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. Here 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.
Projection-based reduced-order models (pROMs) show great promise as a means to accelerate many-query applications such as forward error propagation, solving inverse problems, and design optimization. In order to deploy pROMs in the context of high-consequence decision making, accurate error estimates are required to determine the region(s) of applicability in the parameter space. The following paper considers the dual-weighted residual (DWR) error estimate for pROMs and compares it to another promising pROM error estimate, machine learned error models (MLEM). In this paper, we show how DWR can be applied to ROMs and then evaluate DWR on two partial differential equations (PDEs): a two-dimensional linear convection–reaction–diffusion equation, and a three-dimensional static hyper-elastic beam. It is shown that DWR is able to estimate errors for pROMs extrapolating outside of their training set while MLEM is best suited for pROMs used to interpolate within the pROM training set.
The design of thermal protection systems (TPS), including heat shields for reentry vehicles, rely more and more on computational simulation tools for design optimization and uncertainty quantification. Since high-fidelity simulations are computationally expensive for full vehicle geometries, analysts primarily use reduced-physics models instead. Recent work has shown that projection-based reduced-order models (ROMs) can provide accurate approximations of high-fidelity models at a lower computational cost. ROMs are preferable to alternative approximation approaches for high-consequence applications due to the presence of rigorous error bounds. The following paper extends our previous work on projection-based ROMs for ablative TPS by considering hyperreduction methods which yield further reductions in computational cost and demonstrating the approach for simulations of a three-dimensional flight vehicle. We compare the accuracy and potential performance of several different hyperreduction methods and mesh sampling strategies. This paper shows that with the correct implementation, hyperreduction can make ROMs up to 1-3 orders of magnitude faster than the full order model by evaluating the residual at only a small fraction of the mesh nodes.
Computational simulations of high-speed flow play an important role in the design of hypersonic vehicles, for which experimental data are scarce; however, high-fidelity simulations of hypersonic flow are computationally expensive. Reduced order models (ROMs) have the potential to make many-query problems, such as design optimization and uncertainty quantification, tractable for this domain. Residual minimization-based ROMs, which formulate the projection onto a reduced basis as an optimization problem, are one promising candidate for model reduction of large-scale fluid problems. This work analyzes whether specific choices of norms and objective functions can improve the performance of ROMs of hypersonic flow. Specifically, we investigate the use of dimensionally consistent inner products and modifications designed for convective problems, including ℓ1 minimization and constrained optimization statements to enforce conservation laws. Particular attention is paid to accuracy for problems with strong shocks, which are common in hypersonic flow and challenging for projection-based ROMs. We demonstrate that these modifications can improve the predictability and efficiency of a ROM, though the impact of such formulations depends on the quantity of interest and problem considered.
Computational simulations of high-speed flow play an important role in the design of hypersonic vehicles, for which experimental data are scarce; however, high-fidelity simulations of hypersonic flow are computationally expensive. Reduced order models (ROMs) have the potential to make many-query problems, such as design optimization and uncertainty quantification, tractable for this domain. Residual minimization-based ROMs, which formulate the projection onto a reduced basis as an optimization problem, are one promising candidate for model reduction of large-scale fluid problems. This work analyzes whether specific choices of norms and objective functions can improve the performance of ROMs of hypersonic flow. Specifically, we investigate the use of dimensionally consistent inner products and modifications designed for convective problems, including ℓ1 minimization and constrained optimization statements to enforce conservation laws. Particular attention is paid to accuracy for problems with strong shocks, which are common in hypersonic flow and challenging for projection-based ROMs. We demonstrate that these modifications can improve the predictability and efficiency of a ROM, though the impact of such formulations depends on the quantity of interest and problem considered.
This paper presents the uncertainty propagation of turbulent coefficients for the Spalart– Allmaras (SA) turbulence model using projection-based reduced-order models (ROMs). ROMs are used instead of Reynolds-averaged Navier–Stokes (RANS) solvers and stochastic collocation/ Galerkin and Monte Carlo methods because they are computationally inexpensive and tend to offer more accuracy than a polynomial surrogate. The uncertainty propagation is performed on two benchmark RANS cases documented on NASA’s turbulence modeling resource. Uncertainty propagation of the SA turbulent coefficients using a ROMis shown to compare well against uncertainty propagation performed using only RANS and using a Gaussian process regression (GP) model. The ROM is shown to be more robust to the size and spread of the training data compared to a GP model.
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.
This paper presents an investigation into sampling strategies for reducing the computational expense of creating error models for steady hypersonic flow surrogate models. The error model describes the quantity of interest error between a reduced-order model prediction and a full-order model solution. The sampling strategies are separated into three categories: distinct training sets, single training set, and augmented single training set for the reduced-order model and the error model. Using a distinct training set, three sampling strategies are investigated: latin hypercube sampling, latin hypercube sampling with a maximin criterion, and a D-Optimal design. It was found that using a D-Optimal design was the most effective at producing an accurate error model with the fewest number of training points. When using a single training set, the leave-one-out cross validation approach was used on the D-Optimal design training set. This produced an error model with an R2 value of greater than 0.8, but it had some outliers due to high nonlinearities in the space. Augmenting the training points of the error model helped improve its accuracy. Using a D-Optimal design with distinct training sets cut the computational cost of creating the error model by 15% and using the LOOCV approach with the D-Optimal design cut the cost by 64%.
This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. Finally, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.
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.