Machine learning interatomic potentials (MLIPs) have become a workhorse of modern atomistic simulations, and recently published universal MLIPs, pre-trained on large datasets, have demonstrated remarkable accuracy and generalizability. However, the computational cost of MLIPs limits their applicability to chemically disordered systems requiring large simulation cells or to sample-intensive statistical methods. Here, we report the use of continuous and differentiable alchemical degrees of freedom in atomistic materials simulations, exploiting the fact that graph neural network MLIPs represent discrete elements as real-valued tensors. The proposed method introduces alchemical atoms with corresponding weights into the input graph, alongside modifications to the message-passing and readout mechanisms of MLIPs, and allows smooth interpolation between the compositional states of materials. The end-to-end differentiability of MLIPs enables efficient calculation of the gradient of energy with respect to the compositional weights. Leveraging these gradients, we propose methodologies for optimizing the composition of solid solutions towards target macroscopic properties and conducting alchemical free energy simulations to quantify the free energy of vacancy formation and composition changes. The approach offers an avenue for extending the capabilities of universal MLIPs in the modeling of compositional disorder and characterizing the phase stabilities of complex materials systems.

翻译：机器学习原子间势（MLIPs）已成为现代原子模拟的重要工具，近期发布的基于大数据集预训练的通用MLIPs展现出卓越的准确性和泛化能力。然而，MLIPs的计算成本限制了其在需要大模拟单元的化学无序体系或样本密集型统计方法中的应用。本文报道了在原子材料模拟中利用连续可微炼金术自由度的方法，其关键在于图神经网络MLIPs将离散元素表示为实值张量。所提出的方法将带有相应权重的炼金术原子引入输入图，同时修改MLIPs的消息传递和读出机制，实现了材料组分状态间的平滑插值。MLIPs的端到端可微性使得能够高效计算能量关于组分权重的梯度。利用这些梯度，我们提出了优化固溶体成分以达到目标宏观性质的方法，以及通过炼金术自由能模拟量化空位形成自由能和组分变化的方法。该方法为扩展通用MLIPs在组分无序建模和复杂材料体系相稳定性表征方面的能力提供了新途径。