[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81593-en":3,"doc-seo-81593-105":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},81593,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","Tensor Methods A Unified and Interpretable Approach for Material Design","Material design optimization needs to match target properties such as an ideal Young’s Modulus, but increasing the number of parameters makes the design search space grow exponentially, rendering exhaustive synthesis and evaluation infeasible. Finite Element Analysis (FEA) is computationally intensive, while ML surrogate models are often hard to interpret and struggle under non-uniform sampling and data imbalance. This work proposes tensor completion as an interpretable, unified surrogate approach, rediscovering physical phenomena via tensor factors and improving generalization under non-uniform training, outperforming baseline ML by up to 5%.","Tensor Methods: A Unified and Interpretable Approach for  \nMaterial Design  \nShaan Pakala  \nUniversity of California, Riverside Dept. of Computer Science & Engineering Riverside, CA, USA [spaka002@ucr.edu](spaka002@ucr.edu)  \nAldair E. Gongora  \nLawrence Livermore National Laboratory Materials Engineering Division Livermore, CA, USA [gongora1@llnl.gov](gongora1@llnl.gov)  \nBrian Giera  \nLawrence Livermore National Laboratory Data Science Institute Livermore, CA, USA[giera1@llnl.gov](giera1@llnl.gov)  \nEvangelos E. Papalexakis  \nUniversity of California, Riverside Dept. of Computer Science & Engineering Riverside, CA, USA [epapalex@cs.ucr.edu](epapalex@cs.ucr.edu)  \narXiv :2602 . 10392v 3 [ cs .LG] 9 Jul 2026  \nAbstract  \nWhen designing new materials, it is often necessary to tailor the material design to have some desired properties (e.g., an optimal Young’s Modulus value) . As the set of material design parameters grows, the search space grows exponentially, making the actual synthesis and evaluation of all combinations of designs virtually impossible. Even using traditional computational methods, such as Finite Element Analysis (FEA), becomes too computationally heavy to search this design space. Recent methods use machine learning (ML) surrogate models to more efficiently determine optimal material designs; unfortunately, these methods often (i) are notoriously difficult to interpret and (ii) under perform when the training data comes from a non-uniform sampling of the entire design space. In this work, we suggest the use of tensor completion methods as an all-in-one approach for interpretability and predictions. We observe that classical tensor methods are able to compete with traditional ML methods in predictions, with the added benefit of their interpretable tensor factors (which are given completely for free, as a result of the prediction) . In our experiments, we are able to rediscover physical phenomena via the tensor factors, indicating that our predictions are aligned with the true underlying physics of the problem. This also means these tensor factors could be used by experimentalists to identify potentially novel patterns, given we are able to rediscover existing ones. We also study the effects of both types of surrogate models (traditional ML & tensor-based) when we encounter training data from a non-uniform sampling of the design space. We observe some more specialized tensor methods that are able to give better generalization in these non-uniform sampling scenarios (e.g., neural tensor completion methods), due to the low-rank constraint. We find the best generalization comes from a tensor model, which is able to improve upon the baseline ML methods by up to 5% on aggregate 􀀧2 , and halve the error in some out of distribution sections of the search space.  \nThis work is licensed under a Creative Commons Attribution 4 .0 International License. KDD’26, Jeju Island, Republic of Korea  \n© 2026 Copyright held by the owner/author(s) .  \nACM ISBN 979-8-4007-2259-2/2026/08  \n[https://doi.org/10.1145/3770855.3819008](https://doi.org/10.1145/3770855.3819008)  \nCCS Concepts  \n• Computing methodologies → Machine learning; • Information systems → Data mining; • Applied computing → Physical sciences and engineering.  \nKeywords  \nTensor completion, material design, surrogate modeling, interpretability, data imbalance  \nACM Reference Format:  \nShaan Pakala, Aldair E. Gongora, Brian Giera, and Evangelos E. Papalexakis.  \n2026. Tensor Methods: A Unified and Interpretable Approach for Material Design. In Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2 (KDD’26), August 09–13, 2026, Jeju Island, Republic of Korea. ACM, New York, NY, USA, 11 pages. [https://doi.org/10](https://doi.org/10) . 1145/3770855.3819008  \n1 Introduction  \nDesigning specific structures or materials with desired properties (e.g. Young’s modulus) becomes very challenging as new design variables are added [14, 37] . The nu","cbCaiiqNuDHSUtZr","https://ap.wps.com/l/cbCaiiqNuDHSUtZr","pdf",4029085,3,1,11,"English","en",105,"# Abstract\n# Introduction\n## Challenges in ML surrogate modeling\n# Tensor completion framing","[{\"question\":\"Why is searching the material design space computationally difficult as design variables increase?\",\"answer\":\"The number of design combinations grows exponentially with the number of parameters, making full synthesis and evaluation impractical. Traditional approaches like FEA also become too computationally heavy for large search spaces.\"},{\"question\":\"What limitations do existing ML surrogate models face in this setting?\",\"answer\":\"They are often difficult to interpret and can underperform when training data comes from non-uniform sampling of the design space. Data imbalance further worsens generalization.\"},{\"question\":\"How do tensor completion methods improve both predictions and interpretability?\",\"answer\":\"Tensor completion provides interpretable tensor factors that are obtained directly from the prediction. Experiments show these factors can rediscover underlying physical phenomena, indicating alignment with the true physics and enabling experimentalists to identify novel patterns.\"}]",1784174577,28,{"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},"tensor-methods-a-unified-and-interpretable-approach-for-material-design","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/tensor-methods-a-unified-and-interpretable-approach-for-material-design/81593/",4,{"url":51,"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","2026-07-25","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},"Why is searching the material design space computationally difficult as design variables increase?","Question",{"text":75,"@type":76},"The number of design combinations grows exponentially with the number of parameters, making full synthesis and evaluation impractical. Traditional approaches like FEA also become too computationally heavy for large search spaces.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What limitations do existing ML surrogate models face in this setting?",{"text":80,"@type":76},"They are often difficult to interpret and can underperform when training data comes from non-uniform sampling of the design space. Data imbalance further worsens generalization.",{"name":82,"@type":73,"acceptedAnswer":83},"How do tensor completion methods improve both predictions and interpretability?",{"text":84,"@type":76},"Tensor completion provides interpretable tensor factors that are obtained directly from the prediction. Experiments show these factors can rediscover underlying physical phenomena, indicating alignment with the true physics and enabling experimentalists to identify novel patterns.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]