  This paper presents a first step towards tuning observers for general
nonlinear systems. Relying on recent results around
Kazantzis-Kravaris/Luenberger (KKL) observers, we propose an empirical
criterion to guide the calibration of the observer, by trading off transient
performance and sensitivity to measurement noise. We parametrize the gain
matrix and evaluate this criterion over a family of observers for different
parameter values. We then use neural networks to learn the mapping between the
observer and the nonlinear system, and present a novel method to sample the
state-space efficiently for nonlinear regression. We illustrate the merits of
this approach in numerical simulations.
