The Neural Particle Method – An Updated Lagrangian Physics Informed Neural Network for Computational Fluid Dynamics

03/18/2020
by   Henning Wessels, et al.
0

Numerical simulation is indispensable in industrial design processes. It can replace expensive 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 itself. 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 chances for numerical simulation. It has been shown recently 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 ago [Lagaris et al., 1998], it is only recent 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 easy to implement and gets along without 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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 9

page 11

page 12

page 13

page 15

12/04/2020

DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation

We present a method for learning dynamics of complex physical processes ...
08/01/2021

A-ULMPM: An Arbitrary Updated Lagrangian Material Point Method for Efficient Simulation of Solids and Fluids

We present an arbitrary updated Lagrangian Material Point Method (A-ULMP...
03/19/2021

A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems

In this paper, we show a physics-informed neural network solver for the ...
01/18/2022

Self-similar blow-up profile for the Boussinesq equations via a physics-informed neural network

We develop a new numerical framework, employing physics-informed neural ...
03/11/2021

Frame-independent vector-cloud neural network for nonlocal constitutive modelling on arbitrary grids

Constitutive models are widely used for modelling complex systems in sci...
04/29/2022

AL-PINNs: Augmented Lagrangian relaxation method for Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) has become a prominent applicat...
06/26/2021

Physics-Guided Deep Neural Network to Characterize Non-Newtonian Fluid Flow for Optimal Use of Energy Resources

Numerical simulations of non-Newtonian fluids are indispensable for opti...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.