Hierarchical Embedded Sphere Model: An Interpretable ML-Guided Multiscale Descriptor Engineering Decodes OER Activity on TM@MO

Ziyuan Li, Shan Gao, Yunhan Wang, Yueyu Zhang, Weichao Wang, Xiangmei Duan

Abstract read

In one paragraph

Article in Advanced science (Weinheim, Baden-Wurttemberg, Germany), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it

0cells of the map it votes in

0citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

6 authors.

Ziyuan LiSchool of Physical Science and Technology, Ningbo University, Ningbo, China.

Shan GaoSchool of Physical Science and Technology, Ningbo University, Ningbo, China.

Yunhan WangSchool of Physical Science and Technology, Ningbo University, Ningbo, China.

Yueyu ZhangState Key Laboratory of Materials for Advanced Nuclear Energy & School of Materials Science and Engineering, Shanghai University, Shanghai, China.

Weichao WangCollege of Electronic Information and Optical Engineering, Nankai University, Tianjin, China.

Xiangmei DuanSchool of Physical Science and Technology, Ningbo University, Ningbo, China.ORCID https://orcid.org/0000-0002-7022-753X

Funding

KC Wong Magna Foundation at Ningbo UniversityNational Natural Science Foundation of China 12374061National Natural Science Foundation of China 12404274Zhejiang Provincial Natural Science Foundation of China LD24F040001Zhejiang Provincial Natural Science Foundation of China LQN25A040020

6 · The paper itself

Abstract

Understanding and predicting catalytic activity in transition-metal oxides remains challenging due to the multiscale interplay between geometric and electronic structure. Here, we propose a Hierarchical Embedded Sphere Model (HESM) integrating density functional theory (DFT) with interpretable machine learning (IML) to establish a generalizable descriptor framework for oxide electrocatalysis. By analyzing transition metal-doped anatase MO2 (101) surfaces, HESM disentangles catalytic activity into three hierarchical contributions: Global electronic structure (G-class), atomic-site intrinsic properties (A-class), and local coordination effect (L-class). The combined effect of these three classes leads to the emergence of two catalytic activation paradigms: Rh@MO

Indexed as

descriptor engineeringinterpretable machine learningmultiscale geometric‐electronic couplingsOER electrocatalyssite‐dependent adsorption behavior

Identifiers

PMID41417619

DOI10.1002/advs.202518931

PMCPMC12931158

What OpenQuestion holds

Textmetadata

LicenceCC BY

Read underepoch 390

Registered trials

None linked

Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.