New AI Model Predicts Fluid Dynamics Across Representations

In fluid dynamics, Lagrangian modeling, which tracks individual particle trajectories, is crucial but often less available than Eulerian field data, which describes fluid properties at fixed points. This mismatch presents a challenge for neural operators, which are typically trained and evaluated on Eulerian representations. This research addresses whether a model trained only on Eulerian data can generalize to Lagrangian particle rollout without specific Lagrangian supervision or adaptation. The proposed solution is the Transferable Latent Operator (TLO). TLO learns a unified flow representation that is shared between Eulerian field prediction and Lagrangian particle rollout. It achieves this by decoupling the evolution of the latent flow from coordinate-dependent decoding. This means that by querying the evolving latent representation at fixed spatial coordinates, Eulerian fields can be predicted. Conversely, by querying velocities at particle positions and recursively updating these positions, Lagrangian rollout can be performed. Across five fluid-dynamics benchmarks, TLO consistently outperforms existing neural operators in both Eulerian field prediction and, notably, in zero-shot Lagrangian rollout, with further improvements possible through limited Lagrangian fine-tuning.