GNN-assisted phase space integration with application to atomistics

Overcoming the time scale limitations of atomistics can be achieved by switching from state-space representation Molecular Dynamics (MD) to a statistical-mechanics-based in phase space, where approximations such as maximum-entropy or Gaussian packets (GPP) evolve atomistic ensemble time-coarsened fashion. In practice, this requires computation expensive high-dimensional integrals over all space an ensemble. This, turn, is commonly accomplished efficiently low-order numerical quadrature. We show that quadrature context, unfortunately, comes with set inherent problems, which corrupt accuracy simulations—especially when dealing crystal lattices imperfections. As remedy, we demonstrate Graph Neural Networks, trained on Monte-Carlo data, serve replacement for used rules, overcoming their deficiencies and significantly improving accuracy. This showcased three benchmarks: thermal expansion copper, martensitic transition iron, energy grain boundaries. illustrate benefits proposed technique classically third- fifth-order quadrature, highlight impact predictions, discuss computational efficiency. The latter general importance performing frequent evaluation other integrals, why framework promises applications beyond scope atomistics.