Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation

• URL: http://arxiv.org/abs/2608.01164v1
• Date: Sun, 02 Aug 2026 11:36:08 GMT
• Title: Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation
• Abstract summary: Pure Lagrangian neural simulators offer geometric flexibility and exact advection.<n>The absence of a fixed global reference frame introduces two severe limitations.<n>We propose a Hybrid Lagrangian-Eulerian neural simulator that augments Lagrangian dynamics with an Eulerian representation.
• Score: 39.8019405552335
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Pure Lagrangian neural simulators offer geometric flexibility and exact advection, making them well-suited for modeling moving domains and free surfaces. However, the absence of a fixed global reference frame introduces two severe limitations: a spatial bottleneck, in which model capacity is wasted on uniform regions because the dense particle neighborhoods required for stable gradients are applied indiscriminately, and rapid temporal drift, caused by purely local message passing that lacks a global anchor. Inspired by classical hybrid numerical solvers, we propose a Hybrid Lagrangian-Eulerian neural simulator that augments Lagrangian dynamics with an Eulerian representation. To address the spatial bottleneck, we introduce adaptive downsampling that eliminates kinematic redundancy, preserving micro-scale details on particles while aggregating compressed features onto Eulerian nodes to resolve large-scale dynamics. To counter temporal drift, we employ a cross-attention mechanism that queries these Eulerian features, using the fixed grid as a stable spatial anchor to correct trajectory deviations at every timestep. Comprehensive experiments show that this hierarchical, cross-attended design substantially suppresses error accumulation, establishing a new state-of-the-art for accuracy and rollout stability in Lagrangian fluid simulation.

Related papers

• DyG$^2$T: Modeling Object Dynamics with 3D Gaussian Temporal-Spatial Particle Graph Transformer [86.4618122245946]
  DyG$2$T is a dynamics modeling framework that infers object motion trajectories by spatially completing and temporally discriminating Key Point representations.<n>Experiments on both synthetic and real-world datasets demonstrate that DyG$2$T achieves accurate dynamics modeling and reasoning.
  arXiv  Detail & Related papers  (2026-08-19T03:44:28Z)
• Emulating Cosmic Structure Formation with a Lagrangian Neural Cellular Automaton [0.0]
  We introduce a hybrid deep learning framework that can be applied to structure formation as a local, iterative dynamical process on a comoving lattice.<n>By training the network to learn only the textitresidual displacement corrections to the Zeldovich approximation, we achieve high-fidelity emulation of the non-linear physics.<n>Our trained model supports percent-level precision in the power and cross spectra well into the non-linear regime.
  arXiv  Detail & Related papers  (2026-07-29T18:00:01Z)
• LagrangianSplats: Divergence-Free Transport of Gaussian Primitives for Fluid Reconstruction [26.888819976353957]
  Reconstructing 3D fluid velocity fields from sparse 2D video observations is a highly ill-posed inverse problem.<n>Existing methods typically impose these constraints through soft penalties, often leading to compromised accuracy and convergence issues.<n>We introduce a reconstruction framework that structurally enforces both constraints. Specifically, we parameterize the reconstructed velocity using a continuous Divergence-Free Kernel representation.
  arXiv  Detail & Related papers  (2026-05-10T03:45:50Z)
• Generative modeling of granular flow on inclined planes using conditional flow matching [4.880426970438706]
  This study presents the first conditional flow matching framework for granular-flow reconstruction from sparse boundary observations.<n>A physics decoder maps the reconstructed velocity fields to stress states and energy fluctuation quantities.<n>Results demonstrate that conditional generative modeling offers a practical route for non-invasive inference of hidden bulk mechanics in granular media.
  arXiv  Detail & Related papers  (2026-04-06T05:59:54Z)
• Scalable Spatio-Temporal SE(3) Diffusion for Long-Horizon Protein Dynamics [51.85385061275941]
  Molecular dynamics (MD) simulations remain the gold standard for studying protein dynamics.<n>Recent generative models have shown promise in accelerating simulations, yet they struggle with long-horizon generation.<n>We present STAR-MD, a scalable diffusion model that generates physically plausible protein trajectories over micro-scale timescales.
  arXiv  Detail & Related papers  (2026-02-02T14:13:28Z)
• From Black Hole to Galaxy: Neural Operator: Framework for Accretion and Feedback Dynamics [70.27068115318681]
  We introduce a neural-based ''subgrid black hole'' that learns the small-scale local dynamics and embeds it within direct simulations.<n>Thanks to the great speedup in fine-scale evolution, our approach captures intrinsic variability in accretion-driven feedback, allowing dynamic coupling between the central black hole and galaxy-scale gas.
  arXiv  Detail & Related papers  (2025-12-01T11:47:49Z)
• RainDiff: End-to-end Precipitation Nowcasting Via Token-wise Attention Diffusion [64.49056527678606]
  We propose a Token-wise Attention integrated into not only the U-Net diffusion model but also the radar-temporal encoder.<n>Unlike prior approaches, our method integrates attention into the architecture without incurring the high resource cost typical of pixel-space diffusion.<n>Our experiments and evaluations demonstrate that the proposed method significantly outperforms state-of-the-art approaches, robustness local fidelity, generalization, and superior in complex precipitation forecasting scenarios.
  arXiv  Detail & Related papers  (2025-10-16T17:59:13Z)
• Is memory all you need? Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flows [38.33325744358047]
  We show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions.<n>This opens up a range of new applications, for example, for the control of active Lagrangian agents in turbulence.
  arXiv  Detail & Related papers  (2025-07-21T20:50:55Z)
• Stochastic Reconstruction of Gappy Lagrangian Turbulent Signals by Conditional Diffusion Models [1.7810134788247751]
  We present a method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows. Our approach makes use of conditional generative diffusion models, a recently proposed data-driven machine learning technique.
  arXiv  Detail & Related papers  (2024-10-31T14:26:10Z)
• DeepLag: Discovering Deep Lagrangian Dynamics for Intuitive Fluid Prediction [45.778221193374755]
  This paper introduces a new Lagrangian-Eulerian combined paradigm to tackle the tanglesome fluid dynamics. Instead of solely predicting the future based on Eulerian observations, we propose DeepLag to discover hidden Lagrangian dynamics within the fluid. DeepLag excels in three challenging fluid prediction tasks covering 2D and 3D, simulated and real-world fluids.
  arXiv  Detail & Related papers  (2024-02-04T09:45:35Z)
• Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction [49.66486092259376]
  The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift. Recent works have shown that MFLD globally minimizes an entropy-regularized convex functional in the space of measures. We provide a framework to prove a uniform-in-time propagation of chaos for MFLD that takes into account the errors due to finite-particle approximation, time-discretization, and gradient approximation.
  arXiv  Detail & Related papers  (2023-06-12T16:28:11Z)
• Losing momentum in continuous-time stochastic optimisation [42.617042045455506]
  momentum-based optimisation algorithms have become particularly widespread. In this work, we analyse a continuous-time model for gradient descent with momentum. We also train a convolutional neural network in an image classification problem.
  arXiv  Detail & Related papers  (2022-09-08T10:46:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.