Ghahari, Farid G.; Sargsyan, Khachik S.; Celebi, Mehmet C.; Taciroglu, Ertugrul T.
The use of simple models for response prediction of building structures is preferred in earthquake engineering for risk evaluations at regional scales, as they make computational studies more feasible. The primary impediment in their gainful use presently is the lack of viable methods for quantifying (and reducing upon) the modeling errors/uncertainties they bear. This study presents a Bayesian calibration method wherein the modeling error is embedded into the parameters of the model. Here, the method is specifically described for coupled shear-flexural beam models here, but it can be applied to any parametric surrogate model. The major benefit the method offers is the ability to consider the modeling uncertainty in the forward prediction of any degree-of-freedom or composite response regardless of the data used in calibration. The method is extensively verified using two synthetic examples. In the first example, the beam model is calibrated to represent a similar beam model but with enforced modeling errors. In the second example, the beam model is used to represent the detailed finite element model of a 52-story building. Both examples show the capability of the proposed solution to provide realistic uncertainty estimation around the mean prediction.
A Bayesian inference strategy has been used to estimate uncertain inputs to global impurity transport code (GITR) modeling predictions of tungsten erosion and migration in the linear plasma device, PISCES-A. This allows quantification of GITR output uncertainty based on the uncertainties in measured PISCES-A plasma electron density and temperature profiles (ne, Te) used as inputs to GITR. The technique has been applied for comparison to dedicated experiments performed for high (4 × 1022 m–2 s–1) and low (5 × 1021 m–2 s–1) flux 250 eV He–plasma exposed tungsten (W) targets designed to assess the net and gross erosion of tungsten, and corresponding W impurity transport. The W target design and orientation, impurity collector, and diagnostics, have been designed to eliminate complexities associated with tokamak divertor plasma exposures (inclined target, mixed plasma species, re-erosion, etc) to benchmark results against the trace impurity transport model simulated by GITR. The simulated results of the erosion, migration, and re-deposition of W during the experiment from the GITR code coupled to materials response models are presented. Specifically, the modeled and experimental W I emission spectroscopy data for a 429.4 nm line and net erosion through the target and collector mass difference measurements are compared. Furthermore, the methodology provides predictions of observable quantities of interest with quantified uncertainty, allowing estimation of moments, together with the sensitivities to plasma temperature and density.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.2 offers 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.
Flooding impacts are on the rise globally, and concentrated in urban areas. Currently, there are no operational systems to forecast flooding at spatial resolutions that can facilitate emergency preparedness and response actions mitigating flood impacts. We present a framework for real-time flood modeling and uncertainty quantification that combines the physics of fluid motion with advances in probabilistic methods. The framework overcomes the prohibitive computational demands of high-fidelity modeling in real-time by using a probabilistic learning method relying on surrogate models that are trained prior to a flood event. This shifts the overwhelming burden of computation to the trivial problem of data storage, and enables forecasting of both flood hazard and its uncertainty at scales that are vital for time-critical decision-making before and during extreme events. The framework has the potential to improve flood prediction and analysis and can be extended to other hazard assessments requiring intense high-fidelity computations in real-time.
A new method for computing anharmonic thermophysical properties for adsorbates on metal surfaces is presented. Classical Monte Carlo phase space integration is performed to calculate the partition function for the motion of a hydrogen atom on Cu(111). A minima-preserving neural network potential energy surface is used within the integration routine. Two different sampling schema for generating the training data are presented, and two different density functionals are used. The results are benchmarked against direct state counting results by using discrete variable representation. The phase space integration results are in excellent quantitative agreement with the benchmark results. Additionally, both the discrete variable representation and the phase space integration results confirm that the motion of H on Cu(111) is highly anharmonic. The results were applied to calculate the free energy of dissociative adsorption of H2 and the resulting Langmuir isotherms at 400, 800, and 1200 K in a partial pressure range of 0-1 bar. It shows that the anharmonic effects lead to significantly higher predicted surface site fractions of hydrogen.
We present a new geodesic-based method for geometry optimization in a basis set of redundant internal coordinates. Our method updates the molecular geometry by following the geodesic generated by a displacement vector on the internal coordinate manifold, which dramatically reduces the number of steps required to converge to a minimum. Our method can be implemented in any existing optimization code, requiring only implementation of derivatives of the Wilson B-matrix and the ability to numerically solve an ordinary differential equation.
Kreitz, Bjarne K.; Sargsyan, Khachik S.; Mazeau, Emily J.; Blondal, Katrin B.; West, Richard H.; Wehinger, Gregor W.; Turek, Thomas T.; Goldsmith, Franklin G.
Automatic mechanism generation is used to determine mechanisms for the CO2 hydrogenation on Ni(111) in a two-stage process while considering the correlated uncertainty in DFT-based energetic parameters systematically. In a coarse stage, all the possible chemistry is explored with gas-phase products down to the ppb level, while a refined stage discovers the core methanation submechanism. Five thousand unique mechanisms were generated, which contain minor perturbations in all parameters. Global uncertainty assessment, global sensitivity analysis, and degree of rate control analysis are performed to study the effect of this parametric uncertainty on the microkinetic model predictions. Comparison of the model predictions with experimental data on a Ni/SiO2 catalyst find a feasible set of microkinetic mechanisms within the correlated uncertainty space that are in quantitative agreement with the measured data, without relying on explicit parameter optimization. Global uncertainty and sensitivity analyses provide tools to determine the pathways and key factors that control the methanation activity within the parameter space. Together, these methods reveal that the degree of rate control approach can be misleading if parametric uncertainty is not considered. The procedure of considering uncertainties in the automated mechanism generation is not unique to CO2 methanation and can be easily extended to other challenging heterogeneously catalyzed reactions.
We demonstrate a Bayesian method for the “real-time” characterization and forecasting of partially observed COVID-19 epidemic. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. The estimation problem is posed as one of Bayesian inference and solved using a Markov chain Monte Carlo technique. The data used in this study was sourced before the arrival of the second wave of infection in July 2020. The proposed modeling approach, when applied at the country level, generally provides accurate forecasts at the regional, state and country level. The epidemiological model detected the flattening of the curve in California, after public health measures were instituted. The method also detected different disease dynamics when applied to specific regions of New Mexico.
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.
Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often the largest contributor to the overall predictive uncertainty. This work builds on a recently developed framework of embedded, internal model correction, in order to represent and quantify structural errors, together with model parameters,within a Bayesian inference context. We focus specifically on a Polynomial Chaos representation with additive modification of existing model parameters, enabling a non-intrusive procedure for efficient approximate likelihood construction, model error estimation, and disambiguation of model and data errors’ contributions to predictive uncertainty. The framework is demonstrated on several synthetic examples, as well as on a chemical ignition problem.
Rate coefficients are key quantities in gas phase kinetics and can be determined theoretically via master equation (ME) calculations. Rate coefficients characterize how fast a certain chemical species reacts away due to collisions into a specific product. Some of these collisions are simply transferring energy between the colliding partners, in which case the initial chemical species can undergo a unimolecular reaction: dissociation or isomerization. Other collisions are reactive, and the colliding partners either exchange atoms, these are direct reactions, or form complexes that can themselves react further or get stabilized by deactivating collisions with a bath gas. The input of MEs are molecular parameters: geometries, energies, and frequencies determined from ab initio calculations. While the calculation of these rate coefficients using ab initio data is becoming routine in many cases, the determination of the uncertainties of the rate coefficients are often ignored, sometimes crudely assessed by varying independently just a few of the numerous parameters, and only occasionally studied in detail. In this study, molecular frequencies, barrier heights, well depths, and imaginary frequencies (needed to calculate quantum mechanical tunneling) were automatically perturbed in an uncorrelated fashion. Our Python tool, MEUQ, takes user requests to change all or specified well, barrier, or bimolecular product parameters for a reaction. We propagate the uncertainty in these input parameters and perform global sensitivity analysis in the rate coefficients for the ethyl + O2 system using state-of-the-art uncertainty quantification (UQ) techniques via Python interface to UQ Toolkit (www.sandia.gov/uqtoolkit). A total of 10,000 sets of rate coefficients were collected after perturbing 240 molecular parameters. With our methodology, sensitive mechanistic steps can be revealed to a modeler in a straightforward manner for identification of significant and negligible influences in bimolecular reactions.
A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. The method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function as a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.
The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. Finally, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.
We conduct a global sensitivity analysis (GSA) of the Energy Exascale Earth System Model (E3SM), land model (ELM) to calculate the sensitivity of five key carbon cycle outputs to 68 model parameters. This GSA is conducted by first constructing a Polynomial Chaos (PC) surrogate via new Weighted Iterative Bayesian Compressive Sensing (WIBCS) algorithm for adaptive basis growth leading to a sparse, high-dimensional PC surrogate with 3,000 model evaluations. The PC surrogate allows efficient extraction of GSA information leading to further dimensionality reduction. The GSA is performed at 96 FLUXNET sites covering multiple plant functional types (PFTs) and climate conditions. About 20 of the model parameters are identified as sensitive with the rest being relatively insensitive across all outputs and PFTs. These sensitivities are dependent on PFT, and are relatively consistent among sites within the same PFT. The five model outputs have a majority of their highly sensitive parameters in common. A common subset of sensitive parameters is also shared among PFTs, but some parameters are specific to certain types (e.g., deciduous phenology). The relative importance of these parameters shifts significantly among PFTs and with climatic variables such as mean annual temperature.
Data movement is considered the main performance concern for exascale, including both on-node memory and off-node network communication. Indeed, many application traces show significant time spent in MPI calls, potentially indicating that faster networks must be provisioned for scalability. However, equating MPI times with network communication delays ignores synchronization delays and software overheads independent of network hardware. Using point-to-point protocol details, we explore the decomposition of MPI time into communication, synchronization and software stack components using architecture simulation. Detailed validation using Bayesian inference is used to identify the sensitivity of performance to specific latency/bandwidth parameters for different network protocols and to quantify associated uncertainties. The inference combined with trace replay shows that synchronization and MPI software stack overhead are at least as important as the network itself in determining time spent in communication routines.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.4 offers 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.
A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm−1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.
The UQ Toolkit (UQTk) is a collection of tools for uncertainty quantification, ranging from intrusive and nonintrusive forward propagation of uncertainty to inverse problems and sensitivity analysis. This chapter first outlines the UQTk design philosophy, followed by an overview of the available methods and the way they are implemented in UQTk. The second part of this chapter is a detailed example that illustrates a UQ workflow from surrogate construction, and calibration, to forward propagation and attribution.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.0.3 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sen- sitivity 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.
Proceedings of ScalA 2016: 7th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems - Held in conjunction with SC16: The International Conference for High Performance Computing, Networking, Storage and Analysis
We present a resilient task-based domain-decomposition preconditioner for partial differential equations (PDEs) built on top of User Level Fault Mitigation Message Passing Interface (ULFM-MPI). The algorithm reformulates the PDE as a sampling problem, followed by a robust regression-based solution update that is resilient to silent data corruptions (SDCs). We adopt a server-client model where all state information is held by the servers, while clients only serve as computational units. The task-based nature of the algorithm and the capabilities of ULFM complement each other to support missing tasks, making the application resilient to clients failing.We present weak and strong scaling results on Edison, National Energy Research Scientific Computing Center (NERSC), for a nominal and a fault-injected case, showing that even in the presence of faults, scalability tested up to 50k cores is within 90%. We then quantify the variability of weak and strong scaling due to the presence of faults. Finally, we discuss the performance of our application with respect to subdomain size, server/client configuration, and the interplay between energy and resilience.
Bayesian inference and maximum entropy methods were employed for the estimation of the joint probability density for the Arrhenius rate parameters of the rate coefficient of the H2/O2-mechanism chain branching reaction H + O2 → OH + O. A consensus joint posterior on the parameters was obtained by pooling the posterior parameter densities given each consistent data set. Efficient surrogates for the OH concentration were constructed using a combination of Padé and polynomial approximants. Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation were used resulting in orders of magnitude speedup in data likelihood evaluation. The consistent data sets resulted in nearly Gaussian conditional parameter probability density functions. The resulting pooled parameter probability density function was propagated through stoichiometric H2-air auto-ignition computations to illustrate the necessity for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions to be considered.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncer- tainty in numerical model predictions. Version 3.0 offers intrusive and non-intrusive methods for propagating input uncertainties through computational models, tools for sensitivity anal- ysis, 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.
We discuss algorithm-based resilience to silent data corruption (SDC) in a task- based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDC. The imple- mentation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to [?] 51 K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corrup- tion of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamics voltage/frequency scaling, and its interplay with fault-rates, and application overhead. [?] Sandia National Laboratories, Livermore, CA ( fnrizzi@sandia.gov ). + Sandia National Laboratories, Livermore, CA ( knmorri@sandia.gov ). ++ Sandia National Laboratories, Livermore, CA ( ksargsy@sandia.gov ). SS Duke University, Durham, NC ( paul.mycek@duke.edu ). P Sandia National Laboratories, Livermore, CA ( csafta@sandia.gov ). k Laboratoire d'Informatique pour la M'ecanique et les Sciences de l'Ing'enieur, Orsay, France ( olm@limsi.fr ). [?][?] Duke University, Durham, NC ( omar.knio@duke.edu ). ++ Sandia National Laboratories, Livermore, CA ( bjdebus@sandia.gov ).
We present a domain-decomposition-based pre-conditioner for the solution of partial differential equations (PDEs) that is resilient to both soft and hard faults. The algorithm is based on the following steps: first, the computational domain is split into overlapping subdomains, second, the target PDE is solved on each subdomain for sampled values of the local current boundary conditions, third, the subdomain solution samples are collected and fed into a regression step to build maps between the subdomains' boundary conditions, finally, the intersection of these maps yields the updated state at the subdomain boundaries. This reformulation allows us to recast the problem as a set of independent tasks. The implementation relies on an asynchronous server-client framework, where one or more reliable servers hold the data, while the clients ask for tasks and execute them. This framework provides resiliency to hard faults such that if a client crashes, it stops asking for work, and the servers simply distribute the work among all the other clients alive. Erroneous subdomain solves (e.g. due to soft faults) appear as corrupted data, which is either rejected if that causes a task to fail, or is seamlessly filtered out during the regression stage through a suitable noise model. Three different types of faults are modeled: hard faults modeling nodes (or clients) crashing, soft faults occurring during the communication of the tasks between server and clients, and soft faults occurring during task execution. We demonstrate the resiliency of the approach for a 2D elliptic PDE, and explore the effect of the faults at various failure rates.
The objective of this work is to investigate the efficacy of using calibration strategies from Uncertainty Quantification (UQ) to determine model coefficients for LES. As the target methods are for engineering LES, uncertainty from numerical aspects of the model must also be quantified. 15 The ultimate goal of this research thread is to generate a cost versus accuracy curve for LES such that the cost could be minimized given an accuracy prescribed by an engineering need. Realization of this goal would enable LES to serve as a predictive simulation tool within the engineering design process.
The move towards extreme-scale computing platforms challenges scientific simula- tions in many ways. Given the recent tendencies in computer architecture development, one needs to reformulate legacy codes in order to cope with large amounts of commu- nication, system faults and requirements of low-memory usage per core. In this work, we develop a novel framework for solving partial differential equa- tions (PDEs) via domain decomposition that reformulates the solution as a state-of- knowledge with a probabilistic interpretation. Such reformulation allows resiliency with respect to potential faults without having to apply fault detection, avoids unnecessary communication and is generally well-positioned for rigorous uncertainty quantification studies that target improvements of predictive fidelity of scientific models. We demon- strate our algorithm for one-dimensional PDE examples where artificial faults have been implemented as bit-flips in the binary representation of subdomain solutions. *Sandia National Laboratories, 7011 East Ave, MS 9051, Livermore, CA 94550 (ksargsy@sandia.gov). t Sandia National Laboratories, Livermore, CA (fnrizzi@sandia.gov). IDuke University, Durham, NC (paul .mycek@duke . edu). Sandia National Laboratories, Livermore, CA (csaft a@sandia.gov). i llSandia National Laboratories, Livermore, CA (knmorri@sandia.gov). II Sandia National Laboratories, Livermore, CA (hnnajm@sandia.gov). **Laboratoire d'Informatique pour la Mecanique et les Sciences de l'Ingenieur, Orsay, France (olm@limsi . f r). ttDuke University, Durham, NC (omar . knio@duke . edu). It Sandia National Laboratories, Livermore, CA (bjdebus@sandia.gov).
In this paper we present a basis selection method that can be used with ℓ1-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets that have more terms in important dimensions and limits the number of unimportant terms that increase mutual coherence and thus degrade the performance of ℓ1-minimization. The important features and the accuracy of basis selection are demonstrated with a number of numerical examples. Specifically, we show that for a given computational budget, basis selection produces a more accurate PCE than would be obtained if the basis were fixed a priori. We also demonstrate that basis selection can be applied with non-uniform random variables and can leverage gradient information.
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.
This brief report explains the method used for parameter calibration and model validation in SST/Macro and the set of tools and workflow developed for this purpose.
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.
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.