Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids
2026-06-22 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and ScienceMachine Learning
AI summaryⓘ
The authors address the challenge of simulating complex fluid flows, especially those with changing shapes and materials that are hard to model traditionally due to high computational costs. They developed a neural network using self-attention to understand how parts of the fluid mesh interact, allowing the model to work efficiently with changing geometries. Their approach keeps the mesh structure intact, which helps maintain accuracy and stability over long simulations. Testing on 2D and 3D flows showed their method predicts fluid movement well and handles different materials, including tricky non-Newtonian fluids, all while being faster and scalable for engineering needs.
Particle Finite Element Method (PFEM)Lagrangian methodsfree-surface flownon-Newtonian fluidsself-attention mechanismneural surrogate modelsmesh discretizationremeshingtransient dynamicsstress fields
Authors
Federico Lanteri, Massimiliano Cremonesi
Abstract
High-fidelity simulations of free-surface flows using Lagrangian methods such as the Particle Finite Element Method (PFEM) are computationally demanding due to continuous domain updates and repeated solution of the governing equations. This challenge is further amplified by non-Newtonian rheologies, where material nonlinearities increase computational cost. These limitations motivate the development of efficient surrogate models to approximate PFEM dynamics at reduced cost. While data-driven deep learning approaches are promising, a key challenge is designing models that operate on arbitrary and evolving geometries. We propose a self-attention-based neural surrogate for PFEM simulations of free-surface flows. The architecture leverages attention mechanisms to model node interactions and capture complex spatial dependencies, while preserving the PFEM mesh discretization. This provides a geometric and topological framework for remeshing and node redistribution, maintaining high-quality spatial discretization during rollouts, improving long-term stability, and enabling reconstruction of derived mechanical quantities via standard finite element operators. Two attention formulations are considered: a standard self-attention mechanism and a linear variant that reduces computational cost and improves scalability. The models are evaluated on two- and three-dimensional free-surface flow benchmarks with evolving geometries, varying material parameters, and non-Newtonian fluids. Results show accurate prediction of transient dynamics and final configurations, with significantly improved scalability. The mesh-based formulation also enables direct reconstruction of quantities such as stress fields. Overall, the framework provides an accurate and scalable surrogate strategy for PFEM simulations in engineering-scale applications.