Transformer-based Topology Optimization

2025-09-06

AI Summary

Traditional topology optimization (e.g., SIMP) suffers from high computational cost and sensitivity to initial designs, while existing machine learning approaches either rely on iterative refinement or yield insufficient fidelity. To address these limitations, this paper proposes the first non-iterative, high-fidelity topology generation framework. Our method introduces a physics-informed tokenized domain representation, integrating FFT-based load encoding and transfer learning, and incorporates a manufacturability-oriented auxiliary loss. Leveraging a Transformer architecture, it enables end-to-end mapping from boundary conditions and load configurations to structural topologies. Evaluated on static and dynamic benchmark datasets, the framework achieves significantly reduced compliance error and load deviation, precise volume fraction control, minimal floating material, and topology quality—previously unattainable in non-iterative paradigms—that rivals diffusion models. Moreover, it delivers substantial computational speedup and enhanced design robustness.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Computer Vision: Diffusion Models for Vision

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions. Although machine learning methods have recently shown promise for accelerating topology generation, existing models either remain iterative or struggle to match ground-truth performance. In this work, we propose a transformer-based machine learning model for topology optimization that embeds critical boundary and loading conditions directly into the tokenized domain representation via a class token mechanism. We implement this model on static and dynamic datasets, using transfer learning and FFT encoding of dynamic loads to improve our performance on the dynamic dataset. Auxiliary loss functions are introduced to promote the realism and manufacturability of the generated designs. We conduct a comprehensive evaluation of the model's performance, including compliance error, volume fraction error, floating material percentage, and load discrepancy error, and benchmark it against state-of-the-art non-iterative and iterative generative models. Our results demonstrate that the proposed model approaches the fidelity of diffusion-based models while remaining iteration-free, offering a significant step toward real-time, high-fidelity topology generation.

Problem

• Accelerates topology optimization with transformer model
• Reduces computational cost and sensitivity to initial conditions
• Generates high-fidelity designs without iterative processes

Innovation

• Transformer-based model for topology optimization
• Tokenized domain representation with boundary conditions
• Auxiliary loss functions for design manufacturability