Data Driven Modeling of Complex Systems

The almost paradoxical concept of deterministic chaos describes systems which are so sensitive to initial conditions that long term forecasting becomes impossible. Therefore, despite the fact that there is no randomness in the dynamical equations, even the slightest error in calculation -- for instance numerical precision errors in a computer -- will cause future predictions to be wildly off. Applications of chaotic systems range from weather prediction, turbulent flows in fluids, plasma dynamics, chemical reactions, population dynamics, the motion of celestial bodies, the stock market, and many others. While current techniques tend to use noisy and partial measurement information to constrain a physical model (https://en.wikipedia.org/wiki/Kalman_filter), Therefore it is important to be able to use data driven methods such as machine learning (ML) to forecast such systems.