Computational Modeling and Simulation

Catalog description

Everyone uses modeling and simulation even without being aware of it. This course talks about mathematical and computational modeling and simulation as the tools to solve complex problems in the real world. Topics are divided by the category of modeling method: phenomenological models vs. mechanistic models. For mechanistic models, the course will cover differential equations (including variational principle to construct the differential equations, solutions to ordinary differential equations (ODE), and classical ODE systems) and cellular automaton in detail, and mention other mechanistic models. Similarly, for phenomenological models, the course will cover regression and neural networks in detail, and introduce other phenomenological models such as networks and power-law distributions. In parallel, paper review and discussion will serve as case studies of modeling of real-world complex systems, illustrating application domains. Course projects are required. Note: Knowledge in probability and statistics, linear algebra and calculus, experiences in computer programming/MATLAB, or permission of instructor is required.