Projection-based model reduction: Formulations for physics-based machine learning

Computers & Fluids - Tập 179 - Trang 704-717 - 2019
Renee Swischuk1, Laura Mainini1, Benjamin Peherstorfer2, Karen Willcox1
1Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2University of Wisconsin-Madison, Madison, WI 53706, USA

Tài liệu tham khảo

Coveney, 2016, Big data need big theory too, Philos Trans R Soc Lond A, 374, 1 Antoulas, 2001, A survey of model reduction methods for large-scale systems, Contemp Math, 280, 193, 10.1090/conm/280/04630 Rozza, 2007, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Arch Comput Methods Eng, 15, 1, 10.1007/BF03024948 Chinesta, 2011, A short review on model order reduction based on proper generalized decomposition, Arch Comput Methods Eng, 18, 395, 10.1007/s11831-011-9064-7 Quarteroni A, Rozza G, editors. Reduced order methods for modeling and computational reduction. Springer; 2014. Benner, 2015, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM Rev, 57, 483, 10.1137/130932715 Hesthaven, 2016 Chinesta, 2017, Model reduction methods, 1 Lumley, 1967, The structures of inhomogeneous turbulent flow, 166 Holmes, 1996 Sirovich, 1987, Turbulence and the dynamics of coherent structures. part 1: coherent structures, Q Appl Math, 45, 561, 10.1090/qam/910462 Ly, 2001, Modeling and control of physical processes using proper orthogonal decomposition, J Math Comput Model, 33, 223, 10.1016/S0895-7177(00)00240-5 Bui-Thanh, 2004, Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition, AIAA J, 42, 1505, 10.2514/1.2159 Everson, 1995, The Karhunen-Loeve procedure for gappy data, J Opt Soc Am, 12, 1657, 10.1364/JOSAA.12.001657 Audouze, 2009, Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis, Int J Numer Methods Eng, 80, 1025, 10.1002/nme.2540 Wirtz, 2014, Surrogate modeling of multiscale models using kernel methods, Int J Numer Methods Eng, 101, 1, 10.1002/nme.4767 Audouze, 2013, Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations, Numer Methods Partial Differ Equ, 29, 1587, 10.1002/num.21768 Mainini, 2015, Surrogate modeling approach to support real-time structural assessment and decision making, AIAA J, 53, 1612, 10.2514/1.J053464 Ulu, 2016, A data-driven investigation and estimation of optimal topologies under variable loading configurations, Comput Methods Biomech BiomedEng, 4, 61 Hesthaven, 2018, Non-intrusive reduced order modeling of nonlinear problems using neural networks, J Comput Phys, 363, 55, 10.1016/j.jcp.2018.02.037 Chen, 2017, A greedy non-intrusive reduced order model for fluid dynamics, J Northwest Polytech Univ Ljung, 1987 Viberg, 1995, Subspace-based methods for the identification of linear time-invariant systems, Automatica, 31, 1835, 10.1016/0005-1098(95)00107-5 Kramer, 2016, Tangential interpolation-based Eigensystem realization algorithm for MIMO systems, Math Comput Model Dyn Syst, 22, 282, 10.1080/13873954.2016.1198389 Qin, 2006, An overview of subspace identification, Comput Chem Eng, 30, 1502, 10.1016/j.compchemeng.2006.05.045 Reynders, 2012, System identification methods for (operational) modal analysis: review and comparison, Arch Comput Methods Eng, 19, 51, 10.1007/s11831-012-9069-x Abderrahim, 2010, New approaches to finite impulse response systems identification using higher-order statistics, IET Signal Proc, 4, 488, 10.1049/iet-spr.2008.0190 Rabiner, 1978, FIR system modeling and identification in the presence of noise and with band-limited inputs, IEEE Trans Acoust, 26, 319, 10.1109/TASSP.1978.1163113 Mendel, 1991, Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications, Proc IEEE, 79, 278, 10.1109/5.75086 Antoulas, 1986, On the scalar rational interpolation problem, IMA J Math Control Inf, 3, 61, 10.1093/imamci/3.2-3.61 Lefteriu, 2010, A new approach to modeling multiport systems from frequency-domain data, Comput Aided Des Integr CircuitsSyst IEEE Trans, 29, 14, 10.1109/TCAD.2009.2034500 Mayo, 2007, A framework for the solution of the generalized realization problem, Linear Algebra Appl, 425, 634, 10.1016/j.laa.2007.03.008 Beattie, 2012, Realization-independent H2-approximation, 4953 Schulze, 2018, Data-driven structured realization, Linear Algebra Appl, 537, 250, 10.1016/j.laa.2017.09.030 Ionita, 2012, Matrix pencils in time and frequency domain system identification, 79 Peherstorfer, 2017, Data-driven reduced model construction with time-domain Loewner models, SIAM J Scient Comput, 39, A2152, 10.1137/16M1094750 Drmač, 2015, Quadrature-based vector fitting for discretized H2 approximation, SIAM J Scient Comput, 37, A625, 10.1137/140961511 Drmač, 2015, Vector fitting for matrix-valued rational approximation, SIAM J Scient Comput, 37, A2346, 10.1137/15M1010774 Tu, 2014, On dynamic mode decomposition: theory and applications, J Comput Dyn, 1, 391, 10.3934/jcd.2014.1.391 Proctor, 2016, Dynamic mode decomposition with control, SIAM J Appl Dyn Syst, 15, 142, 10.1137/15M1013857 Proctor, 2014, Exploiting sparsity and equation-free architectures in complex systems, Eur Phys J Spec Top, 223, 2665, 10.1140/epjst/e2014-02285-8 Peherstorfer, 2016, Data-driven operator inference for nonintrusive projection-based model reduction, Comput Methods Appl Mech Eng, 306, 196, 10.1016/j.cma.2016.03.025 Castelletti, 2012, Data-driven dynamic emulation modelling for the optimal management of environmental systems, Environ Model Softw, 34, 30, 10.1016/j.envsoft.2011.09.003 Galelli, 2015, High-performance integrated control of water quality and quantity in urban water reservoirs, Water Resour Res, 51, 9053-9072, 10.1002/2015WR017595 Brunton, 2016, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proc Natl Acad Sci, 113, 3932, 10.1073/pnas.1517384113 Dean, 2017, On the sample complexity of the linear quadratic regulator, ArXiv e-prints Tu, 2017, Least-Squares temporal difference learning for the linear quadratic regulator, ArXiv e-prints Balzano, 2010, Online identification and tracking of subspaces from highly incomplete information, 704 Peherstorfer, 2015, Online adaptive model reduction for nonlinear systems via low-rank updates, SIAM J Scient Comput, 37, A2123, 10.1137/140989169 Zimmermann, 2018, Geometric subspace updates with applications to online adaptive nonlinear model reduction, SIAM J Matrix Anal Appl, 39, 234, 10.1137/17M1123286 Yano, 2013, A model-data weak formulation for simultaneous estimation of state and model bias, CR Math, 351, 937 Maday, 2015, PBDW State estimation: noisy observations; configuration-adaptive background spaces; physical interpretations, 50, 144 Parish, 2016, A paradigm for data-driven predictive modeling using field inversion and machine learning, J Comput Phys, 305, 758, 10.1016/j.jcp.2015.11.012 Singh, 2017, Augmentation of turbulence models using field inversion and machine learning, 1 Lam, 2015, Multifidelity optimization using statistical surrogate modeling for non-hierarchical information sources, 0143 Poloczek, 2017, Multi-information source optimization, 4291 Ghoreishi, 2018 Peherstorfer, 2018, Survey of multifidelity methods in uncertainty propagation, inference, and optimization, SIAM Rev, 10.1137/16M1082469 Bishop, 2006 Hastie, 2009 Murphy, 2012 Haykin, 2008 Akçelik, 2003, High resolution forward and inverse earthquake modeling on terascale computers Rudi, 2015, An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in Earth’s mantle Loéve, 1955 Kosambi, 1943, Statistics in function space, J Indian Math Soc, 7, 76 Hotelling, 1933, Analysis of a complex of statistical variables with principal components, J Educ Psychol, 24, 10.1037/h0070888 North, 1982, Sampling errors in the estimation of empirical orthogonal functions, Mon Weather Rev, 110, 699, 10.1175/1520-0493(1982)110<0699:SEITEO>2.0.CO;2 Raghavan, 2013, A bi-level meta-modeling approach for structural optimization using modified POD bases and diffuse approximation, Comput Struct, 127, 19, 10.1016/j.compstruc.2012.06.008 Hall, 2000, Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows, AIAA J, 38, 1853, 10.2514/2.867 Nielsen, 2015 Rumelhart, 1986, Learning representations by back-propagating errors, Nature, 323, 533, 10.1038/323533a0 Livni, 2014, On the computational efficiency of training neural networks, 855 Bentley, 1975, Multidimensional binary search trees used for associative searching, Commun ACM, 18, 509, 10.1145/361002.361007 Friedman, 1977, An algorithm for finding best matches in logarithmic expected time, ACM Trans Math Softw, 3, 209, 10.1145/355744.355745 Breiman, 2017 Palacios, 2013, Stanford University Unstructured (SU2): an open-source integrated computational environment for multi-physics simulation and design, 1