This report summarizes work done under the Laboratory Directed Research and Development (LDRD) project titled "Incorporating physical constraints into Gaussian process surrogate models?' In this project, we explored a variety of strategies for constraint implementations. We considered bound constraints, monotonicity and related convexity constraints, Gaussian processes which are constrained to satisfy linear operator constraints which represent physical laws expressed as partial differential equations, and intrinsic boundary condition constraints. We wrote three papers and are currently finishing two others. We developed initial software implementations for some approaches. This report summarizes the work done under this LDRD.
We developed a computational strategy to correlate bulk combustion metrics of novel fuels and blends in the low-temperature autoignition regime with measurements of key combustion intermediates in a small-volume, dilute, high-pressure reactor. We used neural net analysis of a large simulation dataset to obtain an approximate correlation and proposed experimental and computational steps needed to refine such a predictive correlation. We also designed and constructed a high-pressure laboratory apparatus to conduct the proposed measurements and demonstrated its performance on three canonical fuels: n-heptane, i-octane, and dimethyl ether.
This report documents a statistical method for the "real-time" characterization of partially observed epidemics. Observations consist of daily counts of symptomatic patients, diagnosed with the disease. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information for the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and is predicated on a model for the distribution of the incubation period. The model parameters are estimated as distributions using a Markov Chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. The method is applied to the COVID-19 pandemic of 2020, using data at the country, provincial (e.g., states) and regional (e.g. county) levels. The epidemiological model includes a stochastic component due to uncertainties in the incubation period. This model-form uncertainty is accommodated by a pseudo-marginal Metropolis-Hastings MCMC sampler, which produces posterior distributions that reflect this uncertainty. We approximate the discrepancy between the data and the epidemiological model using Gaussian and negative binomial error models; the latter was motivated by the over-dispersed count data. For small daily counts we find the performance of the calibrated models to be similar for the two error models. For large daily counts the negative-binomial approximation is numerically unstable unlike the Gaussian error model. Application of the model at the country level (for the United States, Germany, Italy, etc.) generally provided accurate forecasts, as the data consisted of large counts which suppressed the day-to-day variations in the observations. Further, the bulk of the data is sourced over the duration before the relaxation of the curbs on population mixing, and is not confounded by any discernible country-wide second wave of infections. At the state-level, where reporting was poor or which evinced few infections (e.g., New Mexico), the variance in the data posed some, though not insurmountable, difficulties, and forecasts were able to capture the data with large uncertainty bounds. The method was found to be sufficiently sensitive to discern the flattening of the infection and epidemic curve due to shelter-in-place orders after around 90% quantile for the incubation distribution (about 10 days for COVID-19). The proposed model was also used at a regional level to compare the forecasts for the central and north-west regions of New Mexico. Modeling the data for these regions illustrated different disease spread dynamics captured by the model. While in the central region the daily counts peaked in the late April, in the north-west region the ramp-up continued for approximately three more weeks.
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.
Sandia National Laboratories currently has 27 COVID-related Laboratory Directed Research & Development (LDRD) projects focused on helping the nation during the pandemic. These LDRD projects cross many disciplines including bioscience, computing & information sciences, engineering science, materials science, nanodevices & microsystems, and radiation effects & high energy density science.
Transitional Markov Chain Monte Carlo (TMCMC) is a variant of a class of Markov Chain Monte Carlo algorithms known as tempering-based methods. In this report, the implementation of TMCMC in the Uncertainty Quantification Toolkit is investigated through the sampling of high-dimensional distributions, multi-modal distributions, and nonlinear manifolds. Furthermore, the Bayesian model evidence estimates obtained from TMCMC are tested on problems with known analytical solutions and shown to provide consistent results.
The UQ Toolkit (UQTk) is a collection of libraries and tools for the quantification of uncertainty in numerical model predictions. Version 3.1.0 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.
We demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differential equation. The objective function and constraints of the optimization problem are then efficiently framed as non-parametric conditional expectations. Different spatial resolutions of a large-eddy simulation filter are used to explore the robustness of the model to the training dataset and to gain insight into the significance of spatial resolution on optimal design.
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 estimates 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 Bayesian model evidence.
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Itô stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter ε. Currently, ε is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of ε, based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases.