The efficient and reliable estimation of model parameters is important for the simulation and optimization of physical processes. Most models contain variables that have to be adjusted, e.g. in the form of material properties, and the uncertainty of state estimates and predictions is directly linked to the uncertainty of these parameters. Therefore, efficient methods for parameter estimation and uncertainty quantification are required. If the physical system is spatially highly heterogeneous, then the number of model parameters can be very large. At the same time, imaging techniques and time series can provide a large number of measurements for model calibration. Many of the available methods become inefficient or outright unfeasible if both the number of model parameters and the number of state observations are large.
This thesis is concerned with the development of methods that remain efficient when a large number of measurements is used to estimate an even larger number of model parameters. The main result is a special preconditioned Conjugate Gradients method that can achieve both quasilinear complexity in the number of parameters and pseudo-constant complexity in the number of measurements. The thesis also provides randomized methods that allow linearized uncertainty quantification for large systems, taking redundancy in the measurements into account if applicable
