Machine learning of hidden variables in multiscale fluid simulation
- URL: http://arxiv.org/abs/2306.10709v1
- Date: Mon, 19 Jun 2023 06:02:53 GMT
- Title: Machine learning of hidden variables in multiscale fluid simulation
- Authors: Archis S. Joglekar and Alexander G. R. Thomas
- Abstract summary: 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.
- Score: 77.34726150561087
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Solving fluid dynamics equations often requires the use of closure relations
that account for missing microphysics. For example, when solving equations
related to fluid dynamics for systems with a large Reynolds number, sub-grid
effects become important and a turbulence closure is required, and in systems
with a large Knudsen number, kinetic effects become important and a kinetic
closure is required. By adding an equation governing the growth and transport
of the quantity requiring the closure relation, it becomes possible to capture
microphysics through the introduction of ``hidden variables'' that are
non-local in space and time. The behavior of the ``hidden variables'' in
response to the fluid conditions can be learned from a higher fidelity or
ab-initio model that contains all the microphysics. In our study, a partial
differential equation simulator that is end-to-end differentiable is used to
train judiciously placed neural networks against ground-truth simulations. We
show that this method enables an Euler equation based approach to reproduce
non-linear, large Knudsen number plasma physics that can otherwise only be
modeled using Boltzmann-like equation simulators such as Vlasov or
Particle-In-Cell modeling.
Related papers
- Potential quantum advantage for simulation of fluid dynamics [1.4046104514367475]
We show that a potential quantum exponential speedup can be achieved to simulate the Navier-Stokes equations governing turbulence using quantum computing.
This work suggests that an exponential quantum advantage may exist for simulating nonlinear multiscale transport phenomena.
arXiv Detail & Related papers (2023-03-29T09:14:55Z) - Data-driven modeling of Landau damping by physics-informed neural
networks [4.728411962159049]
We construct a multi-moment fluid model with an implicit fluid closure included in the neural network using machine learning.
The model reproduces the time evolution of the electric field energy, including its damping rate, and the plasma dynamics from the kinetic simulations.
This work sheds light on the accurate and efficient modeling of large-scale systems, which can be extended to complex multiscale laboratory, space, and astrophysical plasma physics problems.
arXiv Detail & Related papers (2022-11-02T10:33:38Z) - Data-driven, multi-moment fluid modeling of Landau damping [6.456946924438425]
We apply a deep learning architecture to learn fluid partial differential equations (PDEs) of a plasma system.
The learned multi-moment fluid PDEs are demonstrated to incorporate kinetic effects such as Landau damping.
arXiv Detail & Related papers (2022-09-10T19:06:12Z) - 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) - Deep Random Vortex Method for Simulation and Inference of Navier-Stokes
Equations [69.5454078868963]
Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air.
With the development of AI techniques, several approaches have been designed to integrate deep neural networks in simulating and inferring the fluid dynamics governed by incompressible Navier-Stokes equations.
We propose the emphDeep Random Vortex Method (DRVM), which combines the neural network with a random vortex dynamics system equivalent to the Navier-Stokes equation.
arXiv Detail & Related papers (2022-06-20T04:58:09Z) - 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) - A Gradient-based Deep Neural Network Model for Simulating Multiphase
Flow in Porous Media [1.5791732557395552]
We describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media.
We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses.
arXiv Detail & Related papers (2021-04-30T02:14:00Z) - Machine learning accelerated computational fluid dynamics [9.077691121640333]
We use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows.
For both direct numerical simulation of turbulence and large eddy simulation, our results are as accurate as baseline solvers with 8-10x finer resolution in each spatial dimension.
Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization.
arXiv Detail & Related papers (2021-01-28T19:10:00Z) - 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)
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.