Interpolation and differentiation of alchemical degrees of freedom in
  machine learning interatomic potentials
Juno Nam Rafael Gómez-Bombarelli
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.