[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81769-en":3,"doc-seo-81769-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81769,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Explainable Quantum Neural Networks for Multi Material Topology Optimization","An explainable quantum neural network (XQNN) is proposed for multi-material topology optimization, producing both the load-carrying structural layout and material type assignments under specified boundary and loading conditions. Intermediate optimization histories are converted into element-wise strain energy, sensitivities, densities, and Sobel boundary descriptors, then encoded into a ten-qubit circuit. Qubit-wise Pauli-Z expectation values are mapped to material labels. Trained on fixed-resolution 2D histories only, XQNN generalizes to out-of-distribution boundary/load cases and refined meshes, and extends to voxel-wise 3D problems without extra training. Preserving qubit-wise observables and incorporating boundary information improves accuracy, and selected observables correlate with load paths, material regions, and interfaces as auditable mechanics variables.","arXiv :2607 .00438v 1 [ cs .CE] 1 Jul 2026  \nExplainable quantum neural networks for multi-material topology optimization  \nDahyun Joo 1 , Naruethep Sukulthanasorn2 , Kenjiro Terada2,3 ,  \nDo-Nyun Kim 1,4,5*  \n1 Department of Mechanical Engineering, Seoul National University, Seoul, 08826, Republic of Korea.  \n2 International Research Institute of Disaster Science, Tohoku University, Sendai, 980-8572, Japan.  \n3 Department of Civil and Environmental Engineering, Tohoku University, Sendai, 980-8579, Japan.  \n4 Institute of Advanced Machines and Design, Seoul National University, Seoul, 08826, Republic of Korea.  \n5 Institute of Engineering Research, Seoul National University, Seoul, 08826, Republic of Korea.  \n*Corresponding author(s). E-mail(s): [dnkim@snu.ac.kr](dnkim@snu.ac.kr) ;  \nAbstract  \nWe 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.  \n1  \n1 Introduction  \nTopology optimization (TO) distributes material within a prescribed design domain so that a structural objective, most commonly compliance, is optimized under equilibrium and resource constraints. It has matured through homogenization, density-based formulations, level-set methods, deformable mesh strategies, and broad computational implementations [1–8] . Multi-material topology optimization (MMTO) considers the assignment of material types in addition to the usual layout decision. This coupled layout–type decision creates material–material interfaces, void–material interfaces, and a larger combinatorial design space, motivating the development of specialized formulations for multi-material structural design [9–15] .  \nLearning-assisted TO is attractive in this setting because repeated MMTO calculations are computationally demanding when boundary conditions, loading scenarios, mesh resolutions, or design requirements change. Convolutional neural networks, generative models, multi-stage predictors, reinforcement-learning strategies, and superresolution based accelerators have demonstrated that near-optimized topologies can be inferred directly from physical fields, early optimizer states, or problem specifications [16–23] . While such learned predictors can substantially accelerate the design process, they also impose an interpretability requirement: producing a plausible material map is insufficient if the model cannot account for the signals that support its prediction. A mechanics surrogate should make clear whether its decision is driven by load-carrying regions, material interfaces, or features that separate material types, and these signals should remain accessible when the test case departs from the training distribution. This requirement aligns with a broader view of interpretable and physics-informed machine learning, where physical consistency is regarded as a modeling criterion [24–27] . Although generic post-hoc tools such as SHAP and gradient localization are useful in many domains [28, 29], their explanatory vocabulary in compact numerical sur","cbCait6XdhRmN4wk","https://ap.wps.com/l/cbCait6XdhRmN4wk","pdf",3780225,4,1,40,"English","en",105,"# Introduction\n## Topology optimization and multi-material extensions\n## Learning-assisted optimization and interpretability needs\n## Parameterized quantum circuits and quantum observables","[{\"question\":\"What problem does XQNN address in multi-material topology optimization?\",\"answer\":\"It determines both the structural layout and the assignment of material types for given boundary and loading conditions, capturing both geometry and composition decisions.\"},{\"question\":\"How does XQNN make its predictions explainable?\",\"answer\":\"It converts intermediate optimization histories into physically meaningful element-wise descriptors, encodes them in a quantum circuit, and maps qubit-wise Pauli-Z expectation observables to material type labels, keeping circuit-level measurable variables accessible.\"},{\"question\":\"What does the training setup enable XQNN to generalize to new cases?\",\"answer\":\"Trained only on 2D topology histories with a fixed mesh resolution, XQNN generalizes to out-of-distribution boundary/loading conditions, progressively refined high-resolution meshes, and voxel-wise 3D problems without additional training.\"}]",1784176025,101,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"explainable-quantum-neural-networks-for-multi-material-topology-optimization","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/explainable-quantum-neural-networks-for-multi-material-topology-optimization/81769/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does XQNN address in multi-material topology optimization?","Question",{"text":75,"@type":76},"It determines both the structural layout and the assignment of material types for given boundary and loading conditions, capturing both geometry and composition decisions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does XQNN make its predictions explainable?",{"text":80,"@type":76},"It converts intermediate optimization histories into physically meaningful element-wise descriptors, encodes them in a quantum circuit, and maps qubit-wise Pauli-Z expectation observables to material type labels, keeping circuit-level measurable variables accessible.",{"name":82,"@type":73,"acceptedAnswer":83},"What does the training setup enable XQNN to generalize to new cases?",{"text":84,"@type":76},"Trained only on 2D topology histories with a fixed mesh resolution, XQNN generalizes to out-of-distribution boundary/loading conditions, progressively refined high-resolution meshes, and 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