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PRODID:iCalendar-Ruby
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CATEGORIES:Colloquium/Seminar
DESCRIPTION:Sam Otto\, AI Institute in Dynamic Systems\, University of Wash
ington\n\nModel Reduction and Scientific Machine Learning for Continuum Mec
hanics\n\nA reduced-order model (ROM) is a simplified approximation of a hi
gh-dimensional dynamical system which can be used for qualitative analysis\
, real-time forecasting\, state estimation\, and control. Shear-dominated f
luid flows can be especially difficult to model using data-driven technique
s such as proper orthogonal decomposition (a.k.a.\, principal component ana
lysis)\, kernel-based manifold learning\, and autoencoders because these me
thods discard low-variance variables\, neglecting their importance for futu
re dynamics. We show that this is a fundamental limitation related to the c
urse of dimensionality\, and that additional information is needed to captu
re these sensitivity mechanisms. To extract reliable coordinates for foreca
sting\, we introduce an efficient algorithm called Covariance Balancing Red
uction using Adjoint Snapshots (CoBRAS). This method relies on state and ra
ndomized gradient data obtained by solving linearized adjoint equations to
construct an oblique projection balancing the eﬀects of state variance and
the sensitivity of future outputs to the truncated degrees of freedom. We e
valuate this method against standard techniques on a nonlinear axisymmetric
jet ﬂow simulation with 100\,000 state variables. Nonlinear extensions bas
ed on kernel methods and autoencoders are discussed\, as well as prospects
for techniques that do not require adjoints and are capable of being transf
erred to new spatial domains.
DTEND:20240404T180000Z
DTSTAMP:20241008T143511Z
DTSTART:20240404T170000Z
GEO:40.006791;-105.262818
LOCATION:Engineering Center\, ECCR 257
SEQUENCE:0
SUMMARY:Special Dynamics/Machine Learning Seminar
UID:tag:localist.com\,2008:EventInstance_46047040659297
URL:https://calendar.colorado.edu/event/special-dynamicsmachine-learning-se
minar
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