Walid Taha: Rigorous simulation

Abstract
The falling price of computational and communication components means that they will increasingly be embedded into physical products. Verifying the designs of the resulting “cyber-physical” products is challenging for several reasons. First, closed-form solutions for the behavior of physical systems rarely exist. Second, the most natural mathematical tool for modeling cyber-physical combinations, namely, hybrid (discrete/continuous) systems, exhibit pathologies that arise in neither purely continuous nor purely discrete systems. Third, the expressivity of existing continuous dynamics formalisms is generally lower than those used by domain experts.

To address these problems, we are developing a technology called “rigorous simulation”. The back-end for rigorous simulation uses validated numerics algorithms, which compute guaranteed bounds for the precision of all solutions. We show that these algorithms can be extended to compute trajectories for some hybrid systems exhibiting Zeno behavior. Ongoing work suggests that chattering behavior can be similarly addressed. We make validated numerics more accessible to non-specialists through the use of a domain-specific language, based on hybrid ordinary differential equations, which we also extend to support partial derivatives and certain types of equational modeling. An implementation called “Acumen” has been built and used for several case studies. These include virtual testing of advanced driver assistance functions, bipedal robotics, and a range of model problems for teaching at both graduate and undergraduate levels.

Bio Walid Taha is a Professor of Computer Science at Halmstad University and a Research Professor at the University of Houston. He has held academic positions at Chalmers, Yale, and Rice University, and short-term positions at ABB, Schlumberger, and Lucent Bell Labs. He is a founding chair of the ACM GPCE conference and the IFIP WG on Program Generation (2.11). Taha is a recipient of an NSF CAREER Award. His research interests include software engineering, programming language semantics, modeling and simulation, and cyber-physical systems.