Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory

Abstract

We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $\Delta$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.

References in corpus (24)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Machine Learning Force Fields
• Moment Tensor Potentials: a class of systematically improvable interatomic potentials
• A Spectral Analysis Method for Automated Generation of Quantum-Accurate Interatomic Potentials
• Big Data meets Quantum Chemistry Approximations: The $\Delta$-Machine Learning Approach
• Comparing molecules and solids across structural and alchemical space
• Machine Learning Unifies the Modelling of Materials and Molecules
• Towards Exact Molecular Dynamics Simulations with Machine-Learned Force Fields
• On-the-fly machine learning force field generation: Application to melting points
• Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on-the-fly with Bayesian inference
• Random-phase approximation and its applications in computational chemistry and materials science
• Machine learning a general purpose interatomic potential for silicon
• Alchemical and structural distribution based representation for improved QML
• Regularized SCAN functional
• Efficient global structure optimization with a machine learned surrogate model
• Cubic scaling $GW$: towards fast quasiparticle calculations
• $\Delta$-Machine Learning for Potential Energy Surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) Level of Theory
• Efficient nonparametric $n$-body force fields from machine learning
• Molecular Force Fields with Gradient-Domain Machine Learning: Construction and Application to Dynamics of Small Molecules with Coupled Cluster Forces
• A sparse representation for potential energy surface
• Analytic Interatomic Forces in the Random Phase Approximation
• $\alpha$-$\beta$ phase transition of zirconium predicted by on-the-fly machine-learned force field

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