## UC Berkeley / Lawrence Berkeley Laboratory

#### Multi-fidelity surrogate-based parameter estimation

**Stephen Roberts, Australian National University**

##### September 5th, LBNL 50A-5132, 2:00PM-3:00PM, 2017 at 4:00PM–5:00PM in 891 Evans Hall [Map]

Given a numerical simulation, the objective of parameter estimation is to provide a joint posterior probability distribution for an uncertain input parameter vector, conditional on available experimental data. However, exploring the posterior requires a high number of numerical simulations, which can make the problem impracticable within a given computational budget.

A well-known approach to reduce the number of required simulations is to construct a surrogate, which — based on a set of training simulations — can provide an inexpensive approximation of the simulation output for any parameter configuration. To further reduce the total cost of the simulations, we can introduce low-fidelity as well as high-fidelity training simulations. In this case, a small number of expensive high-fidelity simulations is augmented with a larger number of inexpensive low-fidelity simulations.

In this talk I will present two methods we have investigated to produce such multi-fidelity surrogate-based estimators, one based on kriging and the other based on sparse grid interpolation. The methods will be applied to the design of a sailing yacht hull, and the quantification of uncertainty for the inundation due to a tsunami runup. We can demonstrate a speedup of 20 for a four dimensional parameter estimation problem.