Global Plane Waves from Local Gaussians: Periodic Charge Densities in a Blink

Jonas Elsborg, Felix Aertebjerg, Luca Thiede, Alan Aspuru-Guzik, Tejs Vegge, Arghya Bhowmik
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:27992-28020, 2026.

Abstract

We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the full periodic charge density with a single inverse FFT. By avoiding explicit real-space grid probing, periodic image summation, and spherical harmonic expansions, ELECTRAFI matches or exceeds state-of-the-art accuracy across periodic benchmarks while being up to $633\times$ faster than the strongest competing method, reconstructing crystal charge densities in a fraction of a second. When used to initialize DFT calculations, ELECTRAFI reduces total DFT compute cost by up to $\sim$20 %, whereas slower charge density models negate savings due to high inference times. Our results show that accuracy and inference cost jointly determine end-to-end DFT speedups, and motivate our focus on efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-elsborg26a, title = {Global Plane Waves from Local Gaussians: Periodic Charge Densities in a Blink}, author = {Elsborg, Jonas and Aertebjerg, Felix and Thiede, Luca and Aspuru-Guzik, Alan and Vegge, Tejs and Bhowmik, Arghya}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {27992--28020}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/elsborg26a/elsborg26a.pdf}, url = {https://proceedings.mlr.press/v306/elsborg26a.html}, abstract = {We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the full periodic charge density with a single inverse FFT. By avoiding explicit real-space grid probing, periodic image summation, and spherical harmonic expansions, ELECTRAFI matches or exceeds state-of-the-art accuracy across periodic benchmarks while being up to $633\times$ faster than the strongest competing method, reconstructing crystal charge densities in a fraction of a second. When used to initialize DFT calculations, ELECTRAFI reduces total DFT compute cost by up to $\sim$20 %, whereas slower charge density models negate savings due to high inference times. Our results show that accuracy and inference cost jointly determine end-to-end DFT speedups, and motivate our focus on efficiency.} }
Endnote
%0 Conference Paper %T Global Plane Waves from Local Gaussians: Periodic Charge Densities in a Blink %A Jonas Elsborg %A Felix Aertebjerg %A Luca Thiede %A Alan Aspuru-Guzik %A Tejs Vegge %A Arghya Bhowmik %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-elsborg26a %I PMLR %P 27992--28020 %U https://proceedings.mlr.press/v306/elsborg26a.html %V 306 %X We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the full periodic charge density with a single inverse FFT. By avoiding explicit real-space grid probing, periodic image summation, and spherical harmonic expansions, ELECTRAFI matches or exceeds state-of-the-art accuracy across periodic benchmarks while being up to $633\times$ faster than the strongest competing method, reconstructing crystal charge densities in a fraction of a second. When used to initialize DFT calculations, ELECTRAFI reduces total DFT compute cost by up to $\sim$20 %, whereas slower charge density models negate savings due to high inference times. Our results show that accuracy and inference cost jointly determine end-to-end DFT speedups, and motivate our focus on efficiency.
APA
Elsborg, J., Aertebjerg, F., Thiede, L., Aspuru-Guzik, A., Vegge, T. & Bhowmik, A.. (2026). Global Plane Waves from Local Gaussians: Periodic Charge Densities in a Blink. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:27992-28020 Available from https://proceedings.mlr.press/v306/elsborg26a.html.

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