Multifidelity Failure Probability Estimation with Adaptively Designed Surrogate Models
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Jim Warner↗
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Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification
We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.
Autoencoders↗
Multifidelity Analysis and Optimization for Supersonic Design
Supersonic aircraft design is a computationally expensive optimization problem and multifidelity approaches over a significant opportunity to reduce design time and computational cost. This report presents tools developed to improve supersonic aircraft design capabilities including: aerodynamic tools for supersonic aircraft configurations; a systematic way to manage model uncertainty; and multifidelity model management concepts that incorporate uncertainty. The aerodynamic analysis tools developed are appropriate for use in a multifidelity optimization framework, and include four analysis routines to estimate the lift and drag of a supersonic airfoil, a multifidelity supersonic drag code that estimates the drag of aircraft configurations with three different methods: an area rule method, a panel method, and an Euler solver. In addition, five multifidelity optimization methods are developed, which include local and global methods as well as gradient-based and gradient-free techniques.
Kroo, Ilan↗
Covariance-Free Bifidelity Control Variates Importance Sampling for Rare Event Reliability Analysis
Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world problems, particularly when failure is a rare event. To implement multifidelity modeling, estimators that efficiently combine information from multiple models/sources are necessary. In past works, the variance reduction techniques of control variates (CV) and importance sampling (IS) have been leveraged for this task. In this paper, we present the CVIS framework—a creative take on a coupled CV and IS estimator for bifidelity reliability analysis. The framework addresses some of the practical challenges of the CV method by using an estimator for the control variate mean and sidestepping the need to estimate the covariance between the original estimator and the control variate through a clever choice for the tuning constant. Furthermore, the task of selecting an efficient IS distribution is also considered, with a view towards maximally leveraging the bifidelity structure and maintaining expressivity. Additionally, a diagnostic is provided that indicates both the efficiency of the algorithm as well as the relative predictive quality of the models utilized. Finally, the behavior and performance of the framework is explored through analytical and numerical examples.
Markov chain Monte Carlo↗
Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)
Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Strategies for Automation of Model Tuning in Multifidelity Trajectory Uncertainty Propagation
Multi-model Monte Carlo methods are efficient strategies to perform forward uncertainty quantification studies in entry, descent, and landing (EDL) applications. These multi-model methods are based on the classical Monte Carlo estimator, but fuse predictions from several low-fidelity models to obtain estimators with greater precision given a prescribed computational budget. The effectiveness of these approaches relies on the magnitudes of correlations between the low-fidelity models and the high-fidelity model, as well as the relative computational costs of all models. Identifying and exploiting the best trade-off between correlation and cost, which ultimately depends on the selection of hyperparameters in the low-fidelity models, is a task often performed by hand or simply inspired by the deterministic understanding available for a specific application. This work extends a preliminary effort,
Marten Thompson↗
Multiobjective Multidisciplinary Optimization of Low-Boom Supersonic Transports Using Multifidelity Models
A multidisciplinary optimization (MDO) method has been developed to design a computational fluid dynamics (CFD) based low-boom configuration that can be obtained from a Pareto solution of a low-fidelity multiobjective MDO problem with mission constraints. This paper refines the developed MDO method using multifidelity models for CFD-based multiobjective MDO. The refined MDO method can generate a low-boom configuration that satisfies the mission requirements, has the lowest takeoff gross weight and the longest range for the low-boom mission, trims the low-boom cruise flight with fuel redistributions, and has a reversed equivalent area distribution closely matching a low-boom target with ground noise level below 70 PLdB. The validity of the refined MDO method is demonstrated by a design study of a low-boom supersonic transport that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.7 and range of 3500 nm, and cruises overwater at Mach 1.8 with range of 3882 nm. Moreover, the refined MDO method eliminates the difference between the assumed cruise weight for CFD-based low-boom inverse design optimization and the estimated cruise weight of the optimal inverse design solution with respect to the mission requirements.
multidisciplinary optimization↗
Multiobjective Multidisciplinary Optimization of Low-Boom Supersonic Transports Using Multifidelity Models
A multidisciplinary optimization (MDO) method has been developed to design a computational fluid dynamics (CFD) based low-boom configuration that can be obtained from a Pareto solution of a low-fidelity multiobjective MDO problem with mission constraints. This paper refines the developed MDO method by using multifidelity models for CFD-based multiobjective MDO and a better method for the system-level trade between the target low boom ground noise level and the overland range. The refined MDO method can generate a low-boom configuration that satisfies the mission requirements, has the lowest takeoff gross weight and the longest range for the low-boom mission, trims the low-boom cruise flight with fuel redistributions, and has a reversed equivalent area distribution closely matching a low-boom target with ground noise level below 70 PLdB. The validity of the refined MDO method is demonstrated by a design study of a low-boom supersonic transport that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.7 and range of 3500 nm, and cruises overwater at Mach 1.8 with range of 3882 nm. Moreover, the refined MDO method eliminates the difference between the assumed cruise weight for CFD-based low-boom inverse design optimization and the estimated cruise weight of the optimal inverse design solution with respect to the mission requirements.
MDO↗
Improving Multi-Model Trajectory Simulation Estimators using Model Selection and Tuning
Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation amongst the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.
uncertainty quantification↗