Predicting The Evolution of Interfaces with Fourier Neural Operators

• URL: http://arxiv.org/abs/2505.13463v1
• Date: Mon, 05 May 2025 19:35:23 GMT
• Title: Predicting The Evolution of Interfaces with Fourier Neural Operators
• Authors: Paolo Guida, William L. Roberts,
• Abstract summary: Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations.<n>This work demonstrates that the time scale of neural operators-based predictions is comparable to the time scale of multi-phase applications.
• Score: 0.3069335774032178
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations, such as the Navier-Stokes equations. Some complex problems rely on sophisticated algorithms to deal with strong discontinuities in the computational domain. For example, liquid-vapour multiphase flows are a challenging problem in many configurations, particularly those involving large density gradients or phase change. The complexity mentioned above has not allowed for fine control of fast industrial processes or applications because computational fluid dynamics (CFD) models do not have a quick enough forecasting ability. This work demonstrates that the time scale of neural operators-based predictions is comparable to the time scale of multi-phase applications, thus proving they can be used to control processes that require fast response. Neural Operators can be trained using experimental data, simulations or a combination. In the following, neural operators were trained in volume of fluid simulations, and the resulting predictions showed very high accuracy, particularly in predicting the evolution of the liquid-vapour interface, one of the most critical tasks in a multi-phase process controller.

Related papers

• Neural Operators for Accelerating Scientific Simulations and Design [85.89660065887956]
  An AI framework, known as Neural Operators, presents a principled framework for learning mappings between functions defined on continuous domains. Neural Operators can augment or even replace existing simulators in many applications, such as computational fluid dynamics, weather forecasting, and material modeling.
  arXiv  Detail & Related papers  (2023-09-27T00:12:07Z)
• On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solver [59.13397937903832]
  We introduce a deep learning-based corrector called Neural Vector (NeurVec) NeurVec can compensate for integration errors and enable larger time step sizes in simulations. Our experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability.
  arXiv  Detail & Related papers  (2022-08-07T09:02:18Z)
• Semi-supervised Learning of Partial Differential Operators and Dynamical Flows [68.77595310155365]
  We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.
  arXiv  Detail & Related papers  (2022-07-28T19:59:14Z)
• Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networks [0.0]
  We introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics. We demonstrate this method on advection problems and incompressible fluid dynamics, both fundamental phenomena in oceanic and atmospheric processes. Simulations obtained with MultiScaleGNN are between two and four orders of magnitude faster than those on which it was trained.
  arXiv  Detail & Related papers  (2022-05-05T13:33:03Z)
• Accelerating Part-Scale Simulation in Liquid Metal Jet Additive Manufacturing via Operator Learning [0.0]
  Part-scale predictions require many small-scale simulations. A model describing droplet coalescence for LMJ may include coupled incompressible fluid flow, heat transfer, and phase change equations. We apply an operator learning approach to learn a mapping between initial and final states of the droplet coalescence process.
  arXiv  Detail & Related papers  (2022-02-02T17:24:16Z)
• A fully-differentiable compressible high-order computational fluid dynamics solver [0.0]
  compressible Navier-Stokes equations govern compressible flows and allow for complex phenomena like turbulence and shocks. Despite tremendous progress in hardware and software, the smallest length-scales in fluid flows still introduces prohibitive computational cost for real-life applications. We present a fully-differentiable three-dimensional framework for the computation of compressible fluid flows using high-order state-of-the-art numerical methods.
  arXiv  Detail & Related papers  (2021-12-09T15:18:51Z)
• Machine learning for rapid discovery of laminar flow channel wall modifications that enhance heat transfer [56.34005280792013]
  We present a combination of accurate numerical simulations of arbitrary, flat, and non-flat channels and machine learning models predicting drag coefficient and Stanton number. We show that convolutional neural networks (CNN) can accurately predict the target properties at a fraction of the time of numerical simulations.
  arXiv  Detail & Related papers  (2021-01-19T16:14:02Z)
• Large-scale Neural Solvers for Partial Differential Equations [48.7576911714538]
  Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. Recent numerical solvers require manual discretization of the underlying equation as well as sophisticated, tailored code for distributed computing. We examine the applicability of continuous, mesh-free neural solvers for partial differential equations, physics-informed neural networks (PINNs) We discuss the accuracy of GatedPINN with respect to analytical solutions -- as well as state-of-the-art numerical solvers, such as spectral solvers.
  arXiv  Detail & Related papers  (2020-09-08T13:26:51Z)
• 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)
• Learning Incompressible Fluid Dynamics from Scratch -- Towards Fast, Differentiable Fluid Models that Generalize [7.707887663337803]
  Recent deep learning based approaches promise vast speed-ups but do not generalize to new fluid domains. We propose a novel physics-constrained training approach that generalizes to new fluid domains. We present an interactive real-time demo to show the speed and generalization capabilities of our trained models.
  arXiv  Detail & Related papers  (2020-06-15T20:59:28Z)

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.