论文标题
在Jacobi-Legendre多项式上构建的群集扩展，以进行精确的力场
Cluster expansion constructed over Jacobi-Legendre polynomials for accurate force fields
论文作者
论文摘要
我们介绍了一种紧凑的群集扩展方法，该方法是在雅各比和legendre多项式上构建的，以生成高度准确且柔性的机器学习力场。组成的多体贡献是分离的，可以解释和适应性的，可以复制系统的物理知识。实际上，使用Jacobi多项式引入的灵活性使我们自然地将群集扩展限制并对称性。这具有减少拟合所需的参数数量的影响，并实施了潜力的所需行为。例如，我们表明我们的jacobi-legendre群集扩展可以设计为在短距离距离处具有排斥尾巴的电势，而无需强加任何外部功能。我们的方法在这里与可用的机器学习潜在方案进行比较，例如原子聚类的扩展和在双光谱上建立的电位。作为一个例子，我们通过训练能够描述晶体石墨和钻石以及液体和无定形元素碳的纤细和精确模型来构建碳质潜力。
We introduce a compact cluster expansion method, constructed over Jacobi and Legendre polynomials, to generate highly accurate and flexible machine-learning force fields. The constituent many-body contributions are separated, interpretable and adaptable to replicate the physical knowledge of the system. In fact, the flexibility introduced by the use of the Jacobi polynomials allows us to impose, in a natural way, constrains and symmetries to the cluster expansion. This has the effect of reducing the number of parameters needed for the fit and of enforcing desired behaviours of the potential. For instance, we show that our Jacobi-Legendre cluster expansion can be designed to generate potentials with a repulsive tail at short inter-atomic distances, without the need of imposing any external function. Our method is here continuously compared with available machine-learning potential schemes, such as the atomic cluster expansion and potentials built over the bispectrum. As an example we construct a Jacobi-Legendre potential for carbon, by training a slim and accurate model capable of describing crystalline graphite and diamond, as well as liquid and amorphous elemental carbon.
