  The growing interest in creating a parametric representation of liquid
sloshing inside a container stems from its practical applications in modern
engineering systems. The resonant excitation, on the other hand, can cause
unstable and nonlinear water waves, resulting in chaotic motions and
non-Gaussian signals. This paper presents a novel machine learning-based
framework for nonlinear liquid sloshing representation learning. The proposed
method is a parametric modeling technique that is based on sequential learning
and sparse regularization. The dynamics are categorized into two parts: linear
evolution and nonlinear forcing. The former advances the dynamical system in
time on an embedded manifold, while the latter causes divergent behaviors in
temporal evolution, such as bursting and switching. The proposed framework's
merit is demonstrated using an experimental dataset of liquid sloshing in a
tank under horizontal excitation with a wide frequency range and various
vertical slat screen settings.
