arXiv subjects

Aaron Lutheran

Publications and source records attributed to Aaron Lutheran.

4 recordsLinked to original sources

arXiv2026

Diffusion Transformers with Hybrid Conditioning for Structural Optimization

This work presents a diffusion transformer framework for data-driven structural topology optimization that combines the accuracy of physics-based methods with the efficiency of generative deep learning. Conventional approaches such as the Solid Isotropic Material with Penalization (SIMP) method require repeated finite element analyses at every iteration, making large-scale or real-time optimization computationally expensive. We propose a hybrid conditioning diffusion transformer (DiT) model that learns to generate near-optimal topologies directly from problem definitions, eliminating iterative analysis during inference. The model integrates spatially distributed conditioning through concatenated stress and strain fields and global conditioning via adaptive layer normalization (AdaLN) using scalar descriptors such as load position, magnitude, and prescribed volume fraction. A dataset of 30,000 two-dimensional SIMP-optimized structures was generated for training and evaluation. Results demonstrate that the proposed DiT achieves less than 1% compliance errors relative to ground-truth SIMP solutions while maintaining accurate volume fractions and structural connectivity. Deterministic DDIM sampling enables high-fidelity topology generation in seconds using as few as five denoising steps, enabling near-real-time performance. The hybrid conditioning diffusion transformer thus provides an efficient and scalable alternative to traditional topology optimization methods, with strong potential for integration into interactive computer-aided design workflows.

cs.CE↗

arXiv2026

Physics-Informed Transformer for Real-Time High-Fidelity Topology Optimization

Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design exploration. In this work, we introduce a physics-informed transformer architecture that directly learns a non-iterative mapping from boundary conditions, loading configurations, and derived physical fields to optimized structural topologies. By leveraging global self-attention, the proposed model captures long-range mechanical interactions that govern structural response, overcoming the locality limitations of convolutional architectures. A conditioning-token mechanism embeds global problem parameters, while spatially distributed stress and strain energy fields are encoded as patch tokens within a Vision Transformer framework. To ensure physical realism and manufacturability, we incorporate auxiliary loss functions that enforce volume constraints, load adherence, and structural connectivity through a differentiable formulation. The framework is further extended to dynamic loading scenarios using frequency-domain encoding and transfer learning, enabling efficient generalization from static to time-dependent problems. Comprehensive benchmarking demonstrates that the proposed model achieves fidelity beyond that of diffusion models, while requiring only a single forward pass, thereby eliminating iterative inference entirely. This establishes topology optimization as a real-time operator-learning problem, enabling high-fidelity structural design with significant reductions in computational cost.

cs.CE↗

arXiv2025

Transformer-based Topology Optimization

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.

cs.CE↗

arXiv2025

Latent Space Diffusion for Topology Optimization

Topology optimization enables the automated design of efficient structures by optimally distributing material within a defined domain. However, traditional gradient-based methods often scale poorly with increasing resolution and dimensionality due to the need for repeated finite element analyses and sensitivity evaluations. In this work, we propose a novel framework that combines latent diffusion models (LDMs) with variational autoencoders (VAEs) to enable fast, conditional generation of optimized topologies. Unlike prior approaches, our method conditions the generative process on physically meaningful fields, specifically von Mises stress, strain energy density, volume fraction, and loading information, embedded as dense input channels. To further guide the generation process, we introduce auxiliary loss functions that penalize floating material, load imbalance, and volume fraction deviation, thereby encouraging physically realistic and manufacturable designs. Numerical experiments on a large synthetic dataset demonstrate that our VAE-LDM framework outperforms existing diffusion-based methods in compliance accuracy, volume control, and structural connectivity, providing a robust and scalable alternative to conventional

cs.CE↗