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

arXiv: https://arxiv.org/abs/2407.07611 · HTML: https://mlsanity.com/paper/2407.07611/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 69 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 12 of 12)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [Toward General Design Principles for Generative AI Applications](https://mlsanity.com/paper/2301.05578/) (2023)
- [Kernelized Multiview Subspace Analysis by Self-weighted Learning](https://mlsanity.com/paper/1911.10357/) (2019)
- [Momen(e)t: Flavor the Moments in Learning to Classify Shapes](https://mlsanity.com/paper/1812.07431/) (2018)
- [ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model](https://mlsanity.com/paper/2305.00210/) (2023)
- [Manifold-based Incomplete Multi-view Clustering via Bi-Consistency Guidance](https://mlsanity.com/paper/2405.10987/) (2024)
- [Generative VS non-Generative Models in Engineering Shape Optimization](https://mlsanity.com/paper/2402.08540/) (2024)
- [Reconstruction of convex bodies from moments](https://mlsanity.com/paper/1605.06362/) (2016)
- [Sensitivity indices for multivariate outputs](https://mlsanity.com/paper/1303.3574/) (2013)
- [A curvature and density-based generative representation of shapes](https://mlsanity.com/paper/2009.02494/) (2020)
- [FDSPC: Fast and Direct Smooth Path Planning via Continuous Curvature Integration](https://mlsanity.com/paper/2405.03281/) (2024)

## Abstract (arXiv)

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.