Low-rank statistical finite elements for scalable model-data synthesis

DOI10.1016/j.jcp.2022.111261OpenAlexW3200707909WikidataQ114163291 ScholiaQ114163291MaRDI QIDQ2671375

Edward Cripps, Connor Duffin, Thomas Stemler, Mark A. Girolami

Publication date: 3 June 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.04757

zbMATH Keywords

finite element methodsreaction-diffusionBayesian inverse problemsBayesian filtering

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Stochastic systems and control (93Exx)

Related Items (1)

Statistical Finite Elements via Langevin Dynamics

Uses Software

• EnKF
• FEniCS
• SyFi
• Python
• PMTK
• KeOps
• statFEM

Cites Work

• Hilbert space methods for reduced-rank Gaussian process regression
• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• On the condition number anomaly of Gaussian correlation matrices
• Automated solution of differential equations by the finite element method. The FEniCS book
• Catastrophic filter divergence in filtering nonlinear dissipative systems
• Tidal flow forecasting using reduced rank square root filters
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Hidden physics models: machine learning of nonlinear partial differential equations
• The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Inverse problems: A Bayesian perspective
• Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems
• Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance Matrix
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Statistical finite elements for misspecified models
• Stochastic Equations in Infinite Dimensions
• Learning data-driven discretizations for partial differential equations
• Data Assimilation
• The ensemble Kalman filter for combined state and parameter estimation
• Galerkin Finite Element Methods for Parabolic Problems
• A Reduced-Order Kalman Filter for Data Assimilation in Physical Oceanography
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