We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns latent dynamics from snapshot data, enforcing local operator structure such as skew-symmetry, (semi-)positive definiteness, and gradient preservation, while also reflecting complex dynamics by supporting additive compositions of heterogeneous operators. We present practical training strategies and analyze computational costs relative to linear and quadratic polynomial OpInf (P-OpInf). Numerical experiments across several nonlinear and parametric problems demonstrate improved accuracy, stability, and robustness over P-OpInf and prior NN-ROM formulations, particularly when the dynamics are not well represented by polynomial models. These results suggest that NN-OpInf can serve as an effective drop-in replacement for P-OpInf when the dynamics to be modeled contain non-polynomial nonlinearities, offering potential gains in accuracy and out-of-distribution performance at the expense of higher training computational costs and a more difficult, non-convex learning problem.

This work presents a physics-infused reduced-order modeling (PIROM) framework toward the design optimization of non-linear dynamical systems. It is demonstrated via the modeling of transient thermal behavior in multi-layered hypersonic thermal protection systems. The PIROM architecture integrates a reduced-physics backbone, based on the lumped capacitance model, with data-driven correction dynamics formulated via a coarse-graining approach rooted in the Mori–Zwanzig formalism. While the lumped capacitance model captures the dominant heat transfer mechanisms, the correction terms compensate for residual dynamics arising from higher-order non-linear interactions and heterogeneities across material layers. The proposed PIROM is benchmarked against a non-intrusive ROM (i.e., operator inference) and a surrogate model (i.e., neural ordinary differential equations). The PIROM consistently achieves errors below 1

This work presents an adaptive high-order method for the simulation of parametrized high-speed flows. To obviate the proliferation of degrees of freedom inherent in the discontinuous Galerkin discretization chosen here, we use a hybridized method that decreases the size of the global system along with r-adaptive meshing. For efficiency and robustness, we use a strategy of artificial viscosity continuation, wherein the amount of added dissipation is ramped down until physicality and smoothness constraints are violated. We demonstrate this procedure on problems with greater physical complexity than considered in prior works by incorporating coupled aerothermal interactions between fluid and solid domains. In addition, we have previously found that this choice of mesh adaptation method aids in the creation of surrogate models for flows with shocks. We evaluate whether these advantages persist for viscous flows with multiphysics couplings, demonstrating the use of this method for the forward propagation of uncertain boundary conditions for high-speed flows.

This work investigates the use of the reduced-basis method for multifidelity uncertainty quantification (UQ) with application to the Reynolds-Averaged Navier-Stokes equations. We examine the use of a greedy algorithm that leverages easily computable error estimates for constructing a reduced basis. This reduced basis is used to define a Galerkin reduced-order model that leverages entropy-variable transforms to maintain robustness. We embed our reduced-order model within sampling multifidelity UQ methods and assess its utility for more-efficiently propagating parametric uncertainties with the Spalart-Allmaras turbulence model. Results are presented on several hypersonic turbulent flow configurations.

Projection-based reduced-order models (ROMs) are applied to the hypersonic aerodynamics simulations for aeroheating analysis over a flight path. Simulating the aerodynamics is generally the computational bottleneck for aeroheating so accurate and inexpensive ROMs would significantly accelerate the coupled simulations. This work examines ROMs for hypersonic aerodynamics solved with non-equilibrium chemistry and considers non-constant and non-uniform boundary conditions, surface mass flux, and surface displacement. As the surface materials ablate, mass is released into the boundary layer and the surface of the flight vehicle recesses with time. The ROMs must therefore be solved with varying surface temperatures, mass fluxes, and on a grid in which the surface location changes. This study finds that the ROMs in general are more accurate than interpolation, but have poor accuracy when the boundary conditions are non-constant and non-uniform.

Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning and showcase improved accuracy over traditional linear subspace-reduced order models. A disadvantage of the previously proposed methods is the potential high computational costs of training the networks on high-fidelity solution snapshots. In this work, we propose and analyze a novel method that overcomes this disadvantage by training a neural network only on subsampled versions of the high-fidelity solution snapshots. This method coupled with collocation-based hyper-reduction and Gappy-POD allows for efficient and accurate surrogate models. We demonstrate the validity of our approach on a 2d Burgers problem.

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.

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.

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.

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.

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 ROM is 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.

The solution of conservation laws with parametrized shock waves presents challenges for both high-order numerical methods and model reduction techniques. We introduce an r-adaptivity scheme based on optimal transport and apply it to develop reduced order models for compressible flows. The optimal transport theory allows us to compute high-order r-adaptive meshes from a starting reference mesh by solving the Monge-Ampere equation. A high-order discretization of the conservation laws enables high-order solutions to be computed on the resulting r-adaptive meshes. Furthermore, the Monge-Ampere solutions contain mappings that are used to reduce the spatial locality of the resulting solutions and make them more amenable to model reduction. We use a non-intrusive model reduction method to construct reduced order models of both the mesh and the solution. The procedure is demonstrated on three supersonic and hypersonic test cases, with the hybridizable discontinuous Galerkin method being used as the full order model.

AbstractWe present a novel framework for automatically detecting spatial and temporal events of interest in situ while running high performance computing (HPC) simulations. The new framework – composed from signature, measure, and decision building blocks with well-defined semantics – is tailored for parallel and distributed computing, has bounded communication and storage requirements, is generalizable to a variety of applications, and operates in an unsupervised fashion. We demonstrate the efficacy of our framework on several cases spanning scientific domains and applications of event detection: optimized input/output (I/O) in computational fluid dynamics simulations, detecting events that can lead to irreversible climate changes in simulations of polar ice sheets, and identifying optimal space-time subregions for projection-based model reduction. Additionally, we demonstrate the scalability of our framework using a HPC combustion application on the Cori supercomputer at the National Energy Research Scientific Computing Center (NERSC).

View Video Presentation: https://doi.org/10.2514/6.2022-1247.vid High-fidelity hypersonic aerodynamic simulations require extensive computational resources, hindering their usage in hypersonic vehicle design and uncertainty quantification. Projection-based reduced-order models (ROMs) are a computationally cheaper alternative to full-order simulations that can provide major speedup with marginal loss of accuracy when solving many-query problems such as design optimization and uncertainty propagation. However, ROMs can present robustness and convergence issues, especially when trained over large ranges of input parameters and/or with few training samples. This paper presents the application of several different residual minimization-based ROMs to hypersonic flows around flight vehicles using less training data than in previous work. The ROM demonstrations are accompanied by a comparison to fully data-driven approaches including kriging and radial basis function interpolation. Results are presented for three test cases including one three-dimensional flight vehicle. We show that registration-based ROMs trained on grid-tailored solutions can compute quantities of interest more accurately than data driven approaches for a given sparse training set. We also find that the classic L2 state error metric is not particularly useful when comparing different model reduction techniques on sparse training data sets.