Combined Feed
https://feeds.library.caltech.edu/people/Qian-Elizabeth/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:51:35 +0000Towards scalable parallel-in-time turbulent flow simulations
https://resolver.caltech.edu/CaltechAUTHORS:20220513-557821000
Authors: {'items': [{'id': 'Wang-Qiqi', 'name': {'family': 'Wang', 'given': 'Qiqi'}, 'orcid': '0000-0001-9634-1472'}, {'id': 'Gomez-Steven-A', 'name': {'family': 'Gomez', 'given': 'Steven A.'}}, {'id': 'Blonigan-Patrick-J', 'name': {'family': 'Blonigan', 'given': 'Patrick J.'}}, {'id': 'Gregory-Alistair-L', 'name': {'family': 'Gregory', 'given': 'Alastair L.'}}, {'id': 'Qian-Elizabeth', 'name': {'family': 'Qian', 'given': 'Elizabeth Y.'}, 'orcid': '0000-0001-6713-3746'}]}
Year: 2013
DOI: 10.1063/1.4819390
We present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation can be proven to be well-conditioned time domain boundary value problems. The reformulation can enable scalable parallel-in-time simulation of turbulent flows.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bz9sx-rxz42A Certified Trust Region Reduced Basis Approach to PDE-Constrained Optimization
https://resolver.caltech.edu/CaltechAUTHORS:20220713-96144000
Authors: {'items': [{'id': 'Qian-Elizabeth', 'name': {'family': 'Qian', 'given': 'Elizabeth'}, 'orcid': '0000-0001-6713-3746'}, {'id': 'Grepl-Martin', 'name': {'family': 'Grepl', 'given': 'Martin'}}, {'id': 'Veroy-Karen', 'name': {'family': 'Veroy', 'given': 'Karen'}}, {'id': 'Willcox-Karen', 'name': {'family': 'Willcox', 'given': 'Karen'}}]}
Year: 2017
DOI: 10.1137/16m1081981
Parameter optimization problems constrained by partial differential equations (PDEs) appear in many science and engineering applications. Solving these optimization problems may require a prohibitively large number of computationally expensive PDE solves, especially if the dimension of the design space is large. It is therefore advantageous to replace expensive high-dimensional PDE solvers (e.g., finite element) with lower-dimensional surrogate models. In this paper, the reduced basis (RB) model reduction method is used in conjunction with a trust region optimization framework to accelerate PDE-constrained parameter optimization. Novel a posteriori error bounds on the RB cost and cost gradient for quadratic cost functionals (e.g., least squares) are presented and used to guarantee convergence to the optimum of the high-fidelity model. The proposed certified RB trust region approach uses high-fidelity solves to update the RB model only if the approximation is no longer sufficiently accurate, reducing the number of full-fidelity solves required. We consider problems governed by elliptic and parabolic PDEs and present numerical results for a thermal fin model problem in which we are able to reduce the number of full solves necessary for the optimization by up to 86%.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8fatf-s5084Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices
https://resolver.caltech.edu/CaltechAUTHORS:20220624-673343300
Authors: {'items': [{'id': 'Qian-Elizabeth', 'name': {'family': 'Qian', 'given': 'E.'}, 'orcid': '0000-0001-6713-3746'}, {'id': 'Peherstorfer-B', 'name': {'family': 'Peherstorfer', 'given': 'B.'}}, {'id': "O'Malley-D", 'name': {'family': "O'Malley", 'given': 'D.'}}, {'id': 'Vesselinov-V-V', 'name': {'family': 'Vesselinov', 'given': 'V. V.'}}, {'id': 'Willcox-K', 'name': {'family': 'Willcox', 'given': 'K.'}}]}
Year: 2018
DOI: 10.1137/17m1151006
Variance-based sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This work presents a multifidelity approach for estimating sensitivity indices that leverages cheaper low-fidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convection-diffusion-reaction model that demonstrate up to 10x speedups for fixed convergence levels. For the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/aqj4g-g6151Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
https://resolver.caltech.edu/CaltechAUTHORS:20220513-557886000
Authors: {'items': [{'id': 'Qian-Elizabeth', 'name': {'family': 'Qian', 'given': 'Elizabeth'}, 'orcid': '0000-0001-6713-3746'}, {'id': 'Kramer-Boris', 'name': {'family': 'Kramer', 'given': 'Boris'}, 'orcid': '0000-0002-3626-7925'}, {'id': 'Peherstorfer-Benjamin', 'name': {'family': 'Peherstorfer', 'given': 'Benjamin'}}, {'id': 'Willcox-Karen-E', 'name': {'family': 'Willcox', 'given': 'Karen'}, 'orcid': '0000-0003-2156-9338'}]}
Year: 2020
DOI: 10.1016/j.physd.2020.132401
We present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system's governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHughâ€“Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vv7yc-te185Model Reduction of Linear Dynamical Systems via Balancing for Bayesian Inference
https://resolver.caltech.edu/CaltechAUTHORS:20220426-43806400
Authors: {'items': [{'id': 'Qian-Elizabeth', 'name': {'family': 'Qian', 'given': 'Elizabeth'}, 'orcid': '0000-0001-6713-3746'}, {'id': 'Tabeart-Jemima-M', 'name': {'family': 'Tabeart', 'given': 'Jemima M.'}, 'orcid': '0000-0001-6806-8608'}, {'id': 'Beattie-Christopher', 'name': {'family': 'Beattie', 'given': 'Christopher'}}, {'id': 'Gugercin-Serkan', 'name': {'family': 'Gugercin', 'given': 'Serkan'}}, {'id': 'Jiang-Jiahua', 'name': {'family': 'Jiang', 'given': 'Jiahua'}}, {'id': 'Kramer-Peter-R', 'name': {'family': 'Kramer', 'given': 'Peter R.'}, 'orcid': '0000-0003-4867-5835'}, {'id': 'Narayan-Akil', 'name': {'family': 'Narayan', 'given': 'Akil'}, 'orcid': '0000-0002-5914-4207'}]}
Year: 2022
DOI: 10.1007/s10915-022-01798-8
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large dimension of the dynamical system state poses a computational obstacle to computing the exact posterior distribution. Model reduction offers a variety of computational tools that seek to reduce this computational burden. In particular, balanced truncation is a system-theoretic approach to model reduction which obtains an efficient reduced-dimension dynamical system by projecting the system operators onto state directions which trade off the reachability and observability of state directions as expressed through the associated Gramians. We introduce Gramian definitions relevant to the inference setting and propose a balanced truncation approach based on these inference Gramians that yield a reduced dynamical system that can be used to cheaply approximate the posterior mean and covariance. Our definitions exploit natural connections between (i) the reachability Gramian and the prior covariance and (ii) the observability Gramian and the Fisher information. The resulting reduced model then inherits stability properties and error bounds from system theoretic considerations, and in some settings yields an optimal posterior covariance approximation. Numerical demonstrations on two benchmark problems in model reduction show that our method can yield near-optimal posterior covariance approximations with order-of-magnitude state dimension reduction.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/snhcb-h8k13Multifidelity uncertainty quantification and model validation of large-scale multidisciplinary systems
https://resolver.caltech.edu/CaltechAUTHORS:20220726-996912000
Authors: {'items': [{'id': 'Cataldo-Giuseppe', 'name': {'family': 'Cataldo', 'given': 'Giuseppe'}}, {'id': 'Qian-Elizabeth', 'name': {'family': 'Qian', 'given': 'Elizabeth'}, 'orcid': '0000-0001-6713-3746'}, {'id': 'Auclair-Jeremy', 'name': {'family': 'Auclair', 'given': 'Jeremy'}}]}
Year: 2022
DOI: 10.1117/1.jatis.8.3.038001
A simulation-based framework for multifidelity uncertainty quantification is presented, which informs and guides the design process of complex, large-scale, multidisciplinary systems throughout their life cycle. In this framework, uncertainty in system models is identified, characterized, and propagated in an integrated manner through the analysis cycles needed to quantify the effects of uncertainty on the quantities of interest. This is part of the process to design systems and verify their compliance to performance requirements. Uncertainty quantification is performed through mean and variance estimators as well as global sensitivity analyses. These computational analyses are made tractable by the use of multifidelity methods, which leverage a variety of low-fidelity models to obtain speed-ups, while keeping the main high-fidelity model in the loop to guarantee convergence to the correct result. This framework was applied to the James Webb Space Telescope observatory integrated model used to calculate the wavefront error caused by thermal distortions. The framework proved to reduce the time required to perform global sensitivity analyses from more than 2 months to less than 2 days, while reducing the error in the final estimates of the quantities of interest, including model uncertainty factors. These technical performance improvements are crucial to the optimization of project resources such as schedule and budget and ultimately mission success.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/j6vhm-6hp13