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BEGIN:VEVENT
SUMMARY:POD- and RB-Hierarchical Model Reduction Techniques in a Parametri
zed Setting
DTSTART;VALUE=DATE-TIME:20220401T103000Z
DTEND;VALUE=DATE-TIME:20220401T112000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6215@indico.math.cnrs.fr
DESCRIPTION:Speakers: Simona Perotto (Politecnico Milano)\nDifferent metho
ds have been proposed in the scientific panorama to offer a compromise bet
ween modeling accuracy and computational efficiency. Reduced order models
represent a widespread solution in such a direction. In this presentation\
, we focus on the Hierarchical Model (HiMod) reduction technique\, which p
roved to be an effective approach to discretize CFD configurations where a
principal horizontal dynamics overwhelms the transverse ones (e.g.\, when
modeling hemodynamics or signal propagation in waveguides). In particular
\, we address the generalization of the HiMod procedure to a parametrized
setting. We propose two alternative approaches\, which combine HiMod with
Proper Orthogonal Decomposition (POD) and the Reduced Basis (RB) method\,
respectively. The two strategies will be analyzed and cross-compared in or
der to identify the associated pros and cons.\n\nhttps://indico.math.cnrs.
fr/event/5543/contributions/6215/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6215/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some new developments on the non invasive reduced basis method
DTSTART;VALUE=DATE-TIME:20220330T083000Z
DTEND;VALUE=DATE-TIME:20220330T092000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6200@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yvon Maday (UPMC Paris 6)\nThe efficient implementat
ion of reduced basis methods relying on a high fidelity discretization met
hod to compute the elements of the reduced basis\, requires to enter withi
n the code\, offline\, so that the online solution can be produced very ra
pidly. Since this is sometimes impossible\, in particular for codes used i
n industrial framework\, we have proposed a Non Invasive alternative where
the code is used at two stages : a) offline to build the reduced basis\,
b) online to\, first\, compute a coarse approximation using the code with
few degrees of freedom (thus more rapidly than with the high fidelity requ
irement) then by processing this coarse solution to improve the accuracy a
nd fulfil the high fidelity requirement at much mower cost. This method th
at first appeared with its numerical analysis in [1] for finite element ap
proximations has been generalised in various directions (finite volume\, t
runcation of the domain\, different new rectifications) and implemented in
a library in the frame of a joined project with large and medium size com
panies [2]. \nIn this paper I will present some of the new concepts in thi
s drection\n\n[1] Rachida Chakir\, Yvon Maday :A two-grid finite-element/r
educed basis scheme for the approximation of the solution of parameter dep
endent PDE. In 9e Colloque national en calcul des structures. ISO 690 Y. (
2009\, May). \n[2] Elise Grosjean : Variations and further developments on
the Non-Intrusive Reduced Basis two-grid method\, PhD Thesis at Sorbonne
Université - 2022\n\nElise Grosjean and Yvon Maday\n\nhttps://indico.math
.cnrs.fr/event/5543/contributions/6200/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ROM Closures and Stabilizations for Under-Resolved Turbulent Flows
DTSTART;VALUE=DATE-TIME:20220330T114000Z
DTEND;VALUE=DATE-TIME:20220330T123000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6201@indico.math.cnrs.fr
DESCRIPTION:Speakers: Traian Iliescu (Virginia Tech)\nIn this talk\, I wil
l survey reduced order model (ROM) closures and\nstabilizations for under-
resolved turbulent flows. Over the past\ndecade\, several closure and sta
bilization strategies have been\ndeveloped to tackle the ROM inaccuracy in
the convection-dominated\,\nunder-resolved regime\, i.e.\, when the numbe
r of degrees of freedom is\ntoo small to capture the complex underlying dy
namics. I will present\nregularized ROMs\, which are stabilizations that
employ spatial\nfiltering to alleviate the spurious numerical oscillations
generally\nproduced by standard ROMs in the convection-dominated\, under-
resolved\nregime. I will also survey three classes of ROM closures\, i.e.
\,\ncorrection terms that increase the ROM accuracy: (i) functional\nclosu
res\, which are based on physical insight\; (ii) structural\nclosures\, wh
ich are developed by using mathematical arguments\; and\n(iii) data-driven
closures\, which leverage available data. Throughout\nmy talk\, I will hi
ghlight the impact made by data on classical\nnumerical methods over the p
ast decade. I will also emphasize the role\nplayed by physical constraints
in data-driven modeling of ROM closures\nand stabilizations.\n\nhttps://i
ndico.math.cnrs.fr/event/5543/contributions/6201/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tensor methods for high-dimensional problems and model reduction
DTSTART;VALUE=DATE-TIME:20220401T082000Z
DTEND;VALUE=DATE-TIME:20220401T091000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6213@indico.math.cnrs.fr
DESCRIPTION:Speakers: Damiano Lombardi (Inria Paris)\nWe present several c
ontributions related to Tensor methods for high-dimensional problems and d
iscuss how they are inherently related to model reduction.\nIn particular\
, we will show several ways to introduce a principle of adaptivity\, makin
g tensor representations more suitable to parsimoniously represent certain
solutions sets. In the last part of the talk\, a contribution on a possib
le way to exploit a tensor representation in state estimation is presented
. In this\, we show that variational and sequential state estimation metho
ds can be derived after casting state estimation as an optimal recovery pr
oblem\, using tensors to have a space-time representation of the solutions
set.\n\nhttps://indico.math.cnrs.fr/event/5543/contributions/6213/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6213/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Field reconstruction using manifold learning and structure-preserv
ing metrics
DTSTART;VALUE=DATE-TIME:20220330T123000Z
DTEND;VALUE=DATE-TIME:20220330T132000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6202@indico.math.cnrs.fr
DESCRIPTION:Speakers: Lionel Mathelin (LIMSI-CNRS)\nThe problem of estimat
ing the state of a physical system is ubiquitous in science. However obser
vations are always limited so that the high-dimensional state cannot be ob
served and the associated mathematical problem is ill-posed. Popular worka
rounds include dimension reduction and regularization by imposing some str
ucture to the class of elements in which the estimation is sought.\nWe her
e rely on a purely data-driven approach and learn the map between extended
measurements and the nonlinear manifold the state vector lies on. Specifi
cally\, we use embedding to address the non-Markovianity of the raw measur
ements. Combined with multi-kernel learning\, it results in high-dimension
al measurement features. The state vector nonlinear manifold is approximat
ed and the map from measurement features to the estimated state is the sol
ution to a Sylvester equation.\nThe methodology is illustrated with the es
timation of a fluid flow field from a few wall-mounted sensors.\n\nhttps:/
/indico.math.cnrs.fr/event/5543/contributions/6202/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6202/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Model order reduction for CFD: state of the art\, advances in appl
ications
DTSTART;VALUE=DATE-TIME:20220401T094000Z
DTEND;VALUE=DATE-TIME:20220401T103000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6214@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gianlugi Rozza (SISSA)\nhttps://indico.math.cnrs.fr/
event/5543/contributions/6214/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6214/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beyond PCA by explicitely taking into account system symmetries
DTSTART;VALUE=DATE-TIME:20220401T073000Z
DTEND;VALUE=DATE-TIME:20220401T082000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6212@indico.math.cnrs.fr
DESCRIPTION:Speakers: Denis Sipp (ONERA)\nLinear principal component analy
sis (PCA) experiences an increase in the dimensionality of the latent spac
e when it is applied to configurations that exhibit symmetries. In this st
udy\, we introduce a novel machine learning embedding\, which uses spatial
transformer networks and siamese networks to account for continuous and d
iscrete symmetries\, respectively. This embedding\, which we term symmetry
-aware PCA\, will be applied to three configurations: Burger's equation e
xhibiting a continuous translation symmetry\, flow in sudden expansion\,
a discrete reflexional symmetry\, and Kolmogorov Flow which combines discr
ete shift-reflect and continuous translation symmetries. We will show a dr
astic increase in the number of modes required to represent given trajecto
ries. \n\nSimon Kneer\, Taraneh Sayadi\, Denis Sipp\, Peter J. Schmid\, Ge
orgios Rigas\n\nhttps://indico.math.cnrs.fr/event/5543/contributions/6212/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6212/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBD
DTSTART;VALUE=DATE-TIME:20220331T133000Z
DTEND;VALUE=DATE-TIME:20220331T140000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6211@indico.math.cnrs.fr
DESCRIPTION:Speakers: Guilhem Ferté (EDF)\nhttps://indico.math.cnrs.fr/ev
ent/5543/contributions/6211/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6211/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fear and loathing in Aerodynamics: Are ROMs chimeras or game-chang
ers?
DTSTART;VALUE=DATE-TIME:20220331T123000Z
DTEND;VALUE=DATE-TIME:20220331T130000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6210@indico.math.cnrs.fr
DESCRIPTION:Speakers: Haysam Telib (Optimad)\nOver the last years promisin
g advances in reduced order modelling and machine learning have been repor
ted by the scientific community.\nWithin this talk we will try to project
(some of) these findings on different industrial settings to discuss their
potential.\nWe will try to make this evaluation using all metrices that a
re relevant in industry to identify applications where ROMs can have a rea
l impact.\n\nhttps://indico.math.cnrs.fr/event/5543/contributions/6210/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6210/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBD
DTSTART;VALUE=DATE-TIME:20220331T130000Z
DTEND;VALUE=DATE-TIME:20220331T133000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6209@indico.math.cnrs.fr
DESCRIPTION:Speakers: Florian Bernard (Nurea)\nhttps://indico.math.cnrs.fr
/event/5543/contributions/6209/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6209/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reduced basis Smagorinsky turbulence models
DTSTART;VALUE=DATE-TIME:20220331T100000Z
DTEND;VALUE=DATE-TIME:20220331T105000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6207@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tomás Chacón (Instituto de Matemáticas de la Univ
ersidad de Sevilla)\nhttps://indico.math.cnrs.fr/event/5543/contributions/
6207/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6207/
END:VEVENT
BEGIN:VEVENT
SUMMARY:From handcrafted Galerkin models to automated cluster models
DTSTART;VALUE=DATE-TIME:20220331T091000Z
DTEND;VALUE=DATE-TIME:20220331T100000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6206@indico.math.cnrs.fr
DESCRIPTION:Speakers: Bernd Noack (Harbin Institute ot Technology\, Shenzh
en\, China)\nReduced-order models (ROM) are of paramount importance for ph
ysical understanding\, data\ncompression\, estimation\, control and optimi
zation. Over a century ago\, simple dynamical models\nof coherent structur
es have been facilitated by stability theory (Orr-Sommerfeld equation\n190
7) and by vortex models (von K arm an 1911). Data-driven reduced-order
modeling of coherent\nstructures has been pioneered by Aubry et al. (1988
) with a celebrated POD model of\nthe turbulent boundary layer. Since then
\, machine learning [1] has significantly simplified and\nenriched the spe
ctrum of possibilities for data-driven ROM.\nIn this talk\, we exemplify d
ifferent ROM approaches for the fluidic pinball [2]\, the wake flow\nbehin
d a cluster of three parallel cylinders on an equilateral triangle pointin
g upstream. The\nflow may be actuated by rotating cylinders. First\, the t
ransition scenario of the unforced fluidic\npinball is modeled with a five
-mode mean-field Galerkin model. This model comprises\nsuccessive Hopf and
pitchfork bifucations\, which are typical for a number of wake flows. Sec
ond\,\na cluster-based network model (CNM) [3\, 4] is presented describing
the fluidic pinball\nwake with actuation as free input\, employing thousa
nd differently actuated pinball simulations.\nCNM yields a robust dynamics
from a fully automatable procedure. Finally\, perspectives of\nROM for co
mmon tasks of data management are given.\n[1] BRUNTON\, S. L.\, NOACK\, B.
R. & KOUMOUTASKOS\, P. 2020 Ann. Rev. Fluid Mech. 52:477–\n508.\n[2] DE
NG\, N.\, NOACK\, B. R.\, MORZY N SKI\, M.\, & PASTUR\, L. R. 2020 Low-o
rder model for\nsuccessive bifurcations of the fluidic pinball. J. Fluid M
ech. 884\, A37:1–41.\n[3] LI\, H.\, FERNEX\, D.\, SEMAAN\, R.\, TAN\, J.
\, MORZY N SKI\, M. & NOACK\, B. R. 2021 Clusterbased\nnetwork model. J.
Fluid Mech. 906\, A21:1–41.\n[4] FERNEX\, D.\, NOACK\, B. R. & SEMAAN\,
R. 2021 Cluster-based network model—From snapshots\nto complex dynamica
l systems. Science Advances (online).\n\n\nBernd R. Noack 1\, Nan Deng1\
, Daniel Fernex2\nLuc Pastur3\, Richard Semaan4 Marek Morzy nski5\n1 Ha
rbin Institute of Technology\, Shenzhen\, China\,\n2 EPFL\, Switzerland\,\
n3 ENSTA\, Paris\,\n4 TU Braunschweig\, Germany\,\n5 Poznan University of
Technology\, Poland\n\nhttps://indico.math.cnrs.fr/event/5543/contribution
s/6206/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Model reduction of convection-dominated partial differential equat
ions via optimization-based implicit feature tracking
DTSTART;VALUE=DATE-TIME:20220331T075000Z
DTEND;VALUE=DATE-TIME:20220331T084000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6205@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mattew Zahr (Notre Dame)\nPartial differential equat
ions (PDEs) that model convection-dominated phenomena often arise in engin
eering practice and scientific applications\, ranging from the study of hi
gh-speed\, turbulent flow over vehicles to wave propagation through solid
media. The solutions of these equations are characterized by local feature
s or disturbances that propagate throughout the domain as time evolves or
a system parameter varies. Numerical methods to approximate these solution
s require stabilization and fine\, usually adaptive\, grids to adequately
resolve the local features\, which lead to expensive discretizations with
a large number of degrees of freedom. Projection-based model reduction met
hods tend to be ineffective in reducing the computational cost of such pro
blems due to a slowly decaying Kolmogorov n-width of the solution manifold
.\n\nTo avoid the fundamental linear reducibility limitation associated wi
th convection-dominated problems\, we construct a nonlinear approximation
by composing a low-dimensional linear space with a parametrized domain map
ping. The linear space is constructed using the method of snapshots and PO
D\; prior to compression\, each snapshot is composed with a mapping that c
auses its local features to align (same spatial location) with the corresp
onding features in all other snapshots. The parametrized domain mapping is
chosen such that the local features present in the linear space deform to
the corresponding features in the solution being approximated\, effective
ly removing the convection-dominated nature of the problem. The domain map
ping is determined implicitly through the solution of a residual minimizat
ion problem\, rather than relying on explicit sensing/detection. We provi
de numerous numerical experiments to demonstrate the effectivity of the pr
oposed method on benchmark problems from computational fluid dynamics.\n\n
https://indico.math.cnrs.fr/event/5543/contributions/6205/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6205/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quadratic Approximation Manifold for Mitigating the Kolmogorov Bar
rier in Nonlinear Projection-Based Model Order Reduction
DTSTART;VALUE=DATE-TIME:20220331T070000Z
DTEND;VALUE=DATE-TIME:20220331T075000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6204@indico.math.cnrs.fr
DESCRIPTION:Speakers: Charbel Farhat (Stanford)\nA quadratic approximation
manifold is presented for performing nonlinear\, projection-based\, model
order reduction (PMOR). It constitutes a departure from the traditional a
ffine subspace approximation aimed at mitigating the Kolmogorov barrier fo
r nonlinear PMOR\, particularly for convection-dominated transport problem
s. It builds on the data-driven approach underlying the traditional constr
uction of projection-based reduced-order models (PROMs)\; is application-i
ndependent\; is linearization-free\; and therefore is robust for highly no
nlinear problems. Most importantly\, this approximation leads to quadratic
PROMs that deliver the same accuracy as their traditional counterparts us
ing however the square root of their dimension. The computational advantag
es of the proposed high-order approach to nonlinear PMOR over the traditio
nal approach are highlighted for the detached-eddy simulation-based predic
tion of the Ahmed body turbulent wake flow\, which is a popular CFD benchm
ark problem in the automotive industry. For a fixed accuracy level\, these
advantages include: a reduction of the total offline computational cost b
y a factor greater than five\; a reduction of its online wall clock time b
y a factor greater than 32\; and a reduction of the wall clock time of the
underlying high-dimensional model by a factor greater than two orders of
magnitude.\n\nco-author: Joshua Barnett\n\nhttps://indico.math.cnrs.fr/eve
nt/5543/contributions/6204/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Use of reduced basis techniques for two-phase flows in porous medi
a
DTSTART;VALUE=DATE-TIME:20220330T132000Z
DTEND;VALUE=DATE-TIME:20220330T141000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6203@indico.math.cnrs.fr
DESCRIPTION:Speakers: Guillaume Enchery (IFPEN)\nhttps://indico.math.cnrs.
fr/event/5543/contributions/6203/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hemodynamics examples of reduced order models for clinical applica
tions
DTSTART;VALUE=DATE-TIME:20220330T092000Z
DTEND;VALUE=DATE-TIME:20220330T101000Z
DTSTAMP;VALUE=DATE-TIME:20220808T132949Z
UID:indico-contribution-5543-6199@indico.math.cnrs.fr
DESCRIPTION:Speakers: Irène Vignon-Clémentel (Inria Saclay)\nhttps://ind
ico.math.cnrs.fr/event/5543/contributions/6199/
LOCATION:Inria Bordeaux Sud Ouest Ada Lovelace
URL:https://indico.math.cnrs.fr/event/5543/contributions/6199/
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