Algorithmically-Consistent Deep Learning Frameworks for Structural Topology Optimization
arXiv:2012.05359 · doi:10.1016/j.engappai.2021.104483
Abstract
Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite element analysis iterations required to evaluate the component's performance during the optimization process. Recently, machine learning (ML)-based topology optimization methods have been explored by researchers to alleviate this issue. However, previous ML approaches have mainly been demonstrated on simple two-dimensional applications with low-resolution geometry. Further, current methods are based on a single ML model for end-to-end prediction, which requires a large dataset for training. These challenges make it non-trivial to extend current approaches to higher resolutions. In this paper, we develop deep learning-based frameworks consistent with traditional topology optimization algorithms for 3D topology optimization with a reasonably fine (high) resolution. We achieve this by training multiple networks, each learning a different step of the overall topology optimization methodology, making the framework more consistent with the topology optimization algorithm. We demonstrate the application of our framework on both 2D and 3D geometries. The results show that our approach predicts the final optimized design better (5.76x reduction in total compliance MSE in 2D; 2.03x reduction in total compliance MSE in 3D) than current ML-based topology optimization methods.
29 pages, 28 figures, 9 tables
References in corpus (18)
- Adam: A Method for Stochastic Optimization
- DeepXDE: A deep learning library for solving differential equations
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- 3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation
- Deep Generative Design: Integration of Topology Optimization and Generative Models
- Deep learning for determining a near-optimal topological design without any iteration
- Topology optimization of 2D structures with nonlinearities using deep learning
- Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
- Machine learning materials physics: Integrable deep neural networks enable scale bridging by learning free energy functions
- What Can Neural Networks Reason About?
- Solving inverse-PDE problems with physics-aware neural networks
- A deep Convolutional Neural Network for topology optimization with strong generalization ability
- A Novel Topology Optimization Approach using Conditional Deep Learning
- 3D Topology Optimization using Convolutional Neural Networks
- Convolutional Neural Network-based Topology Optimization (CNN-TO) By Estimating Sensitivity of Compliance from Material Distribution
- Topology Optimization under Uncertainty using a Stochastic Gradient-based Approach