Discovering governing equations of physical phenomena purely from data

Synopsis

Formulating the governing equations of physical systems merely from data is a major challenge in science. Accessibility to collect and treat data together with advances in machine learning and data science gives a new ground to discover equations from measurement data. This is particularly desirable because analytical mathematical models are often elusive to formulate.  This work introduces a method that assumes sparsity in the structure of the model, so few terms are important to dictate the behavior of the system. To determine the fewest terms in the governing equations, sparse regression is used. Finally, the method is illustrated in the chaotic Lorenz system and fluid vortex shedding behind an obstacle. The underlying dynamics are successfully obtained showing the power of this method, in contrast to decades of experts pursuing these solutions.