  We present a data-driven pipeline for model building that combines
interpretable machine learning, hydrodynamic theories, and microscopic models.
The goal is to uncover the underlying processes governing nonlinear dynamics
experiments. We exemplify our method with data from microfluidic experiments
where crystals of streaming droplets support the propagation of nonlinear waves
absent in passive crystals. By combining physics-inspired neural networks,
known as neural operators, with symbolic regression tools, we generate the
solution, as well as the mathematical form, of a nonlinear dynamical system
that accurately models the experimental data. Finally, we interpret this
continuum model from fundamental physics principles. Informed by machine
learning, we coarse grain a microscopic model of interacting droplets and
discover that non-reciprocal hydrodynamic interactions stabilise and promote
nonlinear wave propagation.
