Yadav, Vineet; Michalak, Anna M.; Ray, Jaideep; Shiga, Yoichi P.
Independent verification and quantification of fossil fuel (FF) emissions constitutes a considerable scientific challenge. By coupling atmospheric observations of CO2 with models of atmospheric transport, inverse models offer the possibility of overcoming this challenge. However, disaggregating the biospheric and FF flux components of terrestrial fluxes from CO2 concentration measurements has proven to be difficult, due to observational and modeling limitations. In this study, we propose a statistical inverse modeling scheme for disaggregating winter time fluxes on the basis of their unique error covariances and covariates, where these covariances and covariates are representative of the underlying processes affecting FF and biospheric fluxes. The application of the method is demonstrated with one synthetic and two real data prototypical inversions by using in situ CO2 measurements over North America. Inversions are performed only for the month of January, as predominance of biospheric CO2 signal relative to FF CO2 signal and observational limitations preclude disaggregation of the fluxes in other months. The quality of disaggregation is assessed primarily through examination of a posteriori covariance between disaggregated FF and biospheric fluxes at regional scales. Findings indicate that the proposed method is able to robustly disaggregate fluxes regionally at monthly temporal resolution with a posteriori cross covariance lower than 0.15 µmolm-2 s-1 between FF and biospheric fluxes. Error covariance models and covariates based on temporally varying FF inventory data provide a more robust disaggregation over static proxies (e.g., nightlight intensity and population density). However, the synthetic data case study shows that disaggregation is possible even in absence of detailed temporally varying FF inventory data.
Open-source indicators have been proposed as a way of tracking and forecasting disease outbreaks. Some, such are meteorological data, are readily available as reanalysis products. Others, such as those derived from our online behavior (web searches, media article etc.) are gathered easily and are more timely than public health reporting. In this study we investigate how these datastreams may be combined to provide useful epidemiological information. The investigation is performed by building data assimilation systems to track influenza in California and dengue in India. The first does not suffer from incomplete data and was chosen to explore disease modeling needs. The second explores the case when observational data is sparse and disease modeling complexities are beside the point. The two test cases are for opposite ends of the disease tracking spectrum. We find that data assimilation systems that produce disease activity maps can be constructed. Further, being able to combine multiple open-source datastreams is a necessity as any one individually is not very informative. The data assimilation systems have very little in common except that they contain disease models, calibration algorithms and some ability to impute missing data. Thus while the data assimilation systems share the goal for accurate forecasting, they are practically designed to compensate for the shortcomings of the datastreams. Thus we expect them to be disease and location-specific.
Traditional multiple imputation approaches may perform poorly for datasets with high rates of missingness unless many m imputations are used. This paper implements an alternative machine learning-based approach to imputing data that are missing at high rates. Here, we use boosting to create a strong learner from a weak learner fitted to a dataset missing many observations. This approach may be applied to a variety of types of learners (models). The approach is demonstrated by application to a spatiotemporal dataset for predicting dengue outbreaks in India from meteorological covariates. A Bayesian spatiotemporal CAR model is boosted to produce imputations, and the overall RMSE from a k-fold cross-validation is used to assess imputation accuracy.
Reynolds-Averaged Navier-Stokes models are not very accurate for high-Reynolds-number compressible jet-incrossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-Averaged Navier-Stokes model. In this work, the hypothesis is pursued that Reynolds-Averaged Navier-Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.ABayesian inverse problem is formulated to estimate three Reynolds-Averaged Navier-Stokes parameters (Cμ;Cϵ2;Cϵ1), and a Markov chain Monte Carlo method is used to develop a probability density function for them. The cost of the Markov chain Monte Carlo is addressed by developing statistical surrogates for the Reynolds-Averaged Navier-Stokes model. It is found that only a subset of the (Cμ;Cϵ2;Cϵ1) spaceRsupports realistic flow simulations.Ris used as a prior belief when formulating the inverse problem. It is enforced with a classifier in the current Markov chain Monte Carlo solution. It is found that the calibrated parameters improve predictions of the entire flowfield substantially when compared to the nominal/ literature values of (Cμ;Cϵ2;Cϵ1); furthermore, this improvement is seen to hold for interactions at other Mach numbers and jet strengths for which the experimental data are available to provide a comparison. The residual error is quantifies, which is an approximation of the model-form error; it is most easily measured in terms of turbulent stresses.
We present a general technique to solve Partial Differential Equations, called robust stencils, which make them tolerant to soft faults, i.e. bit flips arising in memory or CPU calculations. We show how it can be applied to a two-dimensional Lax-Wendroff solver. The resulting 2D robust stencils are derived using an orthogonal application of their 1D counterparts. Combinations of 3 to 5 base stencils can then be created. We describe how these are then implemented in a parallel advection solver. Various robust stencil combinations are explored, representing tradeoff between performance and robustness. The results indicate that the 3-stencil robust combinations are slightly faster on large parallel workloads than Triple Modular Redundancy (TMR). They also have one third of the memory footprint. We expect the improvement to be significant if suitable optimizations are performed. Because faults are avoided each time new points are computed, the proposed stencils are also comparably robust to faults as TMR for a large range of error rates. The technique can be generalized to 3D (or higher dimensions) with similar benefits.
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of a system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation.We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equations at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. The goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.
Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO2 (ffCO2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO2 emissions and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.
We demonstrate a Bayesian method that can be used to calibrate computationally expensive 3D RANS models with complex response surfaces. Such calibrations, conditioned on experimental data, can yield turbulence model parameters as probability density functions (PDF), concisely capturing the uncertainty in the estimation. Methods such as Markov chain Monte Carlo construct the PDF by sampling, and consequently a quick-running surrogate is used instead of the RANS simulator. The surrogate can be very difficult to design if the model’s response i.e., the dependence of the calibration variable (the observable) on the parameters being estimated is complex. We show how the training data used to construct the surrogate models can also be employed to isolate a promising and physically realistic part of the parameter space, within which the response is well-behaved and easily modeled. We design a classifier, based on treed linear models, to model the “well-behaved region”. This classifier serves as a prior in a Bayesian calibration study aimed at estimating 3 k-ε parameters C = (Cμ, Cε2, Cε1) from experimental data of a transonic jet-in-crossflow interaction. The robustness of the calibration is investigated by checking its predictions of variables not included in the calibration data. We also check the limit of applicability of the calibration by testing at an off-calibration point.
We demonstrate a Bayesian method that can be used to calibrate computationally expensive 3D RANS (Reynolds Av- eraged Navier Stokes) models with complex response surfaces. Such calibrations, conditioned on experimental data, can yield turbulence model parameters as probability density functions (PDF), concisely capturing the uncertainty in the parameter estimates. Methods such as Markov chain Monte Carlo (MCMC) estimate the PDF by sampling, with each sample requiring a run of the RANS model. Consequently a quick-running surrogate is used instead to the RANS simulator. The surrogate can be very difficult to design if the model's response i.e., the dependence of the calibration variable (the observable) on the parameter being estimated is complex. We show how the training data used to construct the surrogate can be employed to isolate a promising and physically realistic part of the parameter space, within which the response is well-behaved and easily modeled. We design a classifier, based on treed linear models, to model the "well-behaved region". This classifier serves as a prior in a Bayesian calibration study aimed at estimating 3 k - ε parameters ( C μ, C ε2 , C ε1 ) from experimental data of a transonic jet-in-crossflow interaction. The robustness of the calibration is investigated by checking its predictions of variables not included in the cal- ibration data. We also check the limit of applicability of the calibration by testing at off-calibration flow regimes. We find that calibration yield turbulence model parameters which predict the flowfield far better than when the nomi- nal values of the parameters are used. Substantial improvements are still obtained when we use the calibrated RANS model to predict jet-in-crossflow at Mach numbers and jet strengths quite different from those used to generate the ex- perimental (calibration) data. Thus the primary reason for poor predictive skill of RANS, when using nominal values of the turbulence model parameters, was parametric uncertainty, which was rectified by calibration. Post-calibration, the dominant contribution to model inaccuraries are due to the structural errors in RANS.
Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximated Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.
