我们介绍了Ag-Pd的机器学习电位，以描述在广泛的组成范围内合金构型的能量。我们比较两种不同的方法。矩张量势（MTP）是原子间距离和角度的多项式函数。高斯近似势（GAP）框架使用核回归，并且我们使用原子邻域的原子位置（SOAP）表示的平滑重叠，该表示由球形的傅立叶变换的功率谱提供的一组完整的旋转和置换不变量组成邻居密度。两种类型的电势都能为多种成分提供出色的精度，与集群扩展的精度（该系统的基准）相抗衡。虽然两个模型都能够描述远离晶格位置的微小变形，SOAP-GAP在配置之间的合理转换路径上表现出出色的可传输性，并且MTP由于其较低的计算成本而允许组成相图的计算。鉴于这两种方法的性能几乎与簇扩展相同，但会产生非晶格模型，因此我们希望它们为合金的计算材料建模开辟新的途径。
We introduce machine-learned potentials for Ag-Pd to describe the energy of alloy configurations over a wide range of compositions. We compare two different approaches. Moment tensor potentials (MTPs) are polynomial-like functions of interatomic distances and angles. The Gaussian approximation potential (GAP) framework uses kernel regression, and we use the smooth overlap of atomic position (SOAP) representation of atomic neighborhoods that consist of a complete set of rotational and permutational invariants provided by the power spectrum of the spherical Fourier transform of the neighbor density. Both types of potentials give excellent accuracy for a wide range of compositions, competitive with the accuracy of cluster expansion, a benchmark for this system. While both models are able to describe small deformations away from the lattice positions, SOAP-GAP excels at transferability as shown by sensible transformation paths between configurations, and MTP allows, due to its lower computational cost, the calculation of compositional phase diagrams. Given the fact that both methods perform nearly as well as cluster expansion but yield off-lattice models, we expect them to open new avenues in computational materials modeling for alloys.
