Andrew M. Stuart

Orcid: 0000-0001-9091-7266

Affiliations:
  • California Institute of Technology, Pasadena, CA, USA
  • University of Warwick, Department of Mathematics, Coventry, UK (former)


According to our database1, Andrew M. Stuart authored at least 108 papers between 1989 and 2025.

Collaborative distances:

Timeline

Legend:

Book 
In proceedings 
Article 
PhD thesis 
Dataset
Other 

Links

Online presence:

On csauthors.net:

Bibliography

2025
Error analysis of kernel/GP methods for nonlinear and parametric PDEs.
J. Comput. Phys., 2025

2024
Operator Learning Using Random Features: A Tool for Scientific Computing.
SIAM Rev., 2024

The Mean-Field Ensemble Kalman Filter: Near-Gaussian Setting.
SIAM J. Numer. Anal., 2024

Learning Homogenization for Elliptic Operators.
SIAM J. Numer. Anal., 2024

Learning about structural errors in models of complex dynamical systems.
J. Comput. Phys., 2024

Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting.
CoRR, 2024

Autoencoders in Function Space.
CoRR, 2024

Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flows.
CoRR, 2024

Continuum Attention for Neural Operators.
CoRR, 2024

Efficient Prior Calibration From Indirect Data.
CoRR, 2024

Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation.
CoRR, 2024

Discretization Error of Fourier Neural Operators.
CoRR, 2024

Operator Learning: Algorithms and Analysis.
CoRR, 2024

2023
Learning Markovian Homogenized Models in Viscoelasticity.
Multiscale Model. Simul., June, 2023

Convergence Rates for Learning Linear Operators from Noisy Data.
SIAM/ASA J. Uncertain. Quantification, June, 2023

Drift Estimation of Multiscale Diffusions Based on Filtered Data.
Found. Comput. Math., February, 2023

Neural Operator: Learning Maps Between Function Spaces With Applications to PDEs.
J. Mach. Learn. Res., 2023

Modeling groundwater levels in California's Central Valley by hierarchical Gaussian process and neural network regression.
CoRR, 2023

Sampling via Gradient Flows in the Space of Probability Measures.
CoRR, 2023

The curse of dimensionality in operator learning.
CoRR, 2023

The Nonlocal Neural Operator: Universal Approximation.
CoRR, 2023

Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance.
CoRR, 2023

Introduction To Gaussian Process Regression In Bayesian Inverse Problems, With New ResultsOn Experimental Design For Weighted Error Measures.
CoRR, 2023

2022

Derivative-Free Bayesian Inversion Using Multiscale Dynamics.
SIAM J. Appl. Dyn. Syst., 2022

Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods.
SIAM J. Appl. Dyn. Syst., 2022

Ensemble Kalman inversion for sparse learning of dynamical systems from time-averaged data.
J. Comput. Phys., 2022

Iterated Kalman methodology for inverse problems.
J. Comput. Phys., 2022

Ensemble Kalman Methods: A Mean Field Perspective.
CoRR, 2022

Second Order Ensemble Langevin Method for Sampling and Inverse Problems.
CoRR, 2022

Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems.
CoRR, 2022

The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks.
CoRR, 2022

Learning Chaotic Dynamics in Dissipative Systems.
Proceedings of the Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, 2022

2021
The Random Feature Model for Input-Output Maps between Banach Spaces.
SIAM J. Sci. Comput., 2021

Consistency of empirical Bayes and kernel flow for hierarchical parameter estimation.
Math. Comput., 2021

Continuous Time Analysis of Momentum Methods.
J. Mach. Learn. Res., 2021

Calibrate, emulate, sample.
J. Comput. Phys., 2021

Solving and learning nonlinear PDEs with Gaussian processes.
J. Comput. Phys., 2021

Neural Operator: Learning Maps Between Function Spaces.
CoRR, 2021

A Framework for Machine Learning of Model Error in Dynamical Systems.
CoRR, 2021

Markov Neural Operators for Learning Chaotic Systems.
CoRR, 2021

Consensus Based Sampling.
CoRR, 2021

Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods.
CoRR, 2021

Unscented Kalman Inversion.
CoRR, 2021

Fourier Neural Operator for Parametric Partial Differential Equations.
Proceedings of the 9th International Conference on Learning Representations, 2021

2020
Reconciling Bayesian and Perimeter Regularization for Binary Inversion.
SIAM J. Sci. Comput., 2020

Tikhonov Regularization within Ensemble Kalman Inversion.
SIAM J. Numer. Anal., 2020

Inverse Optimal Transport.
SIAM J. Appl. Math., 2020

Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler.
SIAM J. Appl. Dyn. Syst., 2020

Diffusive Optical Tomography in the Bayesian Framework.
Multiscale Model. Simul., 2020

Consistency of Semi-Supervised Learning Algorithms on Graphs: Probit and One-Hot Methods.
J. Mach. Learn. Res., 2020

Posterior Consistency of Semi-Supervised Regression on Graphs.
CoRR, 2020

Model Reduction and Neural Networks for Parametric PDEs.
CoRR, 2020

Neural Operator: Graph Kernel Network for Partial Differential Equations.
CoRR, 2020

Multipole Graph Neural Operator for Parametric Partial Differential Equations.
Proceedings of the Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, 2020

Lessons learned from assimilating knowledge into machine learning to forecast and control glucose in a critical care setting.
Proceedings of the AMIA 2020, 2020

2019
Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data.
SIAM J. Appl. Math., 2019

Strong convergence rates of probabilistic integrators for ordinary differential equations.
Stat. Comput., 2019

Analysis Of Momentum Methods.
CoRR, 2019

Uncertainty quantification for semi-supervised multi-class classification in image processing and ego-motion analysis of body-worn videos.
Proceedings of the Image Processing: Algorithms and Systems XVII, 2019

2018
Posterior consistency for Gaussian process approximations of Bayesian posterior distributions.
Math. Comput., 2018

Uncertainty Quantification in Graph-Based Classification of High Dimensional Data.
SIAM/ASA J. Uncertain. Quantification, 2018

How Deep Are Deep Gaussian Processes?
J. Mach. Learn. Res., 2018

Mechanistic machine learning: how data assimilation leverages physiologic knowledge using Bayesian inference to forecast the future, infer the present, and phenotype.
J. Am. Medical Informatics Assoc., 2018

Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks.
CoRR, 2018

Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms.
CoRR, 2018

Using mechanistic machine learning to forecast glucose and infer physiologic phenotypes in the ICU: what is possible and what are the challenges.
Proceedings of the AMIA 2018, 2018

2017
Analysis of the Ensemble Kalman Filter for Inverse Problems.
SIAM J. Numer. Anal., 2017

Gaussian Approximations for Transition Paths in Brownian Dynamics.
SIAM J. Math. Anal., 2017

Hierarchical Bayesian level set inversion.
Stat. Comput., 2017

Statistical analysis of differential equations: introducing probability measures on numerical solutions.
Stat. Comput., 2017

Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems.
SIAM/ASA J. Uncertain. Quantification, 2017

Gaussian Approximations for Probability Measures on R<sup>d</sup>.
SIAM/ASA J. Uncertain. Quantification, 2017

Geometric MCMC for infinite-dimensional inverse problems.
J. Comput. Phys., 2017

Uncertainty Quantification in the Classification of High Dimensional Data.
CoRR, 2017

Why predicting postprandial glucose using self-monitoring data is difficult.
Proceedings of the AMIA 2017, 2017

2016
Using data assimilation to forecast post-meal glucose for patients with type 2 diabetes.
Proceedings of the AMIA 2016, 2016

2015
Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions.
SIAM J. Sci. Comput., 2015

Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces.
SIAM J. Math. Anal., 2015

Sequential Monte Carlo methods for Bayesian elliptic inverse problems.
Stat. Comput., 2015

Long-Time Asymptotics of the Filtering Distribution for Partially Observed Chaotic Dynamical Systems.
SIAM/ASA J. Uncertain. Quantification, 2015

A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces.
J. Nonlinear Sci., 2015

2014
Analysis of the Gibbs Sampler for Hierarchical Inverse Problems.
SIAM/ASA J. Uncertain. Quantification, 2014

2011
Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem.
SIAM J. Numer. Anal., 2011

Evaluating Data Assimilation Algorithms
CoRR, 2011

2010
Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations.
SIAM J. Numer. Anal., 2010

Approximation of Bayesian Inverse Problems for PDEs.
SIAM J. Numer. Anal., 2010

Inverse problems: A Bayesian perspective.
Acta Numer., 2010

2009
Remarks on Drift Estimation for Diffusion Processes.
Multiscale Model. Simul., 2009

Calculating effective diffusivities in the limit of vanishing molecular diffusion.
J. Comput. Phys., 2009

2006
The Moment Map: Nonlinear Dynamics of Density Evolution via a Few Moments.
SIAM J. Appl. Dyn. Syst., 2006

2005
Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation Times.
Multiscale Model. Simul., 2005

2003
White Noise Limits for Inertial Particles in a Random Field.
Multiscale Model. Simul., 2003

Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations.
LMS J. Comput. Math., 2003

2002
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations.
SIAM J. Numer. Anal., 2002

The dynamical behavior of the discontinuous Galerkin method and related difference schemes.
Math. Comput., 2002

2001
Stiff Oscillatory Systems, Delta Jumps and White Noise.
Found. Comput. Math., 2001

2000
A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations.
SIAM J. Numer. Anal., 2000

1998
Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation.
SIAM J. Sci. Comput., 1998

On the Solution of Convection-Diffusion Boundary Value Problems Using Equidistributed Grids.
SIAM J. Sci. Comput., 1998

1997
Probabilistic and deterministic convergence proofs for software for initial value problems.
Numer. Algorithms, 1997

Waveform relaxation as a dynamical system.
Math. Comput., 1997

1994
Model Problems in Numerical Stability Theory for Initial Value Problems.
SIAM Rev., 1994

Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part II: Problems with Convection.
SIAM J. Appl. Math., 1994

1993
Blowup in a Partial Differential Equation with Conserved First Integral.
SIAM J. Appl. Math., 1993

The Numerical Computation of Heteroclinic Connections in Systems of Gradient Partial Differential Equations.
SIAM J. Appl. Math., 1993

1991
The Dynamics of the Theta Method.
SIAM J. Sci. Comput., 1991

1989
Nonlinear Instability in Dissipative Finite Difference Schemes.
SIAM Rev., 1989


  Loading...