Concurrent multi-parameter learning demonstrated on the Kuramoto-Sivashinsky equation

We develop an algorithm for the concurrent (on-the-fly) estimation of parameters for a system of evolutionary dissipative partial differential equations in which the state is partially observed. The intuitive nature of the algorithm makes its extension to several different systems immediate, and it allows for recovery of multiple parameters simultaneously. We test this algorithm on the Kuramoto-Sivashinsky equation in one dimension and demonstrate its efficacy in this context.