  State estimation from limited sensor measurements is ubiquitously found as a
common challenge in a broad range of fields including mechanics, astronomy, and
geophysics. Fluid mechanics is no exception -- state estimation of fluid flows
is particularly important for flow control and processing of experimental data.
However, strong nonlinearities and spatio-temporal high degrees of freedom of
fluid flows cause difficulties in reasonable estimations. To handle these
issues, neural networks (NNs) have recently been applied to the fluid flow
estimation instead of conventional linear methods. The present study focuses on
the capability of NNs to various fluid flow estimation problems from a
practical viewpoint regarding robust training. Three types of unsteady laminar
and turbulent flows are considered for the present demonstration: 1. square
cylinder wake, 2. turbulent channel flow, and 3. laminar to turbulent
transitional boundary layer. We utilize a convolutional neural network (CNN) to
estimate velocity fields from sectional sensor measurements. To assess the
practicability of the CNN models, physical quantities required for the input
and robustness against lack of sensors are investigated. We also examine the
effectiveness of several considerable approaches for model training to gain
more robustness against the lack of sensors. The knowledge acquired through the
present study in terms of effective training approaches can be transferred
towards practical machine learning in fluid flow modeling.
