2023/05/26 by Fabricio Arend Torres, Torres, F. Arend, Marcello Massimo Negri +7 · 3 citations
Earth and Planetary Sciences · Environmental Science · #Cryospheric studies and observations #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Hydrology and Watershed Management Studies #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Meteorological Phenomena and Simulations #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2305.16846
openalex publication_date 2023/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.