Enhancing Computational Fluid Dynamics with Artificial Intelligence: an AI-based Smoothed Particle Hydrodynamics (SPH) Emulator for Lava Flow Modeling

The combination of Computational Fluid Dynamics (CFD) and Artificial Intelligence (AI) expands the scope of fluid modeling, providing high fidelity and fast simulations. A variety of Eulerian CFD methods integrated with AI has been already successfully presented (\textit{e.g.}, for weather forecasting); on the other hand, the combination of AI and Lagrangian methods remains less consolidated. Smoothed Particle Hydrodynamics (SPH) is a Lagrangian mesh-less CFD numerical method, highly reliable for the simulation of complex fluids. Nevertheless, SPH models exhibit limitations in high-resolution real-time simulations of physical phenomena, due to the high computational costs involved. Specifically, SPH simulations of lava flows are well representative of the difficulties in modeling highly complex fluids. Lava is a fluid with a high physical complexity, generating viscous flows, dependent on temperature and rheology, and it may have significant impacts on the surrounding environment. Thus, it is important to monitor lava flows with accurate and timely forecasting of their spatio-temporal evolution. Here, I present an emulator derived from CFD physics-based models, in which AI algorithms join the equation-based mathematical representation of physics, to solve fluid dynamics problems in shorter times. I developed an AI-based emulator for SPH method, in which the conservation of momentum equation is substituted by an Artificial Neural Network (ANN), which learns from SPH simulations. The ANN is trained to estimate SPH particles interaction forces exploiting as input the state of the particles (position, velocity, density). I verified the reliability of the AI-based emulator to remain as faithful as possible to the SPH reference model. Applications to different kind of fluids are shown, starting from an inviscid fluid, up to the study of a viscous fluid with a thermal component, to finally move towards the description of a lava flow evolution, exploiting the potential of the combined use of numerical and AI models. Simulations and emulations have been compared for each step, reaching a high degree of fidelity, and demonstrating the generalizability of the AI-based emulator, tested over problems with varying levels of complexity, and its robustness to different spatial resolutions.