A reduced order with data assimilation model: Theory and practice

[1]  Ionel M. Navon,et al.  Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes , 2023, Computer Methods in Applied Mechanics and Engineering.

[2]  Julio Amador Díaz López,et al.  Data Learning: Integrating Data Assimilation and Machine Learning , 2021, J. Comput. Sci..

[3]  Vinicius L. S. Silva,et al.  Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19 , 2021, ArXiv.

[4]  R. Arcucci,et al.  Deep Data Assimilation: Integrating Deep Learning with Data Assimilation , 2021, Applied Sciences.

[5]  Rossella Arcucci,et al.  Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilation , 2020, Computer Methods in Applied Mechanics and Engineering.

[6]  D. Xiao,et al.  Error estimation of the parametric non-intrusive reduced order model using machine learning , 2019, Computer Methods in Applied Mechanics and Engineering.

[7]  Christopher C. Pain,et al.  Optimal reduced space for Variational Data Assimilation , 2019, J. Comput. Phys..

[8]  Yike Guo,et al.  A reduced order model for turbulent flows in the urban environment using machine learning , 2019, Building and Environment.

[9]  J. Hesthaven,et al.  Greedy Nonintrusive Reduced Order Model for Fluid Dynamics , 2018, AIAA Journal.

[10]  Yike Guo,et al.  Effective variational data assimilation in air-pollution prediction , 2018, Big Data Min. Anal..

[11]  Giuseppe Scotti,et al.  A Decomposition of the Tikhonov Regularization Functional Oriented to Exploit Hybrid Multilevel Parallelism , 2017, International Journal of Parallel Programming.

[12]  Christopher C. Pain,et al.  Towards non-intrusive reduced order 3D free surface flow modelling , 2017, Ocean Engineering.

[13]  J. Allegrini,et al.  Multiscale interaction between a cluster of buildings and the ABL developing over a real terrain , 2017 .

[14]  Sara Omrani,et al.  Natural ventilation in multi-storey buildings: Design process and review of evaluation tools , 2017 .

[15]  Almerico Murli,et al.  On the variational data assimilation problem solving and sensitivity analysis , 2017, J. Comput. Phys..

[16]  Ionel M. Navon,et al.  Non‐intrusive reduced order modelling with least squares fitting on a sparse grid , 2017 .

[17]  Christopher C. Pain,et al.  Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids , 2017 .

[18]  Ionel M. Navon,et al.  2D Burgers equation with large Reynolds number using POD/DEIM and calibration , 2016 .

[19]  Peter J. Schmid,et al.  Recursive dynamic mode decomposition of transient and post-transient wake flows , 2016, Journal of Fluid Mechanics.

[20]  D. A. Bistrian,et al.  Randomized dynamic mode decomposition for nonintrusive reduced order modelling , 2016, 1611.04884.

[21]  G. Rozza,et al.  POD-Galerkin method for finite volume approximation of Navier–Stokes and RANS equations , 2016 .

[22]  Christopher C. Pain,et al.  Non-intrusive reduced order modelling of fluid–structure interactions , 2016 .

[23]  Jan ter Maten,et al.  Sensitivity analysis and model order reduction for random linear dynamical systems , 2015, Math. Comput. Simul..

[24]  Adrian Sandu,et al.  POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation , 2014, J. Comput. Phys..

[25]  Emiliano Iuliano,et al.  Aerodynamic shape optimization via non-intrusive POD-based surrogate modelling , 2013, 2013 IEEE Congress on Evolutionary Computation.

[26]  David A. Ham,et al.  POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow , 2013, Comput. Math. Appl..

[27]  S-J Cao,et al.  On the construction and use of linear low-dimensional ventilation models. , 2012, Indoor air.

[28]  Charbel Farhat,et al.  The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows , 2012, J. Comput. Phys..

[29]  Hernan G. Arango,et al.  The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems Part I - System overview and formulation , 2011 .

[30]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[31]  Danny C. Sorensen,et al.  Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..

[32]  Christopher C. Pain,et al.  A comparison of mesh-adaptive LES with wind tunnel data for flow past buildings: Mean flows and velocity fluctuations , 2009 .

[33]  P. Nair,et al.  Reduced‐order modeling of parameterized PDEs using time–space‐parameter principal component analysis , 2009 .

[34]  Laurent Cordier,et al.  Calibration of POD reduced‐order models using Tikhonov regularization , 2009 .

[35]  Karen Willcox,et al.  Parametric reduced-order models for probabilistic analysis of unsteady aerodynamic applications , 2007 .

[36]  Ionel M. Navon,et al.  A reduced‐order approach to four‐dimensional variational data assimilation using proper orthogonal decomposition , 2007 .

[37]  M. Piggott,et al.  A Nonhydrostatic Finite-Element Model for Three-Dimensional Stratified Oceanic Flows. Part II: Model Validation , 2004 .

[38]  Wei Huang,et al.  A Three-Dimensional Variational Data Assimilation System for MM5: Implementation and Initial Results , 2004 .

[39]  Philippe Courtier,et al.  The ECMWF implementation of three-dimensional variational assimilation ( 3 D-Var ) . 111 : Experimental results , 2006 .

[40]  P. Courtier,et al.  The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). I: Formulation , 1998 .

[41]  P. Courtier,et al.  A strategy for operational implementation of 4D‐Var, using an incremental approach , 1994 .

[42]  Per Christian Hansen,et al.  Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-Determined Numerical Rank , 1990, SIAM J. Sci. Comput..

[43]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[44]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[45]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[46]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[47]  A. Muggeridge,et al.  Fast Modelling of Gas Reservoirs Using POD-RBF Non-Intrusive Reduced Order Modelling , 2020 .

[48]  R N Meroney,et al.  On the use of numerical modelling for near-field pollutant dispersion in urban environments--A review. , 2016, Environmental pollution.

[49]  Nancy Nichols,et al.  Mathematical Concepts of Data Assimilation , 2010 .

[50]  C. Qiu,et al.  Four-dimensional data assimilation method based on SVD: Theoretical aspect , 2006 .

[51]  Andrew C. Lorenc,et al.  Development of an Operational Variational Assimilation Scheme (gtSpecial IssueltData Assimilation in Meteology and Oceanography: Theory and Practice) , 1997 .