Derive acceptance thresholds for learned GNN-based Lagrangian fluid simulators

Derive quantitative, physics-based threshold criteria for Lagrangian fluid simulations that indicate when a learned graph neural network-based simulator achieves performance sufficient for a specified downstream task, analogous to established standards such as chemical accuracy or the energy-and-forces-within-threshold (EFwT) in computational chemistry.

Background

The paper observes that in some scenarios, such as the 3D reverse Poiseuille flow dataset, baseline GNN simulators already achieve low absolute errors, making further improvements via neural SPH corrections marginal. This highlights the need for principled criteria to decide when a model is accurate enough for practical use.

The authors draw parallels to established acceptance criteria in other fields, such as chemical accuracy and EFwT in computational chemistry, and argue that similar task-relevant thresholds are needed for Lagrangian fluid simulations to determine when corrections are necessary and to assess practical utility.

References

Finally, this 3D RPF result lets us conclude that it is necessary to define a threshold of when a learned GNN-based simulator performs well enough in the sense of the requirements of the downstream task of interest. Here, we refer to physical thresholds like the chemical accuracy in computational chemistry or the energy and forces within threshold (EFwT) quantity used by the Open Catalyst project, both of which are designed to quantify whether a computational model is useful for practical applications. We leave the derivation of such thresholds for Lagrangian fluid simulations to future work.

— Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics  (2402.06275 - Toshev et al., 2024) in Subsection '3D Datasets', Section 'Experiments'