HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition

• URL: http://arxiv.org/abs/2406.08570v1
• Date: Wed, 12 Jun 2024 18:11:32 GMT
• Title: HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition
• Authors: Miao Qi, Ramzi Idoughi, Wolfgang Heidrich,
• Abstract summary: HDNet performs a Helmholtz decomposition of an arbitrary flow field. It decomposes the input flow into a divergence-only and a curl-only component. As a PINN, HDNet is fully differentiable and can easily be integrated into arbitrary flow estimation problems.
• Score: 17.834139646217274
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Flow estimation problems are ubiquitous in scientific imaging. Often, the underlying flows are subject to physical constraints that can be exploited in the flow estimation; for example, incompressible (divergence-free) flows are expected for many fluid experiments, while irrotational (curl-free) flows arise in the analysis of optical distortions and wavefront sensing. In this work, we propose a Physics- Inspired Neural Network (PINN) named HDNet, which performs a Helmholtz decomposition of an arbitrary flow field, i.e., it decomposes the input flow into a divergence-only and a curl-only component. HDNet can be trained exclusively on synthetic data generated by reverse Helmholtz decomposition, which we call Helmholtz synthesis. As a PINN, HDNet is fully differentiable and can easily be integrated into arbitrary flow estimation problems.

Related papers

• Neural Networks-based Random Vortex Methods for Modelling Incompressible Flows [0.0]
  We introduce a novel Neural Networks-based approach for approximating solutions to the (2D) incompressible Navier--Stokes equations. Our algorithm uses a Physics-informed Neural Network, that approximates the vorticity based on a loss function that uses a computationally efficient formulation of the Random Vortex dynamics.
  arXiv  Detail & Related papers  (2024-05-22T14:36:23Z)
• HelmFluid: Learning Helmholtz Dynamics for Interpretable Fluid Prediction [66.38369833561039]
  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.
  arXiv  Detail & Related papers  (2023-10-16T16:38:32Z)
• Speed Limits for Deep Learning [67.69149326107103]
  Recent advancement in thermodynamics allows bounding the speed at which one can go from the initial weight distribution to the final distribution of the fully trained network. We provide analytical expressions for these speed limits for linear and linearizable neural networks. Remarkably, given some plausible scaling assumptions on the NTK spectra and spectral decomposition of the labels -- learning is optimal in a scaling sense.
  arXiv  Detail & Related papers  (2023-07-27T06:59:46Z)
• Predictive Limitations of Physics-Informed Neural Networks in Vortex Shedding [0.0]
  We look at the flow around a 2D cylinder and find that data-free PINNs are unable to predict vortex shedding. Data-driven PINN exhibits vortex shedding only while the training data is available, but reverts to the steady state solution when the data flow stops. The distribution of the Koopman eigenvalues on the complex plane suggests that PINN is numerically dispersive and diffusive.
  arXiv  Detail & Related papers  (2023-05-31T22:59:52Z)
• Forecasting subcritical cylinder wakes with Fourier Neural Operators [58.68996255635669]
  We apply a state-of-the-art operator learning technique to forecast the temporal evolution of experimentally measured velocity fields. We find that FNOs are capable of accurately predicting the evolution of experimental velocity fields throughout the range of Reynolds numbers tested.
  arXiv  Detail & Related papers  (2023-01-19T20:04:36Z)
• FlowX: Towards Explainable Graph Neural Networks via Message Flows [59.025023020402365]
  We investigate the explainability of graph neural networks (GNNs) as a step toward elucidating their working mechanisms. We propose a novel method here, known as FlowX, to explain GNNs by identifying important message flows. We then propose an information-controlled learning algorithm to train flow scores toward diverse explanation targets.
  arXiv  Detail & Related papers  (2022-06-26T22:48:15Z)
• Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flows [0.0]
  A neural network model with a unique network architecture and physics-informed loss function was developed to accelerate CFD simulations. Under the reacting flow dataset, the computational speed of this network model was measured to be about 10 times faster than that of the CFD solver.
  arXiv  Detail & Related papers  (2021-05-07T15:33:49Z)
• Conditional physics informed neural networks [85.48030573849712]
  We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems.
  arXiv  Detail & Related papers  (2021-04-06T18:29:14Z)
• Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction [79.81193813215872]
  We develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. We show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions.
  arXiv  Detail & Related papers  (2020-07-08T21:23:19Z)
• Physics-informed deep learning for incompressible laminar flows [13.084113582897965]
  We propose a mixed-variable scheme of physics-informed neural network (PINN) for fluid dynamics. A parametric study indicates that the mixed-variable scheme can improve the PINN trainability and the solution accuracy.
  arXiv  Detail & Related papers  (2020-02-24T21:51:53Z)

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.