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

2026-04-03

AI Summary

This work addresses the high computational cost of traditional topology optimization, which relies on iterative finite element analyses and hinders real-time design. For the first time, the authors introduce a non-iterative topology optimization framework based on the Transformer architecture, driven by physical priors. The proposed model encodes boundary conditions, loads, and physical fields through conditional tokens and patch-wise physical field embeddings, leveraging global self-attention to capture long-range mechanical interactions. By integrating differentiable constraints and auxiliary loss functions, the method enables end-to-end generation of high-fidelity structures that satisfy volume, load, and connectivity requirements in a single forward pass. This approach drastically reduces computational overhead, supports efficient transfer from static to dynamic loading scenarios, and achieves real-time, high-accuracy design performance surpassing that of diffusion-based models.

Technology Category

• Search and Optimization: Non-convex Optimization
• Computer Vision: Diffusion Models for Vision
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

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.

Problem

• topology optimization
• real-time design
• iterative limitation
• computational cost
• structural design

Innovation

• Physics-Informed Transformer
• Topology Optimization
• Non-iterative Mapping
• Global Self-Attention
• Differentiable Constraints