The NNP Score Completeness Boundary: Physics Decomposition for Crystal Structure Prediction with Neural Network Potentials

Crystal structure prediction (CSP) faces a trade-off between data-driven generative models, which need substantial training data, and physics-based sampling, which is computationally expensive. Pre-trained neural network interatomic potentials (NNPs) offer a middle ground: their energy gradients define conservative scores, so they can in principle sample the Boltzmann distribution without training a generative model. We show that using them directly exposes a fundamental limitation. NNPs are not uniformly complete: they capture long-range chemistry and equilibrium forces accurately, but their training data contain no deep-overlap configurations, leaving short-range Pauli repulsion unconstrained and driving noise-dependent trajectories into an out-of-distribution (OOD) regime. We introduce a physics decomposition that pairs learned long-range chemistry with analytically specified short-range universality. The augmented score is exactly conservative and needs no generative training. Experiments show that the augmented score holds the induced rate to at most a few percent across the entire scan. The frontier where the score stops being complete—the NNP score completeness boundary—is a property of the training data that any machine-learned potential inherits, not an architectural defect. Supplying the missing short-range physics analytically is what makes a pre-trained potential a usable generative score. Our code is available at https://anonymous.4open.science/r/MaterialGen_anoy-3A8B.