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Wu’s computer algorithms win prestigious Chinese prize

Wenyuan Wu and his prize

Wenyuan Wu is one of the two students from Western who has won the 2006 Chinese Government Award for Outstanding Self Financed Studies Abroad

By Mitchell Zimmer

Wenyuan Wu has found ways to mathematically analyze complex systems that have been called, “deep methods that apply to a broad class of problems.” While many researchers work in a highly specific areas, Wu's specialty is combining methods from several different areas, in surprising and deep ways.

This expertise has earned Wu one of the two 2006 Chinese Government Award for Outstanding Self Financed Studies Abroad awarded to Western. Wu is working towards his Ph.D. in Applied Mathematics with Dr. Greg Reid in the area of symbolic numeric computation for equations describing general models in both space and time (partial differential equations). To put it another way, Wu describes his work as taking complex problems that are very general and adapting them so that they are “connected to computer science in that the approach can be automated.”

“In general it’s impossible to compute it by hand” says Wu, “you have to use a computer. When you use a computer you have to design an efficient algorithm. The algorithm should also be stable: small changes in its input should not cause large changes in the output of the algorithm. So when I looked for a numerically stable algorithm, I had to go back to geometry. Geometry always provides you with a very stable view.” That blend of algebra, geometry and computer algorithms was very demanding to work out and required very strong and unusual skills in all three areas. “I think algorithms are closer to algebra” continues Wu. “So here you have computer science algorithms because you want to use computers and you want to look for some stable ways so you have to think about superposing a geometric point of view so you can collect them together.” In building such models, unstable models can be thought of as houses of cards, that the slightest change, will cause them to collapse. Wu uses insights from geometry to build stable models and methods.

An example of this sort of system is demonstrated by the motion of an arm or leg. It helps to visualize each bone as a pendulum and each joint as a link. A pendulum is a fundamental example of motion and, on its own, is fairly easy to analyze. However, if you link a second pendulum that moves independently within the constraints of the first and then a third to the second, (or as in the old song, if you take the leg bone and connect it to the knee bone and take the knee bone and connect it to the ankle bone) describing the motion of each pendulum within that system becomes very complex. In terms of modern geometry, the motion of such multi-link pendula occurs on a very high dimensional space. Wu is an expert in understanding and exploiting the geometry of such spaces.

In the past, these complex mechanisms were studied by the equations worked out by the famous Prof. Wentsun Wu (not related). His work opened up a whole field of study, and recently gained him a 1 million dollar prize from the Shaw Foundation. But there was a problem. The equations required exact numbers or the mathematical model of the system would collapse (like the house of cards). As Greg Reid explains, “in reality systems have approximate numbers so Wenyuan deals with general systems and he shows how to pass from the exact world to the approximate world. This approach is more close to real world situations”.

These algorithms have applications ranging from chemical kinetics to robotics and medical physics.

The $5,000 USD award was presented by Taoying Zhu, Consulate General of China in Toronto on April 25, 2007. There are 302 awards worldwide presented to winners from more than 40 categories which include Art, Science, Engineering, Agriculture, Medicine and Business.