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

• URL: http://arxiv.org/abs/2407.07611v1
• Date: Wed, 10 Jul 2024 12:50:43 GMT
• Title: Physics-Informed Geometric Operators to Support Surrogate, Dimension Reduction and Generative Models for Engineering Design
• Authors: Shahroz Khan, Zahid Masood, Muhammad Usama, Konstantinos Kostas, Panagiotis Kaklis, Wei, Chen,
• Abstract summary: We propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models. GOs exploit the differential and integral properties of shapes to infuse high-level intrinsic geometric information and physics into the feature vector used for training.
• Score: 38.00713966087315
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

Related papers

• (Deep) Generative Geodesics [57.635187092922976]
  We introduce a newian metric to assess the similarity between any two data points. Our metric leads to the conceptual definition of generative distances and generative geodesics. Their approximations are proven to converge to their true values under mild conditions.
  arXiv  Detail & Related papers  (2024-07-15T21:14:02Z)
• Bayesian Mesh Optimization for Graph Neural Networks to Enhance Engineering Performance Prediction [1.6574413179773761]
  In engineering design, surrogate models are widely employed to replace computationally expensive simulations. We propose a Bayesian graph neural network (GNN) framework for a 3D deep-learning-based surrogate model. Our framework determines the optimal size of mesh elements through Bayesian optimization, resulting in a high-accuracy surrogate model.
  arXiv  Detail & Related papers  (2024-06-04T06:27:48Z)
• Generative VS non-Generative Models in Engineering Shape Optimization [0.3749861135832073]
  We compare the effectiveness and efficiency of generative and non-generative models in constructing design spaces. Non-generative models generate robust latent spaces with none or significantly fewer invalid designs when compared to generative models.
  arXiv  Detail & Related papers  (2024-02-13T15:45:20Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Automatic Parameterization for Aerodynamic Shape Optimization via Deep Geometric Learning [60.69217130006758]
  We propose two deep learning models that fully automate shape parameterization for aerodynamic shape optimization. Both models are optimized to parameterize via deep geometric learning to embed human prior knowledge into learned geometric patterns. We perform shape optimization experiments on 2D airfoils and discuss the applicable scenarios for the two models.
  arXiv  Detail & Related papers  (2023-05-03T13:45:40Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Scaling Pre-trained Language Models to Deeper via Parameter-efficient Architecture [68.13678918660872]
  We design a more capable parameter-sharing architecture based on matrix product operator (MPO) MPO decomposition can reorganize and factorize the information of a parameter matrix into two parts. Our architecture shares the central tensor across all layers for reducing the model size.
  arXiv  Detail & Related papers  (2023-03-27T02:34:09Z)
• Graph Neural Network Based Surrogate Model of Physics Simulations for Geometry Design [0.20315704654772412]
  We develop graph neural networks (GNNs) as fast surrogate models for physics simulation. We utilize an encoder-processor-decoder-type architecture which can flexibly make prediction at both node level and graph level. The performance of our proposed GNN-based surrogate model is demonstrated on 2 example applications.
  arXiv  Detail & Related papers  (2023-02-01T16:23:29Z)
• Early-Phase Performance-Driven Design using Generative Models [0.0]
  This research introduces a novel method for performance-driven geometry generation that can afford interaction directly in the 3d modeling environment. The method uses Machine Learning techniques to train a generative model offline. By navigating the generative model's latent space, geometries with the desired characteristics can be quickly generated.
  arXiv  Detail & Related papers  (2021-07-19T01:25:11Z)
• A Compact Spectral Descriptor for Shape Deformations [0.8268443804509721]
  We propose a novel methodology to obtain a parameterization of a component's plastic deformation behavior under stress. Existing parameterizations limit computational analysis to relatively simple deformations. We propose a way to derive a compact descriptor of deformation behavior based on spectral mesh processing.
  arXiv  Detail & Related papers  (2020-03-10T10:34:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.