HelmFluid: Learning Helmholtz Dynamics for Interpretable Fluid Prediction

• URL: http://arxiv.org/abs/2310.10565v3
• Date: Fri, 7 Jun 2024 03:38:15 GMT
• Title: HelmFluid: Learning Helmholtz Dynamics for Interpretable Fluid Prediction
• Authors: Lanxiang Xing, Haixu Wu, Yuezhou Ma, Jianmin Wang, Mingsheng Long,
• Abstract summary: HelmFluid is an accurate and interpretable predictor for fluid. Inspired by Helmholtz theorem, we design a HelmDynamics block to learn Helmholtz dynamics. By embedding the HelmDynamics block into a Multiscale Multihead Integral Architecture, HelmFluid can integrate learned Helmholtz dynamics along temporal dimension in multiple spatial scales.
• Score: 66.38369833561039
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fluid prediction is a long-standing challenge due to the intrinsic high-dimensional non-linear dynamics. Previous methods usually utilize the non-linear modeling capability of deep models to directly estimate velocity fields for future prediction. However, skipping over inherent physical properties but directly learning superficial velocity fields will overwhelm the model from generating precise or physics-reliable results. In this paper, we propose the HelmFluid toward an accurate and interpretable predictor for fluid. Inspired by the Helmholtz theorem, we design a HelmDynamics block to learn Helmholtz dynamics, which decomposes fluid dynamics into more solvable curl-free and divergence-free parts, physically corresponding to potential and stream functions of fluid. By embedding the HelmDynamics block into a Multiscale Multihead Integral Architecture, HelmFluid can integrate learned Helmholtz dynamics along temporal dimension in multiple spatial scales to yield future fluid. Compared with previous velocity estimating methods, HelmFluid is faithfully derived from Helmholtz theorem and ravels out complex fluid dynamics with physically interpretable evidence. Experimentally, HelmFluid achieves consistent state-of-the-art in both numerical simulated and real-world observed benchmarks, even for scenarios with complex boundaries.

Related papers

• Neural Material Adaptor for Visual Grounding of Intrinsic Dynamics [48.99021224773799]
  We propose the Neural Material Adaptor (NeuMA), which integrates existing physical laws with learned corrections. We also propose Particle-GS, a particle-driven 3D Gaussian Splatting variant that bridges simulation and observed images.
  arXiv  Detail & Related papers  (2024-10-10T17:43:36Z)
• Quasi-Lindblad pseudomode theory for open quantum systems [6.184495862486372]
  We introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics. We show that this quasi-Lindblad pseudomode formulation leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials.
  arXiv  Detail & Related papers  (2024-08-28T04:26:13Z)
• Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamics [0.0]
  We study the relaxation of a highly collisional, ultracold but nondegenerate gas of polar molecules. The gas is subject to fluid-gas coupled dynamics that lead to a breakdown of first-order hydrodynamics. We present substantially improved reduced-order models for these same observables.
  arXiv  Detail & Related papers  (2024-06-11T17:50:04Z)
• Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics [10.420017109857765]
  Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines. Due to the particle-like nature of the simulation, graph neural networks (GNNs) have emerged as appealing and successful surrogates. In this work, we identify particle clustering originating from tensile instabilities as one of the primary pitfalls.
  arXiv  Detail & Related papers  (2024-02-09T09:40:12Z)
• Machine learning of hidden variables in multiscale fluid simulation [77.34726150561087]
  Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks. We show that this method enables an equation based approach to reproduce non-linear, large Knudsen number plasma physics.
  arXiv  Detail & Related papers  (2023-06-19T06:02:53Z)
• Using Conservation Laws to Infer Deep Learning Model Accuracy of Richtmyer-meshkov Instabilities [0.0]
  Richtmyer-Meshkov Instability (RMI) is a complicated phenomenon that occurs when a shockwave passes through a perturbed interface. Deep learning was used to learn the temporal mapping of initial geometric perturbations to the full-field hydrodynamic solutions of density and velocity. Predictions from the deep learning model appear to accurately capture temporal RMI formations.
  arXiv  Detail & Related papers  (2022-07-19T02:20:47Z)
• Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management [64.17887333976593]
  Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. We use differentiable programming with a full-physics model and machine learning to determine the fluid extraction rates that prevent over-pressurization.
  arXiv  Detail & Related papers  (2022-06-21T20:38:13Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields [65.07940731309856]
  Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids. In this paper, we consider a partially observable scenario known as fluid dynamics grounding. We propose a differentiable two-stage network named NeuroFluid. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities.
  arXiv  Detail & Related papers  (2022-03-03T15:13:29Z)
• Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics [4.547988283172179]
  We explore the use of Neural Ordinary Differential Equations for fluid flow simulation. Test problems we consider include incompressible flow around a cylinder and real-world applications of shallow water hydrodynamics in riverine and estuarine systems. Our findings indicate that Neural ODEs provide an elegant framework for stable and accurate evolution of latent-space dynamics with a promising potential of extrapolatory predictions.
  arXiv  Detail & Related papers  (2021-04-22T19:20:47Z)

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.