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  • Open Access

Broken Neural Scaling Laws in Learning the Optical Properties of Solids

Max Großmann*, Malte Grunert, and Erich Runge

  • *Contact author: max.grossmann@tu-ilmenau.de
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PRX Intelligence 1, 013011 – Published 13 August, 2026

DOI: https://doi.org/10.1103/wv8r-7zr1

Abstract

In materials science, data are scarce and expensive to generate, whether computationally or experimentally. Therefore, it is crucial to identify how model performance scales with dataset size and model capacity to distinguish between data- and model-limited regimes. Neural scaling laws provide a framework for quantifying this behavior and guide the design of materials datasets and machine learning architectures. Here, we investigate neural scaling laws for predicting the optical properties of solids, using over 200 000 dielectric functions and Drude frequencies of metals from high-throughput ab initio calculations. We study the scaling of three multiobjective graph neural network architectures trained to simultaneously predict the frequency-dependent complex interband dielectric function as a continuous spectral response and the Drude frequency as a scalar quantity. Across two rotationally invariant graph neural networks that differ in their effective body order and an equivariant graph neural network evaluated at different maximum angular degrees, we consistently observe broken neural scaling laws with respect to dataset size. In contrast, scaling with respect to the number of model parameters is well described, in all cases, by saturating power laws.

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PRX Intelligence 1, 013011– Published 13 August, 2026
  • Received 26 March 2026
  • Accepted 15 July 2026
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