The integration of artificial intelligence (AI) into computational fluid dynamics (CFD) has significantly expanded the scope of fluid modeling, allowing enhanced analysis capabilities and improved simulation performance. While Eulerian methods already benefit extensively from AI, notably in reliable weather prediction, the application of AI to Lagrangian methods remains less consolidated. Smoothed particle hydrodynamics (SPH) is a Lagrangian mesh-less numerical method for CFD with well-established advantages for the simulation of highly dynamic free-surface flows. Here, we explore an application of AI to SPH simulations, utilizing an artificial neural network (ANN) to estimate hydrodynamic forces between particle pairs, learning from SPH-simulated results. A model of this nature, which emulates the mathematical representation of physics, is termed an emulator . We examine the physical significance of the emulator, presenting its applications in benchmark tests, assessing its faithfulness to traditional SPH simulations, and highlighting its ability to generalize and simulate test cases with varying levels of complexity beyond its training data.

One of the main issues with naive Smoothed Particle Hydrodynamics (SPH) implementations is the lack of uniform accuracy in the computational domain. If not mastered correctly, this leads to non-physical predictions when dealing with large-domain hydraulic problems or with very fine resolutions. The present article addresses two recommended methodologies to achieve the best numerical accuracy with single-precision SPH implementations, using the GPUSPH engine as reference. A still water test case is examined using different approaches. Instead of operating with the physical particle positions, the use of positions relative to the neighbour-search grid leads to a homogeneous accuracy distribution throughout the domain, with a consequent improvement in energy conservation. Further improvements are attained by evolving the relative density variation in the fluid equations, instead of the physical density. This helps in bounding the numerical errors within the machine epsilon and prevents any spurious behaviour due to error accumulation.

Lava flow modeling is important in many practical applications, such as the simulation of potential hazard scenarios and the planning of risk mitigation measures, as well as in scientific research to improve our understanding of the physical processes governing the dynamics of lava flow emplacement. Existing predictive models of lava flow behavior include various methods and solvers, each with its advantages and disadvantages. Codes differ in their physical implementations, numerical accuracy, and computational efficiency. In order to validate their efficiency and accuracy, several benchmark test cases for computational lava flow modeling have been established. Despite the popularity that the Smoothed Particle Hydrodynamics (SPH) method has gained in Computational Fluid Dynamics (CFD), very few validations against lava flows have been successfully conducted. At the Tecnolab of INGV- Catania we designed GPUSPH, an implementation of the weakly-compressible SPH method running fully on Graphics Processing Units (GPUs). GPUSPH is a particle engine capable of modeling both Newtonian and non-Newtonian fluids, solving the three-dimensional Navier– Stokes equations, using either a fully explicit integration scheme, or a semi-implicit scheme in the case of highly viscous fluids. Thanks to the full coupling with the thermal equation, and its support for radiation, convection and phase transition, GPUSPH can be used to faithfully simulate lava flows. Here we present the preliminary results obtained with GPUSPH for some of the benchmarks introduced by Cordonnier et al. [2016], including analytical, semi- analytical and experimental problems. The results are reported in terms of correctness and performance, highlighting the benefits and the drawbacks deriving from the use of SPH to simulate lava flows.