On the Theoretical Limits of Learning Unconstrained Interatomic Potentials

Key points

• Recent work has shown that relaxing physical inductive biases can improve computational efficiency and predictive accuracy, raising the question of whether energy-and-force matching alone is sufficient to ensure accurate sampling.1
• We show that, for unconstrained hypothesis classes, the relationship between prediction error and sampling accuracy is exponentially ill-conditioned in dimension.1
• The first is kinetic trapping, where relaxation to an accurate learned equilibrium requires exponentially long times, even when simulations are initialized from training configurations at which energies and forces are matched exactly.1
• Under explicit assumptions, we show that equilibrium mismatch can persist even in local, symmetry-preserving models, where small per-atom errors coexist with a distributional discrepancy that approaches its maximum as system size increases.1

Sources (1)

• [1]On the Theoretical Limits of Learning Unconstrained Interatomic Potentials
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 10, 05:23 PM

  Machine-learned interatomic potentials (MLIPs) accelerate molecular dynamics (MD) simulations by learning the energies and forces that govern atomic motion.

  Recent work has shown that relaxing physical inductive biases can improve computational efficiency and predictive accuracy, raising the question of whether energy-and-force matching alone is sufficient to ensure accurate sampling.

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