Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
In this paper, a series of algorithms are proposed to address the problems in the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters based on the available data, whereas a variance-based global sensitivity analysis is used to rank the epistemic and aleatory model parameters. A nested sampling of the aleatory-epistemic space is proposed to propagate uncertainties from model parameters to output quantities of interest.
Stochastic unit commitment models typically handle uncertainties in forecast demand by considering a finite number of realizations from a stochastic process model for loads. Accurate evaluations of expectations or higher moments for the quantities of interest require a prohibitively large number of model evaluations. In this paper we propose an alternative approach based on using surrogate models valid over the range of the forecast uncertainty. We consider surrogate models based on Polynomial Chaos expansions, constructed using sparse quadrature methods. Considering expected generation cost, we demonstrate that the approach can lead to several orders of magnitude reduction in computational cost relative to using Monte Carlo sampling on the original model, for a given target error threshold.
In this project we have developed atmospheric measurement capabilities and a suite of atmospheric modeling and analysis tools that are well suited for verifying emissions of green- house gases (GHGs) on an urban-through-regional scale. We have for the first time applied the Community Multiscale Air Quality (CMAQ) model to simulate atmospheric CO2 . This will allow for the examination of regional-scale transport and distribution of CO2 along with air pollutants traditionally studied using CMAQ at relatively high spatial and temporal resolution with the goal of leveraging emissions verification efforts for both air quality and climate. We have developed a bias-enhanced Bayesian inference approach that can remedy the well-known problem of transport model errors in atmospheric CO2 inversions. We have tested the approach using data and model outputs from the TransCom3 global CO2 inversion comparison project. We have also performed two prototyping studies on inversion approaches in the generalized convection-diffusion context. One of these studies employed Polynomial Chaos Expansion to accelerate the evaluation of a regional transport model and enable efficient Markov Chain Monte Carlo sampling of the posterior for Bayesian inference. The other approach uses de- terministic inversion of a convection-diffusion-reaction system in the presence of uncertainty. These approaches should, in principle, be applicable to realistic atmospheric problems with moderate adaptation. We outline a regional greenhouse gas source inference system that integrates (1) two ap- proaches of atmospheric dispersion simulation and (2) a class of Bayesian inference and un- certainty quantification algorithms. We use two different and complementary approaches to simulate atmospheric dispersion. Specifically, we use a Eulerian chemical transport model CMAQ and a Lagrangian Particle Dispersion Model - FLEXPART-WRF. These two models share the same WRF assimilated meteorology fields, making it possible to perform a hybrid simulation, in which the Eulerian model (CMAQ) can be used to compute the initial condi- tion needed by the Lagrangian model, while the source-receptor relationships for a large state vector can be efficiently computed using the Lagrangian model in its backward mode. In ad- dition, CMAQ has a complete treatment of atmospheric chemistry of a suite of traditional air pollutants, many of which could help attribute GHGs from different sources. The inference of emissions sources using atmospheric observations is cast as a Bayesian model calibration problem, which is solved using a variety of Bayesian techniques, such as the bias-enhanced Bayesian inference algorithm, which accounts for the intrinsic model deficiency, Polynomial Chaos Expansion to accelerate model evaluation and Markov Chain Monte Carlo sampling, and Karhunen-Lo %60 eve (KL) Expansion to reduce the dimensionality of the state space. We have established an atmospheric measurement site in Livermore, CA and are collect- ing continuous measurements of CO2 , CH4 and other species that are typically co-emitted with these GHGs. Measurements of co-emitted species can assist in attributing the GHGs to different emissions sectors. Automatic calibrations using traceable standards are performed routinely for the gas-phase measurements. We are also collecting standard meteorological data at the Livermore site as well as planetary boundary height measurements using a ceilometer. The location of the measurement site is well suited to sample air transported between the San Francisco Bay area and the California Central Valley.
Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 2.0 ffers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity analysis, methods for sparse surrogate construction, and Bayesian inference tools for inferring parameters from experimental data. This manual discusses the download and installation process for UQTk, provides pointers to the UQ methods used in the toolkit, and describes some of the examples provided with the toolkit.