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MAY 11, 2009

    Attendees:

  • C. Lieberman, M. Frangos, M. Buffoni, B. Bond, C. Mitrovski, A. Megretski, K. Willcox, W. Hoburg

    • Summary

  • Review of the semester's events.
  • Discussed the format. Agreed that the informal approach is to be preferred over prepared conference-style talks. Some would like to see a stronger tie to the literature.
  • MRG will recess for the summer and reconvene in the fall.

MAY 4, 2009

    Attendees:

  • C. Lieberman, C. Mitrovski, D. Knezevic, B. Bond, G. Verghese, A. Megretski, M. Buffoni, M. Frangos, Y. Avniel

    • Summary

  • Discussion continued about model reduction for compartmental systems.
  • The need for a reduction to a low-dimensional representation that maintains interpretability, i.e. identifies the critical subset of parameters, brought about discussion of compressed sensing.
  • Compressed sensing attempts to find the relevant parameters by solving a mixed integer linear program (MILP), or a relaxed form of an MILP, with a constraint on the number of nonzero elements the solution may have.
  • Our last meeting is next week, May 11. We will review the semester and discuss the format and potential changes for next semester.

APRIL 27, 2009

    Attendees:

  • C. Lieberman, C. Mitrovski, T. Heldt, D. Knezevic, R. Sredojevic, T. El-Moselhy, B. Bond, G. Verghese

    • Summary

  • Professor G. Verghese led discussion on model reduction for compartmental models. The application of interest is medicine, particularly, to assist doctors at the bedside, e.g. in the ICU.
  • The goal is to derive a reduced model which maintains the integrity of important state variables (interpretability), but which takes advantage of aggregating secondary physics.
  • The discussion of the approach and formulation of this problem will continue next week. We will talk more about compressed sensing, and how this method may be applicable.

APRIL 13, 2009

    Attendees:

  • C. Lieberman, D. Knezevic, M. Buffoni, G. Oxberry, Y. Avniel, W. Hoburg, B. Bond, A. Megretski.

    • Summary

  • NOTES
  • Brad led the discussion of time-varying basis functions. May be good idea if you have regions of fast dynamics and some slow dynamics. In his research, time-varying balanced truncation performed well, but was too costly. (Notes above)
  • In chemical kinetics, dynamics are nonlinear and the fastest time scales are too fast to make linearizing feasible. Far too many interpolation points would be required.
  • Then, Brad and Alex discussed balanced truncation (in the general case). We briefly discussed the Lyapunov equations and the cost of solving them. Balanced truncation comes with guarantees --- but again, it is costly.

APRIL 06, 2009

    Attendees:

  • C. Lieberman, B. Bond, R. Sredojevic, C. Mitrovski, G. Oxberry, D. Knezevic, M. Frangos, M. Buffoni, Y. Avniel, A. Megretski.

    • Summary

  • (1) NOTES
  • (2) NOTES
  • Professor Megretski elaborated on a result from the control community with regard to computing the absolute error in the linear case. There are two sets of notes above -- (1) is the handout provided by A. Megretski and (2) is notes by C. Lieberman taken during the session.
  • Next time -- a change of pace. Please look at Home and let me know (celieber@mit.edu) your preference in the next few days.

MARCH 30, 2009

    Attendees:

  • C. Lieberman, B. Bond, R. Sredojevic, D. Knezevic, T. Heldt, W. Hoburg, A. Megretski, M. Frangos, M. Buffoni.

    • Summary

  • NOTES
  • Defined abstract model reduction scenario --- full-order model and reduced-order model are maps from input/parameter space to outputs of interest through state space. Restricted attention to linear case to start.
  • Proposed several error measures to judge quality of reduced-order model --- absolute and relative --- maximum over some test set, L2 over test set, etc.
  • Understood the distinction between absolute and relative reduced model errors --- absolute errors compare reduced outputs with full outputs, relative errors compare absolute error with the best possible error for a given reduced model dimension.
  • Professor Megretski presented a result from the control community with regard to computing the absolute error in the linear case. He will speak to this subject more exhaustively in our next meeting.

MARCH 23, 2009

    Attendees:

  • C. Lieberman, B. Bond, D. Knezevic, G. Verghese, Y-C Hsiao, M. Frangos, M. Buffoni, G. Oxberry, Y. Avniel, W. Hoburg, A. Megretski, J. Barbic.

    • Summary

  • J. Barbic discussed nonlinear model reduction set up for computer graphics and simulation (in particular for deformable objects). Error difficult to quantify in this setting because aesthetics (physical deformations) are most important.
  • D. Knezevic demonstrated a posteriori error estimation in the reduced basis context by leveraging finite element theory.
  • We had a short discussion of philosophical type: should the inputs over which you desire reduced-order model accuracy be described in the problem formulation, and not affect the method by which you reduce? What does one do in the case when you do not know a priori the inputs over which you need reduced model accuracy (e.g. inverse problems, computer graphics)?

MARCH 16, 2009

    Attendees:

  • C. Lieberman, D. Knezevic, B. Bond, M. Frangos, M. Buffoni, Z. Mahmood, L. Baldasarre, Y-C Hsiao, G. Oxberry, Y. Avniel, J. Barbic, A. Megretski, G. Verghese.

    • Summary

  • Projection framework re-introduced. Push toward error estimation.
  • Discussion of error measures, e.g. L_2 error gain, H_\infty, etc.
  • Parameterized systems, FEM error estimation, greedy sampling, (next time -- DK)
  • Balanced truncation, optimal Hankel norm reduction.
  • Next week: J. Barbic and D. Knezevic PLUS lots of discussion.

MARCH 09, 2009

    Attendees:

  • B. Bond, T. Heldt, G. Verghese, G. Oxberry, A. Megretski, M. Levashov, Z. Mahmood, L. Baldasarre, D. Knezevic.

    • Summary

  • Discussed `Topics for Discussion' list
  • Classification of problems
  • Topics of interest include: Projection framework (selection of bases), system identification approaches, error bounds, formulation of model reduction problems
  • Next week will focus on projection framework and the various methods for constructing the basis

MARCH 02, 2009

FEBRUARY 25, 2009

FEBRUARY 18, 2009

    Attendees:

  • B. Bond, C. Lieberman, Y-C Hsiao, M. Frangos, W. Hoburg, G. Oxberry, L. Daniel, G. Verghese, A. Megretski, T. Heldt, J. Barbic.

    • Summary:

  • Introductions
  • Meeting format discussion: Decided that members should prepare a single-page summary or outline of their research area. Within the next two meetings, each member will be given 10-15 minutes at the chalkboard to summarize their interest and highlight the challenges they face. From this blitzkrieg, we hope that everyone will get a sense of where each other person is coming from. As the talks go by, we will populate a list of discussion topics to be treated in future meetings.
  • Directors to e-mail link to Google survey to determine regular meeting time and place.
  • Future announcements sent to MRG list. If you are not on the list, e-mail one of the directors.