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 a paradigmatic materials science task: predicting the dielectric function of metals, a high-dimensional response that governs how solids interact with light. Using over 200,000 dielectric functions from high-throughput ab initio calculations, we study two multi-objective graph neural networks trained to predict the frequency-dependent complex interband dielectric function and the Drude frequency. We observe broken neural scaling laws with respect to dataset size, whereas scaling with the number of model parameters follows a simple power law that rapidly saturates.

翻译：在材料科学领域，无论是通过计算还是实验手段，数据都极为稀缺且生成成本高昂。因此，确定模型性能如何随数据集规模和模型容量变化，以区分数据受限与模型受限的机制至关重要。神经标度律为量化这一行为提供了框架，并指导材料数据集与机器学习架构的设计。本文研究了一个典型材料科学任务中的神经标度律：预测金属的介电函数——这是一种决定固体与光相互作用的高维响应。利用来自高通量第一性原理计算的超过200,000个介电函数数据，我们研究了两种多目标图神经网络，它们被训练用于预测频率依赖的复带间介电函数及Drude频率。我们观察到关于数据集规模的神经标度律出现失效现象，而关于模型参数数量的标度则遵循简单的幂律关系且迅速达到饱和。