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Gradient-based optimization of complex nanoparticle heterostructures enabled by deep learning on heterogeneous graphs

Nature Computational Science volume 6, pages 83–95 (2026)Cite this article

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A preprint version of the article is available at ChemRxiv.

Abstract

Applications of deep learning (DL) to design nanomaterials are hampered by a lack of suitable data representations and training data. Here we report efforts to overcome these limitations and leverage DL to optimize the nonlinear optical properties of core–shell upconverting nanoparticles (UCNPs). UCNPs, which have applications in fields such as biosensing, super-resolution microscopy and three-dimensional printing, can emit visible and ultraviolet light from near-infrared excitations. We report a large-scale dataset of UCNP emission spectra based on accurate but expensive kinetic Monte Carlo simulations (N > 6,000) and use these data to train a heterogeneous graph neural network using a physically motivated representation of UCNP nanostructure. Applying gradient-based optimization on the trained graph neural network, we identify structures with 6.5× higher predicted emission under 800-nm illumination than any UCNP in our training set. Our work reveals design principles for UCNP heterostructures and presents a roadmap for DL-based inverse design of nanomaterials.

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Fig. 1: DL approach to enable UCNP heterostructure optimization.
Fig. 2: Description of SUNSET datasets.
Fig. 3: UCNP graph representation and hetero-GNN model architecture.
Fig. 4: Increasing hetero-GNN accuracy using on-the-fly data augmentation to promote subdivision invariance.
Fig. 5: Gradient-based optimization of UCNP heterostructure.

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Data availability

The SUNSET dataset is freely available via Figshare at https://doi.org/10.6084/m9.figshare.25130921 (ref. 61). Each subset (for instance, SUNSET-1) is presented in Javascript Object Notation (JSON) format; separate JSON files are also provided for ID and OOD collections for each subset. The hetero-GNN models used for UCNP optimization are freely available via Figshare at https://doi.org/10.6084/m9.figshare.27941694.v1 (ref. 62). The nanoparticle structures discovered by optimizing the hetero-GNN model are available via Figshare at https://doi.org/10.6084/m9.figshare.27973206 (ref. 63). Data for Figs. 2 and 5 are available via Figshare at https://doi.org/10.6084/m9.figshare.29916992 (ref. 64).

Code availability

The RNMC program, which contains the NPMC kMC tool, is available via GitHub at https://github.com/BlauGroup/RNMC and via Zenodo at https://doi.org/10.5281/zenodo.14360064 (ref. 65). Code defining the ML representations, data featurization and model training is available via GitHub at https://github.com/BlauGroup/NanoParticleTools and via Zenodo at https://doi.org/10.5281/zenodo.16878169 (ref. 66).

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Acknowledgements

This work was primarily funded by the Charter Hill Laboratory Directed Research and Development program of Lawrence Berkeley National Laboratory (LBNL), supported by the Office of Science, Office of Basic Energy Sciences (BES), of the US Department of Energy (DOE) under contract no. DE-AC02-05CH11231. This DOE-BES contract also supported work at the Molecular Foundry as well as computational resources at the National Energy Research Scientific Computing Center (NERSC, award no. BES-ERCAP0023292) and the Lawrencium computational cluster provided by the LBNL IT Division. We are especially grateful for the NERSC and Lawrencium low-priority queues, without which this work would not have been possible. L.A. was supported by the DOE Computational Science Graduate Fellowship under award no. DE-SC0022158. E.W.C.S.-S. was supported by the Carnegie Bosch Institute Postdoctoral Fellowship. We thank K. Chiao for helpful discussions related to optimizing C++ code.

Author information

Author notes

  1. Benjamin Sanchez-Lengeling

    Present address: Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada

  2. Benjamin Sanchez-Lengeling

    Present address: Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada

Authors and Affiliations

  1. Energy Technologies Area, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Eric Sivonxay, Lucas Attia, Daniel Barter & Samuel M. Blau

  2. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Lucas Attia

  3. Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    Evan Walter Clark Spotte-Smith

  4. Google DeepMind, Cambridge, MA, USA

    Benjamin Sanchez-Lengeling

  5. The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Xiaojing Xia & Emory M. Chan

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Contributions

E.S. and D.B. implemented nanoparticle kMC in C++, and X.X. provided validation against a previous implementation. E.S. and X.X. built simulation analysis capabilities in Python. E.S. implemented the high-throughput workflow infrastructure. E.S. and X.X. ran kMC simulations to construct SUNSET. E.S. implemented RFR, FCNN, CNN and homo-GNN models and trained on SUNSET data. E.S. and L.A. implemented the hetero-GNN model and trained on SUNSET data. L.A. and E.S. implemented the on-the-fly data augmentation scheme. E.S. implemented and carried out global optimization, and then ran kMC on the optimized particles to validate predicted intensities. B.S.-L. provided important input on components of the GNN architecture and global optimization. E.S., L.A., E.W.C.S.-S., E.M.C. and S.M.B. wrote the manuscript. E.M.C. and S.M.B. conceived and supervised the project.

Corresponding authors

Correspondence to Emory M. Chan or Samuel M. Blau.

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Nature Computational Science thanks Kuan Sun and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Katilin McCardle, in collaboration with the Nature Computational Science team. Peer reviewer reports are available.

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Supplementary information

Supplementary Information (download PDF )

Supplementary Figs. 1–11, Discussion and Tables 1–3.

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Supplementary Video 1 (download MP4 )

Visualization of a local optimization trajectory for a particle with eight regions, illustrating how the layer geometry and dopant concentrations are modified to maximize emission intensity.

Source data

Source Data Fig. 2 (download XLSX )

Data used to generate the subfigures in Fig. 2.

Source Data Fig. 5 (download XLSX )

Data used to plot the heat map in Fig. 5.

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Sivonxay, E., Attia, L., Spotte-Smith, E.W.C. et al. Gradient-based optimization of complex nanoparticle heterostructures enabled by deep learning on heterogeneous graphs. Nat Comput Sci 6, 83–95 (2026). https://doi.org/10.1038/s43588-025-00917-3

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