A comparison of reduced-order modeling approaches for PDEs with bifurcating solutions

by   Martin W. Hess, et al.

This paper focuses on reduced-order models (ROMs) built for the efficient treatment of PDEs having solutions that bifurcate as the values of multiple input parameters change. First, we consider a method called local ROM that uses k-means algorithm to cluster snapshots and construct local POD bases, one for each cluster. We investigate one key ingredient of this approach: the local basis selection criterion. Several criteria are compared and it is found that a criterion based on a regression artificial neural network (ANN) provides the most accurate results for a channel flow problem exhibiting a supercritical pitchfork bifurcation. The same benchmark test is then used to compare the local ROM approach with the regression ANN selection criterion to an established global projection-based ROM and a recently proposed ANN based method called POD-NN. We show that our local ROM approach gains more than an order of magnitude in accuracy over the global projection-based ROM. However, the POD-NN provides consistently more accurate approximations than the local projection-based ROM.



There are no comments yet.


page 6

page 8

page 9

page 10

page 11

page 12


Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks

We propose a nonlinear reduced basis method for the efficient approximat...

Physics-informed cluster analysis and a priori efficiency criterion for the construction of local reduced-order bases

Nonlinear model order reduction has opened the door to parameter optimiz...

Standardized Non-Intrusive Reduced Order Modeling Using Different Regression Models With Application to Complex Flow Problems

We present a non-intrusive reduced basis method (RBM) for unsteady non-l...

Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks

We present a method for solving linear and nonlinear PDEs based on the v...

A hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic ...

An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

This work deals with the investigation of bifurcating fluid phenomena us...

Classification based on invisible features and thereby finding the effect of tuberculosis vaccine on COVID-19

In the case of clustered data, an artificial neural network with logcosh...
This week in AI

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