The neural particle method

An updated Lagrangian physics informed neural network for computational fluid dynamics

verfasst von: Henning Wessels, Christian Weißenfels, Peter Wriggers
Abstract: Today numerical simulation is indispensable in industrial design processes. It can replace cost and time intensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement, this must also be true for numerical simulation techniques themselves. Up to date, no general purpose numerical method is available which can accurately resolve a variety of physics ranging from fluid to solid mechanics including large deformations and free surface flow phenomena. These complex multi-physics problems occur for example in Additive Manufacturing processes. In this sense, the recent developments in Machine Learning display promise for numerical simulation. It has recently been shown that instead of solving a system of equations as in standard numerical methods, a neural network can be trained solely based on initial and boundary conditions. Neural networks are smooth, differentiable functions that can be used as a global ansatz for Partial Differential Equations (PDEs). While this idea dates back to more than 20 years (Lagaris et al., 1998), it is only recently that an approach for the solution of time dependent problems has been developed (Raissi et al., 2019). With the latter, implicit Runge–Kutta schemes with unprecedented high order have been constructed to solve scalar-valued PDEs. We build on the aforementioned work in order to develop an Updated Lagrangian method for the solution of incompressible free surface flow subject to the inviscid Euler equations. The method is straightforward to implement and does not require any specific algorithmic treatment which is usually necessary to accurately resolve the incompressibility constraint. Due to its meshfree character, we will name it the Neural Particle Method (NPM). It will be demonstrated that the NPM remains stable and accurate even if the location of discretization points is highly irregular.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Externe Organisation(en): Technische Universität Braunschweig
Typ: Artikel
Journal: Computer Methods in Applied Mechanics and Engineering
Band: 368
ISSN: 0045-7825
Publikationsdatum: 15.08.2020
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Physik und Astronomie (insg.), Angewandte Informatik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2003.10208 (Zugang: Offen)
https://doi.org/10.1016/j.cma.2020.113127 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{ed354c4a7b5046abbf865ab38d25009f,
title = "The neural particle method: An updated Lagrangian physics informed neural network for computational fluid dynamics",
abstract = "Today numerical simulation is indispensable in industrial design processes. It can replace cost and time intensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement, this must also be true for numerical simulation techniques themselves. Up to date, no general purpose numerical method is available which can accurately resolve a variety of physics ranging from fluid to solid mechanics including large deformations and free surface flow phenomena. These complex multi-physics problems occur for example in Additive Manufacturing processes. In this sense, the recent developments in Machine Learning display promise for numerical simulation. It has recently been shown that instead of solving a system of equations as in standard numerical methods, a neural network can be trained solely based on initial and boundary conditions. Neural networks are smooth, differentiable functions that can be used as a global ansatz for Partial Differential Equations (PDEs). While this idea dates back to more than 20 years (Lagaris et al., 1998), it is only recently that an approach for the solution of time dependent problems has been developed (Raissi et al., 2019). With the latter, implicit Runge–Kutta schemes with unprecedented high order have been constructed to solve scalar-valued PDEs. We build on the aforementioned work in order to develop an Updated Lagrangian method for the solution of incompressible free surface flow subject to the inviscid Euler equations. The method is straightforward to implement and does not require any specific algorithmic treatment which is usually necessary to accurately resolve the incompressibility constraint. Due to its meshfree character, we will name it the Neural Particle Method (NPM). It will be demonstrated that the NPM remains stable and accurate even if the location of discretization points is highly irregular.",
keywords = "Computational fluid dynamics, Constraint problem, Implicit Runge–Kutta, Incompressibility, Machine learning, Physics-informed neural network",
author = "Henning Wessels and Christian Wei{\ss}enfels and Peter Wriggers",
year = "2020",
month = aug,
day = "15",
doi = "10.48550/arXiv.2003.10208",
language = "English",
volume = "368",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}