Data Assimilation: A Mathematical Introduction

Abstract

These notes provide a systematic mathematical treatment of the subject of data assimilation.

References in corpus (13)

• Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems
• Can local particle filters beat the curse of dimensionality?
• Sharp failure rates for the bootstrap particle filter in high dimensions
• MAP Estimators and Their Consistency in Bayesian Nonparametric Inverse Problems
• Evaluating Data Assimilation Algorithms
• On the Convergence of the Ensemble Kalman Filter
• Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time
• Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations
• Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters
• A Gaussian mixture ensemble transform filter
• Accuracy and Stability of Filters for Dissipative PDEs
• Interpolation and Iteration for Nonlinear Filters
• Stochastic Analysis Seminar on Filtering Theory

Cited by in corpus (46)

• Calibrate, Emulate, Sample
• Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks
• Multilevel ensemble Kalman filtering
• Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation
• Ensemble Kalman Methods With Constraints
• State estimation in turbulent channel flow from limited observations
• Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion
• A stochastic version of Stein Variational Gradient Descent for efficient sampling
• Controlling Unpredictability with Observations in the Partially Observed Lorenz '96 Model
• A comparison of nonlinear extensions to the ensemble Kalman filter: Gaussian Anamorphosis and Two-Step Ensemble Filters
• Model and Data Reduction for Data Assimilation: Particle Filters Employing Projected Forecasts and Data with Application to a Shallow Water Model
• Convergence Analysis of a Viscosity Parameter Recovery Algorithm for the 2D Navier-Stokes Equations
• Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation
• On the Mathematical Theory of Ensemble (Linear-Gaussian) Kalman-Bucy Filtering
• On the continuous time limit of the Ensemble Kalman Filter
• A coherent structure approach for parameter estimation in Lagrangian Data Assimilation
• Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion
• Low-rank statistical finite elements for scalable model-data synthesis
• State and Parameter Estimation from Observed Signal Increments
• Uniform in time error estimates for fully discrete numerical schemes of a data assimilation algorithm
• Combining Dynamic Mode Decomposition with Ensemble Kalman Filtering for Tracking and Forecasting
• Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building walls
• Inference via low-dimensional couplings
• Quantum mechanics and data assimilation
• An Explicit Probabilistic Derivation of Inflation in a Scalar Ensemble Kalman Filter for Finite Step, Finite Ensemble Convergence
• Multilevel ensemble Kalman filtering for spatially extended models
• Randomised one-step time integration methods for deterministic operator differential equations
• The Role of Network Analysis in Industrial and Applied Mathematics
• Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
• On the Incorporation of Box-Constraints for Ensemble Kalman Inversion
• Bayesian Approach to Inverse Time-harmonic Acoustic Scattering from Sound-soft Obstacles with Phaseless Data
• A Metric Tensor Approach to Data Assimilation with Adaptive Moving Meshes
• A Stochastic Covariance Shrinkage Approach to Particle Rejuvenation in the Ensemble Transform Particle Filter
• Minimax state estimates for abstract Neumann problems
• An adaptive multi-fidelity PC-based ensemble Kalman inversion for inverse problems
• Continuous Data Assimilation for the Double-Diffusive Natural Convection
• Experimental Study of Nonlinear Resonances and Anti-resonances in a Forced, Ordered Granular Chain
• State-space deep Gaussian processes with applications
• Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy Case
• A non-intrusive reduced basis EKI for time-fractional diffusion inverse problems
• Feedback Particle Filter With Stochastically Perturbed Innovation And Its Application to Dual Estimation
• Spatial localization for nonlinear dynamical stochastic models for excitable media
• Derivation and Analysis of Simplified Filters for Complex Dynamical Systems
• The convergence of stochastic differential equations to their linearisation in small noise limits
• From limited observations to the state of turbulence: Fundamental difficulties of flow reconstruction
• On the asymptotical regularization for linear inverse problems in presence of white noise