Physics-Informed Geometric Operators to Support Surrogate, Dimension Reduction and Generative Models for Engineering Design

TL;DR

This paper introduces physics-informed geometric operators that incorporate high-level shape and physics information into models, improving surrogate accuracy, dimension reduction, generative design, and optimization in engineering applications.

Contribution

The work develops geometric operators that embed physics-based shape features into models, enhancing their performance and generalization for design and optimization tasks.

Findings

GOs act as regularizers, reducing overfitting in surrogate models.

Incorporating GOs improves the quality of latent spaces in generative models.

GOs accelerate convergence in shape optimization processes.

Abstract

In this work, we propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models, dimension reduction, and generative models, typically employed for performance prediction, dimension reduction, and creating data-driven parameterisations, respectively. However, as both the input and output streams of these models consist of low-level shape representations, they often fail to capture shape characteristics essential for performance analyses. Therefore, the proposed GOs exploit the differential and integral properties of shapes--accessed through Fourier descriptors, curvature integrals, geometric moments, and their invariants--to infuse high-level intrinsic geometric information and physics into the feature vector used for training, even when employing simple model architectures or low-level parametric descriptions. We showed that for surrogate modelling, along with the inclusion of the notion of physics, GOs enact regularisation to reduce over-fitting and enhance generalisation to new, unseen designs. Furthermore, through extensive experimentation, we demonstrate that for dimension reduction and generative models, incorporating the proposed GOs enriches the training data with compact global and local geometric features. This significantly enhances the quality of the resulting latent space, thereby facilitating the generation of valid and diverse designs. Lastly, we also show that GOs can enable learning parametric sensitivities to a great extent. Consequently, these enhancements accelerate the convergence rate of shape optimisers towards optimal solutions.