  Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering
and scientific disciplines. SPH is a class of Lagrangian schemes that
discretize fluid dynamics via finite material points that are tracked through
the evolving velocity field. Due to the particle-like nature of the simulation,
graph neural networks (GNNs) have emerged as appealing and successful
surrogates. However, the practical utility of such GNN-based simulators relies
on their ability to faithfully model physics, providing accurate and stable
predictions over long time horizons - which is a notoriously hard problem. In
this work, we identify particle clustering originating from tensile
instabilities as one of the primary pitfalls. Based on these insights, we
enhance both training and rollout inference of state-of-the-art GNN-based
simulators with varying components from standard SPH solvers, including
pressure, viscous, and external force components. All Neural SPH-enhanced
simulators achieve better performance than the baseline GNNs, often by orders
of magnitude in terms of rollout error, allowing for significantly longer
rollouts and significantly better physics modeling. Code available at
https://github.com/tumaer/neuralsph.
