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 nite 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 de ned over complex domains.
Tutti gli interessati sono invitati a partecipare.
Cordiali saluti, Laura Sangalli