EYAWKAJKOS
Financiado
Everything You Always Wanted to Know About the JKO Scheme
The project deals with the so-called Jordan-Kinderlehrer-Otto scheme, a time-discretization procedure consisting in a sequence of
iterated optimization problems involving the Wasserstein distance W_2 between probability measures....
The project deals with the so-called Jordan-Kinderlehrer-Otto scheme, a time-discretization procedure consisting in a sequence of
iterated optimization problems involving the Wasserstein distance W_2 between probability measures. This scheme allows to
approximate the solutions of a wide class of PDEs (including many diffusion equations with possible aggregation effects) which have
a variational structure w.r.t. the distance W_2 but not w.r.t. Hilbertian distances. It has been used both for theoretical purposes
(proving existence of solutions for new equations and studying their properties) and for numerical applications. Indeed, it naturally
provides a time-discretization and, if coupled with efficient computational techniques for optimal transport problems, can be used for
numerics.
This project will cover both equations which are well-studied (Fokker-Planck, for instance) and less classical ones (higher-order
equations, crowd motion, cross-diffusion, sliced Wasserstein flow...). For the most classical ones, we will systematically consider
estimates and properties which are known for solutions of the continuous-in-time PDEs and try to prove sharp and equivalent
analogues in the discrete setting: some of these results (L^p, Sobolev, BV...) have already been proven in the simplest cases ; the
results in the classical case will provide techniques to be applied to the other equations, allowing to prove existence of solutions and
to study their qualitative properties. Moreover, some estimates proven on each step of the JKO scheme can provide useful
information for the numerical schemes, reducing the computational complexity or improving the quality of the convergence.
During the project, the study of the JKO scheme will be of course coupled with a deep study of the corresponding continuous-in-time
PDEs, with the effort to produce efficient numerical strategies, and with the attention to the modeling of other phenomena which
could take advantage of this techniques.
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Duración del proyecto: 68 meses
Fecha Inicio: 2022-12-05
Fecha Fin: 2028-08-31
Fecha Fin: 2028-08-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2022-12-05
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2021-ADG:
ERC ADVANCED GRANTS
Cerrada
hace 3 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
UNIVERSITE LYON 1 CLAUDE BERNARD
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5