[Forum SIS] Politecnico di Milano - Seminari Jim Ramsay e Michelle Carey

[Laura M. Sangalli]

Si avvisa che in data 6-11-2015, alle ore 10:30 precise,
presso l'Aula Seminari "F. Saleri" VI piano - Dipartimento di 
Matematica, Politecnico di Milano,
nell'ambito delle iniziative MOX, si svolgeranno i seguente seminari:

ore 10:30
Jim Ramsay, McGill University,
Exploring Functional Data with Dynamic Models

ore 11:30
Michelle Carey, McGill University,
Data2PDE: an iterative scheme for obtaining data driven estimates of the 
parameters of PDEs defined over complex domains


Seguono gli abstracts dei due seminari.


Jim Ramsay
Exploring Functional Data with Dynamic Models

Discrete observations of curves are often smoothed by attaching a 
penalty to the error sum of squares, and the most popular penalty is the 
integrated squared second derivative of the function that fits the 
data.  But it has been known since the earliest days of smoothing 
splines that, if the linear differential operator D^2 is replaced by a 
more general differential operator L that annihilates most of the 
variation in the observed curves, then the resulting smooth has less 
bias and greatly reduced mean squared error.
This talk will show how we can use the data to estimate such an 
operator.  The differential equation estimated in this way is already an 
interesting model for the data that represents the dynamics of  the 
processes being estimated. But, in addition to the advantages in bias 
and MSE, it emerges that exciting new ways of representing the data 
emerge that use an orthogonal basis system defined by the estimated 
operator.


M. Carey
Data2PDE: an iterative scheme for obtaining data driven estimates of the 
parameters of PDEs defined over complex domains

Spatial data are abundant in many scientific fields, some examples 
include; satellite images of the earth, temperature readings from 
multiple weather stations and the spread of an infectious disease over a 
particular region. In many instances the spatial data are accompanied by 
mathematical models expressed in terms of partial differential equations 
(PDEs). These PDEs determine the theoretical aspects of the behaviour of 
the physical, chemical or biological phenomena considered. The 
parameters of the PDEs are typically unknown and must be inferred from 
expert knowledge of the phenomena considered. In this talk I will 
discuss extending the profiling with parameter
cascading procedure outlined in Ramsay et al (2007) to incorporate PDE 
parameter estimation. Furthermore, following from Sangalli et al. (2013) 
the estimation procedure is extended to include finite element methods 
(FEMs). This allows the proposed method to account for attributes of the 
geometry of the physical problem such as irregular shaped domains, 
external and internal boundary features and strong concavities. Thus 
this talk introduces a methodology for data driven estimates of the 
parameters of PDEs defined over complex domains.


Tutti gli interessati sono invitati a partecipare.

Cordiali saluti,
Laura Sangalli

-- 
Laura Maria Sangalli
MOX - Dipartimento di Matematica
Politecnico di Milano
Piazza Leonardo da Vinci 32
20133 Milano - Italy
tel: +39 02 2399 4554
fax: +39 02 2399 4568
email: laura.sangalli at polimi.it
url: http://mox.polimi.it/~sangalli