Prolate spheroidal wave functions enable fast and exponent-aware long-range machine learning interatomic potentials
For researchers developing machine learning interatomic potentials, PSWF-LR provides a more efficient and accurate method for handling long-range interactions, enabling larger-scale simulations.
PSWF-LR uses prolate spheroidal wave functions to efficiently model long-range interactions in machine learning interatomic potentials, reducing Fourier modes, improving accuracy, and accelerating simulations by about threefold while extending memory limits.
Long-range interactions such as electrostatics and dispersion remain a central bottleneck for machine learning interatomic potentials (MLIPs), especially in ionic, polar and interfacial systems. Ewald-based reciprocal-space mechanisms provide a physically grounded route for capturing these nonlocal effects, but often require dense Fourier grids and can become memory-limited at scale. This problem is particularly pronounced in molecular dynamics, where high efficiency requirements make accurate long-range modelling particularly costly. Here we introduce PSWF-LR, an exponent-aware long-range framework based on prolate spheroidal wave functions (PSWFs) that can be easily incorporated into existing model architectures. Its core components are PSWF-based mollification and atom-grid spreading, which enable compact and efficient representation of arbitrary inverse-power channels $1/r^p$ while treating the decay exponent as a physical prior. Across diverse long-range benchmarks, PSWF-LR reduces Fourier-mode requirements, improves energy and force accuracy, accelerates production-level simulations by about threefold, and extends long-range MLIP simulations beyond the memory limits of conventional MLIPs.