Physics-informed machine learning for reduced-order modeling of nonlinear problems
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Jan S. Hesthaven | Qian Wang | Wenqian Chen | Chuhua Zhang | J. Hesthaven | Chuhua Zhang | Qian Wang | Wenqian Chen
[1] Y. Ju,et al. A multidomain multigrid pseudospectral method for incompressible flows , 2018, Numerical Heat Transfer, Part B: Fundamentals.
[2] F. Chinesta,et al. A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .
[3] Philip S. Beran,et al. Reduced-order modeling - New approaches for computational physics , 2001 .
[4] A. Quarteroni,et al. Reduced Basis Methods for Partial Differential Equations: An Introduction , 2015 .
[5] Danny C. Sorensen,et al. Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..
[6] Boris Lohmann,et al. Parametric Model Order Reduction by Matrix Interpolation , 2010, Autom..
[7] Karthik Duraisamy,et al. Challenges in Reduced Order Modeling of Reacting Flows , 2018, 2018 Joint Propulsion Conference.
[8] Martin A. Riedmiller,et al. Advanced supervised learning in multi-layer perceptrons — From backpropagation to adaptive learning algorithms , 1994 .
[9] H. P. Lee,et al. PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY , 2002 .
[10] Wei Zhang,et al. An explicit Chebyshev pseudospectral multigrid method for incompressible Navier–Stokes equations , 2010 .
[11] George Em Karniadakis,et al. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations , 2020, Science.
[12] G. Karniadakis,et al. Physics-informed neural networks for high-speed flows , 2020, Computer Methods in Applied Mechanics and Engineering.
[13] Jean-Antoine Désidéri,et al. Stability Properties of POD–Galerkin Approximations for the Compressible Navier–Stokes Equations , 2000 .
[14] Siep Weiland,et al. Missing Point Estimation in Models Described by Proper Orthogonal Decomposition , 2004, IEEE Transactions on Automatic Control.
[15] R. Peyret. Spectral Methods for Incompressible Viscous Flow , 2002 .
[16] Lawrence Sirovich,et al. Karhunen–Loève procedure for gappy data , 1995 .
[17] Arthur Veldman,et al. Proper orthogonal decomposition and low-dimensional models for driven cavity flows , 1998 .
[18] I. Kevrekidis,et al. Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylinders , 1991 .
[19] Yvon Maday,et al. Reduced basis method for the rapid and reliable solution of partial differential equations , 2006 .
[20] Karen Willcox,et al. A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..
[21] Natalia Gimelshein,et al. PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.
[22] Anthony Nouy,et al. Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems , 2016, SIAM J. Sci. Comput..
[23] Jan S. Hesthaven,et al. Reduced order modeling for nonlinear structural analysis using Gaussian process regression , 2018, Computer Methods in Applied Mechanics and Engineering.
[24] Paris Perdikaris,et al. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , 2019, J. Comput. Phys..
[25] J. Hesthaven,et al. Non-intrusive reduced order modeling of nonlinear problems using neural networks , 2018, J. Comput. Phys..
[26] R. Murray,et al. Model reduction for compressible flows using POD and Galerkin projection , 2004 .
[27] Luning Sun,et al. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data , 2019, Computer Methods in Applied Mechanics and Engineering.
[28] Miss A.O. Penney. (b) , 1974, The New Yale Book of Quotations.
[29] Yaping Ju,et al. A parallel inverted dual time stepping method for unsteady incompressible fluid flow and heat transfer problems , 2020, Comput. Phys. Commun..
[30] J. Hesthaven,et al. Certified Reduced Basis Methods for Parametrized Partial Differential Equations , 2015 .
[31] Paul Van Dooren,et al. Model reduction via tangential interpolation , 2002 .
[32] Benjamin Stamm,et al. EFFICIENT GREEDY ALGORITHMS FOR HIGH-DIMENSIONAL PARAMETER SPACES WITH APPLICATIONS TO EMPIRICAL INTERPOLATION AND REDUCED BASIS METHODS ∗ , 2014 .
[33] Qian Wang,et al. Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism , 2020, J. Comput. Phys..
[34] N. Nguyen,et al. An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .
[35] C. Eckart,et al. The approximation of one matrix by another of lower rank , 1936 .
[36] Fabien Casenave,et al. A nonintrusive reduced basis method applied to aeroacoustic simulations , 2014, Adv. Comput. Math..
[37] Erich Novak,et al. High dimensional polynomial interpolation on sparse grids , 2000, Adv. Comput. Math..
[38] Jonathan R Clausen,et al. Entropically damped form of artificial compressibility for explicit simulation of incompressible flow. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.