[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118498-en":3,"doc-seo-118498-105":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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118498,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","A framework to evaluate machine learning crystal stability predictions - Supplementary information","Supplementary information describes foundational concepts in crystal structures and how they are represented for materials discovery datasets. It defines unit cells, crystal systems, symmetry, atomic positions, and common database fields such as cell parameters, fractional coordinates, and optional site properties. It then formalizes energy quantities used for stability assessment, including formation energy and energy above hull with hull-threshold guidance. Finally, it presents the Matbench Discovery record format and evaluation metrics on full and deduplicated test sets, explaining how dataset composition affects DAF and related model performance measures.","| nature machine intelligence |  |\n| --- | --- |\n| Supplementary information [https://doi.org/10.1038/s42256-025-01055-1](https://doi.org/10.1038/s42256-025-01055-1) |  |\n| A framework to evaluate machine learning crystal stability predictions |  |\n| In the format provided by the authors and unedited |  |\n\nS1 Primer on Crystal Structures  \nAs suggested during review, this section provides a brief introduction to crystal structures for readers unfamiliar with crystallography. We outline why they are foundational to materials science, and how they are represented in the Matbench Discovery dataset.  \nUnit Cell  \nThe unit cell is the basic building block making up a crystal. It is defined by three lattice vectors (⃗a, ⃗b,⃗c) and three angles (α , β , γ) between these vectors determining the shape and volume of the cell. The entire crystal can be constructed by translating the unit cell along all three lattice vectors.  \nCrystal Systems and Symmetry  \nCrystals are classified into seven crystal systems (cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, and triclinic) based on their symmetry. These systems are further divided into 230 space groups that describe all possible sets of symmetry operations (rotations, reflections, and translations) an arrangement of points can have in 3d periodic structures.  \nAtomic Positions  \nWithin a unit cell, atomic positions are specified by 3 fractional coordinates (values between 0 and 1) along each lattice vector. These positions, combined with atomic types, fully define the crystal structure. Wyckoff positions denote sets of equivalent atomic sites that transform into each other through the crystal’s symmetry operations.  \nStructure Representation in Databases  \nIn materials databases like the Materials Project, crystal structures are typically stored with the following information:  \n• Crystal structure: Cell parameters (a, b, c, α , β , γ)  \n• Atomic positions: List of element type and fractional coordinates of each atom in the unit cell  \n• Site properties: Optional information about atomic sites (oxidation states, magnetic moments, etc.)  \nEnergy Quantities  \nSeveral energy quantities are used to characterize crystal stability:  \n• Formation energy (Eform ): Energy released or required when a compound forms from its constituent elements in their lowest-energy pure-element states  \n• Energy above hull (Eabove hull ): Energy relative to the thermodynamic convex hull in a chemical system, indicating stability against decomposition to other competing phases. Eabove hull = 0, the material is said to be on the hull and thermodynamically stable. If Eabove hull > 0, the material may still exist with varying degrees of metastability. If Eabove hull > 100 meV/atom, material’s are very rarely observed in nature.  \n• Decomposition energy: The energy released during decomposition into more stable phases. Can be negative if a material is lower in any energy than any decomposition products on the known convex hull of its chemical system.  \nMatbench Discovery Data Format  \nMatbench Discovery records structures along with DFT-calculated energies and model predictions for 257k materials in the WBM test set. Each entry includes:  \n• Crystal structure information (lattice, sites, unique material ID)  \nModel F1 ↑ DAF ↑ Prec ↑ Acc ↑ TPR ↑ TNR ↑ MAE ↓ RMSE ↓ R2 ↑  \nTable S1: Same as Table 1 in the main text but computed for all 257k structures in the WBM test set, no duplicate protostructures excluded. The prevalence of stable structures is 16.7%(42,825 out of 256,963), placing a ceiling of 6 on the maximum possible DAF.  \n• Ground truth DFT energies (formation energy, energy above hull)  \n• Model predictions for comparison  \nThis standardized format enables consistent evaluation of machine learning models for crystal stability prediction and materials discovery.  \nS2 Metrics on full test set and for 10k materials predicted most stable  \nAs discussed in [riebesell_phd_ 2024], unlike Table 1 in the","cbCairYbJutjVpPv","https://ap.wps.com/l/cbCairYbJutjVpPv","pdf",2819274,1,20,"English","en",105,"# S1 Primer on Crystal Structures\n## Unit Cell\n## Crystal Systems and Symmetry\n## Atomic Positions\n## Structure Representation in Databases\n## Energy Quantities\n# S2 Metrics on full test set and for 10k materials predicted most stable","[{\"question\":\"What is the unit cell and how does it build a crystal structure?\",\"answer\":\"A unit cell is defined by three lattice vectors and three inter-vector angles. The full crystal is constructed by translating the unit cell along the lattice vectors in all directions.\"},{\"question\":\"How are formation energy and energy above hull used to characterize crystal stability?\",\"answer\":\"Formation energy measures the energy change when a compound forms from lowest-energy elemental states. Energy above hull measures stability relative to the convex hull; values on the hull indicate thermodynamic stability, while positive values indicate metastability and larger values are rarely observed.\"},{\"question\":\"Why does DAF change between the full test set and the deduplicated subset?\",\"answer\":\"DAF is tied to the ratio of stability-prediction precision to the prevalence of stable structures. The full dataset has a higher fraction of stable structures, which shifts the prevalence term and leads to different DAF values across models.\"}]","A framework to evaluate machine learning crystal stability predictions - Supplementary information | PDF",1785683879,50,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"a-framework-to-evaluate-machine-learning-crystal-stability-predictions-supplementary-information","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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":53},"https://docshare.wps.com/document/a-framework-to-evaluate-machine-learning-crystal-stability-predictions-supplementary-information/118498/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the unit cell and how does it build a crystal structure?","Question",{"text":75,"@type":76},"A unit cell is defined by three lattice vectors and three inter-vector angles. The full crystal is constructed by translating the unit cell along the lattice vectors in all directions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are formation energy and energy above hull used to characterize crystal stability?",{"text":80,"@type":76},"Formation energy measures the energy change when a compound forms from lowest-energy elemental states. Energy above hull measures stability relative to the convex hull; values on the hull indicate thermodynamic stability, while positive values indicate metastability and larger values are rarely observed.",{"name":82,"@type":73,"acceptedAnswer":83},"Why does DAF change between the full test set and the deduplicated subset?",{"text":84,"@type":76},"DAF is tied to the ratio of stability-prediction precision to the prevalence of stable structures. The full dataset has a higher fraction of stable structures, which shifts the prevalence term and leads to different DAF values across models.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,114,119,122,126,129,133],{"id":20,"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":53,"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":29,"slug":113},6,"Technology","technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":21,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":21,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":106,"slug":136},19,"General","general"]