Title: Sampling Lattices in Semi-Grand Canonical Ensemble with Autoregressive Machine Learning

Abstract: Calculating thermodynamic potentials and observables efficiently and accurately is key for the application of statistical mechanics simulations to materials science. However, naive Monte Carlo approaches, on which such calculations are often dependent, struggle to scale to complex materials in many state-of-the-art disciplines such as the design of high entropy alloys or multicomponent catalysts. To address this issue, we adapt sampling tools built upon machine-learning based generative modeling to the materials space by transforming them into the semi-grand canonical ensemble. Furthermore, we show that the resulting models are transferable across wide-ranges of thermodynamic conditions and can be implemented with any internal energy model U, allowing integration into many existing materials workflows. We demonstrate the applicability of this approach to the simulation of benchmark systems (AgPd, CuAu) that exhibit diverse thermodynamic behavior in their phase diagrams. Finally, we discuss remaining challenges in model development and promising research directions for future improvements.