使用基于物理信息的卷积神经网络求解Navier–Stokes方程的物理合理且守恒解.pdfVIP

Article

Received:November28,2022;Accepted:May04,2023

PhysicallyplausibleandconservativesolutionstoNavier–Stokes

equationsusingphysics-informedCNNs

✉

Jianfeng

Li,

Liangying

Zhou,

Jingwei

Sun

,

and

Guangzhong

Sun

SchoolofComputerScienceandTechnology,UniversityofScienceandTechnologyofChina,Hefei230027,China

✉Correspondence:

Jingwei

Sun,

E-mail:

sunjw@

©

2024

The

Author(s).

This

is

an

open

access

article

under

the

CC

BY-NC-ND

4.0

license

(/licenses/by-nc-nd/4.0/).

CiteThis:JUSTC,2024,54(4):0403(12pp)

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Abstract:The

physics-informed

neural

network

(PINN)

is

an

emerging

approach

for

efficiently

solving

partial

differen-

tial

equations

(PDEs)

using

neural

networks.

The

physics-informed

convolutional

neural

network

(PICNN),

a

variant

of

PINN

enhanced

by

convolutional

neural

networks

(CNNs),

has

achieved

better

results

on

a

series

of

PDEs

since

the

parameter-sharing

property

of

CNNs

is

effective

in

learning

spatial

dependencies.

However,

applying

existing

PICNN-

based

methods

to

solve

Navier–Stokes

equations

can

generate

oscillating

predictions,

which

are

inconsistent

with

the

laws

of

physics

and

the

conservation

properties.

To

address

this

issue,

we

propose

a

novel

method

that

combines

PICNN

with

the

finite

volume

method

to

obtain

physically

plausible

and

conservative

solutions

to

Navier–Stokes

equations.

We

derive

the

second-order

upwind

difference

scheme

of

Navier–Stokes

equations

using

the

finite

volume

method.

Then

we

use

the

derived

scheme

to

calculate

the

partial

derivatives

and

construct

the

physics-informed

loss