Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics (2402.06275v2)

Abstract: 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.

• The paper proposes neural SPH, a hybrid approach that integrates SPH stabilizing forces into GNN-based simulations, effectively mitigating particle clustering and tensile instabilities.
• It introduces refined pressure, viscous, and external force computations during evaluation to significantly improve metrics like MSE and kinetic energy.
• Experimental results on 2D and 3D scenarios, including dam breaks and lid-driven cavity flows, demonstrate an order of magnitude improvement in simulation accuracy and stability.

Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics

The paper "Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics" proposes advancements in modeling Lagrangian fluid dynamics through enhancements to Graph Neural Networks (GNNs) by incorporating elements from Smoothed Particle Hydrodynamics (SPH) solvers. SPH, a method prevalent in computational fluid dynamics (CFD), models fluid flow by tracking discrete particles, making it an exemplary candidate for integration with GNN-based simulators. However, traditional GNN-based simulators face challenges in modeling physics accurately over extended time horizons due to issues such as particle clustering from tensile instabilities. This paper addresses these limitations through the introduction of neural SPH—a methodology that integrates SPH solver components into GNN simulators, achieving superior performance in fluid dynamics simulations.

Key Contributions and Methodology

The authors identify particle clustering, especially when negative pressures induce tensile instabilities, as a significant hurdle for accurate fluid simulations. To mitigate this, they propose augmenting GNN simulators with SPH-based pressure, viscous, and external force components. This enhancement is achieved without retraining the models, relying instead on novel improvements during the evaluation phase. Specifically, the paper leverages insights from traditional SPH methodologies to correct these instabilities through modifications such as:

1. Pressure and Density Computation Enhancements: By introducing pressure-related stabilizing forces, the paper addresses inaccuracies in density distribution, particularly at free surfaces where standard SPH density approximations encounter difficulties.
2. Incorporation of SPH-Based Force Computation: The paper outlines methodologies for correcting particle interactions by incorporating SPH-derived force computations during the GNN inference stage. This includes distinguishing between instantaneous and effective forces for improved temporal coarsening.
3. SPH Relaxation: A novel relaxation step is applied post-GNN integration to redistribute particles more evenly and correct unphysical cluster formations. This involves temporarily running a few steps of SPH computations to stabilize and refine the predicted states.
4. Handling of External Forces: Differentiating gravitational and non-gravitational forces to improve model generalizability and consistency across different force vector scenarios.

Experimental Results

The efficacy of neural SPH is demonstrated across diverse datasets involving both 2D and 3D fluid dynamics scenarios, including dam breaks, reverse Poiseuille flow, and lid-driven cavity flow. The introduction of neural SPH led to significant improvements in metrics like mean-squared error (MSE) in positions and kinetic energy, and Sinkhorn divergence, with enhanced stability and accuracy in long-rollout simulations—an order of magnitude improvement over baseline GNN-based models.

A particularly notable result is the improvement in modeling the complex dynamics of 2D and 3D dam break scenarios, where traditional GNN models struggle with particle artifacts such as clumping and void formation. The authors showed that applying SPH-based pressure gradients and effective force corrections garnered more accurate representations of the fluid dynamics over extended time steps.

Implications and Future Directions

The integration of SPH components into neural network-based fluid dynamics simulators represents a considerable advancement in computational fluid dynamics, particularly in the accurate and stable reproduction of Lagrangian dynamics. By resolving particle clustering through numerical physics enhancement, neural SPH has significant implications for improving the utility of GNNs in physics-based simulations across various engineering and scientific applications.

Future developments could explore the extension of this framework to more complex, multi-phase flow scenarios, further refinement of SPH hyperparameters for generalized cases, and the application of SPH relaxations to other graph-based models and simulators. Another potential exploration is the expansion of neural SPH to larger-scale, real-time simulations, providing a practical solution for industries reliant on accurate fluid modeling. Additionally, this work prompts further examination into the theoretical underpinnings of GNN-driven physics models, particularly in understanding and controlling physical accuracy and computational efficiency trade-offs.

In summary, the neural SPH approach brings a significant step forward in bridging the gap between traditional numerical solvers and contemporary machine learning-based fluid simulations, offering a robust framework that harnesses the strengths of both domains.