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Andrew M. Stuart

  1. Fourier Neural Operator for Parametric Partial Differential Equations
    2020/10/18 by Zongyi Li, Nikola Kovachki, Li, Zongyi +12 · 2 voices · 442 citations
    Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #cs.LG #math.NA
  2. Neural Operator: Graph Kernel Network for Partial Differential Equations
    2020/03/07 by Zongyi Li, Li, Zongyi, Nikola Kovachki +11 · 95 citations
    Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning in Healthcare #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical Analysis (math.NA)
  3. Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
    2002/01/01 by Desmond J. Higham, Xuerong Mao, Andrew M. Stuart · 38 citations
    Economics, Econometrics and Finance · Mathematics · Engineering · #Stochastic processes and financial applications #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics
  4. Multipole Graph Neural Operator for Parametric Partial Differential Equations
    2020/06/16 by Zongyi Li, Li, Zongyi, Nikola Kovachki +11 · 39 citations
    Physics and Astronomy · Engineering · Computer Science · #Model Reduction and Neural Networks #Electromagnetic Simulation and Numerical Methods #Computational Physics and Python Applications
  5. Solving and Learning Nonlinear PDEs with Gaussian Processes
    2021/03/24 by Yifan Chen, Chen, Yifan, Bamdad Hosseini +5 · 19 citations
    Computer Science · Decision Sciences · Physics and Astronomy · #34B15 #35R30 #41A15 #47B34 #60G15 #65M75 #65N35 #65N75 #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
  6. 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)
  7. Data Assimilation: A Mathematical Introduction
    2015/06/25 by Kody J. H. Law, Andrew M. Stuart, Law, K. J. H. +3 · 11 citations
    Earth and Planetary Sciences · Environmental Science · #Atmospheric and Environmental Gas Dynamics #Climate variability and models #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Meteorological Phenomena and Simulations #Methodology (stat.ME) #Optimization and Control (math.OC)
  8. 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
  9. 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)
  10. Learning Dissipative Dynamics in Chaotic Systems
    2021/06/13 by Zongyi Li, Li, Zongyi, Miguel Liu-Schiaffini +13 · 6 citations
    Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Model Reduction and Neural Networks
  11. Nonlocality and Nonlinearity Implies Universality in Operator Learning
    2023/04/26 by Samuel Lanthaler, Lanthaler, Samuel, Zongyi Li +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)
  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. Consensus‐based sampling
    2022/01/05 by José A. Carrillo, J. A. Carrillo, F. Hoffmann +5 · 4 citations
    Mathematics · Computer Science · #Markov Chains and Monte Carlo Methods #Bayesian Methods and Mixture Models #Gaussian Processes and Bayesian Inference
  14. An Adaptive Euler-Maruyama Scheme For SDEs: Convergence and Stability
    2006/01/02 by Harbir Lamba, Lamba, H., Jonathan C. Mattingly +3 · 2 citations
    Economics, Econometrics and Finance · Physics and Astronomy · #Stochastic processes and financial applications #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis
  15. Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs
    2023/05/08 by Pau Batlle, Yifan Chen, Batlle, Pau +7 · 5 citations
    Physics and Astronomy · Mathematics · Computer Science · #Model Reduction and Neural Networks #Statistical Methods and Inference #Gaussian Processes and Bayesian Inference
  16. The Mean Field Ensemble Kalman Filter: Near-Gaussian Setting
    2022/12/26 by José A. Carrillo, Franca Hoffmann, Carrillo, J. A. +9 · 4 citations
    Computer Science · Earth and Planetary Sciences · Environmental Science · #62F15 #65C35 #70F45 #93E11 #Dynamical Systems (math.DS) #FOS: Mathematics #Geology and Paleoclimatology Research #Geophysics and Gravity Measurements #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Soil Geostatistics and Mapping #Target Tracking and Data Fusion in Sensor Networks
  17. Sequential Monte Carlo Methods for Bayesian Elliptic Inverse Problems
    2014/12/15 by Alex Beskos, Beskos, Alex, Ajay Jasra +5 · 2 citations
    Decision Sciences · Earth and Planetary Sciences · Environmental Science · #Computation (stat.CO) #FOS: Computer and information sciences #Groundwater flow and contamination studies #Probabilistic and Robust Engineering Design #Seismic Imaging and Inversion Techniques
  18. 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
  19. 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
  20. 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)
  21. Contextual computation by competitive protein dimerization networks
    2025/02/19 by Jacob Parres-Gold, Matthew E. Levine, Benjamin Emert +2 · 1 voice · 4 citations
    Biochemistry, Genetics and Molecular Biology · Chemistry · #Bioinformatics and Genomic Networks #Gene Regulatory Network Analysis #Advanced Proteomics Techniques and Applications
  22. Hard Constraint Guided Flow Matching for Gradient-Free Generation of PDE Solutions
    2024/12/02 by Chaoran Cheng, Boran Han, Cheng, Chaoran +11 · 6 citations
    Engineering · #Advanced Control Systems Optimization #FOS: Computer and information sciences #Iterative Learning Control Systems #Machine Learning (cs.LG) #Reservoir Engineering and Simulation Methods
  23. Sampling via Gradient Flows in the Space of Probability Measures
    2023/10/05 by Yifan Chen, Chen, Yifan, Daniel Zhengyu Huang +6 · 3 citations
    Computer Science · Physics and Astronomy · #Adversarial Robustness in Machine Learning #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Statistical Mechanics and Entropy
  24. Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning\n Algorithms
    2018/05/23 by Matthew M. Dunlop, Dunlop, Matthew M., Dejan Slepčev +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
  25. 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)
  26. 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
  27. 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
  28. 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
  29. Learning About Structural Errors in Models of Complex Dynamical Systems
    2023/12/29 by Jinlong Wu, Matthew E. Levine, Wu, Jin-Long +5 · 3 citations
    Earth and Planetary Sciences · Environmental Science · #68T01 #Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Hydrology and Watershed Management Studies #Machine Learning (cs.LG) #Meteorological Phenomena and Simulations
  30. Second Order Ensemble Langevin Method for Sampling and Inverse Problems
    2022/08/09 by Ziming Liu, Liu, Ziming, Andrew M. Stuart +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)
  31. Approximation of Bayesian Inverse Problems for PDEs
    2009/09/11 by Simon L. Cotter, Cotter, S. L., Masoumeh Dashti +3 · 1 citation
    Computer Science · Engineering · Mathematics · #65C05 #65P99 #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Numerical Analysis (math.NA) #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Statistical and numerical algorithms
  32. 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
  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. 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)
  35. Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation
    2020/05/22 by Yifan Chen, Houman Owhadi, Chen, Yifan +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)
  36. Hyperparameter Estimation in Bayesian MAP Estimation: Parameterizations\n and Consistency
    2019/05/10 by Matthew M. Dunlop, Dunlop, Matthew M., Tapio Helin +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)
  37. Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods
    2021/04/07 by Oliver R. A. Dunbar, Dunbar, Oliver R. A., A. Duncan +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
  38. DreamBlend: Advancing Personalized Fine-tuning of Text-to-Image Diffusion Models
    2024/11/28 by Sabita Ram, Ram, Shwetha, Tal Neiman +9 · 2 citations
    Computer Science · Biochemistry, Genetics and Molecular Biology · Engineering · #Image Retrieval and Classification Techniques #Biomedical Text Mining and Ontologies #3D Modeling in Geospatial Applications
  39. 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
  40. Learning Optimal Filters Using Variational Inference
    2024/06/26 by Eviatar Bach, Ricardo Baptista, Bach, Eviatar +5 · 1 citation
    Computer Science · Engineering · #Neural Networks and Applications #Speech and Audio Processing #Advanced Algorithms and Applications
  41. Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulation
    2024/05/21 by Yifan Chen, Bamdad Hosseini, Chen, Yifan +5 · 1 citation
    Environmental Science · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Probability (math.PR) #Soil Geostatistics and Mapping
  42. Learning Enhanced Ensemble Filters
    2025/04/24 by Eviatar Bach, Ricardo Baptista, Bach, Eviatar +7 · 2 citations
    Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering