Model reduction and inverse problems and data assimilation with geophysical applications. A special issue in honor of I. Michael Navon's 75th birthday

Abstract

EDITORIALModel reduction and inverse problems and data assimilation with geophysical applications. A special issue in honor of I. Michael Navon's 75th birthdayProfessor Ionel Michael Navon retired in September 2014 from the Scientific Computing Department, Florida State University, Tallahassee, Florida, after a brilliant academic career. Since 1997, he is a fellow of the American Meteorological Society, and recently, he became an honorary member of the Academy of Romanian Scientists. His distinguished pioneering achievements in the domains of data assimilation, inverse problems, and reduced order modeling during the last few decades have greatly contributed to the establishment and development of these aforementioned fields. In particular, his rich interdisciplinary expertise allowed him to advance the science reduced order modeling and inverse modeling as core techniques for data-driven modeling. He generalized predictive computational modeling leading to fast novel solution approaches for real-world inverse problems of oceanography and weather forecast. At the same time, Professor Ionel Michael Navon has been an outstanding mentor, advisor, role model, and friend to his 9 PhD students and 11 postdoctoral scholars, with the large majority of them pursuing successful academic, scientific, and industry careers. This year Professor Ionel Michael Navon celebrates his 75th anniversary, and this special issue recognizes his accomplishments. The contributors to this special issue are former students, postdoctoral scholars, colleagues, close collaborators, and friends of Professor Ionel Michael Navon. The next three paragraphs describe his most important contributions to data assimilation and reduced order modeling fields in the last 10 years, while the last part of the editorial focuses on the special issue's contributions.Professor Navon's work addressed fundamental issues in both variational and statistical data assimilation with applications in fluid dynamics and atmospheric flows. Professor Navon extended and proposed frameworks to tackle non-differentiability in models and objective functions. For example, he formulated the maximum likelihood ensemble filter (MLEF) equations without the differentiability requirement for the prediction model and for the observation operators [1] and measured the impact of non-smooth observation operators on variational and sequential data assimilation [2]. Other efforts include coupling a Gaussian resampling method to generate more effective and efficient Particle Filter posterior analysis ensembles [3], improvement on the ensemble Kalman filters [4][5][6][7], and MLEF [8]. Professor Navon is also the co-author of a recent book [9] and several book chapters [10][11][12][13] describing the recent advancements and methodologies in variational data assimilation and non-linear sensitivity analysis. Goal-oriented adjoint sensitivity methods were proposed to guide to the adaptivity of finite element meshes [14,15]. Moreover, he developed different approaches to model error formulation [...

Surrogate Modeling of Aerodynamic Simulations for Multiple Operating Conditions Using Machine Learning

“…The surrogate modeling of high-dimensional vector-valued functions is mainly performed with a reduced-order approach, called reduced-order modeling (ROM). Originally developed for the study of coherent structures in the turbulent boundary layer [1], ROM methods have shown various applications such as aeroelasticity [2], optimal flow control [3], turbulent flows [4,5] or geophysics [6]. Most ROM methods are applied to CFD problems by approximating the high fidelity model as a linear combination of low-dimensional basis vectors, weighted by purposely-tuned parameters.…”

A non‐linear non‐intrusive reduced order model of fluid flow by auto‐encoder and self‐attention deep learning methods

“…In this case, the reduced‐order models (ROMs) technology plays an important role as they are able to simulate physical systems accurately with several orders of magnitude CPU speed‐up. The ROMs have been applied successfully to a number of research fields such as data assimilation, 3 ocean modeling, 4 shallow water equations, 5,6 air pollution prediction, 7 polynomial systems, 8 viscous and inviscid flows, 9 fluid‐structure interaction, 10 aerodynamic shape optimization, 11 large‐scale time‐dependent systems, 12 optimal control, 13 circuit systems, 14,15 inverse problems, 16 fluids, 17 reservoir history matching, 18 and turbulent flows 19,20 …”

Randomization for the Efficient Computation of Parametric Reduced Order Models for Inversion

“…Before we continue, we point out that different model reduction techniques have been employed in a wide variety of inverse problems; see, e.g., [12,14,17,19,22,27,[38][39][40][41]47] and the references therein. However, as we explain below, interpolatory model reduction methods [2,3,7] are perfectly suited for the DOT problem and have proven very effective in this setting [20,42].…”