  In this work, we ask and answer the question: when is the viscosity of a
fluid uniquely determined from spatially sparse measurements of its velocity
field? We pose the question mathematically as an optimization problem using the
determining map (the mapping of data to an approximation made via a nudging
algorithm) to define a loss functional, the minimization of which solves the
inverse problem of identifying the true viscosity given the measurement data.
We give explicit a priori conditions for the well-posedness of this inverse
problem. In addition, we show that smallness of the loss functional implies
proximity to the true viscosity. We then present an algorithm for solving the
inverse problem and prove its convergence.
