Physics-Informed Feature-to-Feature Learning for Design-Space Dimensionality Reduction in Shape Optimisation

Abstract

High-dimensional parametric design problems cause optimisers and physics simulations to suffer from the curse-of-dimensionality, resulting in high computational cost. In this work, to release this computational burden, we adopted a two-step feature-to-feature learning methodology to discover a lower-dimensional latent space, based on the combination of geometry-and physics-informed principal component analysis and the active subspace method. At the first step, statistical dependencies implicit in the design parameters encode important geometric features of the underline shape. During the second step, functional features of designs are extracted in term of previously learned geometric features. Afterwards, both geometric and functional features are augmented together to create a functionally-active subspace, whose basis not only captures the geometric variance of designs but also induces the variability in the designs' physics. As the new subspace accumulates both the functional and geometric variance, therefore, it can be exploited for efficient design exploration and the construction of improved surrogate models for designs' physics prediction. The validation and experimental studies presented in this work show the beneficial effects of the current approach in comparison to a conventional single-step feature learning.

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls

“…9 For multidisciplinary analysis and optimization involving reduction in both input and output spaces we cite References 10 and 11, while for a specific naval engineering application we suggest. 12 In this work, we propose an optimization framework, to be used in the preliminary design phase, involving many reduced order models to assess the structural behavior of modern passenger ship hulls under different parametric configurations and loading conditions. Many studies have been conducted to assess the structural behavior of passenger ship hulls.…”

“…Recently a component‐based data‐driven approach has been proposed to assess the structural integrity of aircraft components 7,8 in the context of modern digital twins incorporating not only data but also physical models, also referred to as hybrid twins 9 . For multidisciplinary analysis and optimization involving reduction in both input and output spaces we cite References 10 and 11, while for a specific naval engineering application we suggest 12 …”

A Data-Driven Interactive System for Aerodynamic and User-centred Generative Vehicle Design

“…The objective of qualitative search process is to find a set of uniformly distributed N designs, where N is a user-defined parameter. This search process is based on Principal Component Analysis (PCA) [20], [21] and k-means clustering [22] approach. First, a dataset is created by randomly sampling a set of designs from a design space, which is formed with design parameters and their bounding limits.…”

Bayesian shape optimisation in high dimensional design spaces using isogeometric boundary element analysis

“…Even then, one can guarantee neither the identification of all relevant parameters nor exclude redundancies that increase unnecessarily the design space dimensions [10]. In this work, we employ dimensionality reduction techniques [11,12] and a Bayesian optimisation [13] approach to cure the curse of dimensionality and ease the design space exploration by reducing the number of required design evaluations. In the first step, statistical dependencies implicit in the design parameters encode essential latent features of the underlining shape and form a lower-dimensional subspace while maintaining the maximum geometric variance of the original space.…”