Structural Design Through Reinforcement Learning

This paper introduces the Structural Optimization gym (SOgym), a novel open-source reinforcement learning environment designed to advance the application of machine learning in topology optimization. SOgym aims for RL agents to learn to generate physically viable and structurally robust designs by integrating the physics of TO directly into the reward function. To enhance scalability, SOgym leverages feature mapping methods as a mesh-independent interface between the environment and the agent, allowing for efficient interaction with the design variables regardless of the mesh resolution. Baseline results are presented using a model-free proximal policy optimization agent and a model-based DreamerV3 agent. Three observation space configurations were tested. The TopOpt game inspired configuration, an interactive educational tool that improves students' intuition in designing structures to minimize compliance under volume constraints, performed best in terms of performance and sample efficiency. The 100M parameter version of DreamerV3 produced structures within 54% of the baseline compliance achieved by traditional optimization methods as well as a 0% disconnection rate, an improvement over supervised learning approaches that often struggle with disconnected load paths. When comparing the learning rates of the agents to those of engineering students from the TopOpt game experiment, the DreamerV3-100M model shows a learning rate approximately four orders of magnitude lower, an impressive feat for a policy trained from scratch through trial and error. These results suggest RL's potential to solve continuous TO problems and its capacity to explore and learn from diverse design solutions. SOgym provides a platform for developing RL agents for complex structural design challenges and is publicly available to support further research in the field.

From Density to Geometry: YOLOv8 Instance Segmentation for Reverse Engineering of Optimized Structures

This paper introduces YOLOv8-TO, a novel approach for reverse engineering of topology-optimized structures into interpretable geometric parameters using the YOLOv8 instance segmentation model. Density-based topology optimization methods require post-processing to convert the optimal density distribution into a parametric representation for design exploration and integration with CAD tools. Traditional methods such as skeletonization struggle with complex geometries and require manual intervention. YOLOv8-TO addresses these challenges by training a custom YOLOv8 model to automatically detect and reconstruct structural components from binary density distributions. The model is trained on a diverse dataset of both optimized and random structures generated using the Moving Morphable Components method. A custom reconstruction loss function based on the dice coefficient of the predicted geometry is used to train the new regression head of the model via self-supervised learning. The method is evaluated on test sets generated from different topology optimization methods, including out-of-distribution samples, and compared against a skeletonization approach. Results show that YOLOv8-TO significantly outperforms skeletonization in reconstructing visually and structurally similar designs. The method showcases an average improvement of 13.84% in the Dice coefficient, with peak enhancements reaching 20.78%. The method demonstrates good generalization to complex geometries and fast inference times, making it suitable for integration into design workflows using regular workstations. Limitations include the sensitivity to non-max suppression thresholds. YOLOv8-TO represents a significant advancement in topology optimization post-processing, enabling efficient and accurate reverse engineering of optimized structures for design exploration and manufacturing.

De-homogenization using Convolutional Neural Networks

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogenization approaches and save time correspondingly. To train the neural network, a two-step custom loss function has been developed which ensures a periodic output field that follows the local lamination orientations. A key feature of the proposed method is that the training is carried out without any use of or reference to the underlying structural optimization problem, which renders the proposed method robust and insensitive wrt. domain size, boundary conditions, and loading. A post-processing procedure utilizing a distance transform on the output field skeleton is used to project the desired lamination widths onto the output field while ensuring a predefined minimum length-scale and volume fraction. To demonstrate that the deep learning approach has excellent generalization properties, numerical examples are shown for several different load and boundary conditions. For an appropriate choice of parameters, the de-homogenized designs perform within $7-25\%$ of the homogenization-based solution at a fraction of the computational cost. With several options for further improvements, the scheme may provide the basis for future interactive high-resolution topology optimization.