Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations

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Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “(Other applications of RB, in particular to optimization and control, can be found in [109, 123].”
A low‐cost, goal‐oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems (2011, background): “Unlike real-time problems, offlineonline decomposition strategies are ill-suited for this class of problems due to the existence of a ‘break-even’ point [7, 8, 9, 10], which is characterized by the number of online analyses required for computational cost savings to be achieved for the overall offli”
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, background): “The bounds may thus serve to ensure a feasible design(5), a “good” design, and a fast design process or real-time decision [29].”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, methodology): “The methodology we describe in this paper is motivated by, optimized for, and applied within two particular contexts: the real-time context (e.g., parameterestimation [54,96,154] or control [124]); and the manyquery context (e.g., design optimization [ 107 ] or multimodel/scale simulation [26,49]).”