雖然新材料的計算發現可以簡化實驗合成前的篩選過程，但由於材料組分和結構的潛在組合潛力巨大，這一篩選過程仍然困難而漫長，系統地探索材料組成和結構空間也具有挑戰性。
fig. 1 performance ()of prediction of various test datasets using the ce feature models with different center atom definitions.
如果目標材料的資料有限，則難度更大，從其他材料已知的大資料集中遷移習晶體結構已成為材料設計中的重要策略之一。
fig. 2 formation energies predicted by the ml with ce features (dnn-ce) and dft using various datasets.
上海大學材料基因組工程研究所劉毅教授和馮凌燕教授團隊提出了一種基於大規模尖晶石氧化物計算資料集的熱力學穩定鈣鈦礦氧化物深度遷移習方法。
fig. 3 heat map of formation energies of 5329 abo3 perovskite oxide structures predicted by the transferred learning model in this work, containing 73 constitution elements at the a and b sites, respectively, sorted by the atom number.
利用計算出的5329尖晶石氧化物結構的形成能，建立了具有“中心環境（CE）”特徵的深度神經元網路（DNN）源域模型，然後通過習對855個鈣鈦礦氧化物結構的小資料集對DNN模型引數進行微調，得到了目標域中鈣鈦礦氧化物中具有良好遷移率的遷移習模型。
fig. 4 heat map of tolerance factor of 5329 perovskite oxide structures calculated in this work, containing 73 constitution elements at the a and b sites, sorted by the atom number.
遷移習模型**對鈣鈦礦結構形成能的平均絕對誤差（MAE）僅為0106 EV 原子，優於 0132 ev/atom。基於遷移習模型，作者快速估計了包含73種元素的5329個潛在鈣鈦礦結構的形成能。
fig. 5 tolerance factor (t) vs. octahedral factor (μscatter plot ofperovskite oxide structures, where the colormap corresponds tothe transfer learning predicted formation energy of perovskitestructure.
結合**的形成能和公差因子（0.）的包含。7 < t ≤ 1.1） 和八面體因子 （045 < 0.7）他們鑑定了1314種潛在的熱力學穩定的鈣鈦礦氧化物。在1314種潛在的鈣鈦礦氧化物中，144種已經通過實驗合成證實，10種已經通過其他計算確定，301種已經記錄在材料專案資料庫中，其餘859種氧化物尚未在文獻中報道。
fig. 6 statistical distribution of the formation energy of perovskite structures predicted by machine learning and the screening process for stable perovskite structures.
本研究結合了基於結構資訊的機器習表徵和遷移習方法，利用豐富的已知結構資料以較低的額外計算成本建立新結構，為昂貴的高通量計算篩選材料設計提供了一種新的有效加速策略。
fig. 7 crystal structures and constituent elements of spinel oxides and perovskite oxides studied in this work.
*新型鈣鈦礦氧化物為可再生能源和電子材料應用的實驗合成和探索提供了豐富的候選材料。 相關**最近發表在NPJ Computational Materials上106 (2023)。在手機上閱讀原文，請點選本文底部左下角的“閱讀原文”，輸入後也可以**全文pdf檔案。
fig. 8 general schematic diagram of dnn-ce models and the workflow of transfer learning method in this work.
editorial summary
transfer learning across crystal structures: “center-environment” feature accelerates materials predicting
discovering new materials through computational methods has simplified the screening process before experimental synthesis. however, systematically exploring the material space remains challenging due to the vast potential combinations of material compositions and structures. in cases where data on the target material is limited, cross-crystal structure transfer learning from large-scale known datasets of other materials has become an important strategy in materials design.
this study proposes a deep transfer learning approach based on a large-scale dataset of spinel oxide compounds to predict the thermodynamically stable perovskite oxides. prof. liu and prof. feng’s team at materials genome institute of shanghai university utilized the formation energy of 5,329 spinel oxide structures to develop a deep neural network (dnn) source domain model with “center-environment” (ce) features. the ce-dnn model was then fine-tuned using a small dataset of 855 perovskite oxide structures to achieve a transferable learning model with good performance in the perovskite oxide target domain.
the mean absolute error (mae) of the perovskite structure formation energy predicted by the transfer learning model is 0.106 ev/atom, which is better than the mae of 0.132 ev/atom of the model trained solely using small perovskite data. based on the transfer learning model, the formation energy of 5,329 potential perovskite structures containing 73 different elements was further predicted. combining the predicted formation energies with structural factor criteria, including tolerance factor (0.7 < t ≤ 1.1) and octahedral factor (0.45 < 0.7), a total of 1,314 potentially thermodynamically stable perovskite oxides were predicted.
among 1,314 predicted potential perovskite oxides, 144 were experimentally synthesized, 10 were predicted by other computational works, and 301 are documented in the materials project database, while the remaining 859 oxides h**e not been reported in literatures. the combination of structural information features and transfer learning methods in this study enables the low-cost prediction of new structures using existing big data, providing an effective acceleration strategy for expensive high-throughput computational material design. the predicted stable novel perovskite oxides offer a rich platform for exploring novel perovskite experimental synthesis, renewable energy and electronic materials applications.this article was recently published in npj computational materials
原文摘要及其翻譯
跨晶體結構的中心環境深度轉移機器學習：從尖晶石氧化物到鈣鈦礦氧化物 習 s
yihang li, ruijie zhu, yuanqing wang, lingyan feng & yi liu
abstractin data-driven materials design where the target materials h**e limited data, the transfer machine learning from large known source materials, becomes a demanding strategy especially across different crystal structures. in this work, we proposed a deep transfer learning approach to predict thermodynamically stable perovskite oxides based on a large computational dataset of spinel oxides. the deep neural network (dnn) source domain model with “center-environment” (ce) features was first developed using the formation energy of 5329 spinel oxide structures and then was fine-tuned by learning a small dataset of 855 perovskite oxide structures, leading to a transfer learning model with good transferability in the target domain of perovskite oxides. based on the transferred model, we further predicted the formation energy of potential 5329 perovskite structures with combination of 73 elements. combining the criteria of formation energy and structure factors including tolerance factor (0.7 < t ≤ 1.1) and octahedron factor (0.45 < 0.7), we predicted 1314 thermodynamically stable perovskite oxides, among which 144 oxides were reported to be synthesized experimentally, 10 oxides were predicted computationally by other literatures, 301 oxides were recorded in the materials project database, and 859 oxides h**e been first reported. combing with the structure-informed features the transfer machine learning approach in this work takes the advantage of existing data to predict new structures at a lower cost, providing an effective acceleration strategy for the expensive high-throughput computational screening in materials design. the predicted stable novel perovskite oxides serve as a rich platform for exploring potential renewable energy and electronic materials applications.
總結：
在資料驅動的材料設計中，當目標材料的資料有限時，基於大量已知源材料資料，特別是跨越不同晶體結構的轉移機習已成為具有實際需求和應用場景的研究策略。 本文基於已知的大規模尖晶石氧化物計算資料和新新增的少量鈣鈦礦氧化物計算資料，以及新的熱力學穩定的新型鈣鈦礦氧化物跨晶體結構，提出了一種深度遷移習方法。
首先，利用計算得到的5329個尖晶石氧化物結構的形成能，建立了基於包含結構資訊的“中心環境”（CE）特徵的深度神經網路（DNN）源域模型，然後通過習學習855個鈣鈦礦氧化物結構的小資料集對DNN模型引數進行微調，得到具有良好遷移率的鈣鈦礦氧化物在目標域的遷移習模型。 基於CE-DNN遷移習模型，進一步估計了包含73種元素組合的5329個鈣鈦礦結構的形成能。 結合形成能**和結構因子（包括公差因子（0.）。7 < t ≤ 1.1） 和八面體因子 （045 < 0.7）），共鑑定出1314種具有潛在熱力學穩定性的鈣鈦礦氧化物，其中144種氧化物已被實驗合成，10種氧化物已被記錄在其他計算文獻中，301種氧化物被記錄在材料專案資料庫中，另外859種氧化物是本文首次報道。
基於包含結構資訊的特徵工程，本研究的遷移機習方法利用豐富的可用資料，以較低的額外計算成本為昂貴的新晶體結構特性的高通量計算篩選提供了有效的加速策略。 本研究的新型鈣鈦礦氧化物為探索可再生能源和電子材料應用提供了豐富的候選材料和改進平台。