Queridos Estudiantes,
El Dr. Raúl Tempone, egresado en nuestra casa de estudios y primer ganador del reconocido Premio Dahlquist, va a ofrecer una charla sobre sus investigaciones recientes. Será el martes 23 de 11:00 a 12:00 en el Salón de Seminarios del IMERL.
Sean muy bienvenidos; ver detalles en Posdata.
Cordiales saludos,
Pablo.
PD: Resumen:
En esta charla, hablaré sobre nuestro trabajo reciente, en el que abordamos la aproximación de funcionales dependientes de un sistema de partículas, descrito por ecuaciones diferenciales estocásticas de Ito (SDE), en el límite cuando el número de partículas es infinito. Este problema es equivalente a estimar la solución débil de la SDE de McKean-Vlasov. Con ese fin, nuestro enfoque utiliza sistemas con números finitos de partículas y un esquema discreto de pasos en el tiempo. En esta configuración, hay dos parámetros de discretización: el número de pasos de tiempo y el número de partículas. Basándonos en estos dos parámetros, consideramos diferentes variantes de los métodos de Monte Carlo, de Monte Carlo Multi-nivel (MLMC) y de Monte Carlo Multi-Indices. Demostramos que, en base a algunas suposiciones que se verifican numéricamente, podemos lograr un valor óptimo de trabajo computacional. También discutiré los desafíos teóricos involucrados al probar los supuestos necesarios para nuestros métodos y algunos resultados más recientes en esa dirección.
"Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equation”, by Abdul-Lateef Haji-Ali, Raul Tempone, Preprint: arXiv:1610.09934, 2017. Published in Vol. 28, Issue 4, pp. 923–935. Statistics and Computing, 2018.
Shortest Bio
Raúl Tempone graduated as an industrial engineer in 1995 from the University of the Republic, Montevideo, Uruguay. After graduation, he worked on the optimal dispatch of electricity for the Uruguayan system using techniques from nonlinear stochastic programming and visited the Royal Institute of Technology (KTH) in Stockholm, Sweden, to study numerical analysis. He obtained a Master in Engineering Mathematics in 1999 (inverse problems for incompressible flows, supervised by Jesper Oppelstrup, KTH) and a Ph.D. in Numerical Analysis in 2002 (a posteriori error estimation and control for stochastic differential equations, supervised by Anders Szepessy, KTH). He later moved to ICES, UT Austin, to work as a postdoctoral fellow from 2003 until 2005 in the area of numerical methods for PDEs with random coefficients (supervised by Ivo Babuska and Mary Wheeler). In 2005 he became an assistant professor (joint appointment) with the School of Computational Sciences and the Department of Mathematics at Florida State University, Tallahassee. In 2007 he was awarded the first Dahlquist fellowship by KTH and COMSOL for his contributions to the field of numerical approximation of deterministic and stochastic differential equations. In 2009 he joined King Abdullah University of Science and Technology as Associate Professor (founding faculty) and was promoted in 2015 to the rank of Full Professor in Applied Mathematics. Since 2012, he has been directing the KAUST Strategic Research Center for Uncertainty Quantification. In May 2018, he has been recently awarded an Alexander von Humboldt Professorship (hosted by RWTH Aachen) by the German Ministry of Education and Research.
Raúl Tempone graduated as an industrial engineer in 1995 from the University of the Republic, Montevideo, Uruguay. After graduation, he worked on the optimal dispatch of electricity for the Uruguayan system using techniques from nonlinear stochastic programming and visited the Royal Institute of Technology (KTH) in Stockholm, Sweden, to study numerical analysis. He obtained a Master in Engineering Mathematics in 1999 (inverse problems for incompressible flows, supervised by Jesper Oppelstrup, KTH) and a Ph.D. in Numerical Analysis in 2002 (a posteriori error estimation and control for stochastic differential equations, supervised by Anders Szepessy, KTH). He later moved to ICES, UT Austin, to work as a postdoctoral fellow from 2003 until 2005 in the area of numerical methods for PDEs with random coefficients (supervised by Ivo Babuska and Mary Wheeler). In 2005 he became an assistant professor (joint appointment) with the School of Computational Sciences and the Department of Mathematics at Florida State University, Tallahassee. In 2007 he was awarded the first Dahlquist fellowship by KTH and COMSOL for his contributions to the field of numerical approximation of deterministic and stochastic differential equations. In 2009 he joined King Abdullah University of Science and Technology as Associate Professor (founding faculty) and was promoted in 2015 to the rank of Full Professor in Applied Mathematics. Since 2012, he has been directing the KAUST Strategic Research Center for Uncertainty Quantification. In May 2018, he has been recently awarded an Alexander von Humboldt Professorship (hosted by RWTH Aachen) by the German Ministry of Education and Research.