Unscented Kalman Inversion: Efficient Gaussian Approximation to the Posterior Distribution
arXiv:2103.00277
Abstract
The unscented Kalman inversion (UKI) method presented in [1] is a general derivative-free approach for the inverse problem. UKI is particularly suitable for inverse problems where the forward model is given as a black box and may not be differentiable. The regularization strategies, convergence property, and speed-up strategies [1,2] of the UKI are thoroughly studied, and the method is capable of handling noisy observation data and solving chaotic inverse problems. In this paper, we study the uncertainty quantification capability of the UKI. We propose a modified UKI, which allows to well approximate the mean and covariance of the posterior distribution for well-posed inverse problems with large observation data. Theoretical guarantees for both linear and nonlinear inverse problems are presented. Numerical results, including learning of permeability parameters in subsurface flow and of the Navier-Stokes initial condition from solution data at positive times are presented. The results obtained by the UKI require only iterations, and match well with the expected results obtained by the Markov Chain Monte Carlo method.
arXiv comment23 pages, 10 figures
References in corpus (8)
- The Ensemble Kalman Filter for Inverse Problems
- Learning Constitutive Relations from Indirect Observations Using Deep Neural Networks
- Learning Constitutive Relations using Symmetric Positive Definite Neural Networks
- Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM
- High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit-explicit Runge-Kutta schemes
- High-order partitioned spectral deferred correction solvers for multiphysics problems
- Learned convex regularizers for inverse problems
- Improve Unscented Kalman Inversion With Low-Rank Approximation and Reduced-Order Model