Session A6 - Mathematical Foundations of Data Assimilation and Inverse Problems
July 11, 15:00 ~ 15:30 - Room T1
Optimal experimental design for large-scale PDE-constrained Bayesian inverse problems
The University of Texas at Austin, USA - email@example.com
We address the problem of optimal experimental design (OED) for infinite-dimensional nonlinear Bayesian inverse problems. We seek an A-optimal design, i.e., we aim to minimize the average variance of a Gaussian approximation to the inversion parameters at the MAP point, i.e. the Laplace approximation. The OED problem includes as constraints the optimality condition PDEs defining the MAP point as well as the PDEs describing the action of the posterior covariance. A randomized trace estimator along with low rank approximations of the Hessian of the data misfit lead to efficient OED cost function computation, and an adjoint approach leads to efficient gradient computation for the OED problem. We provide numerical results for the optimal sensor locations for inference of the permeability field in a porous medium flow problem. The results indicate that the cost of the proposed method (measured by the number of forward PDE solves) is independent of the parameter and data dimensions.
Joint work with Alen Alexanderian (North Carolina State University), Noemi Petra (University of California, Merced) and George Stadler (New York University).