HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization

2026-07-08 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Engineering Design & Optimization · Depth: Expert, quick

Summary

HPG-Diff, a novel Hierarchical Physics-Guided Diffusion framework, addresses key limitations in deep generative models for topology optimization, specifically their lack of intrinsic physics guidance and issues with generalizability and floating material artifacts. This framework enforces physics consistency through two synergistic mechanisms. First, a hierarchical physics-guided strategy aligns precomputed physics features with the denoising process, directing material distribution along optimal load paths to improve generalizability. Second, a differentiable connectivity constraint, inspired by thermal conduction, introduces a floating material suppression loss that explicitly penalizes floating material during training by simulating virtual heat propagation from load positions. Quantitative evaluations show HPG-Diff achieves average compliance errors of 0.87% in-distribution and 5.29% out-of-distribution, while reducing floating material ratios to 2.90% and 2.44% respectively. Preliminary case studies also indicate that lightweight LoRA fine-tuning enables adaptation to rectangular non-square domains using small datasets.

Key takeaway

For Machine Learning Engineers developing generative models for structural design, HPG-Diff offers a robust approach to overcome common challenges. You should consider integrating physics-guided strategies and differentiable connectivity constraints, like those inspired by thermal conduction, into your diffusion models to significantly improve generalizability and reduce material artifacts. This framework demonstrates how lightweight LoRA fine-tuning can efficiently adapt models to new geometric domains, streamlining your design workflows.

Key insights

HPG-Diff integrates physics guidance and connectivity constraints into diffusion models for robust topology optimization.

Principles

• Physics guidance improves generalizability.
• Thermal conduction models connectivity.
• Hierarchical features enhance denoising.

Method

HPG-Diff uses a hierarchical physics-guided strategy and a floating material suppression loss, based on virtual heat propagation, to enforce physics consistency during diffusion model training for topology optimization.

In practice

• Apply LoRA for domain adaptation.
• Use physics features for load paths.
• Penalize floating material via heat simulation.

Topics

• Topology Optimization
• Diffusion Models
• Physics-Guided AI
• Generative Design
• LoRA Fine-tuning
• Material Connectivity

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.