Conservative adaptive-precision interatomic potentials

TL;DR

The paper introduces a Hamiltonian-consistent, conservative adaptive-precision interatomic potential by energy-bridging fast and accurate models through a differentiable, locally averaged switching parameter. Forces and energies are constructed to preserve both energy and momentum, addressing shortcomings of previous force-mixing approaches. By coupling a fast EAM potential to a high-accuracy ACE potential (demonstrated on tungsten), they achieve substantial speedups (up to 1–2 orders of magnitude) while maintaining quantifiable force and energy fidelity, controlled by the averaging radius and descriptor choice. This framework enables efficient, energy-conserving simulations in microcanonical ensembles, unlocking larger systems or longer times with reduced computational cost. The approach integrates seamlessly into LAMMPS via the APIP package, with detailed supplementary material on transition functions, force decomposition, and differentiable CSP implementations.

Abstract

Adaptive precision molecular dynamics simulations have developed along energy- and force-coupling approaches, which allow for a continuous transition between different particle descriptions or interaction potentials. Most approaches consider different (fixed) spatial regions, which control the transition between the descriptions and consequently avoid a consistent momentum-conserving Hamiltonian description. We present here a new approach to fully integrate the coupling into a Hamiltonian, therefore allowing for a conservative description, which, by design, guarantees both energy and momentum conservation. By coupling a fast EAM potential to a highly accurate ACE potential, we verify numerically the conservation properties and show that one can achieve - dependent on both the potential and the atomistic system - a speedup of one or two orders of magnitude compared to a pure ACE simulation.

Figures (8)

• Figure 1: The deviation $\pmb{d}_i$ (a) is measured in the descriptor space and used to calculate (b) the switching parameter $\lambda_i$ (c) between fast and precise model for all atoms $i$.
• Figure 2: Switching parameters $\lambda_i$ -- calculated from $g_i$ via \ref{['eq:cp:lambda', 'eq:cp:descriptor']} -- and dislocation lines. Not shown are the atoms in the lower part of the simulation box, which are calculated with the fast potential, i.e., $\lambda_i=1$.
• Figure 3: RMSE of the a) potential energies $E_i$ and b) force components $F_{i\alpha}$ of an AP potential compared with the precise ACE potential dependent on the radius $r_\text{w}^\text{cut}$ of the averaging region of the descriptor for the atoms shown in (c) (inset of (a)). The RMSE of EAM is given for comparison.
• Figure 4: Achievable speedup factor $s$ (cf. \ref{['eq:cp:speedup']}) and computing time aside_cpu per atom dependent on the fraction $x$ of ACE atoms and the averaging radius $r^\text{cut}_\text{w}$ of the AP potential.
• Figure 5: a) Momentum, b) energy and c) temperature change in a NVE simulation dependent on the combination method of EAM and ACE potential.