Aaron Lutheran

Aaron Lutheran, Srijan Das, Alireza Tabarraei

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.

Aaron Lutheran, Srijan Das, Alireza Tabarraei

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.