Special Session on Symbolic and numeric approaches to dynamical modeling and simulation


Held at the conference ACA'2009, June 25-28, 2009, in Montreal, Canada.

Session Organizers:
Jürgen Gerhard, Maplesoft, Canada.      jgerhard (at) maplesoft (dot) com
Austin Roche, Maplesoft, Canada.      aroche (at) maplesoft (dot) com
Elena Shmoylova, Maplesoft, Canada.      eshmoylova (at) maplesoft (dot) com

There are a few software packages such as Dymola and MapleSim that support high-level physics-based modeling and simulation of large-scale continuous and hybrid discrete-continuous dynamical systems. Internally these models are represented by so-called lumped parameter models or differential-algebraic equations (DAEs), and significant parts of the software perform symbolic manipulations of the equations before sending them to a numerical integrator, in order to reduce simulation time or even to enable the numerical integrator to handle the problem.

In this session, we will consider such symbolic and symbolic-numeric techniques for purely continuous DAEs and hybrid discrete-continuous models, including the following topics:

  • index reduction and causalization
  • graph-theory based modeling and simplification
  • model order reduction
  • multi- and cross-domain modeling
  • finding consistent initial conditions for hybrid systems
  • solvers for higher index DAEs
  • nonlinear model reduction
  • reducing the number of static parameters
  • differential elimination
  • reducing the number of discrete modes for hybrid systems
  • model size reduction
  • straight-line program techniques
  • optimized code generation
  • singular perturbation methods
  • parallel algorithms for dynamical simulation
  • multi-body dynamics

Another question that could be considered is related to "real world models". Many of the symbolic methods prevalent in dynamical modeling were designed specifically for a certain class of "nice" models, such as, e.g., polynomials with integer coefficients. However, in practice many models contain components that are not easily accessible to purely symbolic manipulations, such as floating point coefficients and exponents, lookup tables, or piecewise defined functions. The challenge is to apply symbolic techniques to such models appropriately and effectively.

Call for Contributions:
If you are interested in giving a presentation at this session, please email an abstract to one of the organizers. Presentations will be up to 30 min in length, including time for discussion. The tentative deadline for submissions is May 29th, 2009.


Thursday June 25th, 2009
10:30 Jürgen Gerhard (Maplesoft) Industrial Dynamical Modeling and Simulation (abstract, .zip)
11:00 Marc Moreno Maza (Massachusetts Institute of Technology) Regular Chains and Differential Elimination (abstract, .zip)
11:30 Gregory Reid (University of Western Ontario) Numeric-Geometric Techniques for Differential Equations I. Introduction (abstract, .pdf)
12:00 Niloofar Mani (University of Western Ontario) Numeric-Geometric Techniques for Differential Equations II. Applications (abstract, .pdf)
12:30 Lunch
14:00 Allan Wittkopf (Maplesoft)
Presented by Austin Roche (Maplesoft)
Symbolic Preprocessing of DAE Systems (abstract, .zip)
14:30 Henrik Tidefelt (Linköping University) Unstructured matrix-valued singular perturbations -- tackle or avoid? (abstract, .pdf)
15:00 Thomas Wolf (Brock University) Applications of the package CRACK to simplify large systems (abstract, .pdf)
15:30 Coffee Break
16:00 Benjamin J. Spivey (*), John D. Hedengren (**), Thomas F. Edgar (*)
*University of Texas, Austin; **ExxonMobil Chemical Company, Baytown
Presented by John D. Hedengren
Monitoring of Process Fouling Using First Principles
Monitoring and Moving Horizon Estimation (abstract, .ppt)
16:30 Erik Postma, Elena Shmoylova (Maplesoft)
Presented by Elena Shmoylova
Computer Algebra versus Reality (abstract, .ppt)
17:00 Thomas Wolf (Brock University) A hybrid discrete-polynomial dynamical system modeling board positions in the game of go (abstract, .pdf)
17:30 Jay Bardhan (Argonne National Laboratory, Rush University) Challenges in Coupling Simulation and Optimization: Biomolecule Design (abstract)