Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending

• URL: http://arxiv.org/abs/2112.00648v1
• Date: Wed, 1 Dec 2021 16:54:56 GMT
• Title: Remixing Functionally Graded Structures: Data-Driven Topology Optimization with Multiclass Shape Blending
• Authors: Yu-Chin Chan, Daicong Da, Liwei Wang, Wei Chen
• Abstract summary: We propose a data-driven framework for multiclass functionally graded structures. The key is a new multiclass shape blending scheme that generates smoothly graded microstructures. It transforms the microscale problem into an efficient, low-dimensional one without confining the design to predefined shapes.
• Score: 15.558093285161775
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To create heterogeneous, multiscale structures with unprecedented functionalities, recent topology optimization approaches design either fully aperiodic systems or functionally graded structures, which compete in terms of design freedom and efficiency. We propose to inherit the advantages of both through a data-driven framework for multiclass functionally graded structures that mixes several families, i.e., classes, of microstructure topologies to create spatially-varying designs with guaranteed feasibility. The key is a new multiclass shape blending scheme that generates smoothly graded microstructures without requiring compatible classes or connectivity and feasibility constraints. Moreover, it transforms the microscale problem into an efficient, low-dimensional one without confining the design to predefined shapes. Compliance and shape matching examples using common truss geometries and diversity-based freeform topologies demonstrate the versatility of our framework, while studies on the effect of the number and diversity of classes illustrate the effectiveness. The generality of the proposed methods supports future extensions beyond the linear applications presented.

Related papers

• Cliqueformer: Model-Based Optimization with Structured Transformers [102.55764949282906]
  We develop a model that learns the structure of an MBO task and empirically leads to improved designs. We evaluate Cliqueformer on various tasks, ranging from high-dimensional black-box functions to real-world tasks of chemical and genetic design.
  arXiv  Detail & Related papers  (2024-10-17T00:35:47Z)
• Consistent machine learning for topology optimization with microstructure-dependent neural network material models [0.0]
  We present a framework for multiscale structures with spatially varying microstructural symmetry and differentiably different microstructural descriptors. Our findings highlight the potential of integrating consistency with density-based design optimization.
  arXiv  Detail & Related papers  (2024-08-25T14:17:43Z)
• Smooth Like Butter: Evaluating Multi-Lattice Transitions in Property-Augmented Latent Spaces [0.0]
  This work implements and evaluates a hybrid geometry/property Variational Autoencoder (VAE) for generating multi-lattice transition regions. In our study, we found that hybrid VAEs demonstrate enhanced performance in maintaining stiffness continuity through transition regions.
  arXiv  Detail & Related papers  (2024-07-10T22:28:13Z)
• ComboStoc: Combinatorial Stochasticity for Diffusion Generative Models [65.82630283336051]
  We show that the space spanned by the combination of dimensions and attributes is insufficiently sampled by existing training scheme of diffusion generative models. We present a simple fix to this problem by constructing processes that fully exploit the structures, hence the name ComboStoc.
  arXiv  Detail & Related papers  (2024-05-22T15:23:10Z)
• A Pareto-optimal compositional energy-based model for sampling and optimization of protein sequences [55.25331349436895]
  Deep generative models have emerged as a popular machine learning-based approach for inverse problems in the life sciences. These problems often require sampling new designs that satisfy multiple properties of interest in addition to learning the data distribution.
  arXiv  Detail & Related papers  (2022-10-19T19:04:45Z)
• Differentiable Spline Approximations [48.10988598845873]
  Differentiable programming has significantly enhanced the scope of machine learning. Standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable. We show that leveraging this redesigned Jacobian in the form of a differentiable "layer" in predictive models leads to improved performance in diverse applications.
  arXiv  Detail & Related papers  (2021-10-04T16:04:46Z)
• Data-Driven Multiscale Design of Cellular Composites with Multiclass Microstructures for Natural Frequency Maximization [14.337297795182181]
  We propose a data-driven topology optimization (TO) approach to enable the multiscale design of cellular structures. The framework can be easily extended to other multi-scale TO problems, such as thermal compliance and dynamic response optimization.
  arXiv  Detail & Related papers  (2021-06-11T15:59:33Z)
• Bilinear Classes: A Structural Framework for Provable Generalization in RL [119.42509700822484]
  Bilinear Classes is a new structural framework which permits generalization in reinforcement learning. The framework incorporates nearly all existing models in which a sample complexity is achievable. Our main result provides an RL algorithm which has sample complexity for Bilinear Classes.
  arXiv  Detail & Related papers  (2021-03-19T16:34:20Z)
• Isometric Multi-Shape Matching [50.86135294068138]
  Finding correspondences between shapes is a fundamental problem in computer vision and graphics. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis.
  arXiv  Detail & Related papers  (2020-12-04T15:58:34Z)
• Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems [20.659457956055366]
  We propose a novel data-driven metamaterial design framework based on deep generative modeling. We show in this study that the latent space of VAE provides a distance metric to measure shape similarity. We demonstrate our framework by designing both functionally graded and heterogeneous metamaterial systems.
  arXiv  Detail & Related papers  (2020-06-27T03:56:55Z)
• Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process [18.17435834037483]
  We develop a multi-response latent-variable Gaussian process (LVGP) model for the microstructure libraries of metamaterials. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses. We show that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.
  arXiv  Detail & Related papers  (2020-06-27T03:55:52Z)

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.