Machine-learned force fields (MLFFs) enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. Two major challenges, however, are i) the accurate description of anharmonic interactions, which are crucial for predicting key thermodynamic properties such as the phase transitions and lattice thermal conductivity in solids, and ii) that MLFFs are generally trained from density-functional theory (DFT) data and thus suffer the same limitations as DFT. This talk will discuss the on-the-fly learning technique implemented in VASP, based on molecular dynamics and Bayesian inference, and a Δ-machine learning approach that allows to generate MLFFs with beyond-DFT accuracy at an affordable computational cost. Specifically, we train MLFFs based on the random phase approximation (RPA).

Three applications will be discussed. First, for the paradigmatic 

example of zirconia, an important transition metal oxide, we will show 

that our MLFF correctly captures the temperature-induced phase 

transitions below the melting point. We also calculate the heat 

transport on the basis of Green-Kubo theory, accounting for anharmonic effects to all orders. Second, we will focus on strontium titanate, a prototypical perovskite oxide with strongly anharmonic lattice dynamics and a building block for a variety of technologies. We employ MLFFs in combination with the stochastic self-consistent harmonic approximation method in order to investigate the cubic to tetragonal transition and the quantum paraelectric behavior at low temperature, which is accurately described by the RPA. Third, we investigate carbon monoxide (CO) adsorption on transition metal surfaces, an important problem in surface science and catalysis where DFT is often inaccurate. We show that our RPA-derived MLFF is capable to accurately predict the Rh(111) surface energy, CO adsorption site preference, as well as adsorption energies at different coverages. Taken together, the results demonstrate the feasibility of many-body calculations of finite-temperature properties of materials.