This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.
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.
This paper describes an efficient reverse-mode differentiation algorithm for contraction operations for arbitrary and unconventional tensor network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have a single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve eficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.
The TChem open-source software is a toolkit for computing thermodynamic properties, source term, and source term’s Jacobian matrix for chemical kinetic models that involve gas and surface reactions.
CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE/DAE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems.
We present a simple, near-real-time Bayesian method to infer and forecast a multiwave outbreak, and demonstrate it on the COVID-19 pandemic. The approach uses timely epidemiological data that has been widely available for COVID-19. It provides short-term forecasts of the outbreak’s evolution, which can then be used for medical resource planning. The method postulates one- and multiwave infection models, which are convolved with the incubation-period distribution to yield competing disease models. The disease models’ parameters are estimated via Markov chain Monte Carlo sampling and information-theoretic criteria are used to select between them for use in forecasting. The method is demonstrated on two- and three-wave COVID-19 outbreaks in California, New Mexico and Florida, as observed during Summer-Winter 2020. We find that the method is robust to noise, provides useful forecasts (along with uncertainty bounds) and that it reliably detected when the initial single-wave COVID-19 outbreaks transformed into successive surges as containment efforts in these states failed by the end of Spring 2020.
This report investigates the use of unsupervised probabilistic learning techniques for the analysis of hypersonic trajectories. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. Using the diffusion coordinates on the graph of training samples, the probabilistic framework augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path-planing algorithm. In this framework the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time. A 3DOF model was employed to generate optimal hypersonic trajectories that comprise the training datasets. The diffusion map algorithm identfied that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. In addition to the path-planing worflow we also propose an algorithm that utilizes the diffusion map coordinates along the manifold to label and possibly remove outlier samples from the training data. This algorithm can be used to both identify edge cases for further analysis as well as to remove them from the training set to create a more robust set of samples to be used for the path-planing process.
In this paper we investigate the utility of one-dimensional convolutional neural network (CNN) models in epidemiological forecasting. Deep learning models, in particular variants of recurrent neural networks (RNNs) have been studied for ILI (Influenza-Like Illness) forecasting, and have achieved a higher forecasting skill compared to conventional models such as ARIMA. In this study, we adapt two neural networks that employ one-dimensional temporal convolutional layers as a primary building block—temporal convolutional networks and simple neural attentive meta-learners—for epidemiological forecasting. We then test them with influenza data from the US collected over 2010-2019. We find that epidemiological forecasting with CNNs is feasible, and their forecasting skill is comparable to, and at times, superior to, plain RNNs. Thus CNNs and RNNs bring the power of nonlinear transformations to purely data-driven epidemiological models, a capability that heretofore has been limited to more elaborate mechanistic/compartmental disease models.
Bayesian inference is used to calibrate a bottom-up home PLC network model with unknown loads and wires at frequencies up to 30 MHz. A network topology with over 50 parameters is calibrated using global sensitivity analysis and transitional Markov Chain Monte Carlo (TMCMC). The sensitivity-informed Bayesian inference computes Sobol indices for each network parameter and applies TMCMC to calibrate the most sensitive parameters for a given network topology. A greedy random search with TMCMC is used to refine the discrete random variables of the network. This results in a model that can accurately compute the transfer function despite noisy training data and a high dimensional parameter space. The model is able to infer some parameters of the network used to produce the training data, and accurately computes the transfer function under extrapolative scenarios.
We have extended the computational singular perturbation (CSP) method to differential algebraic equation (DAE) systems and demonstrated its application in a heterogeneous-catalysis problem. The extended method obtains the CSP basis vectors for DAEs from a reduced Jacobian matrix that takes the algebraic constraints into account. We use a canonical problem in heterogeneous catalysis, the transient continuous stirred tank reactor (T-CSTR), for illustration. The T-CSTR problem is modelled fundamentally as an ordinary differential equation (ODE) system, but it can be transformed to a DAE system if one approximates typically fast surface processes using algebraic constraints for the surface species. We demonstrate the application of CSP analysis for both ODE and DAE constructions of a T-CSTR problem, illustrating the dynamical response of the system in each case. We also highlight the utility of the analysis in commenting on the quality of any particular DAE approximation built using the quasi-steady state approximation (QSSA), relative to the ODE reference case.
Jivani, Aniket; Huan, Xun; Safta, Cosmin S.; Zhou, Beckett Y.; Gauger, Nicolas R.
Understanding the behavior of turbulent jets under variable environment and uncertain conditions is critical for predicting and mitigating aircraft jet noise. However, uncertainty quantification (UQ) for jet noise, which requires repeated expensive eddy-resolving simulations, is often computationally prohibitive. We thus build surrogate models, in particular Karhunen-Loève expansions (KLEs) for field quantities of interest in three-dimensional turbulent round jets. We build them in a multifidelity manner by combining simulation data from high-fidelity enhanced delayed detached-eddy simulation (EDDES) and low-fidelity Reynolds-averaged Navier-Stokes (RANS), generated under uncertain nozzle exit stagnation pressure and inlet eddy viscosity ratio. Furthermore, we form the KLEs in conjunction with polynomial chaos expansions in order to explicitly associate their randomness to each physical source of uncertainty, and so justifying the combining procedure in the multifidelity construct. We illustrate advantages of the new multifidelity KLE against single-fidelity KLEs, with the former achieving more accurate predictions at locations away from existing high-fidelity training data. With the KLE surrogate, we conduct UQ inexpensively.
CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems. The software provides support for: General ODE models (gODE model class) for computing source terms and Jacobians for a generic ODE system; TChem model (ChemElemODETChem model class) for computing source term, Jacobian, other necessary chemical reaction data, as well as the rates of progress for a homogenous batch reactor using an elementary step detailed chemical kinetic reaction mechanism. This class relies on the TChem [2] library; A set of functions to compute essential elements of CSP analysis (Kernel class). This includes computations of the eigensolution of the Jacobian matrix, CSP basis vectors and co-vectors, time scales (reciprocals of the magnitudes of the Jacobian eigenvalues), mode amplitudes, CSP pointers, and the number of exhausted modes. This class relies on the Tines library; A set of functions to compute the eigensolution of the Jacobian matrix using Tines library GPU eigensolver; A set of functions to compute CSP indices (Index Class). This includes participation indices and both slow and fast importance indices.
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.
Chemical kinetics simulations are used to explore whether detailed measurements of relevant chemical species during the oxidation of very dilute fuels (less than 1 Torr partial pressure) in a high-pressure plug flow reactor (PFR) can predict autoignition propensity. We find that for many fuels the timescale for the onset of spontaneous oxidation in dilute fuel/air mixtures in a simple PFR is similar to the 1st-stage ignition delay time (IDT) at stoichiometric engine-relevant conditions. For those fuels that deviate from this simple trend, the deviation is closely related to the peak rate of production of OH, HO2, CH2O, and CO2 formed during oxidation. We use these insights to show that an accurate correlation between simulated profiles of these species in a PFR and 1st-stage IDT can be developed using convolutional neural networks. Our simulations suggest that the accuracy of such a correlation is 10–50%, which is appropriate for rapid fuel screening and may be sufficient for predictive fuel performance modeling.
In this report we describe an enhanced methodology for performing stochastic Bayesian inversions of atmospheric trace gas inversions that allows the time variation of model parameters to be inferred. We use measurements of methane atmospheric mixing ratio made in Livermore, California along with atmospheric transport modeling and published prior estmates of emissions to estimate the regional emissions of methane and the temporal variations in inferred bias parameters. We compute Bayesian model evidence and continuous rank probability score to optimize the model with respect to temporal resolution. Using two different emissions inventories, we perform inversions for a series of models with increasing temporal resolution in the model bias representation. We show that temporal variation in the model bias can improve the model fit and can also increase the likelihood that the parameterization is appropriate, as measured by the Baysian model evidence. .
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.
The computational burden of a large-eddy simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer samples. Such procedures, if successful, will greatly enhance the predictability of models in the sense of improving exploration and characterization of uncertainty due to model error and input dependencies, all while being constrained by the size of the associated statistical samples. In this paper, it is shown how a recently developed procedure for probabilistic learning on manifolds can serve to improve the predictability in a probabilistic framework of a scramjet simulation. The estimates of the probability density functions of the quantities of interest are improved together with estimates of the statistics of their maxima. It is also demonstrated how the improved statistical model adds critical insight to the performance of the model.
In this work, we provide a method for enhancing stochastic Galerkin moment calculations to the linear elliptic equation with random diffusivity using an ensemble of Monte Carlo solutions. This hybrid approach combines the accuracy of low-order stochastic Galerkin and the computational efficiency of Monte Carlo methods to provide statistical moment estimates which are significantly more accurate than performing each method individually. The hybrid approach involves computing a low-order stochastic Galerkin solution, after which Monte Carlo techniques are used to estimate the residual. We show that the combined stochastic Galerkin solution and residual is superior in both time and accuracy for a one-dimensional test problem and a more computational intensive two-dimensional linear elliptic problem for both the mean and variance quantities.
This study explores a Bayesian calibration framework for the RAMPAGE alloy potential model for Cu-Ni and Cu-Zr systems, respectively. In RAMPAGE potentials, it is proposed that once calibrated potentials for individual elements are available, the inter-species interac- tions can be described by fitting a Morse potential for pair interactions with three parameters, while densities for the embedding function can be scaled by two parameters from the elemen- tal densities. Global sensitivity analysis tools were employed to understand the impact each parameter has on the MD simulation results. A transitional Markov Chain Monte Carlo al- gorithm was used to generate samples from the multimodal posterior distribution consistent with the discrepancy between MD simulation results and DFT data. For the Cu-Ni system the posterior predictive tests indicate that the fitted interatomic potential model agrees well with the DFT data, justifying the basic RAMPAGE assumtions. For the Cu-Zr system, where the phase diagram suggests more complicated atomic interactions than in the case of Cu-Ni, the RAMPAGE potential captured only a subset of the DFT data. The resulting posterior distri- bution for the 5 model parameters exhibited several modes, with each mode corresponding to specific simulation data and a suboptimal agreement with the DFT results.
Increasing penetration levels of renewables have transformed how power systems are operated. High levels of uncertainty in production make it increasingly difficulty to guarantee operational feasibility; instead, constraints may only be satisfied with high probability. We present a chance-constrained economic dispatch model that efficiently integrates energy storage and high renewable penetration to satisfy renewable portfolio requirements. Specifically, we require that wind energy contribute at least a prespecified proportion of the total demand and that the scheduled wind energy is deliverable with high probability. We develop an approximate partial sample average approximation (PSAA) framework to enable efficient solution of large-scale chance-constrained economic dispatch problems. Computational experiments on the IEEE-24 bus system show that the proposed PSAA approach is more accurate, closer to the prescribed satisfaction tolerance, and approximately 100 times faster than standard sample average approximation. Finally, the improved efficiency of our PSAA approach enables solution of a larger WECC-240 test system in minutes.
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.
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 uncertainparameters involvedandthe high computational costofflow simulations. These difficulties are addressedin this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying themin the current studyto large-eddy simulations ofajet incrossflow 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. 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.
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.
Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.
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.
A general strategy for analysis and reduction of uncertain chemical kinetic models is presented, and its utility is illustrated in the context of ignition of hydrocarbon fuel–air mixtures. The strategy is based on a deterministic analysis and reduction method which employs computational singular perturbation analysis to generate simplified kinetic mechanisms, starting from a detailed reference mechanism. We model uncertain quantities in the reference mechanism, namely the Arrhenius rate parameters, as random variables with prescribed uncertainty factors. We propagate this uncertainty to obtain the probability of inclusion of each reaction in the simplified mechanism. We propose probabilistic error measures to compare predictions from the uncertain reference and simplified models, based on the comparison of the uncertain dynamics of the state variables, where the mixture entropy is chosen as progress variable. We employ the construction for the simplification of an uncertain mechanism in an n-butane–air mixture homogeneous ignition case, where a 176-species, 1111-reactions detailed kinetic model for the oxidation of n-butane is used with uncertainty factors assigned to each Arrhenius rate pre-exponential coefficient. This illustration is employed to highlight the utility of the construction, and the performance of a family of simplified models produced depending on chosen thresholds on importance and marginal probabilities of the reactions.
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).
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.