|Marquette||MS in Computing||Dr. Corliss||Teach||Research||Pubs||Service|
Projects of Current
Testing COSY interval arithmetic
During the Spring 2002, the reliable computing list serve email@example.com entertained an active discussion of COSY Infinity, software by Berz et al. available from cosy.pa.msu.edu. COSY Infinity is an arbitrary order beam dynamics simulation and analysis code using interval arithmetic and Taylor models for the validated solution of systems of ordinary differential equations. The list serve discussions raised concerns about the reliability of COSY's interval and Taylor model arithmetics, which we set about to test.
This project is execution-based testing of the interval arithmetic facilities of COSY. We developed test cases for each of COSY's interval arithmetic operations and intrinsic functions, executed them, and compared COSY's results with highly accurate values computed by Maple.
Joint with student Jun Yu and with Martin Berz, Michigan State University
Taylor series solution of ordinary differential equations
We use automatic differentiation to generate long (30-100 term) Taylor series expansions for the solution to initial value problems in ordinary differential equations. Pattern matching the tails of the series locates primary singularities, which we use for integration steps.
Joint with Ned Nedialkov, McMaster Univeristy, and Robert Corless, University of Western Ontario
Hybrid differential equations with multiple active switching functions
A hybrid differential equation may have several different right hand sides, depending on values of state variables, for example Berz' computation of the trajectory of a particle in a high-energy physics accelerator, where a particle encounters thousands of magnets in a single orbit. One task is to compute an enclosure of a trajectory as it switches from state to state. Uncertainty in the trajectory translates into uncertainty in switching times, which usually further smears the trajectory. Another concern is the long-term stability of the orbits.
Joint with Ned Nedialkov, McMaster Univeristy, and Martin Berz, Michigan State University
Projects I'd like to pursue:
Applications of global optimization
Many applications of optimization are characterized by many local minima. Interval techniques can potentially guarantee to find the true global min.
Everyone thinks their work is central, but optimization really is. Consider the largest problem in scientific computation you know: global climate modeling, nuclear explosion simulation, Big Bang, whatever. We want to compute that to control or optimize something. That is, the largest problems in scientific computing are just one evaluation of the objective function of the optimization problem we really want to solve - Jorge More
Applications of automatic differentiation
Automatic differentiation computes derivative objects accurately and quickly.
Numerical optimization of neural networks
Training a neural network is an optimization problem
"All together" method for parameter identification and control
Optimization in self-organizing maps