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

03/11/2021
by   Xu-Hui Zhou, et al.
0

Constitutive models are widely used for modelling complex systems in science and engineering, where first-principle-based, well-resolved simulations are often prohibitively expensive. For example, in fluid dynamics, constitutive models are required to describe nonlocal, unresolved physics such as turbulence and laminar-turbulent transition. In particular, Reynolds stress models for turbulence and intermittency transport equations for laminar-turbulent transition both utilize convection–diffusion partial differential equations (PDEs). However, traditional PDE-based constitutive models can lack robustness and are often too rigid to accommodate diverse calibration data. We propose a frame-independent, nonlocal constitutive model based on a vector-cloud neural network that can be trained with data. The learned constitutive model can predict the closure variable at a point based on the flow information in its neighborhood. Such nonlocal information is represented by a group of points, each having a feature vector attached to it, and thus the input is referred to as vector cloud. The cloud is mapped to the closure variable through a frame-independent neural network, which is invariant both to coordinate translation and rotation and to the ordering of points in the cloud. As such, the network takes any number of arbitrarily arranged grid points as input and thus is suitable for unstructured meshes commonly used in fluid flow simulations. The merits of the proposed network are demonstrated on scalar transport PDEs on a family of parameterized periodic hill geometries. Numerical results show that the vector-cloud neural network is a promising tool not only as nonlocal constitutive models and but also as general surrogate models for PDEs on irregular domains.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 7

page 9

page 11

12/28/2021

Frame invariance and scalability of neural operators for partial differential equations

Partial differential equations (PDEs) play a dominant role in the mathem...
05/18/2021

PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence

Recent research has used deep learning to develop partial differential e...
02/25/2021

SPINN: Sparse, Physics-based, and Interpretable Neural Networks for PDEs

We introduce a class of Sparse, Physics-based, and Interpretable Neural ...
03/18/2020

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

Numerical simulation is indispensable in industrial design processes. It...
09/14/2021

Non-linear Independent Dual System (NIDS) for Discretization-independent Surrogate Modeling over Complex Geometries

Numerical solutions of partial differential equations (PDEs) require exp...
07/08/2020

Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction

Solving large complex partial differential equations (PDEs), such as tho...
01/14/2020

Turbulent scalar flux in inclined jets in crossflow: counter gradient transport and deep learning modelling

A cylindrical and inclined jet in crossflow is studied under two distinc...
This week in AI

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