Prediction of phase diagrams using machine-learning-backed nested sampling

Abstract

Predicting phase diagrams from first principles requires efficient and reliable access to free energies across broad regions of configuration space. Nested sampling (NS) provides a principled statistical-mechanical framework for this task, offering direct access to the configurational partition function and enabling the determination of thermodynamic observables and phase boundaries from a single simulation. When combined with modern machine-learning interatomic potentials (MLIPs), NS achieves near-first-principles accuracy at dramatically reduced computational cost. Nevertheless, the computational cost of NS for larger systems remains prohibitive, and further advances in the underlying Monte Carlo machinery will be indispensable. Its overall efficiency, however, depends critically on robust exploration of rugged potential-energy landscapes and on the availability of representative, high-quality training data. A central methodological contribution of this work is the development of replica-exchange nested sampling (RENS). By introducing occasional configuration swaps between parallel NS replicas, RENS substantially enhances ergodicity and facilitates barrier crossing, enabling reliable sampling of multimodal and highly anisotropic energy landscapes. The resulting exploration naturally yields diverse and physically relevant configurations suitable for training MLIPs. To harness the computational capabilities of modern hardware accelerators, we develop JAXNEST, a fully JAX-based NS implementation that executes large RENS simulations concurrently on single or multiple GPUs. These performance gains allowed RENS to be embedded directly into a fully automated active learning (AL) workflow. Our AL strategy combines uncertainty quantification with the thermodynamically representative sampling of NS to identify and label only the most informative configurations with ab initio calculations, thereby maintaining MLIP accuracy while minimizing computational cost. In this thesis, we therefore carefully rederive the constant-pressure NS formalism within the language of Monte Carlo statistical methods. Building on this foundation, we compare NS to other common free-energy techniques, highlighting its unique advantages, and reformulate our RENS approach in terms of Markov kernels. Finally, we discuss some of the computational challenges we faced with machine learning (ML)-backed NS and describe how they were addressed in practice.

Die Arbeit verbessert die Vorhersage von Phasendiagrammen durch die Kombination von Nested Sampling (NS) mit maschinellen Lernpotenzialen (MLIPs). Mit der entwickelten Methode Replica-Exchange Nested Sampling (RENS) und der GPU-optimierten Software JAXNEST werden komplexe Energielandschaften effizienter erkundet. Ein automatisierter Active-Learning-Workflow reduziert zusätzlich den Aufwand für quantenmechanische Berechnungen. Ziel ist es, thermodynamische Eigenschaften und Phasengrenzen genauer und kostengünstiger zu bestimmen.