Explainable quantum neural networks for multi-material topology optimization

2026-07-01

AI Summary

This work addresses the challenge of jointly optimizing structural layout and material assignment in multi-material topology optimization by introducing, for the first time, an interpretable quantum neural network. The method encodes optimization history—including strain energy, sensitivity, density, and Sobel edge features—into a ten-qubit quantum circuit, and correlates material labels with Z-basis observables to establish an auditable link between quantum outputs and mechanical pathways, material regions, and interfaces. Remarkably, the approach generalizes effectively—without additional training—to out-of-distribution loading and boundary conditions, high-resolution meshes, and three-dimensional voxelized domains, thereby significantly enhancing both optimization accuracy and model interpretability.

Abstract

We propose an explainable quantum neural network for multi-material topology optimization, XQNN, that determines both load-carrying structural layout and material type assignment for given boundary/loading conditions. Intermediate solution histories are first converted into element-wise strain energy, sensitivity, density, and Sobel boundary descriptors. Then, they are encoded in a ten-qubit circuit and qubit-wise $Z$ observables are mapped onto material type labels. Trained only on two-dimensional topology optimization histories obtained with a fixed mesh resolution, XQNN can be generalized to handle out-of-distribution boundary/loading conditions, progressively refined high-resolution meshes, and voxel-wise three-dimensional problems without additional training. We find that it is important to preserve qubit-wise observables and add boundary information for improving the optimization accuracy, and certain observables have consistent links to load paths, material type regions, and interfaces, demonstrating their usability as auditable mechanics-facing variables.

Problem

• multi-material topology optimization
• explainable AI
• quantum neural networks
• structural design
• material assignment

Innovation

• explainable quantum neural network
• multi-material topology optimization
• quantum encoding
• out-of-distribution generalization
• mechanics-facing observables