基于材料性质外推的原子系统的小波散射网络
Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties
摘要：
材料科学中机器学习的梦想是让模型学习原子系统的底层物理，使其能够超越训练集的插值，预测原始训练数据中不存在的属性。除了机器学习架构和训练技术的进步之外，实现这一雄心勃勃的目标还需要一种方法将3D原子系统转换为特征表示，该特征表示保持旋转和平移对称性，在小扰动下保持平滑性，以及在重新排序下保持不变性。原子轨道小波散射变换通过构造保持了这些对称性，并作为机器学习能量预测的特征化方法取得了巨大成功。无论是在小分子还是在块状无定形$\text{Li}_α\text{Si}$系统中，使用小波散射系数作为特征的机器学习模型都以计算成本的一小部分证明了与密度泛函理论相当的准确性。在这项工作中，我们测试了我们的$\text{Li}_α\text{Si}$能量预测器的泛化能力，不包括在训练集中的属性，如弹性常数和迁移障碍。我们证明，统计特征选择方法可以减少过度拟合，并导致显着的准确性，在这些外推任务。
英文摘要：
The dream of machine learning in materials science is for a model to learn the underlying physics of an atomic system, allowing it to move beyond interpolation of the training set to the prediction of properties that were not present in the original training data. In addition to advances in machine learning architectures and training techniques, achieving this ambitious goal requires a method to convert a 3D atomic system into a feature representation that preserves rotational and translational symmetry, smoothness under small perturbations, and invariance under re-ordering. The atomic orbital wavelet scattering transform preserves these symmetries by construction, and has achieved great success as a featurization method for machine learning energy prediction. Both in small molecules and in the bulk amorphous $\text{Li}_α\text{Si}$ system, machine learning models using wavelet scattering coefficients as features have demonstrated a comparable accuracy to Density Functional Theory at a small fraction of the computational cost. In this work, we test the generalizability of our $\text{Li}_α\text{Si}$ energy predictor to properties that were not included in the training set, such as elastic constants and migration barriers. We demonstrate that statistical feature selection methods can reduce over-fitting and lead to remarkable accuracy in these extrapolation tasks.
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