New Trends in Computational Mechanics: Model Order Reduction, Manifold Learning and Data‐Driven

Abstract

Engineering sciences and technology is experiencing the data revolution. In the past models were more abundant than data, too expensive to be collected and analyzed at that time. However, nowadays, the situation is radically different, data is much more abundant (and accurate sometimes) than existing models, and a new paradigm is emerging in engineering sciences and technology. This paper retraces some incipient applications based on data within the framework of computational mechanics. Three main topics are addressed in the present work: (i) construction of solution manifolds and its use for interpolating new solutions on the manifold; (ii) constructing parametric solutions on the just extracted manifold; and (iii) defining behavior manifolds to perform data-driven simulation while avoiding the use of usual constitutive equations.

Review of the Brain’s Behaviour after Injury and Disease for Its Application in an Agent-Based Model (ABM)

“…These techniques are mainly algebraic, redefining the full system into a reduced version represented by their greatest eigenvalues (principal component analysis) [ 428 ] or user-defined modes (proper orthogonal/generalised decomposition) [ 429 , 430 , 431 ]—which involves taking lower resolution snapshots representing the evolution of the system—or locally overcoming nonlinearities (locally linear embedding) [ 432 ]. A more detailed overview on MOR can be found in [ 433 ].…”

Spurious-free interpolations for non-intrusive PGD-based parametric solutions: Application to composites forming processes

“…The assigned problems are managed by classical PGD decomposition procedures [1,6,11]. Another way of constructing a computational vademecum through the use of non-intrusive PGD relies on the calculation of snapshots to later on construct a manifold of solutions using the locally linear embedding (LLE) for example or other manifold learning techniques [2,4,5,12,15,17,21,23]. Despite numerous developments during the recent years towards the development of computational vademecums in both intrusive and non-intrusive manners [11], the calculation of solution handbooks using any of the aforementioned methods faces a major challenge when changing a parameter induces drastic changes in the solution map.…”