Machine-learning interatomic potentials have emerged as a revolutionary class of force-field models in molecular simulations, delivering quantum-mechanical accuracy at a fraction of the computational cost and enabling the simulation of large-scale systems over extended timescales. However, they often focus on modeling local environments, neglecting crucial long-range interactions. We propose a sum-of-Gaussians neural network (SOG-Net), a lightweight and versatile framework for integrating long-range interactions into a machine-learning force field. The SOG-Net employs a latent-variable learning network that seamlessly bridges short-range and long-range components, coupled with an efficient Fourier convolution layer that incorporates long-range effects. By learning sum-of-Gaussians multipliers across different convolution layers, the SOG-Net adaptively captures diverse long-range decay behaviors while maintaining close-to-linear computational complexity during training and simulation via nonuniform fast Fourier transforms. The method is demonstrated effective for a broad range of long-range systems.

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• Classical statistical mechanics
• Long-range interactions
• Potential energy surfaces
• Density functional theory
• Machine learning
• Molecular dynamics
• Neuronal network models