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DTSTART:20201025T030000
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UID:calendar.124522.field_date.0@www.tse-fr.eu
DTSTAMP:20210421T041801Z
CREATED:20210225T081001Z
DESCRIPTION:Philippe LeFloch (Université Pierre et Marie Curie\; CNRS)\, “A
Class of Mesh-free Algorithms for Finance\, Machine Learning and Fluid Dy
namics”\, MAD-Stat. Seminar\, Toulouse: TSE\, April 8\, 2021\, 11:00–12:15
\, Zoom.\n\nWe introduce a numerical methodology which applies to a broad
class of partial differential equations and discrete models\, and is refer
red to here as the {\sl transport-based mesh-free method}. It led us to se
veral numerical algorithms which are now implemented in a Python library\,
called CodPy. We develop a mesh-free discretization technique based on th
e (so-called RKHS) theory of reproducing kernels and the theory of transpo
rt mappings\, in a way that is reminiscent of Lagrangian methods in comput
ational fluid dynamics. The strategy is relevant when a large number of di
mensions or degrees of freedom are present\, as is the case in mathematica
l finance and machine learning\, but is also applicable in fluid dynamics.
We present our algorithms primarily for the Fokker-Planck-Kolmogorov syst
em of mathematical finance and for neural networks based on support vector
machines. The proposed algorithms are nonlinear in nature and enjoy quant
itative error estimates based on the notion of discrepancy error\, which a
llow one to evaluate the relevance and accuracy of given data and numerica
l solutions. Joint with Jean Marc Mercier
DTSTART;TZID=Europe/Paris:20210408T120000
DTEND;TZID=Europe/Paris:20210408T131500
LAST-MODIFIED:20210331T001001Z
LOCATION:Toulouse: TSE\, April 8\, 2021\, 11:00–12:15\, Zoom
SUMMARY:MAD-Stat. Seminar
URL;TYPE=URI:https://www.tse-fr.eu/seminars/2021-class-mesh-free-algorithms
-finance-machine-learning-and-fluid-dynamics
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