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.

Team

Georg Kresse
PI

Sylwia Gutowska
Co-PI

Payal Wadhwa
PostDoc

Bernhard Schmiedmayer
PhD Student

Former Members

Carla Verdi
co-PI

Peitao Liu
PostDoc

Carolin Faller PhD Student, Student Representative 22–24

Publications

13 entries « 1 of 2 »

2025

Quantum Delocalization Enables Water Dissociation on Ru(0001)

Cao, Yu; Wang, Jiantao; Liu, Mingfeng; Liu, Yan; Ma, Hui; Franchini, Cesare; Sun, Yan; Kresse, Georg; Chen, Xing-Qiu; Liu, Peitao

Quantum Delocalization Enables Water Dissociation on Ru(0001)

Journal ArticleOpen Access

In: Physical Review Letters, vol. 134, iss. 17, pp. 178001, 2025.

Abstract | Links | BibTeX | Tags: P03, P07

Structure and Dynamics of the Magnetite(001)/Water Interface from Molecular Dynamics Simulations Based on a Neural Network Potential

Romano, Salvatore; de Hijes, Pablo Montero; Meier, Matthias; Kresse, Georg; Franchini, Cesare; Dellago, Christoph

Structure and Dynamics of the Magnetite(001)/Water Interface from Molecular Dynamics Simulations Based on a Neural Network Potential

Journal ArticleOpen Access

In: Journal of Chemical Theory and Computation, vol. 21, iss. 4, pp. 1951–1960, 2025.

Abstract | Links | BibTeX | Tags: P03, P07, P12

2024

Density-Based Long-Range Electrostatic Descriptors for Machine Learning Force Fields

Faller, Carolin; Kaltak, Merzuk; Kresse, Georg

Density-Based Long-Range Electrostatic Descriptors for Machine Learning Force Fields

Journal ArticleOpen Access

In: The Journal of Chemical Physics, vol. 161, iss. 21, pp. 214701, 2024, (submitted to the Journal of Chemical Physics).

Abstract | Links | BibTeX | Tags: P03

Density isobar of water and melting temperature of ice: Assessing common density functionals

de Hijes, Pablo Montero; Dellago, Christoph; Jinnouchi, Ryosuke; Kresse, Georg

Density isobar of water and melting temperature of ice: Assessing common density functionals

Journal ArticleOpen Access

In: The Journal of Chemical Physics, vol. 161, pp. 131102, 2024.

Abstract | Links | BibTeX | Tags: P03, P12

Stoichiometric reconstruction of the Al2O3(0001) surface

Hütner, Johanna I.; Conti, Andrea; Kugler, David; Mittendorfer, Florian; Kresse, Georg; Schmid, Michael; Diebold, Ulrike; Balajka, Jan

Stoichiometric reconstruction of the Al2O3(0001) surface

Journal ArticleOpen Access

In: Science, vol. 385, pp. 1241–1244, 2024, ISSN: 1095-9203.

Abstract | Links | BibTeX | Tags: P02, P03

Derivative learning of tensorial quantities—Predicting finite temperature infrared spectra from first principles

Schmiedmayer, Bernhard; Kresse, Georg

Derivative learning of tensorial quantities—Predicting finite temperature infrared spectra from first principles

Journal ArticleOpen Access

In: The Journal of Chemical Physics, vol. 161, iss. 8, pp. 084703, 2024.

Abstract | Links | BibTeX | Tags: P03

Comparing machine learning potentials for water: Kernel-based regression and Behler–Parrinello neural networks

de Hijes, Pablo Montero; Dellago, Christoph; Jinnouchi, Ryosuke; Schmiedmayer, Bernhard; Kresse, Georg

Comparing machine learning potentials for water: Kernel-based regression and Behler–Parrinello neural networks

Journal ArticleOpen Access

In: The Journal of Chemical Physics, vol. 160, iss. 11, no. 114107, 2024.

Abstract | Links | BibTeX | Tags: P03, P12

2023

Quantum paraelectricity and structural phase transitions in strontium titanate beyond density functional theory

Verdi, Carla; Ranalli, Luigi; Franchini, Cesare; Kresse, Georg

Quantum paraelectricity and structural phase transitions in strontium titanate beyond density functional theory

Journal Article

In: Physical Review Materials, vol. 7, no. 3, pp. l030801, 2023.

Abstract | Links | BibTeX | Tags: P03, P07

Temperature-dependent anharmonic phonons in quantum paraelectric KTaO3 by first principles and machine-learned force fields

Ranalli, Luigi; Verdi, Carla; Monacelli, Lorenzo; Kresse, Georg; Calandra, Matteo; Franchini, Cesare

Temperature-dependent anharmonic phonons in quantum paraelectric KTaO3 by first principles and machine-learned force fields

Journal ArticleOpen Access

In: Advanced Quantum Technology, vol. 6, iss. 4, 2023.

Abstract | Links | BibTeX | Tags: P03, P07

Combining Machine Learning and Many-Body Calculations: Coverage-Dependent Adsorption of CO on Rh(111)

Liu, Peitao; Wang, Jiantao; Avargues, Noah; Verdi, Carla; Singraber, Andreas; Karsai, Ferenc; Chen, Xing-Qiu; Kresse, Georg

Combining Machine Learning and Many-Body Calculations: Coverage-Dependent Adsorption of CO on Rh(111)

Journal Article

In: Physical Review Letters, vol. 130, no. 7, pp. 078001, 2023.

Abstract | Links | BibTeX | Tags: P03

13 entries « 1 of 2 »