Data Assimilation: The Schrödinger Perspective

Abstract

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger's boundary value problem for stochastic processes in particular.

References in corpus (4)

• Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems
• Particle Filters and Data Assimilation
• Convergence of the Square Root Ensemble Kalman Filter in the Large Ensemble Limit
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Cited by in corpus (11)

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• McKean-Vlasov SDEs in nonlinear filtering
• State and Parameter Estimation from Observed Signal Increments
• An Optimal Control Derivation of Nonlinear Smoothing Equations
• Filtering Dynamical Systems Using Observations of Statistics
• Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach
• Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering
• Analysis of the Ensemble Kalman--Bucy Filter for correlated observation noise
• A Unification of Weighted and Unweighted Particle Filters
• Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes
• Gradient-Free Score-Based Sampling Methods with Ensembles