Unraveling the Size Determination Mechanism of Nanocrystal Synthesis via Interpretable Neural Networks

[2608.14734] Unraveling the Size Determination Mechanism of Nanocrystal Synthesis via Interpretable Neural Networks Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14734 (cs) [Submitted on 13 Aug 2026] Title: Unraveling the Size Determination Mechanism of Nanocrystal Synthesis via Interpretable Neural Networks Authors: Kai Gu , Haizheng Zhong View a PDF of the paper titled Unraveling the Size Determination Mechanism of Nanocrystal Synthesis via Interpretable Neural Networks, by Kai Gu and Haizheng Zhong View PDF Abstract: Deep learning models of nanocrystal synthesis enable the prediction of size and shape by encoding precursors and reaction conditions. However, their black-box nature hinders gaining deep insights into the underlying synthetic mechanisms. Here, we develop the Nanocrystal Equation Learner (NanoEQL), a fully white-box neural network to unravel the size determination mechanisms of nanocrystal synthesis. Building on the EQL architecture, eight operators are introduced to replace standard activation functions to fit the mathematical equations in nanocrystal synthesis. Among these operators, three smoothed operators address the gradient explosion of singular operators at zero. To evaluate the weights of different precursors, we develop a temperature-gated attention pooling strategy that encodes concentration-driven and reactivity-driven chemical synthesis mechanisms into the temperature gate. The NanoEQL model illustrates that the final nanocrystal size can be described by a linear equation composed of three scalars representing nanocrystallization capability (-Zp), growth capability (Zrea), and external input potential (-Zops). These interpretable scalars not only advance the rational design of nanocrystal synthesis but also establish a generalizable paradigm for deciphering chemical reaction mechanisms through white-box machine learning. Subjects: Machine Learning (cs.LG) ; Materials Science (cond-mat.mtrl-sci); Artificial Intelligence (cs.AI) Cite as: arXiv:2608.14734 [cs.LG] (or arXiv:2608.14734v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14734 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kai Gu [ view email ] [v1] Thu, 13 Aug 2026 07:43:27 UTC (1,647 KB) Full-text links: Access Paper: View a PDF of the paper titled Unraveling the Size Determination Mechanism of Nanocrystal Synthesis via Interpretable Neural Networks, by Kai Gu and Haizheng Zhong View PDF view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cond-mat cond-mat.mtrl-sci cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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