Bayesian regression for
multi-level machine-learned potentials

Subproject P03

The first-principles description of the properties of multi-component metal oxides is an exceedingly challenging problem. The reasons are that the configurational space grows exponentially with the number of species and standard Density Functional Theory (DFT) is often not accurate enough. The long-term objective of P03 is to accelerate first-principles calculations by developing machine-learning approaches for the description of the interatomic forces, Born effective charges, and other tensorial properties of multivalent oxides. The project will rely on kernel-based methods and Bayesian inference to implement fully automatic “on-the-fly” learning.

In the first project period, we will develop machine-learned force fields (MLFF) for DFT and DFT+U, whereby the number of components in the FF will be gradually increased. A concise framework for learning tensorial properties will be implemented. We will use this to simulate infrared spectra of oxide materials, which can be readily compared to the finite-temperature spectra measured by the experimental groups.

The difference between DFT and hybrid functionals will be machine-learned to go beyond semi-local functionals (Delta-learning). The long-term perspective is to extend this approach to highly accurate beyond-DFT methods, such as the random phase approximation and quantum chemistry (coupled cluster) methods. Although kernel-based methods are exceedingly accurate, they are often less efficient than NN. We will collaborate with other projects to recast the on-the-fly trained FF into NN potentials to address this issue.

In the second funding period, the project is structured around four principal components:

Δ-Learning Beyond Local Density Functional Theory:

Significant progress was made in the first funding period by integrating the random phase approximation (RPA) with machine learning, yielding improved agreement with experimental data for various materials, including surface science applications. To enhance robustness, the approach will be refined by adopting message-passing neural networks, which are less data-intensive than kernel-based methods. This methodology will be applied to multivalent oxides, specifically iron oxides and other complex oxide surfaces. Furthermore, the project intends to explore advanced methods beyond RPA, such as coupled cluster and auxiliary field quantum Monte Carlo methods.

Transition from Kernel-Based Methods to Message-Passing Networks:

Equivariant message-passing networks demonstrate substantial accuracy gains over traditional approaches, albeit at a higher computational cost, necessitating GPU-based computations. The utilization of graph-ACE (atomic cluster expansion) is expected to advance the learning of force fields for complex materials, the differentiation between RPA and DFT, and the learning of tensorial quantities. A transition to graph-ACE will occur whenever the current methodology exhibits unsatisfactory accuracy.

Learning Polarization, Polarizabilities, and Simulating IR Spectra:

During the first funding period, polipy4vasp was developed for predicting IR spectra. While prediction accuracy for polarization and electric field gradient (NMR data) is generally very good to excellent across many systems, challenges persist. Kernel-based methods encounter some difficulties in learning tensorial quantities. Plans include improving accuracy through the use of higher-order body descriptors and ACE. Additionally, the project aims to explore advanced message-passing approaches like graph-ACE and migrate to contemporary software platforms such as PyTorch. Finally, training will be conducted on the electrical enthalpy and its derivatives.

Bayesian Regression and Global Optimization:

Active learning strategies, including Bayesian regression, are routinely and reliably employed. However, the predicted errors occasionally display an unsatisfactory distribution, which is partly attributed to the use of local descriptors. The project will investigate global descriptors to mitigate prediction errors and generate more accurate error estimates that align with expected distributions. This refined methodology will extend and enhance the active learning strategy, increasing its robustness. We also plan to implement global optimization strategies based on Bayesian regression and global descriptor-based force fields.

Georg Kresse
PI

Expertise

The main research efforts of the group are directed towards the development of quantum-mechanical tools for atomic-scale simulations of properties and processes in materials and the application of these methodologies to key areas of condensed matter physics and materials research. An important pillar of the research is the Vienna Ab initio Simulation Package (VASP), a general-purpose ab initio code for solving the many-electron Schrödinger equation. The code is among the world leaders in its field, with more than 3500 licensees worldwide. We have expertise with simulations for a vast number of properties using many different techniques:

Density functional theory (DFT), including spin and non-collinear DFT
Linear response theory to calculate phonons and dielectric properties
Hartree-Fock techniques and many flavors of hybrid functionals
Many-body perturbation theory, including GW and Bethe-Salpeter
Wavefunction-based correlated methods (Møller-Plesset perturbation theory)
Surface science, including growth and oxide formation
Simulation of nanostructures
Semiconductor physics: charge trapping, polarons
Electronic excitations
Defect energies in extended systems

For TACO, we will adapt our machine-learning techniques to tensorial properties and correlated wavefunction techniques. These techniques are directly integrated into VASP and allow to accelerate finite-temperature simulations by many orders of magnitudes.