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Stuart, Andrew M.

  1. Model Reduction and Neural Networks for Parametric PDEs
    2020/05/07 by Bhattacharya, Kaushik, Hosseini, Bamdad, Kovachki, Nikola B. +1 · 32 citations
    #60H15 #60H30 #62M45 #65N75 #68T05 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
  2. The Bayesian Approach To Inverse Problems
    2013/02/27 by Dashti, Masoumeh, Stuart, Andrew M. · 18 citations
    #FOS: Mathematics #Probability (math.PR)
  3. Operator Learning: Algorithms and Analysis
    2024/02/24 by Nikola Kovachki, Kovachki, Nikola B., Samuel Lanthaler +3 · 24 citations
    Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Neural Networks and Applications #Numerical Analysis (math.NA)
  4. Optimal tuning of the Hybrid Monte-Carlo Algorithm
    2010/01/25 by Alexandros Beskos, Natesh S. Pillai, Beskos, Alexandros +7 · 8 citations
    Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics #Stochastic processes and statistical mechanics
  5. Analysis of the ensemble Kalman filter for inverse problems
    2016/02/05 by Schillings, Claudia, Stuart, Andrew M. · 8 citations
    #FOS: Mathematics #Numerical Analysis (math.NA)
  6. Inverse optimal transport
    2019/05/10 by Stuart, Andrew M., Wolfram, Marie-Therese · 7 citations
    #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Optimization and Control (math.OC)
  7. The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks
    2022/03/24 by de Hoop, Maarten V., Huang, Daniel Zhengyu, Qian, Elizabeth +1 · 9 citations
    #FOS: Mathematics #Numerical Analysis (math.NA)
  8. Inverse Problems and Data Assimilation
    2018/10/15 by Daniel Sanz-Alonso, Andrew M. Stuart, Sanz-Alonso, Daniel +3 · 6 citations
    Computer Science · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME)
  9. Nonlocality and Nonlinearity Implies Universality in Operator Learning
    2023/04/26 by Samuel Lanthaler, Zongyi Li, Lanthaler, Samuel +3 · 7 citations
    Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical Analysis (math.NA)
  10. Uncertainty quantification and weak approximation of an elliptic inverse problem
    2011/02/01 by Dashti, Masoumeh, Stuart, Andrew M. · 3 citations
    #FOS: Mathematics #Statistics Theory (math.ST)
  11. Tikhonov Regularization Within Ensemble Kalman Inversion
    2019/01/29 by Chada, Neil K., Stuart, Andrew M., Tong, Xin T. · 4 citations
    #35Q93 #58E25 #65F22 #65M32 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
  12. Iterated Kalman Methodology For Inverse Problems
    2021/02/02 by Daniel Zhengyu Huang, Tapio Schneider, Huang, Daniel Zhengyu +3 · 5 citations
    Mathematics · Physics and Astronomy · #Statistical and numerical algorithms #Scientific Research and Discoveries
  13. The Parametric Complexity of Operator Learning
    2023/06/28 by Lanthaler, Samuel, Stuart, Andrew M. · 6 citations
    #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
  14. Discretization Error of Fourier Neural Operators
    2024/05/03 by Lanthaler, Samuel, Stuart, Andrew M., Trautner, Margaret · 7 citations
    #41A35 (Primary) 65T50 #68T07 (Secondary) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
  15. A Bayesian Level Set Method for Geometric Inverse Problems
    2015/03/31 by Iglesias, Marco A., Lu, Yulong, Stuart, Andrew M. · 2 citations
    #FOS: Computer and information sciences #Methodology (stat.ME)
  16. Gaussian approximations for transition paths in Brownian dynamics
    2016/04/22 by Yulong Lu, Andrew M. Stuart, Lu, Yulong +3 · 2 citations
    Computer Science · Mathematics · Physics and Astronomy · #28C20 #60F10 #60G15 #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Probability (math.PR) #Statistical Mechanics and Entropy #Statistical Methods and Inference
  17. Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems
    2022/04/09 by Huang, Daniel Zhengyu, Huang, Jiaoyang, Reich, Sebastian +1 · 3 citations
    #FOS: Mathematics #Numerical Analysis (math.NA)
  18. How Deep Are Deep Gaussian Processes?
    2017/11/30 by Matthew M. Dunlop, Mark Girolami, Dunlop, Matthew M. +5 · 2 citations
    Computer Science · #Gaussian Processes and Bayesian Inference
  19. Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance
    2023/02/21 by Yifan Chen, Chen, Yifan, Daniel Zhengyu Huang +6 · 3 citations
    Computer Science · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Machine Learning (stat.ML) #Machine Learning and Data Classification #Numerical Analysis (math.NA)
  20. Memorization and Regularization in Generative Diffusion Models
    2025/01/27 by Baptista, Ricardo, Dasgupta, Agnimitra, Kovachki, Nikola B. +2 · 6 citations
    #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC)
  21. Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning\n Algorithms
    2018/05/23 by Matthew M. Dunlop, Dejan Slepčev, Dunlop, Matthew M. +5 · 2 citations
    Decision Sciences · Engineering · Mathematics · #49J55 #62C10 #62F15 #62G20 #Advanced Bandit Algorithms Research #Advanced Optimization Algorithms Research #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques
  22. Learning Homogenization for Elliptic Operators
    2023/06/21 by Kaushik Bhattacharya, Bhattacharya, Kaushik, Nikola Kovachki +7 · 3 citations
    Computer Science · Engineering · #35B27 #35J47 #74H15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
  23. Learning Markovian Homogenized Models in Viscoelasticity
    2022/05/27 by Kaushik Bhattacharya, Burigede Liu, Bhattacharya, Kaushik +5 · 3 citations
    Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Model Reduction and Neural Networks
  24. A Framework for Machine Learning of Model Error in Dynamical Systems
    2021/07/14 by Matthew E. Levine, Levine, Matthew E., Andrew M. Stuart +1 · 2 citations
    Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications
  25. Drift Estimation of Multiscale Diffusions Based on Filtered Data
    2020/09/28 by Abdulle, Assyr, Garegnani, Giacomo, Pavliotis, Grigorios A. +2 · 2 citations
    #FOS: Mathematics #Numerical Analysis (math.NA)
  26. Learning Stochastic Closures Using Ensemble Kalman Inversion
    2020/04/17 by Tapio Schneider, Schneider, Tapio, Andrew M. Stuart +3 · 2 citations
    Computer Science · #Computation (stat.CO) #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Target Tracking and Data Fusion in Sensor Networks
  27. Second Order Ensemble Langevin Method for Sampling and Inverse Problems
    2022/08/09 by Ziming Liu, Andrew M. Stuart, Liu, Ziming +3 · 2 citations
    Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Numerical Analysis (math.NA)
  28. Ensemble Kalman Methods: A Mean Field Perspective
    2022/09/23 by Calvello, Edoardo, Reich, Sebastian, Stuart, Andrew M. · 2 citations
    #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
  29. Evaluation of Gaussian approximations for data assimilation in reservoir models
    2012/12/08 by Marco Iglesias, Kody J. H. Law, Iglesias, Marco A. +3 · 2 citations
    Engineering · Environmental Science · #Applications (stat.AP) #Atmospheric and Environmental Gas Dynamics #FOS: Computer and information sciences #Groundwater flow and contamination studies #Reservoir Engineering and Simulation Methods
  30. Complexity Analysis of Accelerated MCMC Methods for Bayesian Inversion
    2012/07/10 by Hoang, Viet Ha, Schwab, Christoph, Stuart, Andrew M. · 1 citation
    #FOS: Mathematics #Numerical Analysis (math.NA) #Statistics Theory (math.ST)
  31. Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions
    2014/08/08 by Pinski, Frank J., Simpson, Gideon, Stuart, Andrew M. +1 · 1 citation
    #34A55 #60G15 #62G05 #65C05 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)
  32. The Bayesian Formulation of EIT: Analysis and Algorithms
    2015/08/17 by Dunlop, Matthew M., Stuart, Andrew M. · 1 citation
    #62G05 #65N21 #92C55 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)
  33. Autoencoders in Function Space
    2024/08/02 by Justin Bunker, Mark Girolami, Bunker, Justin +7 · 3 citations
    Computer Science · #Neural Networks and Applications
  34. Hierarchical Bayesian Level Set Inversion
    2016/01/14 by Dunlop, Matthew M., Iglesias, Marco A., Stuart, Andrew M. · 1 citation
    #35R30 #62G05 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR)
  35. Gaussian Approximations for Probability Measures on Rd
    2016/11/26 by Yulong Lu, Lu, Yulong, Andrew M. Stuart +3 · 1 citation
    Computer Science · Mathematics · #60B10 #60H07 #62F15 #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Probability (math.PR)
  36. Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation
    2020/05/22 by Yifan Chen, Chen, Yifan, Houman Owhadi +3 · 2 citations
    Computer Science · #65F12 62C10 41A05 35Q62 #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Machine Learning and Algorithms #Numerical Analysis (math.NA) #Statistics Theory (math.ST)
  37. Dimension-Robust MCMC in Bayesian Inverse Problems
    2018/03/09 by Chen, Victor, Dunlop, Matthew M., Papaspiliopoulos, Omiros +1 · 1 citation
    #35R30 #62G05 #62G35 #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME)
  38. Parameter estimation for macroscopic pedestrian dynamics models from microscopic data
    2018/09/21 by Gomes, Susana N., Stuart, Andrew M., Wolfram, Marie-Therese · 1 citation
    #Analysis of PDEs (math.AP) #FOS: Mathematics
  39. Hyperparameter Estimation in Bayesian MAP Estimation: Parameterizations\n and Consistency
    2019/05/10 by Matthew M. Dunlop, Tapio Helin, Dunlop, Matthew M. +3 · 1 citation
    Computer Science · Mathematics · #45Q05 #62C10 #62G05 #62G20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Numerical Analysis (math.NA) #Statistical Methods and Inference #Statistics Theory (math.ST)
  40. Efficient Prior Calibration From Indirect Data
    2024/05/28 by Akyildiz, O. Deniz, Girolami, Mark, Stuart, Andrew M. +1 · 3 citations
    #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  41. Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
    2019/09/13 by Hoffmann, Franca, Hosseini, Bamdad, Oberai, Assad A. +1 · 1 citation
    #05C50 #35B20 #47A75 #62H30 #68T10 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Spectral Theory (math.SP)
  42. Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flows
    2024/06/25 by Chen, Yifan, Huang, Daniel Zhengyu, Huang, Jiaoyang +2 · 2 citations
    #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
  43. Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods
    2021/04/07 by Oliver R. A. Dunbar, A. Duncan, Dunbar, Oliver R. A. +5 · 1 citation
    Computer Science · Environmental Science · #60J22 #65C05 #65C40 #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Soil Geostatistics and Mapping #Target Tracking and Data Fusion in Sensor Networks
  44. Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization
    2016/02/12 by Bréhier, Charles-Edouard, Hairer, Martin, Stuart, Andrew M. · 1 citation
    #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)
  45. Continuum Attention for Neural Operators
    2024/06/10 by Calvello, Edoardo, Kovachki, Nikola B., Levine, Matthew E. +1 · 2 citations
    #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
  46. Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting
    2024/09/15 by Calvello, Edoardo, Monmarché, Pierre, Stuart, Andrew M. +1 · 2 citations
    #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Statistics Theory (math.ST)
  47. Interacting Langevin Diffusions: Gradient Structure And Ensemble Kalman\n Sampler
    2019/03/21 by Alfredo Garbuno-Iñigo, Franca Hoffmann, Garbuno-Inigo, Alfredo +5 · 1 citation
    Computer Science · Decision Sciences · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Probabilistic and Robust Engineering Design
  48. Efficient Deconvolution in Populational Inverse Problems
    2025/05/26 by Vadeboncoeur, Arnaud, Girolami, Mark, Stuart, Andrew M. · 3 citations
    #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  49. Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
    2025/01/28 by Baptista, Ricardo, Calvello, Edoardo, Darcy, Matthieu +3 · 2 citations
    #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)