces, Journal of Machine Learning Research 24, (2023) 1-97.
[Online Publication] [pdf]
2022
[184] M. de Hoop, D. Z. Huang, E. Qian, and A.M. Stuart; The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks, Journal of Machine Learning (2022) 1:3, 299-341.
[Online Publication] [pdf]
[183] D. Z. Huang, J. Huang,
S. Reich, A. M. Stuart; Efficient Derivative-free Bayesian Inference
for Large-scale Inverse Problems, (2022) Inverse Problems 38 125006
[Online Publication]
[pdf]
[182] M. E. Levine, A. M. Stuart; A Framework for Machine Learning of Model Error in Dynamical Systems, Comm. Amer. Math. Soc. 2 (2022), 283-344.
[Online Publication] [pdf]
[181] O. R. A. Dunbar, M. F. Howland, T. Schneider, A. M. Stuart; Ensemble-Based Experimental Design for Targeting Data Acquisition to Inform Climate Models, Journal of Advances in Modeling Earth Systems 10.1029/2022MS002997
[Online Publication] [pdf]
[180] T. Schneider, A. M. Stuart, J.-L. Wu; Ensemble Kalman Inversion for Sparse Learning of Dynamical Systems from Time-averaged Data, Journal of Computational Physics 470 (2022) 111559.
[Online Publication]
[pdf]
[179] D. Z. Huang, T. Schneider, A. M.Stuart; Iterated Kalman Methodology for Inverse Problems, Journal of Computational Physics 463 (2022) 111262.
[Online Publication] [pdf]
[178] O. R. A. Dunbar, A. B. Duncan, A. M. Stuart, and Marie-Therese Wolfram; Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods, SIAM J. Applied Dynamical Systems, Vol. 21, No. 2, pp. 1539-1572.
[Online Publication] [pdf]
[177] J. A. Carrillo, F. Hoffmann, A. M. Stuart, U. Vaes; Consensus-based Sampling, Stud Appl Math. 2022;148:1069–1140.
[Online Publication] [pdf]
[176] N. Kovachki, B. Liu, X. Sun, H. Zhou, K. Bhattacharya, M. Ortiz, A. Stuart; Multiscale Modeling of Materials: Computing, Data Science, Uncertainty and Goal-oriented Optimization, Mechanics of Materials 165 (2022) 104156.
[Online Publication]
[pdf]
[175] B. Liu, N. Kovachki, Z. Li, K. Azizzadenesheli, A. Anandkumar, A. M. Stuart, K. Bhattacharya; A Learning-based Multiscale Method and its Application to Inelastic
Impact Problems, J. Mech. Phys. Solids 158 (2022) 104668.
[Online Publication] [pdf]
[174] F. Hoffmann, B. Hosseini, A. A. Oberai, A. M. Stuart; Spectral Analysis of Weighted Laplacians Arising in Data Clustering, Applied and Computational Harmonic Analysis
Volume 56, January 2022, Pages 189-249.
[Online Publication] [pdf]
[173] G. A. Pavliotis, A. M. Stuart, U. Vaes; Derivative-Free Bayesian Inversion Using Multiscale Dynamics, SIAM J. Applied Dynamical Systems, Vol. 21, No. 1, pp. 284-326.
[Oline Publication] [pdf]
2021
[172] A. Abdulle, G. Garegnani, G. A. Pavliotis, A. M. Stuart, A. Zanoni; Drift Estimation of Multiscale Diffusions Based on Filtered Data, Foundations of Computational Mathematics, October 2021.
[Online Publication]
[pdf]
[171] T. Schneider, A. M. Stuart, J.-L. Wu; Learning Stochastic Closures Using Ensemble Kalman Inversion, Transactions of Mathematics and Its Applications, Volume 5, Issue 1, January 2021.
[Online Publication] [pdf]
[170] N. H. Nelsen, A. M. Stuart; The Random Feature Model for Input-Output Maps between Banach Spaces, SIAM J. Sci. Comput., 43(5), A3212–A3243.
[Online Publication] [pdf]
[169] A. L. Bertozzi, B. Hosseini, H. Li, K. Miller, A. M. Stuart, Posterior consistency of semi-supervised regression on graphs, Inverse Problems 37 (10 2021), pp 105011.
[Online Publication] [pdf]
[168] Y. Chen, H. Owhadi, A. M. Stuart; Consistency of Empirical Bayes and Kernel Flow for Hierarchial Parameter Estimation, Mathematics of Computation,
Volume 90, Number 332, November 2021, Pages 2527–2578.
[Online Publication] [pdf]
[167] Y. Chen, B. Hosseini, H. Owhadi, A. M. Stuart; Solving and Learning Nonlinear PDEs with Gaussian Processes, Journal of Computational Physics 447 (2021) 110668.
[Online Publication] [pdf]
[166] O. R. A. Dunbar, A. Garbuno-Inigo, T. Schneider, A. M. Stuart; Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM, Journal of Advances in Modeling Earth Systems, Volume13, Issue 9, September 2021.
[Online Publication] [pdf]
[165] K. Bhattacharya; B. Hosseini; N. B. Kovachki; A. M. Stuart; Model Reduction And Neural Networks For Parametric PDEs, SMAI journal of computational mathematics, Volume 7 (2021), pp. 121-157.
[Online Publication]
[pdf]
[164] D. Burov, D. Giannakis, K. Manohar, A. Stuart; Kernel Analog Forecasting: Multiscale Test Problems, Multiscale Modeling & Simulation, 19(2), 1011–1040, 2021.
[Online Publication]
[pdf]
[163] N. B. Kovachki, A. M. Stuart; Continuous Time Analysis of Momentum Methods, JMLR 22(17):1−40, 2021.
[Online Publication] [pdf]
[162] E. Cleary, A. Garbuno-Inigo, S. Lan, T. Schneider, A. M. Stuart; Calibrate, emulate, sample, Journal of Computational Physics,
Volume 424, 1 January 2021, 109716.
[Online Publication]
[pdf]
2020
[161] O.R.A. Dunbar, M. M. Dunlop, C. M. Elliott, V. H. Hoang, A. M. Stuart; Reconciling Bayesian and Perimeter Regularization for Binary Inversion, SIAM J. Sci. Comput. Vol. 42, No. 4, pp. A1984−A2013.
[Online Publication] [pdf]
[160] F. Hoffmann, B. Hosseini, Z. Ren, A. M. Stuart; Consistency of Semi-Supervised Learning Algorithms on Graphs: Probit and One-Hot Methods, Journal of Machine Learning Research, 21(186):1−55, 2020.
[Online Publication] [pdf]
[159] A. Garbuno-Inigo, F. Hoffmann, W. Li, and A. M. Stuart; Interacting Langevin Diffusions:
Gradient Structure And Ensemble Kalman Sampler, SIAM J. Appl. Dyn. Syst. 19-1 (2020), pp. 412-441.
[Online Publication] [pdf]
[158] M. M. Dunlop, D. Slepcev, A. M. Stuart, M. Thorpe; Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms, Applied & Computational Harmonic Analysis, 49-2 (2020), pp. 655-697.
[Online Publication] [pdf]
[157] K. Newton, Q. Li, and A. M. Stuart; Diffusive Optical Tomography in the Bayesian Framework, Multiscale Model. Simul. 18-2 (2020), pp. 589-611.
[Online Publicaton] [pdf]
[156] M. M. Dunlop, T. Helin, A. M. Stuart; Hyperparameter Estimation in Bayesian MAP Estimation: Parame- terizations and Consistency. SMAI J. of Computational Mathematics. 6 (2020), 69–100.
[Online Publicaton] [pdf]
[155] E. Seylabi, A. Stuart, D. Asimaki; Site Characterization at Downhole Arrays by Joint Inversion of Dispersion Data and Acceleration Time Series. Bulletin of the Seismological Society of America. 110 (2020), 1323–1337.
[Online Publication] [pdf]
[154] N. K. Chada, A. M. Stuart, X. T. Tong; Tikhonov Regularization Within Ensemble Kalman Inversion. SIAM J. Numer. Anal., 58(2), 1263–1294.
[Online Publication] [pdf]
[153] A. M. Stuart and M.-T. Wolfram; Inverse Optimal Transport. SIAM J. Appl. Math. 80-1 (2020), pp. 599-619.
[Online Publication] [pdf]
2019
[152] H. C. Lie, A. M. Stuart, and T. J. Sullivan; Strong Convergence Rates of Probabilistic Integrators for Ordinary Differential Equations. Statistics and Computing, Vol. 29, Issue 6, (2019) 1265–1283.
[Online Publication] [pdf]
[151] M. Ottobre, A. M. Stuart, and J. Kuntz; Diffusion Limit for the Random Walk Metropolis Algorithm Out of Stationarity. Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Vol. 55, No. 3, (2019) 1599–1648.
[Online Publication] [pdf]
[150] D. Kelly, and A. M. Stuart; Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation. Chin. Ann. Math. Ser. B, 40(5), (2019) 811–842.
[Online Publication]
[pdf]
[149] D. J. Albers, P. Blancquart, M. E. Levine, E. E. Seylabi, and A. M. Stuart;
Ensemble Kalman Methods With Constraints. Inverse Problems, Vol. 35, Number 9, (2019).
[Online Publication] [pdf]
[148] N. B. Kovachki, and A. M. Stuart;
Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks. Inverse Problems, Vol. 35, Number 9, (2019).
[Online Publication] [pdf]
[147] S. N. Gomes, A. M. Stuart, and M.-T. Wolfram;
Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data. SIAM J. APPL. MATH. Vol. 79, No. 4, (2019) 1475-1500.
[Online Publication] [pdf]
[146] Y. Qiao, C. Shi, C. Wang, H. Li, M. Haberland, X. Luo, A. M. Stuart, and A. L. Bertozzi; Uncertainty Quantification for Semi-supervised Multi-class Classification in Image Processing and Ego-Motion Analysis of Body-Worn Videos. Electronic Imaging, Image Processing: Algorithms and Systems XVII, (2019) 264-1-264-7(7).
[Online Publication] [pdf]
2018
[145] C. Schillings and A. M. Stuart; Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy Case. Applicable Analysis 97(2018), 107-123.
[Online Publication] [pdf]
[144] M. M. Dunlop, M. A. Girolami, A. M. Stuart, and A. L. Teckentrup; How Deep Are Deep Gaussian Processes? Journal of Machine Learning Research 19(54):1−46, 2018.
[Online Publication] [pdf]
[143] A. L. Bertozzi, X. Luo, A. M. Stuart, and K. C. Zygalakis; Uncertainty Quantification in the Classification of High Dimensional Data. SIAM-ASA JUQ, 6(2) (2018) 568-595.
[Online Publication] [pdf]
[142] N. K. Chada, M. A. Iglesias, L. Roininen, and A. M. Stuart; Parameterizations for Ensemble Kalman Inversion. Inverse Problems, 34 (2018) 055009.
[Online Publication] [pdf]
[141] J. Kuntz, M. Ottobre, and A. M. Stuart; Non-stationary Phase of the MALA Algorithm. Stochastic PDE: Anal. Comp. (2018).
[Online Publication] [pdf]
[140] D. Calvetti, M. M. Dunlop, E. Somersalo, and A. M. Stuart; Iterative Updating of Model Error for Bayesian Inversion. Inverse Problems, 34 (2018) 025008.
[Online Publication] [pdf]
[139] A. M. Stuart and A. L. Teckentrup; Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions. Mathematics of Computation, 87(310) (2018) 721-753.
[Online Publication] [pdf]
[138] C.-E. Brehier, M. Hairer and A. M. Stuart; Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin discretization. Journal of Computational Mathematics, 36(2) (2018) 159-182.
[Online Publication] [pdf]
2017
[137] Y. Lu, A. Stuart, and H. Weber; Gaussian Approximations For Transition Paths In Brownian Dynamics. SIAM J. Math. Anal. 49(4) (2017) 3005-3047.
[Online Publication] [pdf]
[136] Y. Lu, A. M. Stuart, and H. Weber; Gaussian Approximations for Probability Measures on Rd. SIAM/ASA J. Uncertainty Quantification 5 (2017) 1136-1165.
[Online Publication] [pdf]
[135] T. Schneider, S. Lan, A. Stuart, and J. Teixeira; Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations. Geophysical Research Letters 44 (2017).
[Online Publication] [pdf]
[134] D. Sanz-Alonso, and A. M. Stuart; Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence. Communications in Mathematical Sciences 15(7) (2017), 2087-2097.
[Online Publication] [pdf]
[133] M. A. Iglesias, K. Lin, S. Lu, A. M. Stuart; Filter Based Methods for Statistical Linear Inverse Problems. Communications in Math. Sciences 15(7) (2017), 1867-1896.
[Online Publication] [pdf]
[132] S. Agapiou, O. Papaspiliopoulos, D. Sanz-Alonso, and A. M. Stuart; Importance Sampling: Computational Complexity and Intrinsic Dimension. Statistical Science 32(3) (2017), 405-431.
[Online Publication] [pdf]
[131] C. Schillings and A. M. Stuart; Analysis of the Ensemble Kalman Filter for Inverse Problems. SIAM J Numerical Analysis 55(3) (2017), 1264-1290.
[Online publication] [pdf]
[130] A. Beskos, M. Girolami, S. Lan, P. E. Farrell and A. M. Stuart; Geometric MCMC for Infinite-Dimensional Inverse Problems. Journal of Computational Physics 335 (2017), 327-351.
[Online Publication] [pdf]
[129] R. Scheichl, A. M. Stuart and A. L. Teckentrup; Quasi-Monte Carlo and Multi-level Monte Carlo for Computing Posterior Expectations in Elliptic Inverse Problems. JUQ 5(1) (2017), 493-518.
[Online Publication] [pdf]
[128] W. Lee and A. M. Stuart; Derivation and Analysis of Simplified Filters for Complex Dynamical Systems. Communications in Mathematical Sciences 15(2) (2017), 413-450.
[Online Publication] [pdf]
2016
[127] M. Iglesias, Y. Lu and A. M. Stuart; A Bayesian Level Set Method for Geometric Inverse Problems. Interfaces and Free Boundaries 18 (2016), 181-217.
[Online Publication] [pdf]
[126] M. M. Dunlop and A. M. Stuart; The Bayesian Formulation of EIT: Analysis and Algorithms. Inverse Problems and Imaging 10(4)(2016) 1007-1036.
[Online Publication] [pdf]
[125] M. M. Dunlop, M. A. Iglesias and A. M. Stuart; Hierarchical Bayesian Level Set Inversion. Statistics and Computing (2016).
[Online Publication] [pdf]
[124] M. M. Dunlop and A. M. Stuart; MAP Estimators for Piecewise Continuous Inversion. Inverse Problems 32(10) (2016) 105003.
[Online Publication] [pdf]
[123] P. R. Conrad, M. Girolami, S. Sarkka, A. M. Stuart, and K. C. Zygalakis; Statistical Analysis of Differential Equations: Introducing Probability Measures on Numerical Solutions. Statistics and Computing (2016).
[Online Publication] [pdf]
[122] K. J. H. Law, D. Sanz-Alonso, A. Shukla and A. M. Stuart; Filter Accuracy for the Lorenz 96 model: Fixed Versus Adaptive Observation Operators. Physica D: Nonlinear Phenomena 325 (2016) 1-13.
[Online Publication] [pdf]
[121] M. Ottobre, N. S. Pillai, F. J. Pinski and A. M. Stuart; A function Space HMC Algorithm with Second Order Langevin Diffusion Limit. Bernoulli 22/1(2016) 60-106.
[Online Publication] [pdf]
2015
[120] F. J. Pinski, G. Simpson, A. M. Stuart and H. Weber; Algorithms for Kullback-Leibler Approximation for Probability Measures in Infinite Dimensions. SIAM J. Sci. Comp. 37(6) (2015) A2733–A2757.
[Online Publication] [pdf]
[119] D. Sanz-Alonso and A. M. Stuart; Long-Time Asymptotics of the Filtering Distribution for Partially Observed Chaotic Dynamical Systems. SIAM/ASA J. Uncertainty Quantification, 3(1) (2015) 1200-1220.
[Online Publication] [pdf]
[118] F. J. Pinski, G. Simpson, A. M. Stuart and H. Weber; Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces. SIAM J. Mathematical Analysis 47(2015) 4091-4122.
[Online Publication] [pdf]
[117] A. Beskos, A. Jasra, E. A. Muzaffer and A. M. Stuart; Sequential Monte Carlo Methods for Bayesian Elliptic Inverse Problems. Stat. Comp. 25/4 (2015) 727-737.
[Online Publication] [pdf]
[116] A. B. Duncan, C. M. Elliot, G. A. Pavliotis, A. M. Stuart; A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces. J. Nonlinear Science 25/2 (2015)389-449.
[Online Publication] [pdf]
2014
[115] M. A. Iglesias, K. Lin, A. M. Stuart, Well-posed Bayesian Geometric Inverse Problems Arising in Subsurface Flow. Inverse Problems, 30 (2014) 114001.
[Online Publication] [pdf]
[114] S. Agapiou, J. M. Bardsley, O. Papaspiliopoulos and A. M. Stuart; Analysis of the Gibbs Sampler for Hierarchical Inverse Problems. SIAM JUQ, 2 (2014) 514-544.
[Online Publication] [pdf]
[113] D. T. B. Kelly, K. J. H. Law, and A. M. Stuart; Well-posedness and Accuracy of the Ensemble Kalman Filter In Discrete and Continuous Time. Nonlinearity, 27 (2014) 2579-2603.
[Online Publication] [pdf]
[112] M. Hairer, A. M. Stuart and S. J. Vollmer; Spectral Gaps for a Metropolis–Hastings Algorithm in Infinite Dimensions. The Annals of Applied Probability, 24/6(2014), 2455-2490
[Online Publication] [pdf]
[111] N. S. Pillai, A. M. Stuart and A. H. Thiery; Noisy Gradient Flow From a Random Walk in Hilbert Space. Stochastic PDEs: Analysis and Computation, 2(2014), 196-232.
[Online Publication] [pdf]
[110] V. H Hoang, K. J. H. Law and A. M. Stuart, Determining White Noise Forcing From Eulerian Observations in the Navier-Stokes Equation. Stochastic PDEs: Analysis and Computation, 2(2014), 233-261.
[Online Publication] [pdf]
[109] S. Agapiou, A. M. Stuart and Y-X. Zhang; Bayesian Posterior Contraction Rates for Linear Severely Ill-posed Inverse Problems. Journal of Inverse and Ill-Posed Problems, 22(2014), 297-321.
[Online Publication] [pdf]
[108] K. J. H. Law, A. Shukla and A. M. Stuart; Analysis of the 3DVAR Filter for the Partially Observed Lorenz '63 Model. Discrete and Continuous Dynamical Systems A, 34(2014), 1061-1078.
[Online Publication] [pdf]
2013
[107] D. Bloemker, K. J. H. Law, A. M. Stuart and K. Zygalalkis; Accuracy and Stability of the Continuous-time 3DVAR Filter for the Navier-Stokes Equation. Nonlinearity 26(2013), 2193--2219.
[Online Publication] [pdf]
[106] A. Beskos, N. Pillai, G. Roberts, J.-M. Sanz-Serna, and A. M. Stuart; Optimal Tuning of the Hybrid Monte Carlo Algorithm. Bernoulli 19(2013), 1501-1534.
[Online Publication] [pdf]
[105] M. A. Iglesias, K. J. H. Law and A. M. Stuart; Evaluation of Gaussian Approximations for Data Assimilation in Reservoir Models. Computational Geosciences. 17(2013), 851-885.
[Online Publication] [pdf]
[104] M. Dashti, K. J. H. Law, A. M. Stuart and J. Voss; MAP Estimators and Posterior Consistency in Bayesian Nonparametric Inverse Problems. Inverse Problems, 29(2013) 095017.
[Online Publication] [pdf]
[103] S. L. Cotter, G. O. Roberts, A. M. Stuart and D. White; MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster. Statistical Science, 28 (2013) 424-446).
[Online Publication] [pdf]
[102] V. H. Hoang, C. Schwab and A. M. Stuart; Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion. Inverse Problems, 29/8 (2013) 085010
[Online Publication] [pdf]
[101] S. Agapiou, S. Larsson and A. M. Stuart; Posterior Consistency of the Bayesian Approach to Linear Ill-posed Inverse Problems. Stochastic Processes and Applications, 123/10 (2013) 3828-3860.
[Online Publication] [pdf]
[100] Y. Pokern, A. M. Stuart and J. H. Van Zanten; Posterior Consistency via Precision Operators for Nonparametric Drift Estimation in SDEs. Stochastic Processes and Their Applications, 123/2 (2013) 603-628.
[Online Publication] [pdf]
[99] M. A. Iglesias, K. J. H. Law and A. M. Stuart; Ensemble Kalman Methods for Inverse Problems. Inverse Problems, 29(2013) 045001.
[Online Publication] [pdf]
[98] C. E. A. Brett, K. F. Lam, K. J. H. Law, D. S. McCormick, M. R. Scott, A. M. Stuart, Accuracy and Stability of Filters for Dissipative PDEs. Physica D 245(2013) 34-45
[Online Publication] [pdf]
2012
[97] N. S. Pillai, A. M. Stuart and A. H. Thiery; Optimal Scaling and Ddiffusion Limits for the Langevin Algorithm in High Dimensions. Annals of Applied Probability 22 (2012) 2320-2356.
[Online Publication] [pdf]
[96] K. J. H. Law and A. M. Stuart; Evaluating Data Assimilation Algorithms. Monthly Weather Review 140(2012), 3757-3782.
[Online Publication] [pdf]
[95] O. Papaspiliopoulos, Y. Pokern, G. O. Roberts and A. M. Stuart; Nonparametric Estimation of Diffusions: A Differential Equations Approach. Biometrika 2012.
[Online Publication] [pdf]
[94] M. Dashti, S. Harris and A. M. Stuart; Besov Priors for Bayesian Inverse Problems. Inverse Problems and Imaging 6 (2012) 183-200.
[Online Publication] [pdf]
[93] J. C. Mattingly, N. Pillai and A. M. Stuart; Diffusion Limits of the Random Walk Metropolis Algorithm in High Dimensions. Annals of Applied Probability 22 (2012) 881-930.
[Online Publication] [pdf]
[92] C. Schwab and A. M. Stuart; Sparse Determinisitc Approximation of Bayesian Inverse Problems. Inverse Problems 28 (2012) 045003.
[Online Publication] [pdf]
[91] F. Pinski, A. M. Stuart and F. Theil; Gamma Limit for Transition Paths of Maximal Probability. Journal of Statistical Physics 146/5 (2012) 955-974.
[Online Publication] [pdf]
[90] S. L. Cotter, M. Dashti and A. M. Stuart; Variational Data Assimilation Using Targetted Random Walks. International Journal of Numerical Methods in Fluids 68(4) (2012) 403-421
[Online Publication] [pdf]
2011
[89] M. Dashti and A. M. Stuart; Uncertainty quantification and weak approximation of an elliptic inverse problem. SIAM Journal of Numerical Analysis 49(2011), 2524--2542.
[Online Publication] [pdf]
[88] W. Lee, D. McDougall and A. M. Stuart; Kalman filtering and smoothing for linear wave equations with model error. Inverse Problems 27 (2011) 095008.
[Online Publication] [pdf]
[87] A. Beskos, F. J. Pinski, J.-M. Sanz-Serna and A. M. Stuart; Hybrid Monte-Carlo on Hilbert Spaces. Stochastic Processes and their Applications 121 (2011) 2201-2230.
[Online Publication] [pdf]
[86] M. Hairer, A. M. Stuart and J. Voss; Sampling Conditioned Hypoelliptic Diffusions. Annals of Applied Probability 21 (2011) 669-698.
[Online Publication] [pdf]
[85] I. Melbourne and A. M. Stuart; A Note on Diffusion Limits of Chaotic Skew Product Flows. Nonlinearity 24 (2011) 1361-1367.
[Online Publication] [pdf] [Correction] [Corrected Version]
2010
[84] P. Fearnhead, O. Papaspiliopoulos, G. O. Roberts and A. M. Stuart; Random-weight Particle Filtering of Continuous Time Stochastic Processes. Journal of the Royal Statistical Society B 72(4) (2010) 497-512.
[Online Publication] [pdf]
[83] J. C. Mattingly, A. M. Stuart and M. Tretyakov; Convergence of Numerical Time-averaging and Stationary Measures via the Poisson Equation. SIAM Journal of Numerical Analysis 48(2) (2010) 552-577.
[Online Publication] [pdf]
[82] F. J. Pinski and A. M. Stuart; Transition Paths in Molecules: Gradient Descent in Pathspace. Journal of Chemical Physics 132 (2010), 184104.
[Online Publication] [pdf]
[81] S. L. Cotter, M. Dashti and A. M. Stuart; Approximation of Bayesian Inverse Problems. SIAM Journal of Numerical Analysis 48 (2010) 322-345.
[Online Publication] [pdf]
2009
[80] S. L. Cotter, M. Dashti, J. C. Robinson and A. M. Stuart; Bayesian Inverse Problems for Functions and Applications to Fluid Mechanics. Inverse Problems 25 (2009) 115008. doi: 10.1088/0266-5611/25/11/115008.
[Online Publication] [pdf]
[79] Y. Pokern, A. M. Stuart and E. Vanden Eijnden; Remarks on Drift Estimation for Diffusion Processes. SIAM Multiscale Modelling and Simulation 8 (2009) 69-95. doi:10.1137/070694806.
[Online Publication] [pdf]
[78] A. Beskos, G. O. Roberts and A. M. Stuart; Optimal scalings of Metropolis-Hastings algorithms for non-product targets in high dimensions. Annals of Applied Probability 19 (2009) 863-898.
[Online Publication] [pdf]
[77] A. Papavasiliou, G. Pavliotis and A. M. Stuart; Maximum likelihood estimation for multiscale diffusions. Stochastic Processes and their Applications 19 (2009) 3173-3210.
[Online Publication] [pdf]
[76] Y. Pokern, A. M. Stuart and P. Wiberg; Parameter Estimation for Partially Observed Hypo-elliptic Diffusions. Journal of the Royal Statistical Society B 71 (2009) 49-73.
[Online Publication] [pdf]
[75] G. Pavliotis, A. M. Stuart and K. Zygalakis; Calculating effective diffusivities in the limit of vanishing molecular diffusion. Journal of Computational Physics 228 (2009) 1030-1055.
[Online Publication] [pdf]
2008
[74] A. Beskos, G. Roberts, A. M. Stuart and J. Voss; An MCMC method for diffusion bridges. Stochastics and Dynamics 8 (2008) 319-350.
[Online Publication] [pdf]
[73] A. Apte, C.K.R.T. Jones, A. M. Stuart and J. Voss; Data Assimilation: Mathematical and Statistical Perspectives. International Journal of Numerical Methods in Fluids 56 (2008) 1033-1046.
[Online Publication] [pdf]
[72] A. Apte, C.K.R.T. Jones and A. M. Stuart; A Bayesian Approach to Lagrangian Data Assimilation. Tellus A 60 (2008) 336-347.
[Online Publication] [pdf]
2007
[71] G. Pavliotis, A. M. Stuart and K. Zygalakis; Homogenization for Inertial Particles in a Random Flow. Communications in Mathematical Sciences 5 (2007) 507-531.
[Online Publication] [pdf]
[70] M. Hairer, A. M. Stuart and J. Voss; Analysis of SPDEs arising in path sampling part II: the nonlinear case. Annals of Applied Probability 17(5-6) (Oct 2007) 1657-1706.
[Online Publication] [pdf]
[69] G. Pavliotis and A. M. Stuart; Parameter estimation for multiscale diffusions. Journal of Statistical Physics 127 (2007) 741-781.
[Online Publication] [pdf]
[68] A. Apte, M. Hairer, A. M. Stuart and J. Voss; A Bayesian Approach to Data Assimilation. Physica D Nonlinear Phenomena 230 (2007) 50-64.
[Online Publication] [pdf]
[67] H. Lamba, J. C. Mattingly and A. M. Stuart; An Adaptive Euler-Maruyama Scheme for SDEs: Convergence and Stability. IMA Journal of Numerical Analysis 27 (2007) 479-506.
[Online Publication] [pdf]
2006
[66] D. Barkley, I. G. Kevrekidis and A. M. Stuart; The moment map: nonlinear dynamics of density evolution via a few moments. SIAM Journal of Applied Dynamical Systems 5 (2006) 403-434.
[Online Publication] [pdf]
2005
[65] M. Hairer, A. M. Stuart, J. Voss and P. Wiberg; Analysis of SPDEs arising in path sampling part I: the Gaussian case. Communications in Mathematical Sciences 3(4) (2005) 587-603.
[Online Publication] [pdf]
[64] G. A. Pavliotis and A. M. Stuart; Periodic Homogenization for Inertial Particles. Physica D Nonlinear Phenomena 204 (2005) 161-187.
[Online Publication] [pdf]
[63] G. Pavliotis and A. M. Stuart; Analysis of White Noise Limits for Stochastic Systems With Two Fast Relaxation Times. SIAM Multiscale Modelling and Simulation 4 (2005) 1-35.
[Online Publication] [pdf]
2004
[62] R. Kupferman and A. M. Stuart; Fitting SDE Models to Nonlinear Kac-Zwanzig Heat Bath Models. Physica D Nonlinear Phenomena 199 (2004) 279-316.
[Online Publication] [pdf]
[61] A. M. Stuart, P. Wiberg and J. Voss; Conditional Path Sampling of SDEs and the Langevin MCMC Method. Communications in Mathematical Sciences 2(4) (Dec 2004) 685-697.
[Online Publication] [pdf]
[60] R. Kupferman, G. Pavliotis and A. M. Stuart; Ito versus Stratonovich white noise limits for systems with inertia and colored multiplicative noise. Physical Review E 70 (2004) 036120.
[Online Publication] [pdf]
[59] D. Givon, R. Kupferman, and A. M. Stuart, Extracting Macroscopic Dynamics: Model Problems and Algorithms. Nonlinearity 17 (2004) 55-127.
[Online Publication] [pdf]
2003
[58] D. J. Higham, X. Mao and A. M. Stuart; Mean Square Stability of Numerical Solutions to Stochastic Differential Equations. LMS Journal of Computational Mathematics 6 (2003) 297-313.
[Online Publication] [pdf]
[57] G. Pavliotis and A. M. Stuart; White Noise Limits for Inertial Particles in a Random Field. SIAM Multiscale Modelling and Simulation 1 (2003) 527-553.
[Online Publication] [pdf]
[56] W. Husinga, C. Schutte and A. M. Stuart; Extracting Macroscopic Stochastic Models from Dynamics. Communications in Pure and Applied Mathematics LVI (2003) 234-269.
[Online Publication] [pdf]
2002
[55] H. Sigurgeirsson and A. M. Stuart; A Model for Preferential Concentration. Physics of Fluids 14 (2002) 4352-4361.
[Online Publication] [pdf]
[54] H. Sigurgeirsson and A. M. Stuart; Inertial Particles in a Random Field. Stochastics and Dynamics 2 (2002) 295-310.
[Online Publication] [pdf]
[53] R. Kupferman, A. M. Stuart, J. Terry and P. Tupper; Long Time Behaviour of Large Mechanical Systems with Random Initial Data. Stochastics and Dynamics 2 (2002) 533-562.
[Online Publication] [pdf]
[52] J. Mattingly and A. M. Stuart; Geometric Ergodicity of Some Hypo-elliptic Diffusions for Particle Motions. Markov Processes and Related Fields 8 (2002) 199-214.
[Online Publication] [pdf]
[51] D. J. Higham, X. Mao and A. M. Stuart; Strong Convergence of Euler Type Methods for Nonlinear Stochastic Differential Equations. SIAM Journal of Numerical Analysis 40(3) (Aug 2002) 1041-1063. 10.1137/S0036142901389530
[Online Publication] [pdf]
[50] J. Mattingly, A. M. Stuart and D. J. Higham; Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Stochastic Processes and their Applications 101(2) (Oct 2002) 185-232. 10.1016/S0304-4149(02)00150-3
[Online Publication] [pdf]
[49] D. J. Estep and A. M. Stuart; The Dynamical Behaviour of the Discontinuous Galerkin Method and Related Difference Schemes. Mathematics of Computation 71 (2002) 1075-1103.
[Online Publication] [pdf]
2001
[48] H. Sigurgeirsson, A. M. Stuart and J. Wan; Algorithms for Particle-Field Simulations with Collisions. J. Comp. Phys. 172 (2001),766-807.
[Online Publication] [pdf]
[47] B. Cano and A. M. Stuart, Under-resolved Simulations of Heat Baths. J. Comp. Phys. 169 (2001) 193-214.
[Online Publication] [pdf]
[46] B. Cano, E. Suli, A. M. Stuart and J. Warren; Stiff Oscillatory Systems, Delta Jumps and White Noise. Found. Comp. Math. 1 (2001) 69-100.
[Online Publication] [pdf]
2000
[45] T. Shardlow and A. M. Stuart; A perturbation theory for ergodic Markov chains with application to numerical approximation. SIAM J. Num. Anal. 37 (2000) 1120-1137.
[Online Publication] [pdf]
1999
[44] A. M. Stuart and J. Warren; Analysis and Experiments for a Computational Model of a Heat Bath. J. Stat. Phys. 97 (1999) 687-723.
[Online Publication] [pdf]
[43] O. Gonzalez, D. J. Higham and A. M. Stuart; Qualitative Properties of Modified Equations. IMA J. Num. Anal. 19 (1999) 169-190.
[Online Publication] [pdf]
[42] J. M. Sanz-Serna and A. M. Stuart; Ergodic Properties of Dissipative Differential Equations Subject to Random Impulses. J. Diff. Eq., 155 (1999) 262-284.
[Online Publication] [pdf]
1998
[41] H. Lamba and A. M. Stuart; Convergence Results for the MATLAB ode23 Routine. BIT 38 (1998), 751-780.
[Online Publication] [pdf]
[40] D. A. Jones, A. M. Stuart and E. S. Titi; Persistence of Invariant Sets for Dissipative Evolution Equations. J. Math. Anal. and Applic. 219 (1998), 479-502.
[Online Publication] [pdf]
[39] M. Gander and A. M. Stuart; Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation. SIAM J. Sci. Comp. 19 (1998), 2014-2031.
[Online Publication] [pdf]
[38] C. J. Budd, G. P. Koomullil and A. M. Stuart; On the solution of convection-diffusion boundary-value problems by grid adaptation. SIAM J. Sci. Stat. Comp. 20 (1998), 591-618.
[Online Publication] [pdf]
[37] D. J. Higham and A. M. Stuart; Analysis of the Dynamics of Error Control via a Piecewise Continuous Residual. BIT 38 (1998), 44-57.
[Online Publication] [pdf]
1997
[36] A. M. Stuart; Probabilistic and Deterministic Convergence Proofs for Software for Initial Value Problems. Numerical Algorithms 14 (1997) 227-260.
[Online Publication] [pdf]
[35] M. Bjorhus and A. M. Stuart; Waveform Relaxation as a Dynamical System. Math. Comp. 66 (1997) 1101-1117.
[Online Publication] [pdf]
1996
[34] C. M. Elliott and A. M. Stuart; The Viscous Cahn-Hilliard Equation. Part II: Analysis. J. Diff. Equations. 128 (1996) 387-414.
[Online Publication] [pdf]
1995
[33] D. A. Jones and A. M. Stuart; Attractive Invariant Manifolds Under Approximation. Part I: Inertial Manifolds. J. Diff. Eq. 123 (1995) 588-637.
[Online Publication] [pdf]
[32] A. M. Stuart and A. R. Humphries; The Essential Stability of Local Error Control for Dissipative and Gradient Dynamical Systems. SIAM J. Num. Anal. 32 (1995) 1940-1971.
[Online Publication] [pdf]
[31] G. J. Lord and A. M. Stuart; Discrete Gevrey Regularity Attractors and
Uppers–semicontinuity for a Finite Difference
Approximation to the Ginzburg–landau Equation. Num. Func. Anal. Appl. 16 (1995) 1003-1047.
[Online Publication] [pdf]
[30] D. J. Estep and A. M. Stuart; The Rate of Error Growth in Hamiltonian Conserving Integrators. ZAMP 46 (1995) 407-418.
[Online Publication] [pdf]
[29] F. Bai, C. M. Elliott, A. Gardiner, A. Spence, and A. M. Stuart; The Viscous Cahn- Hilliard Equation. Part I: Computations. Nonlinearity 8 (1995) 131-160.
[Online Publication] [pdf]
1994
[28] F. Bai, A. Spence, and A. M. Stuart; Numerical Computations of Coarsening in the Cahn-Hilliard model of phase separation. Physica D. 78 (1994), 155-165.
[Online Publication] [pdf]
[27] A. M. Stuart and A. R. Humphries; Model Problems in Numerical Stability for Initial Value Problems. SIAM Review 36 (1994), 226-257.
[Online Publication] [pdf]
[26] A. R. Humphries and A. M. Stuart; Runge-Kutta Methods for Dissipative and Gradient Dynamical Systems. SIAM J. Num. Anal. 31 (1994), 1452-1485.
[Online Publication] [pdf]
[25] C. J. Budd, J. W. Dold and A. M. Stuart; The Study of Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part II: Non-zero convection. SIAM J. Appl. Math. 54 (1994) 610-640.
[Online Publication] [pdf]
1993
[24] F. Bai, A. Spence, and A. M. Stuart; The Numerical Computation of Heteroclinic Connections in Systems of Gradient Partial Differential Equations. SIAM J. Appl. Math. 35 (1993) 743-769.
[Online Publication] [pdf]
[23] C. J. Budd, J. W. Dold and A. M. Stuart; The Study of Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part I: Zero convection. SIAM J. Appl. Math. 53 (1993) 718-742.
[Online Publication] [pdf]
[22] C. M. Elliott and A. M. Stuart; The Global Dynamics of Discrete Semilinear Parabolic Equations. SIAM J. Num. Anal. 30 (1993) 1622-1663.
[Online Publication] [pdf]
[21] M. A. J. Chaplain and A. M. Stuart; A Model Mechanism for the Chemotactic Response of Endothelial Cells to Tumour Angiogenesis Factor. IMA J. Math. Appl. Med. Biol. 10 (1993), 149-168.
[Online Publication] [pdf]
1992
[20] J. M. Sanz-Serna and A. M. Stuart; A Note on Uniform in Time Error Estimates for Reaction-diffusion Equations. IMA J. Num. Anal. 12 (1992) 457-462.
[Online Publication] [pdf]
[19] D. F. Griffiths, A. M. Stuart and H. C. Yee; Numerical Wave Propagation in Hyperbolic Equations with Source Terms. SIAM J. Num. Anal. 29 (1992) 1244-1260.
[Online Publication] [pdf]
[18] A. Iserles and A. M. Stuart; A Unified Approach to Spurious Solutions Introduced by Timediscretisation. Part II. BDF-like methods. IMA J. Num. Anal. 12 (1992) 487-502.
[Online Publication] [pdf]
1991
[17] M. A. J. Chaplain and A. M. Stuart; A Mathematical Model for the Diffusion of Tumour Angiogenesis Factor into the Surrounding Host Tissue. IMA J. Math. Appl. Med. Biol. 8 (1991) 191-220.
[Online Publication] [pdf]
[16] A. Iserles, A. T. Peplow and A. M. Stuart; A Unified Approach to Spurious Solutions Introduced by Time-discretisation. Part I Basic Theory. SIAM J. Num. Anal. 28 (1991) 1723-1751.
[Online Publication] [pdf]
[15] A. M. Stuart and A. T. Peplow; The Dynamics of the Theta Method. SIAM J. Sci. Stat. Comp. 12 (1991) 1351-1372.
[Online Publication] [pdf]
[14] A. M. Stuart; Singular Limits In Free Boundary Problems. Rocky Mountain J. Math. 21 (1991) 809-811.
[Online Publication] [pdf]
1990
[13] A. M. Stuart and M. S. Floater; On the Computation of Blow-up. Euro. J. Appl. Math. 1 (1990) 47-71.
[Online Publication] [pdf]
1989
[12] A. M. Stuart; Linear Instability Implies Spurious Periodic Solutions. IMA J. Num. Anal. 9 (1989)465-486.
[Online Publication] [pdf]
[11] J. Norbury and A. M. Stuart; A Model For Porous Medium Combustion. Quart. J. Mech. Appl. Math. 42 (1989)159-178.
[Online Publication] [pdf]
[10] A. M. Stuart; A Note On High/Low Wave Number Interactions In Spatially Discrete Parabolic Equations. IMA J. Appl. Math. 42 (1989) 27-42.
[Online Publication] [pdf]
[9] A. M. Stuart; Nonlinear Instability In Dissipative Finite Difference Schemes. SIAM Review 31 (1989) 191-220.
[Online Publication] [pdf]
[8] A. M. Stuart; Singular Free Boundary Problems And Local Bifurcation Theory. SIAM J. Appl. Math. 49 (1989) 72-85.
[Online Publication] [pdf]
1988
[7] A. M. Stuart; Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity. IMA J. Appl. Math. 40 (1988) 217-234.
[Online Publication] [pdf]
[6] J. Norbury and A. M. Stuart; Parabolic Free Boundary Problems Arising in Porous Medium Combustion. IMA J. Appl. Math. 39 (1988) 241-257.
[Online Publication] [pdf]
[5] J. Norbury and A. M. Stuart; Travelling Combustion Waves in a Porous Medium. Part II — Stability. SIAM J. Appl. Math. 48 (1988) 374-392.
[Online Publication] [pdf]
[4] J. Norbury and A. M. Stuart; Travelling Combustion Waves in a Porous Medium. Part I — Existence. SIAM J. Appl. Math. 48 (1988) 155-169.
[Online Publication] [pdf]
1987
[3] A. M. Stuart; Existence of Solutions of a Two-Point Free Boundary Problem Arising in the Theory of Porous Medium Combustion. IMA J. Appl. Math. 38 (1987) 23-34.
[Online Publication] [pdf]
[2] J. Norbury and A. M. Stuart; Volterra Integral Equations and a New Gronwall Inequality. Part II: The Nonlinear Case. Proc. Roy. Soc. Edin. 106A (1987) 375-384.
[Online Publication] [pdf]
[1] J. Norbury and A. M. Stuart; Volterra Integral Equations and a New Gronwall Inequality. Part I: The Linear Case. Proc. Roy. Soc. Edin. 106A (1987) 361-373.
[Online Publication] [pdf]
