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Efficient uncertainty quantification methodologies for high-dimensional climate land models

Sargsyan, Khachik S.; Safta, Cosmin S.; Berry, Robert D.; Ray, Jaideep R.; Debusschere, Bert D.; Najm, H.N.

In this report, we proposed, examined and implemented approaches for performing efficient uncertainty quantification (UQ) in climate land models. Specifically, we applied Bayesian compressive sensing framework to a polynomial chaos spectral expansions, enhanced it with an iterative algorithm of basis reduction, and investigated the results on test models as well as on the community land model (CLM). Furthermore, we discussed construction of efficient quadrature rules for forward propagation of uncertainties from high-dimensional, constrained input space to output quantities of interest. The work lays grounds for efficient forward UQ for high-dimensional, strongly non-linear and computationally costly climate models. Moreover, to investigate parameter inference approaches, we have applied two variants of the Markov chain Monte Carlo (MCMC) method to a soil moisture dynamics submodel of the CLM. The evaluation of these algorithms gave us a good foundation for further building out the Bayesian calibration framework towards the goal of robust component-wise calibration.

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TYPE SAND Report YEAR 2011
OSTIDOI

Real-time characterization of partially observed epidemics using surrogate models

Safta, Cosmin S.; Ray, Jaideep R.; Sargsyan, Khachik S.; Lefantzi, Sophia L.

We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiological parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.

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TYPE SAND Report YEAR 2011
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TChem - A Software Toolkit for the Analysis of Complex Kinetic Models

Safta, Cosmin S.; Najm, H.N.

The TChem toolkit is a software library that enables numerical simulations using complex chemistry and facilitates the analysis of detailed kinetic models. The toolkit provide capabilities for thermodynamic properties based on NASA polynomials and species production/consumption rates. It incorporates methods that can selectively modify reaction parameters for sensitivity analysis. The library contains several functions that provide analytically computed Jacobian matrices necessary for the efficient time advancement and analysis of detailed kinetic models.

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TYPE SAND Report YEAR 2011
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Uncertainty quantification given discontinuous climate model response and a limited number of model runs

Sargsyan, Khachik S.; Safta, Cosmin S.; Debusschere, Bert D.; Najm, H.N.

Uncertainty quantification in complex climate models is challenged by the sparsity of available climate model predictions due to the high computational cost of model runs. Another feature that prevents classical uncertainty analysis from being readily applicable is bifurcative behavior in climate model response with respect to certain input parameters. A typical example is the Atlantic Meridional Overturning Circulation. The predicted maximum overturning stream function exhibits discontinuity across a curve in the space of two uncertain parameters, namely climate sensitivity and CO2 forcing. We outline a methodology for uncertainty quantification given discontinuous model response and a limited number of model runs. Our approach is two-fold. First we detect the discontinuity with Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve shape and location for arbitrarily distributed input parameter values. Then, we construct spectral representations of uncertainty, using Polynomial Chaos (PC) expansions on either side of the discontinuity curve, leading to an averaged-PC representation of the forward model that allows efficient uncertainty quantification. The approach is enabled by a Rosenblatt transformation that maps each side of the discontinuity to regular domains where desirable orthogonality properties for the spectral bases hold. We obtain PC modes by either orthogonal projection or Bayesian inference, and argue for a hybrid approach that targets a balance between the accuracy provided by the orthogonal projection and the flexibility provided by the Bayesian inference - where the latter allows obtaining reasonable expansions without extra forward model runs. The model output, and its associated uncertainty at specific design points, are then computed by taking an ensemble average over PC expansions corresponding to possible realizations of the discontinuity curve. The methodology is tested on synthetic examples of discontinuous model data with adjustable sharpness and structure.

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TYPE Conference YEAR 2010
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Results 201–225 of 239
Results 201–225 of 239