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

arXiv: https://arxiv.org/abs/2604.03522 · HTML: https://mlsanity.com/paper/2604.03522/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2026.

## Built on by (most cited first, 2 of 2)

- [Trajectory-Aware Flow Matching for Topology Optimisation](https://mlsanity.com/paper/2607.14652/) (2026)
- [TopoMamba: A Load-Support Relation-Guided Multi-Directional State-Space Model for Topology Optimization](https://mlsanity.com/paper/2609.33688/) (2026)

## Abstract (arXiv)

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.