Computational science is a driver of our society’s technological advancement, playing a key role for design, decision making and risk assessment. The ``extreme-scale'' computing era we are living in is enabling a paradigm shift: we no longer approach a problem with a few, target runs for specific choices of parameters and conditions, but we aim increasingly more at combining higher fidelity models with uncertainty quantification (UQ) methods to address, e.g., design optimization and parameter-space exploration. This approach allows us to discover rare events and critical behaviors of a target system, which is key information for high-consequence systems and cutting-edge engineering. If the system of interest is expensive to query, UQ can become impractical to complete within a reasonable amount of time. Reduced-order models (ROMs), due to their accuracy, computational efficiency and certification, constitute a promising technique to overcome this computational barrier, and make high-fidelity predictive simulations feasible for UQ. This mini-symposium aims at presenting recent advances in algorithms, software and applications in the context of reduced-order models and their broad impact for UQ. The talks will cover a broad range of applications, ranging from hypersonics to multiscale flows and plasma microturbulence.
16:30
Windowed Least–Squares Reduced-Order Models for Dynamical Systems
Eric Parish | Sandia National Labs | United States
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Eric Parish | Sandia National Labs | United States
Kevin Carlberg | Facebook Reality Labs | United States
We present a windowed least-squares (WLS) reduced-order modeling formulation for dynamical systems. The approach sequentially minimizes the time-continuous full-order model residual within a low-dimensional trial space over a series of time windows, and comprises a generalization of the Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG methods. The stationary conditions are obtained via the Euler–Lagrange equations and comprise a coupled two-point Hamiltonian boundary value problem containing a forward and backward system. We examine two differing methods to solve the minimization problems: direct (discretize then minimize) and indirect (minimize and then discretize). Lastly, we present numerical experiments demonstrating that, at an increased computational cost, the WLS formulation can yield more accurate and physically relevant solutions than the Galerkin and Least-Squares Petrov–Galerkin approaches. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525
17:00
Context-aware multifidelity Monte Carlo sampling
Ionut-Gabriel Farcas | Technical University of Munich | Germany
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Ionut-Gabriel Farcas | Technical University of Munich | Germany
Benjamin Peherstorfer | Courant Institute for Mathematical Sciences | United States
Frank Jenko | Max Planck Institute for Plasma Physics | Germany
Hans-Joachim Bungartz | Technical University of Munich | Germany
Traditional model reduction aims to construct low-cost low-fidelity models to replace computationally expensive high-fidelity models for speeding up computations. In contrast, in multifidelity methods, low- and high-fidelity models are used together and so the primary purpose of low-fidelity models is supporting computations with the high-fidelity models rather than approximating and replacing them. In this presentation, we introduce low-fidelity models that are explicitly constructed for being used together with high-fidelity models in multifidelity settings. We discuss the Context-aware multifidelity Monte Carlo algorithm that learns contextaware low-fidelity models for the estimation of statistics of high-fidelity model outputs. These low-fidelity models are constructed by quasi-optimally trading off refining the low-fidelity models (to improve their deterministic approximation quality) with sampling the models (to reduce the statistical error). Our analysis shows that the quasi-optimal computational effort to spend on improving the low-fidelity models is bounded, which means that low-fidelity models can become too accurate for multifidelity methods, which is in stark contrast to traditional model reduction. We test the power and usefulness of the proposed approach in two test cases in which we construct several context-aware low-fidelity models of different kinds, and in a real-world plasma microturbulence analysis problem in which we employ a sparse grid surrogate.
17:30
- CANCELED - Least-Squares Petrov-Galerkin Reduced-Order Models for Hypersonic Flight Vehicles
Patrick Blonigan | Sandia National Labs | United States
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Patrick Blonigan | Sandia National Labs | United States
Francesco Rizzi | NexGen Analytics | United States
Micah Howard | Sandia National Labs | United States
Jeff Fike | Sandia National Labs | United States
High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis due to the expense and difficulty of flight tests and experiments. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ). However, it is very computationally expensive to run CFD for hypersonic flows due to high grid resolution requirements. Additionally, UQ approaches are “many-query” problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model. In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems including subsonic CFD applications. This work presents the first application of LSPG to hypersonic CFD applications including the Blottner sphere and HiFIRE experimental flight vehicle. This shows the ability of LSPG ROMs to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525
18:00
Scalable Closure of Nonlinear Manifold Reduced-Order Models
Christopher Wentland | University of Michigan | United States
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Christopher Wentland | University of Michigan | United States
Karthik Duraisamy | University of Michigan | United States
As projection-based reduced-order models (ROMs) are applied to increasingly complex dynamical systems, the assumption that dominant system dynamics evolve on a linear subspace has displayed extreme accuracy and stability limitations. Recent developments in neural networks, specifically convolutional autoencoders and recurrent neural networks, have improved approximations of system dynamics on a learned low-dimensional nonlinear manifold or modeled memory effects inherent in ROMs. In this work, we combine, refine, and expand upon both concepts, utilizing convolutional neural networks to realize significant dimension reduction on a nonlinear manifold, and implementing neural networks to predict closure dynamics and improve simulation accuracy. This approach formally separates the Markovian coarse-scale dynamics from the memory effects, as described by the Mori-Zwanzig formalism. Additionally, whereas many neural network ROMs have dealt with small proof-of-concept systems, we test this method for several large, highly nonlinear, multiscale fluid flow problems which stand to benefit greatly from improved dimension reduction. Results are compared against standard linear projection and nonlinear manifold ROMs. The computational cost of each network architecture is discussed, and analysis of network parameterizations is performed to develop improved heuristics for implementing such neural networks for large-scale simulations.