Parameter estimation in the Burgers equation using retrospective-cost model refinement

We apply retrospective cost model refinement to parameter estimation in a nonlinear partial differential equation. Specifically, for the scalar Burgers equation, we estimate the viscosity from measurements of flow velocity at a single grid point. We also consider the analogous problem for a modified Burgers equation as a proxy for a large eddy simulation to estimate a parameter that relates subgrid-scale stresses to the resolved strain rate.