Machine Learning Seminar presentation

Topic: A Physics-guided Machine Learning Model Based on Peridynamics

Speaker: Dr Lars Beex, FSTM, University of Luxembourg

Authors: S. Vijayaraghavan (1; 2), L.A.A.Beex (1), L.Noels (2), and S.P.A.Bordas (1)

1) University of Luxembourg, Ave. de la Fonte 6, L-4364 Belval, Luxembourg.

2) University of Liege, CM3 B52, Alle de la découverte 9, B4000 Liege, Belgium

Time: Wednesday 2021.01.13, 10:00 CET

How to join: Please contact Jakub Lengiewicz

Abstract:

Many model order reduction approaches use solutions of a few ‘offline’ training simulations to reduce the number of degrees of freedom of the many ‘online’ simulations of interest. In proper orthogonal decomposition, singular value decomposition is applied to a matrix with the training solutions in order to capture the most essential characteristics in the first few modes – which are used as global interpolation bases.

Proper orthogonal decomposition has proven itself as an accurate reduced-order model approach for elliptical partial differential equations. In the field of solid mechanics, this means that it is accurate for (hyper)elastic material models, but not for (hyper)elastoplasticity. Based on the study of [1], the current contribution investigates how clustering of the training solutions and extracting global modes from each cluster can improve the accuracy of proper orthogonal decomposition for hyperelastoplasticity. Both centroid-based clustering (i.e. k-means clustering) and connectivity-based clustering (based on Chinese whispers) are investigated.

The approach is applied to a hyperelastoplastic representative volume element exposed to monotonic loading, quasi-monotonic loading, and quasi-random loading. In case of monotonic and quasi-monotonic loading, the components of the macroscopic deformation tensor are the variables to which clustering is applied. In case of quasi-random loading, however, not only the components of the macroscopic deformation tensor and the incremental changes of these components are the variables to which clustering is applied, but also all history variables of all integration points.

Additional material:

[1] David Amsallem, Matthew J. Zahr and Charbel Farhat. Nonlinear model order reduction based on local reduced-order bases. Int. J. Numer. Meth. Engng. VOL 92 IS-10 SN-0029-5981