Due to slow convergence, classical Monte-Carlo approaches are ineffective for computationally
intensive studies of complex models as they require prohibitively many sampled
simulations for reasonable accuracy. Targeting high-dimensional systems, we build computationally
inexpensive surrogate models in order to accelerate both forward (e.g., uncertainty
propagation and sensitivity analysis) and inverse (e.g., calibration) uncertainty quantification
studies. We apply Polynomial Chaos (PC) spectral expansions to build surrogate relationships
between output quantities and model parameters using as few forward model simulations as
possible.
For a complex model with a large number of input parameters, building a PC surrogate
model is challenged by high dimensionality: there is typically insufficient model simulation
data as well as a prohibitively large number of spectral basis terms. Bayesian compressive
sensing (BCS) approach is employed in order to detect a sparse polynomial basis set that best
captures the model outputs. We enhance the BCS algorithm with iterative basis growth and
reweighing that effectively searches polynomial space for an optimal, sparse basis set.
Besides proof-of-concept studies for synthetic models, the technique is demonstrated on the
Community Land Model with more than 50 input parameters. The outcome of the algorithm
is then employed for forward uncertainty propagation and variance-based sensitivity analysis,
leading to dimensionality reduction. Furthermore, we illustrate how the computationally inexpensive
surrogate greatly accelerates statistical methods for parameter estimation, where one
relies on observational data to estimate input parameters with quantified uncertainty, using
Markov Chain Monte Carlo sampling.
Talk given by Kenny Chowdhary.