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DTSTAMP:20190719T085743Z
LOCATION:HG F 1
DTSTART;TZID=Europe/Stockholm:20190612T133000
DTEND;TZID=Europe/Stockholm:20190612T140000
UID:submissions.pasc-conference.org_PASC19_sess138_msa199@linklings.com
SUMMARY:Scalable Multi-Fidelity Machine Learning
DESCRIPTION:Minisymposium\nComputer Science and Applied Mathematics, Emerg
ing Application Domains, Chemistry and Materials, Physics, Engineering\n\n
Scalable Multi-Fidelity Machine Learning\n\nZaspel\n\nThe solution of para
metric partial differential equations or other parametric problems is the
main component of many applications in scientific computing. To avoid the
re-implementation of scientific simulation codes, the use of snapshot-base
d (non-intrusive) techniques for the solution of parametric problems becom
es very attractive. We will report on ongoing work to solve parametric pro
blems with a higher-dimensional parameter space by means of kernel ridge r
egression, i.e. machine learning. Results on the use of machine learning t
o for an efficient approximation of parametric problems will be discussed
for examples in computational fluid mechanics and quantum chemistry. One c
hallenge in parametric problems with high-dimensional parameter space is t
he high number of expensive simulation snapshots that has to be computed i
n order to get a low approximation error with respect to the parameter spa
ce. To overcome this, we have introduced a multi-fidelity kernel ridge reg
ression approach. This approach allows to significantly reduce the number
of expensive calculations by adding coarser and coarser simulation snapsho
ts. To solve large-scale training problems, we have developed a hierarchic
al matrix approach that allows to solve related dense linear systems in lo
g-linear time. This hierarchical matrix approach was parallelized on clust
ers of graphics hardware (GPUs).
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