Publications

Ray, Jaideep R.; Swiler, Laura P.; Huang, Maoyi H.; Zhangshuan, Hou Z.

Abstract not provided.

Hou, Z H.; Ray, Jaideep R.; Huang, M H.; Swiler, Laura P.

Abstract not provided.

Ray, Jaideep R.; Hou, Zhangshuan H.; Huang, Maoyi H.; Swiler, Laura P.

Abstract not provided.

Drohmann, M.D.; Tuminaro, Raymond S.; Boggs, Paul T.; Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Carlberg, Kevin T.

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.

Ray, Jaideep R.; Swiler, Laura P.

Abstract not provided.

Ray, Jaideep R.; Swiler, Laura P.

Abstract not provided.

SIAM Journal of Uncertainty Quantification

Ray, Jaideep R.; Swiler, Laura P.; Sargsyan, Khachik S.

Abstract not provided.

Swiler, Laura P.; Ray, Jaideep R.; Sargsyan, Khachik S.

Abstract not provided.

Ray, Jaideep R.; Swiler, Laura P.

We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural error in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.

Atmospheric Chemistry and Physics

Ray, Jaideep R.; van Bloemen Waanders, Bart G.

Abstract not provided.

Ray, Jaideep R.; Lee, Jina L.; Lefantzi, Sophia L.; van Bloemen Waanders, Bart G.

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. The limited nature of the measured data leads to a severely-underdetermined estimation problem. If the estimation is performed at fine spatial resolutions, it can also be computationally expensive. In order to enable such estimations, advances are needed in the spatial representation of ffCO2 emissions, scalable inversion algorithms and the identification of observables to measure. To that end, we investigate parsimonious spatial parameterizations of ffCO2 emissions which can be used in atmospheric inversions. We devise and test three random field models, based on wavelets, Gaussian kernels and covariance structures derived from easily-observed proxies of human activity. In doing so, we constructed a novel inversion algorithm, based on compressive sensing and sparse reconstruction, to perform the estimation. We also address scalable ensemble Kalman filters as an inversion mechanism and quantify the impact of Gaussian assumptions inherent in them. We find that the assumption does not impact the estimates of mean ffCO2 source strengths appreciably, but a comparison with Markov chain Monte Carlo estimates show significant differences in the variance of the source strengths. Finally, we study if the very different spatial natures of biogenic and ffCO2 emissions can be used to estimate them, in a disaggregated fashion, solely from CO2 concentration measurements, without extra information from products of incomplete combustion e.g., CO. We find that this is possible during the winter months, though the errors can be as large as 50%.

Ray, Jaideep R.; Lee, Jina L.; Lefantzi, Sophia L.; van Bloemen Waanders, Bart G.

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. To that end, we construct a multiresolution spatial parametrization for fossil-fuel CO2 emissions (ffCO2), to be used in atmospheric inversions. Such a parametrization does not currently exist. The parametrization uses wavelets to accurately capture the multiscale, nonstationary nature of ffCO2 emissions and employs proxies of human habitation, e.g., images of lights at night and maps of built-up areas to reduce the dimensionality of the multiresolution parametrization. The parametrization is used in a synthetic data inversion to test its suitability for use in atmospheric inverse problem. This linear inverse problem is predicated on observations of ffCO2 concentrations collected at measurement towers. We adapt a convex optimization technique, commonly used in the reconstruction of compressively sensed images, to perform sparse reconstruction of the time-variant ffCO2 emission field. We also borrow concepts from compressive sensing to impose boundary conditions i.e., to limit ffCO2 emissions within an irregularly shaped region (the United States, in our case). We find that the optimization algorithm performs a data-driven sparsification of the spatial parametrization and retains only of those wavelets whose weights could be estimated from the observations. Further, our method for the imposition of boundary conditions leads to a 10computational saving over conventional means of doing so. We conclude with a discussion of the accuracy of the estimated emissions and the suitability of the spatial parametrization for use in inverse problems with a significant degree of regularization.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Mckenna, Sean A.

Abstract not provided.

Proposed for publication in Computer methods in applied mechanics and engineering.

van Bloemen Waanders, Bart G.; Ray, Jaideep R.

Abstract not provided.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Mckenna, Sean A.

Abstract not provided.

Ray, Jaideep R.; Lefantzi, Sophia L.; Mckenna, Sean A.; van Bloemen Waanders, Bart G.

Abstract not provided.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Mckenna, Sean A.

Abstract not provided.

Ray, Jaideep R.; Lefantzi, Sophia L.; Mckenna, Sean A.; van Bloemen Waanders, Bart G.

Abstract not provided.

Lefantzi, Sophia L.; Mckenna, Sean A.; Ray, Jaideep R.; van Bloemen Waanders, Bart G.

Abstract not provided.

Lefantzi, Sophia L.; Klise, Katherine A.; Salazar, Luke S.; Mckenna, Sean A.; van Bloemen Waanders, Bart G.; Ray, Jaideep R.

We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loeve expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman filter. We conclude with a demonstration of the use of multiscale stochastic finite elements to reconstruct permeability fields. This method, though computationally intensive, is general and can be used for multiscale inference in cases where a subgrid model cannot be constructed.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Lefantzi, Sophia L.

Abstract not provided.

Advances in Water Resources

Mckenna, Sean A.; van Bloemen Waanders, Bart G.; Ray, Jaideep R.

Abstract not provided.

Advances in Water Resources

Mckenna, Sean A.; Ray, Jaideep R.; Marzouk, Youssef; van Bloemen Waanders, Bart G.

Truncated Gaussian fields provide a flexible model for defining binary media with dispersed (as opposed to layered) inclusions. General properties of excursion sets on these truncated fields are coupled with a distance-based upscaling algorithm and approximations of point process theory to develop an estimation approach for effective conductivity in two-dimensions. Estimation of effective conductivity is derived directly from knowledge of the kernel size used to create the multiGaussian field, defined as the full-width at half maximum (FWHM), the truncation threshold and conductance values of the two modes. Therefore, instantiation of the multiGaussian field is not necessary for estimation of the effective conductance. The critical component of the effective medium approximation developed here is the mean distance between high conductivity inclusions. This mean distance is characterized as a function of the FWHM, the truncation threshold and the ratio of the two modal conductivities. Sensitivity of the resulting effective conductivity to this mean distance is examined for two levels of contrast in the modal conductances and different FWHM sizes. Results demonstrate that the FWHM is a robust measure of mean travel distance in the background medium. The resulting effective conductivities are accurate when compared to numerical results and results obtained from effective media theory, distance-based upscaling and numerical simulation. © 2011 Elsevier Ltd.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Mckenna, Sean A.

Abstract not provided.

Ray, Jaideep R.; van Bloemen Waanders, Bart G.; Mckenna, Sean A.

We present results from a recently developed multiscale inversion technique for binary media, with emphasis on the effect of subgrid model errors on the inversion. Binary media are a useful fine-scale representation of heterogeneous porous media. Averaged properties of the binary field representations can be used to characterize flow through the porous medium at the macroscale. Both direct measurements of the averaged properties and upscaling are complicated and may not provide accurate results. However, it may be possible to infer upscaled properties of the binary medium from indirect measurements at the coarse scale. Multiscale inversion, performed with a subgrid model to connect disparate scales together, can also yield information on the fine-scale properties. We model the binary medium using truncated Gaussian fields, and develop a subgrid model for the upscaled permeability based on excursion sets of those fields. The subgrid model requires an estimate of the proportion of inclusions at the block scale as well as some geometrical parameters of the inclusions as inputs, and predicts the effective permeability. The inclusion proportion is assumed to be spatially varying, modeled using Gaussian processes and represented using a truncated Karhunen-Louve (KL) expansion. This expansion is used, along with the subgrid model, to pose as a Bayesian inverse problem for the KL weights and the geometrical parameters of the inclusions. The model error is represented in two different ways: (1) as a homoscedastic error and (2) as a heteroscedastic error, dependent on inclusion proportionality and geometry. The error models impact the form of the likelihood function in the expression for the posterior density of the objects of inference. The problem is solved using an adaptive Markov Chain Monte Carlo method, and joint posterior distributions are developed for the KL weights and inclusion geometry. Effective permeabilities and tracer breakthrough times at a few 'sensor' locations (obtained by simulating a pump test) form the observables used in the inversion. The inferred quantities can be used to generate an ensemble of permeability fields, both upscaled and fine-scale, which are consistent with the observations. We compare the inferences developed using the two error models, in terms of the KL weights and fine-scale realizations that could be supported by the coarse-scale inferences. Permeability differences are observed mainly in regions where the inclusions proportion is near the percolation threshold, and the subgrid model incurs its largest approximation. These differences also reflected in the tracer breakthrough times and the geometry of flow streamlines, as obtained from a permeameter simulation. The uncertainty due to subgrid model error is also compared to the uncertainty in the inversion due to incomplete data.