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This is an investigation on two experimental datasets of laminar hypersonic flows, over a double-cone geometry, acquired in Calspan--University at Buffalo Research Center's Large Energy National Shock (LENS)-XX expansion tunnel. These datasets have yet to be modeled accurately. A previous paper suggested that this could partly be due to mis-specified inlet conditions. The authors of this paper solved a Bayesian inverse problem to infer the inlet conditions of the LENS-XX test section and found that in one case they lay outside the uncertainty bounds specified in the experimental dataset. However, the inference was performed using approximate surrogate models. In this paper, the experimental datasets are revisited and inversions for the tunnel test-section inlet conditions are performed with a Navier-Stokes simulator. The inversion is deterministic and can provide uncertainty bounds on the inlet conditions under a Gaussian assumption. It was found that deterministic inversion yields inlet conditions that do not agree with what was stated in the experiments. An a posteriori method is also presented to check the validity of the Gaussian assumption for the posterior distribution. This paper contributes to ongoing work on the assessment of datasets from challenging experiments conducted in extreme environments, where the experimental apparatus is pushed to the margins of its design and performance envelopes. [ABSTRACT FROM AUTHOR]

This paper explores automated approaches for the analysis and categorization of turbulent flow data as a means of assessing the quality of a turbulence dataset used for constructing data-driven turbulence closures. Single-point statistics from several high-fidelity turbulent flow simulation datasets are differentiated into groups using a Gaussian mixture model clustering algorithm. Candidate features are proposed, and a feature selection algorithm is applied to the data in a sequential fashion, flow by flow, to identify a good feature set and an optimal number of clusters for each dataset. Clusters are first identified for plane channel flows, producing results that agree with existing theory and empirical observations. Further clusters are then identified in an incremental fashion for flow over a wavy-walled channel, flow over a bump in a channel, and flow past a square cylinder. Some clusters are closely identified with the anisotropy state of the turbulence, whereas others can be connected to physical phenomena, such as boundary-layer separation and free shear layers. Exemplar points from the clusters, or prototypes, are then identified using a prototype placement method. These exemplars effectively summarize the dataset using a greatly reduced collection of data points. The clusters and their prototypes are used to assess the quality of a training dataset constructed by simply pooling the four flows. We enumerate the dataset's shortcomings and state the limits of generalizability of any data-driven closure trained on it. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Compressible jet-in-crossflow interactions are difficult to simulate accurately using Reynolds-averaged Navier-Stokes (RANS) models. This could be due to simplifications inherent in RANS or the use of inappropriate RANS constants estimated by fitting to experiments of simple or canonical flows. Our previous work on Bayesian calibration of a k-ε model to experimental data had led to a weak hypothesis that inaccurate simulations could be due to inappropriate constants more than model-form inadequacies of RANS. In this work, Bayesian calibration of k-ε constants to a set of experiments that span a range of Mach numbers and jet strengths has been performed. The variation of the calibrated constants has been checked to assess the degree to which parametric estimates compensate for RANS's model-form errors. An analytical model of jet-in-crossflow interactions has also been developed, and estimates of k-ε constants that are free of any conflation of parametric and RANS's model-form uncertainties have been obtained. It has been found that the analytical k-ε constants provide mean-flow predictions that are similar to those provided by the calibrated constants. Further, both of them provide predictions that are far closer to experimental measurements than those computed using "nominal" values of these constants simply obtained from the literature. It can be concluded that the lack of predictive skill of RANS jet-in-crossflow simulations is mostly due to parametric inadequacies, and our analytical estimates may provide a simple way of obtaining predictive compressible jet-in-crossflow simulations. [ABSTRACT FROM AUTHOR]

In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability. [ABSTRACT FROM AUTHOR]

Reynolds-averaged Navier-Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow 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. A Bayesian inverse problem is formulated to estimate three Reynolds-averaged Navier-Stokes parameters (C956,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 (C956,Cε2,Cε1) space RR supports realistic flow simulations. RR is 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 (C956,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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: A high-order projection scheme was developed for the study of chemically reacting flows in the low-Mach number limit. The numerical approach for the momentum transport uses a combination of cell-centered/cell-averaged discretizations to achieve a fourth order formulation for the pressure projection algorithm. This scheme is coupled with a second order in time operator-split stiff approach for the species and energy equations. The code employs a fourth order, block-structured, adaptive mesh refinement approach to address the challenges posed by the large spectrum of spatial scales encountered in reacting flow computations. Results for advection–diffusion-reaction configurations are used to illustrate the performance of the numerical construction. [ABSTRACT FROM AUTHOR]

Block-structured adaptive mesh refinement (AMR) is used for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order derivative, interpolation, and filter stencils and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by the discretized operators for derivatives, interpolations, and filters. We develop general expressions for high-order derivative, interpolation, and filter stencils applicable in multiple dimensions, using a Fourier approach, to facilitate high-order block-structured AMR implementations. These stencils are derived under the assumption that the fields that they are applied to are smooth. For a given derivative stencil (and thus a given order of accuracy), the necessary interpolation order is found to be dependent on the highest spatial derivative in the PDE being solved. This is demonstrated empirically, using one- and two-dimensional model equations, by observing the increase in delivered accuracy as the order of accuracy of the interpolation stencil is increased. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of derivative, interpolation, and filter stencils. The procedure devised here is modular and its various pieces, i.e., the derivative, interpolation, and filter stencils, can be extended independently to higher orders and dimensions (in the case of interpolation stencils). The application of these methods often requires nontrivial logic, especially near domain boundaries; this logic, along with the stencils used in this study, are available as a freely downloadable software library. [ABSTRACT FROM AUTHOR]

The article focuses on the development of a model that predicts the suitability of a structured adaptive mesh for purely domain-based or patch-based decomposition. The model could be used to determine one of the parameters used to configure a partitioner or choose the optimal one for a given problem. The predictions were validated against data obtained from four different SAMR simulations. Optimal partitioning of structured adaptive mesh applications necessitates dynamically determining and optimizing for the most time-inhibiting factor, such as load imbalance and communication volume. This model contributes to the meta-partitioner, able to select and configure the optimal partitioner based on the mesh configuration, the simulation and computer characteristics. The results show that the proposed model generally captures the inherent optimization-need in structured adaptive mesh refinement applications. The article concludes that the model could be useful for decreasing execution time for large SAMR applications.

We examine the vortex dynamics and interfacial evolution of "reacceleration" and "reshock" for single interface density-stratified fluid (Richtmyer-Meshkov) environments. In the former case, we simulate, visualize, and quantify the parameter range of the free falling tank laboratory experiment of J. Jacobs and C. F. Niederhaus, where the impulsive subsequent acceleration of the interface occurs after several rolls from the initial impulsive acceleration. We interpret the rapid onset of chaotic motion in the roll-up region as due to the formation of intertwined close-laying layers of opposite-signed vorticity. In the latter case, we make compressible simulations at low Mach number (M=1.2) and compare with incompressible simulations. We juxtapose the results and find an excellent agreement in large and intermediate size features and their magnitudes before the "reshock." At the "reshock," discrepancies arise due to highly compressible regime. The simulations were made with incompressible vorticity-based methods, vortex-in-cell (VIC) and vortex blob (VB), and compressible second-order Godunov codes. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Previous efforts determined a set of calibrated, optimal model parameter values for Reynolds-averaged Navier-Stokes (RANS) simulations of a compressible jet in crossflow (JIC) using a k-e turbulence model. These parameters were derived by comparing simulation results to particle image velocimetry (PIV) data of a complementary JIC experiment under a limited set of flow conditions. Here, a k-e model using both nominal and calibrated parameters is validated against PIV data acquired from a much wider variety of JIC cases, including a realistic flight vehicle. The results from the simulations using the calibrated model parameters showed considerable improvements over those using the nominal values, even for cases that were not used in the calibration procedure that defined the optimal parameters. This improvement is demonstrated using a number of quality metrics that test the spatial alignment of the jet core, the magnitudes of multiple flow variables, and the location and strengths of vortices in the counter-rotating vortex cores on the PIV planes. These results suggest that the calibrated parameters have applicability well outside the specific flow case used in defining them and that with the right model parameters, RANS solutions for the JIC can be improved significantly over those obtained from the nominal model. [ABSTRACT FROM AUTHOR]

Explores the generation of baroclinic circulation on shock accelerated gas interfaces. Refraction of incident shock at slow/fast interfaces; Production of a transmitted shock and reflected waves; Calculation of the total circulation deposited on sinusoidal interfaces.

In this study, we focus on a hydrogeological inverse problem specifically targeting monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data. Technical challenges exist in the inversion of GPR tomographic data for handling non-uniqueness, nonlinearity and high-dimensionality of unknowns. We have developed a new method for estimating soil moisture fields from crosshole GPR data. It uses a pilot-point method to provide a low-dimensional representation of the relative dielectric permittivity field of the soil, which is the primary object of inference: the field can be converted to soil moisture using a petrophysical model. We integrate a multi-chain Markov chain Monte Carlo (MCMC)-Bayesian inversion framework with the pilot point concept, a curved-ray GPR travel time model, and a sequential Gaussian simulation algorithm, for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as the corresponding geostatistical parameters (i.e., spatial correlation range). We infer the dielectric permittivity as a probability density function, thus capturing the uncertainty in the inference. The multi-chain MCMC enables addressing high-dimensional inverse problems as required in the inversion setup. The method is scalable in terms of number of chains and processors, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. The proposed inversion approach can successfully approximate the posterior density distributions of the pilot points, and capture the true values. The computational efficiency, accuracy, and convergence behaviors of the inversion approach were also systematically evaluated, by comparing the inversion results obtained with different levels of noises in the observations, increased observational data, as well as increased number of pilot points. [ABSTRACT FROM AUTHOR]

We identify two different modes, types I and II, of the interaction for planar shocks accelerating heavy prolate gaseous ellipses. These modes arise from different interactions of the incident shock (IS) and transmitted shock (TS) on the leeward side of the ellipse. A time ratio t T/t I(M,η,λ,γ 0,γ b), which characterizes the mode of interaction, is derived heuristically. Here, the principal parameters governing the interaction are the Mach number of the shock (M), the ratio of the density of the ellipse to the ambient gas density, (η>1), γ 0, γ b (the ratios of specific heats of the two gases), λ (the aspect ratio). Salient events in shock-ellipse interactions are identified and correlated with their signatures in circulation budgets and on-axis space-time pressure diagrams. The two modes yield different mechanisms of the baroclinic vorticity generation. We present a heuristic model for the net baroclinic circulation generated on the interface at the end of the early-time phase by both the IS and TS and validate the model via numerical simulations of the Euler equations. In the range 1.2<=M<=3.5, 1.54<=η<=5.04, and λ=1.5 and 3.0, our model predicts the baroclinic circulation on the interface within a band of ±10% in comparison to converged numerical simulations. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A “buffer zone” methodology is introduced to impose the solid–fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed. [Copyright &y& Elsevier]

To increase situational awareness and support evidence-based policymaking, we formulated a mathematical model for coronavirus disease transmission within a regional population. This compartmental model accounts for quarantine, self-isolation, social distancing, a nonexponentially distributed incubation period, asymptomatic persons, and mild and severe forms of symptomatic disease. We used Bayesian inference to calibrate region-specific models for consistency with daily reports of confirmed cases in the 15 most populous metropolitan statistical areas in the United States. We also quantified uncertainty in parameter estimates and forecasts. This online learning approach enables early identification of new trends despite considerable variability in case reporting. [ABSTRACT FROM AUTHOR]

In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate models are essential for many-query applications e.g., engineering design optimization and parameter estimation, where it is necessary to invoke the high-fidelity model sequentially, many times. Surrogate models are usually constructed for individual scalar quantities. However there are scenarios where a spatially varying field needs to be modeled as a function of the model's input parameters. We develop a method to do so, using projections to represent spatial variability while a machine-learned model captures the dependence of the model's response on the inputs. The method is demonstrated on modeling the heat flux and pressure on the surface of the HIFiRE-1 geometry in a Mach 7.16 turbulent flow. The surrogate model is then used to perform Bayesian estimation of freestream conditions and parameters of the SST (Shear Stress Transport) turbulence model embedded in the high-fidelity (Reynolds-Averaged Navier–Stokes) flow simulator, using shock-tunnel data. The paper provides the first-ever Bayesian calibration of a turbulence model for complex hypersonic turbulent flows. We find that the primary issues in estimating the SST model parameters are the limited information content of the heat flux and pressure measurements and the large model-form error encountered in a certain part of the flow. • We study data-driven ROM-based surrogate model construction for application in hypersonic flows. • Complementary software compatible with scikit-learn is available here: https://www.github.com/kennychowdhary/tesuract. • First-ever Bayesian calibration of a hypersonic flow model using data-driven ROM surrogates. [ABSTRACT FROM AUTHOR]

• Identify emergent technologies from open-source indicators using binary classifier. • Transition between emergence and growth is encoded in the shape of the curve. • Artificial neural network learns technology maturity based on derivatives of curve. • Data augmentation improves classifier performance by increasing training corpus. The capability to identify emergent technologies based upon easily accessed open-source indicators, such as publications, is important for decision-makers in industry and government. The scientific contribution of this work is the proposition of a machine learning approach to the detection of the maturity of emerging technologies based on publication counts. Time-series of publication counts have universal features that distinguish emerging and growing technologies. We train an artificial neural network classifier, a supervised machine learning algorithm, upon these features to predict the maturity (emergent vs. growth) of an arbitrary technology. With a training set comprised of 22 technologies we obtain a classification accuracy ranging from 58.3% to 100% with an average accuracy of 84.6% for six test technologies. To enhance classifier performance, we augmented the training corpus with synthetic time-series technology life cycle curves, formed by calculating weighted averages of curves in the original training set. Training the classifier on the synthetic data set resulted in improved accuracy, ranging from 83.3% to 100% with an average accuracy of 90.4% for the test technologies. The performance of our classifier exceeds that of competing machine learning approaches in the literature, which report an average classification accuracy of only 85.7% at maximum. Moreover, in contrast to current methods our approach does not require subject matter expertise to generate training labels, and it can be automated and scaled. [ABSTRACT FROM AUTHOR]

This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and displacement fields. The proposed methodology develops a low-dimensional parametrization of these quantities of interest using space–time bases combined with machine learning methods. In particular, the space–time solutions are sought in a low-dimensional space–time linear trial subspace that can be obtained by computing tensor decompositions of usual state-snapshots data. The mapping between the input parameters and the basis expansion coefficients (or generalized coordinates) is approximated using four different machine learning techniques: multivariate polynomial regression, k -nearest-neighbors, random forests and neural networks. The relative costs and effectiveness of the four machine learning techniques are explored through three engineering problems: steady heat conduction, unsteady heat conduction and unsteady advective–diffusive–reactive system. Numerical results demonstrate that the proposed method performs well in terms of both accuracy and computational cost, and highlights the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models. • A novel non-intrusive reduced-order model (ROM) method to solve systems of parameterized unsteady nonlinear algebraic equations is developed. • Various machine learning techniques to approximate the mapping between input parameters and output space–time bases expansion coefficients are examined: multivariate polynomial regression, k-nearest neighbors, random forest and neural network. • In the offline stage, we collect usual (space–time) state snapshots to build space–time bases and train the machine learning surrogate models. • In the online stage, for an arbitrary input parameter we express the space–time solution as linear combinations of those space–time bases and compute the coefficients using the trained surrogate models. • The space–time basis expansion coefficients only depend on input parameters and not on time. • The proposed method is verified on three benchmark problems: parameterized steady heat conduction PDE, parameterized unsteady heat conduction PDE and parameterized advective–diffusive–reactive problem. • Numerical results show that the online computation of machine learning surrogate models is extremely fast and the relative solution error is less than 1% on average. • We show that while our proposed approach is less accurate than the least-square Petrov–Galerkin (LSPG) model reduction (without hyper-reduction), it is significantly faster. [ABSTRACT FROM AUTHOR]