BOZEMAN_2003.TEX
PDE Model Reduction Using Clustering

I attended the 8th Conference on Computation, Control, and Biological Systems, at Montana State University in Bozeman, Montana, held from July 29 to August 1, 2003. I gave a 25 minute presentation there with the title

PDE Model Reduction Using Clustering

A PDF version is available as ../../presentations/bozeman_2003.pdf.

The following files constitute the LaTeX file used to create the slides:

• bozeman_2003.tex, the LaTeX file;
• inout_001_dir.png, the direction field for the IN/OUT flow field at time step 1;
• inout_100_flow.png, the velocity field for the IN/OUT flow field at time step 100;
• inout_sinusoid_cvt_g.png, plots of the error between an IN/OUT simulation and a CVT approximation using 4, 8 and 16 basis vectors, with a sinusoidal inflow parameter ALPHA (and the input snapshots were NOT normalized);
• inout_sinusoid_cvt_n.png, plots of the error between an IN/OUT simulation and a CVT approximation using 4, 8 and 16 basis vectors, with a sinusoidal inflow parameter ALPHA (and the input snapshots WERE normalized);
• inout_cvt81_dir.png, the direction field for the IN/OUT flow, for CVT basis vector 1 of 8;
• inout_cvt81_vec.png, the velocity field for the IN/OUT flow, for CVT basis vector 1 of 8;
• inout_cvt82_dir.png, the direction field for the IN/OUT flow, for CVT basis vector 2 of 8;
• inout_cvt82_vec.png, the velocity field for the IN/OUT flow, for CVT basis vector 2 of 8;
• inout_cvt83_dir.png, the direction field for the IN/OUT flow, for CVT basis vector 3 of 8;
• inout_cvt83_vec.png, the velocity field for the IN/OUT flow, for CVT basis vector 3 of 8;
• inout_cvt84_dir.png, the direction field for the IN/OUT flow, for CVT basis vector 4 of 8;
• inout_cvt84_vec.png, the velocity field for the IN/OUT flow, for CVT basis vector 4 of 8;
• inout_energies.png, a bar graph of the energies of the first 16 POD modes for the IN/OUT flow;
• inout_hat.png, a graph illustrating the behavior of the IN/OUT inflow parameter ALPHA for the HAT problem;
• inout_pod1_dir.png, the direction field for the IN/OUT flow, for POD basis vector 1;
• inout_pod1_vec.png, the velocity field for the IN/OUT flow, for POD basis vector 1;
• inout_pod2_dir.png, the direction field for the IN/OUT flow, for POD basis vector 2;
• inout_pod2_vec.png, the velocity field for the IN/OUT flow, for POD basis vector 2;
• inout_pod3_dir.png, the direction field for the IN/OUT flow, for POD basis vector 3;
• inout_pod3_vec.png, the velocity field for the IN/OUT flow, for POD basis vector 3;
• inout_pod4_dir.png, the direction field for the IN/OUT flow, for POD basis vector 4;
• inout_pod4_vec.png, the velocity field for the IN/OUT flow, for POD basis vector 4;
• inout_sinusoid.png, a graph illustrating the behavior of the IN/OUT inflow parameter ALPHA for the SINUSOID problem;
• steady_dir.png, the steady state direction field for the IN/OUT flow;
• steady_vec.png, the steady state velocity vector field for the IN/OUT flow;
• supreme.png, an article from the New York Times about the application of model reduction to decisions of the Supreme Court;
• uniform_02_00100_dot.png, an illustration of 100 "random" points in the unit square;
• uniform_02_00100_km5.png, an illustration of 100 "random" points in the unit square, organized into 5 clusters using the K-Means algorithm;