Differentiable Particle-Mesh Ewald with Cartesian Tensor Message Passing for Learning Long-Range Electrostatics and Dipole Response
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918534498484224 |
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| author | Guo, Zhiyue Wang, Junjie Zhang, Haoting Liang, Zhixin Yang, Ziyang Pan, Yujian Sun, Jian |
| author_facet | Guo, Zhiyue Wang, Junjie Zhang, Haoting Liang, Zhixin Yang, Ziyang Pan, Yujian Sun, Jian |
| contents | Machine learning interatomic potentials (MLIPs) can approach quantum accuracy for short-range chemistry, but most architectures remain local and fail to capture the long-range electrostatic and polarization interactions essential for ionic, polar, and interfacial systems. Recent Ewald-based MLIPs show that locally predicted electrostatic variables can recover important long-range physics, including multipolar response. However, many energy-based implementations still compute reciprocal-space terms by direct summation over k vectors, leaving a gap with production molecular dynamics, where particle-mesh Ewald (PME) with O(NlogN) scaling is standard. Here we introduce a fully differentiable PME framework for learned charges and learned atomic dipoles within an E(n)-equivariant Cartesian tensor message passing network. Charges are predicted from scalar local features, while dipoles are predicted from equivariant vector features and enter the same particle-mesh solver as an effective bound charge density. This dipolar density is constructed using analytic real-space gradients of Hockney-Eastwood spline assignment weights, enabling charge-dipole and dipole-dipole long-range forces to be trained end-to-end through FFT-space electrostatics without direct charge or dipole supervision. On a charged-dimer test case, the differentiable PME module reproduces explicit Ewald energies and forces to numerical precision when assignment-kernel deconvolution is enabled. On molten NaCl, the charge and dipole long-range channel gives the lowest force RMSE among the tested models, while all energy RMSE values remain in the sub-meV per atom regime. Timing tests show the expected crossover from explicit Ewald summation to particle-mesh scaling. These results establish differentiable dipole PME as a scalable route toward polarization-aware MLIPs for condensed-phase and interfacial systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_01598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Differentiable Particle-Mesh Ewald with Cartesian Tensor Message Passing for Learning Long-Range Electrostatics and Dipole Response Guo, Zhiyue Wang, Junjie Zhang, Haoting Liang, Zhixin Yang, Ziyang Pan, Yujian Sun, Jian Computational Physics Machine learning interatomic potentials (MLIPs) can approach quantum accuracy for short-range chemistry, but most architectures remain local and fail to capture the long-range electrostatic and polarization interactions essential for ionic, polar, and interfacial systems. Recent Ewald-based MLIPs show that locally predicted electrostatic variables can recover important long-range physics, including multipolar response. However, many energy-based implementations still compute reciprocal-space terms by direct summation over k vectors, leaving a gap with production molecular dynamics, where particle-mesh Ewald (PME) with O(NlogN) scaling is standard. Here we introduce a fully differentiable PME framework for learned charges and learned atomic dipoles within an E(n)-equivariant Cartesian tensor message passing network. Charges are predicted from scalar local features, while dipoles are predicted from equivariant vector features and enter the same particle-mesh solver as an effective bound charge density. This dipolar density is constructed using analytic real-space gradients of Hockney-Eastwood spline assignment weights, enabling charge-dipole and dipole-dipole long-range forces to be trained end-to-end through FFT-space electrostatics without direct charge or dipole supervision. On a charged-dimer test case, the differentiable PME module reproduces explicit Ewald energies and forces to numerical precision when assignment-kernel deconvolution is enabled. On molten NaCl, the charge and dipole long-range channel gives the lowest force RMSE among the tested models, while all energy RMSE values remain in the sub-meV per atom regime. Timing tests show the expected crossover from explicit Ewald summation to particle-mesh scaling. These results establish differentiable dipole PME as a scalable route toward polarization-aware MLIPs for condensed-phase and interfacial systems. |
| title | Differentiable Particle-Mesh Ewald with Cartesian Tensor Message Passing for Learning Long-Range Electrostatics and Dipole Response |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2606.01598 |