PGD-Based Computational Vademecum for Efficient Design, Optimization and Control

By Francisco Chinesta, Adrien Leygue, Felipe Bordeu, José Vicente Aguado, Elías Cueto, David González, Icíar Alfaro, Amine Ammar, Antonio Huerta. Archives of Computational Methods in Engineering, 2013

312 citations recorded by the source corpus.

In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/892066c9e5088afb50a3ffaf889da2e3bddd4170

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Citations in the corpus

Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation (2015, background): “This generalized solution, recently called computational vademecum [7] in a more general framework, provides the engineer a way to evaluate in real-time any tentative scattering situation (e.”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “We refer to the review papers [46, 49], the literature [6, 45, 50, 77, 153, 154] and the references therein for details on PGD and its applications.”
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “Successful applications of the NTFA [58–60], POD [54,55,61,62] and PGD [63] demonstrate the usefulness of these approaches.”