Metamodeling techniques for CPU-intensive simulation-based design optimization: a survey

Abstract

In design optimization of complex systems, the surrogate model approach relying on progressively enriched Design of Experiments (DOE) avoids efficiency problems encountered when embedding simulation codes within optimization loops. However, an efficient a priori sampling of the design space rapidly becomes costly when using High-Fidelity (HF) simulators, especially in high dimension. On the other hand, in applications such as aeronautical design, multiple simulation tools are frequently available for the same problem, generally with a degree of precision inversely proportional to the CPU cost. Thus, the concept of multi-fidelity proposes to merge different levels of fidelity within a single model with controlled variance. Based on recent Reduced-Order Modeling (ROM) techniques, an alternative approach allows to pursue the objective of mastering the simulation budget by replacing costly models with their approximate full-field counterparts, providing additional insight to scalar surrogates built directly from the Quantities of Interest (QoI). Both approaches: multi-fidelity and ROM, may be combined, allowing for additional flexibility in choosing the degree of fidelity required in different zones of the design space. This paper reviews the strategies that seek to improve surrogate-based optimization efficiency, including ROM, multi-fidelity metamodeling, and DOE enrichment strategies.

Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation

“…These responses may be obtained through numerical simulations or experimental measurements. The surrogate is subsequently trained employing Machine Learning and Model Order Reduction techniques [26][27][28][29][30][31]. It is important to emphasize that during the surrogate training process, we assume precise knowledge of the values of each feature in p. This assumption enables the collection of the corresponding quantity of interest for the parameters' samples within the DoE.…”

Different Numerical Techniques, Modeling and Simulation in Solving Complex Problems

“…In [7] drew from two different but related concepts of modeling and simulation. The [8] describe modeling and simulation as providing inputs to a model of a system and watching the resulting outputs, whereas [9] defines modeling and simulation as "the act of developing a model of a conceptual system and utilizing it to conduct experiments with the aim of understanding the performance of the system and/or assessing different management strategies and decision-making processes using simulation result as inputs and outputs" Modeling and simulation may be used for a wide variety of purposes, such as testing hypotheses, making predictions, learning new information, teaching, and even providing amusement. Research into computer systems, industrial processes, social systems, political structures, corporate structures, ecological environments, and other complex processes and systems all make use of simulation.…”

Parametric Curves Metamodelling Based on Data Clustering, Data Alignment, POD-Based Modes Extraction and PGD-Based Nonlinear Regressions

“…The uncertainty propagation in such models is also fundamental to operate efficiently in diagnosis and prognosis. In a non-intrusive framework, given an engineering problem, a Design of Experiments-DoE-based on the problem parameters is established and the corresponding responses of the system are collected into databases, which are used as training data to build the surrogate model via Machine Learning-ML-and Model Order Reduction-MOR-algorithms (Wang and Shan, 2007;Benner et al, 2015;Hesthaven and Ubbiali, 2018;Rajaram et al, 2020;Franchini et al, 2022;Khatouri et al, 2022). Such responses are usually the ensemble of several Quantities of Interest-QoI-observed, for instance, over time (i.e., time series) and can come both from experiments and numerical simulations.…”