  State estimation is key to both analyzing physical mechanisms and enabling
real-time control of fluid flows. A common estimation approach is to relate
sensor measurements to a reduced state governed by a reduced-order model (ROM).
(When desired, the full state can be recovered via the ROM). Current methods in
this category nearly always use a linear model to relate the sensor data to the
reduced state, which often leads to restrictions on sensor locations and has
inherent limitations in representing the generally nonlinear relationship
between the measurements and reduced state. We propose an alternative
methodology where a neural network architecture is used to learn this nonlinear
relationship. Neural network is a natural choice for this estimation problem,
as a physical interpretation of the reduced state-sensor measurement
relationship is rarely obvious. The proposed estimation framework is agnostic
to the ROM employed, and can be incorporated into any choice of ROMs derived on
a linear subspace (e.g., proper orthogonal decomposition) or a nonlinear
manifold. The proposed approach is demonstrated on a two-dimensional model
problem of separated flow around a flat plate, and is found to outperform
common linear estimation alternatives.
