PDE Model Reduction Using SVD

Huge amounts of data are pouring into storage systems, the
result of satellite measurements, computer simulations,
automatic record keeping.  This data surely contains a great
deal of hidden information.  We may be unable to imagine 
an underlying physical law to explain the data.  However, 
we can apply techniques of reduced order modeling to the
data.  This approach can compress the data, extract hidden
information and structures, exhibit an underlying natural
basis, and enable us to recognize whether new items belong
or don't belong to the dataset.  

While the primary discussion will focus on a fluid flow 
problem, each point will also be discussed for a facial 
recognition problem, which begins with 600 photographs, 
and tries to answer the questions 
  * "What do these faces have in common?", 
  * "Is this another picture of a face in the set?"
  * "Is this a picture of (a brand new) face?"