Bayesian regression for
multilevel machinelearned potentials
Subproject P03
The firstprinciples description of the properties of multicomponent 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 longterm objective of P03 is to accelerate firstprinciples calculations by developing machinelearning approaches for the description of the interatomic forces, Born effective charges, and other tensorial properties of multivalent oxides. The project will rely on kernelbased methods and Bayesian inference to implement fully automatic “onthefly” learning.
In the first project period, we will develop machinelearned 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 finitetemperature spectra measured by the experimental groups.
The difference between DFT and hybrid functionals will be machinelearned to go beyond semilocal functionals (Deltalearning). The longterm perspective is to extend this approach to highly accurate beyondDFT methods, such as the random phase approximation and quantum chemistry (coupled cluster) methods. Although kernelbased methods are exceedingly accurate, they are often less efficient than NN. We will collaborate with other projects to recast the onthefly trained FF into NN potentials to address this issue.
Expertise
The main research efforts of the group are directed towards the development of quantummechanical tools for atomicscale 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 generalpurpose ab initio code for solving the manyelectron 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 noncollinear DFT
 Linear response theory to calculate phonons and dielectric properties
 HartreeFock techniques and many flavors of hybrid functionals
 Manybody perturbation theory, including GW and BetheSalpeter
 Wavefunctionbased correlated methods (MøllerPlesset 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 machinelearning techniques to tensorial properties and correlated wavefunction techniques. These techniques are directly integrated into VASP and allow to accelerate finitetemperature simulations by many orders of magnitudes.
Team
Publications
2021 

Liu, Peitao; Verdi, Carla; Karsai, Ferenc; Kresse, Georg αβ phase transition of zirconium predicted by onthefly machinelearned force field Journal Article Physical Review Materials, 5 (5), pp. 053804, 2021. Abstract  Links  BibTeX  Tags: P03, preTACO @article{Liu2021, title = {αβ phase transition of zirconium predicted by onthefly machinelearned force field}, author = {Peitao Liu and Carla Verdi and Ferenc Karsai and Georg Kresse}, doi = {10.1103/physrevmaterials.5.053804}, year = {2021}, date = {20210524}, journal = {Physical Review Materials}, volume = {5}, number = {5}, pages = {053804}, publisher = {American Physical Society (APS)}, abstract = {The accurate prediction of solidsolid structural phase transitions at finite temperature is a challenging task, since the dynamics is so slow that direct simulations of the phase transitions by firstprinciples (FP) methods are typically not possible. Here, we study the α−β phase transition of Zr at ambient pressure by means of onthefly machinelearned force fields. These are automatically generated during FP molecular dynamics (MD) simulations without the need of human intervention, while retaining almost FP accuracy. Our MD simulations successfully reproduce the firstorder displacive nature of the phase transition, which is manifested by an abrupt jump of the volume and a cooperative displacement of atoms at the phase transition temperature. The phase transition is further identified by the simulated xray powder diffraction, and the predicted phase transition temperature is in reasonable agreement with experiment. Furthermore, we show that using a singular value decomposition and pseudo inversion of the design matrix generally improves the machinelearned force field compared to the usual inversion of the squared matrix in the regularized Bayesian regression.}, keywords = {P03, preTACO}, pubstate = {published}, tppubtype = {article} } The accurate prediction of solidsolid structural phase transitions at finite temperature is a challenging task, since the dynamics is so slow that direct simulations of the phase transitions by firstprinciples (FP) methods are typically not possible. Here, we study the α−β phase transition of Zr at ambient pressure by means of onthefly machinelearned force fields. These are automatically generated during FP molecular dynamics (MD) simulations without the need of human intervention, while retaining almost FP accuracy. Our MD simulations successfully reproduce the firstorder displacive nature of the phase transition, which is manifested by an abrupt jump of the volume and a cooperative displacement of atoms at the phase transition temperature. The phase transition is further identified by the simulated xray powder diffraction, and the predicted phase transition temperature is in reasonable agreement with experiment. Furthermore, we show that using a singular value decomposition and pseudo inversion of the design matrix generally improves the machinelearned force field compared to the usual inversion of the squared matrix in the regularized Bayesian regression.  
Jinnouchi, Ryosuke; Karsai, Ferenc; Verdi, Carla; Kresse, Georg Firstprinciples hydration free energies of oxygenated species at water–platinum interfaces Journal Article The Journal of Chemical Physics, 154 (9), pp. 094107, 2021. Abstract  Links  BibTeX  Tags: P03, preTACO @article{Jinnouchi2021, title = {Firstprinciples hydration free energies of oxygenated species at water–platinum interfaces}, author = {Ryosuke Jinnouchi and Ferenc Karsai and Carla Verdi and Georg Kresse}, doi = {10.1063/5.0036097}, year = {2021}, date = {20210301}, journal = {The Journal of Chemical Physics}, volume = {154}, number = {9}, pages = {094107}, publisher = {AIP Publishing}, abstract = {The hydration free energy of atoms and molecules adsorbed at liquid–solid interfaces strongly influences the stability and reactivity of solid surfaces. However, its evaluation is challenging in both experiments and theories. In this work, a machine learning aided molecular dynamics method is proposed and applied to oxygen atoms and hydroxyl groups adsorbed on Pt(111) and Pt(100) surfaces in water. The proposed method adopts thermodynamic integration with respect to a coupling parameter specifying a path from welldefined noninteracting species to the fully interacting ones. The atomistic interactions are described by a machinelearned interatomic potential trained on firstprinciples data. The free energy calculated by the machinelearned potential is further corrected by using thermodynamic perturbation theory to provide the firstprinciples free energy. The calculated hydration free energies indicate that only the hydroxyl group adsorbed on the Pt(111) surface attains a hydration stabilization. The observed trend is attributed to differences in the adsorption site and surface morphology.}, keywords = {P03, preTACO}, pubstate = {published}, tppubtype = {article} } The hydration free energy of atoms and molecules adsorbed at liquid–solid interfaces strongly influences the stability and reactivity of solid surfaces. However, its evaluation is challenging in both experiments and theories. In this work, a machine learning aided molecular dynamics method is proposed and applied to oxygen atoms and hydroxyl groups adsorbed on Pt(111) and Pt(100) surfaces in water. The proposed method adopts thermodynamic integration with respect to a coupling parameter specifying a path from welldefined noninteracting species to the fully interacting ones. The atomistic interactions are described by a machinelearned interatomic potential trained on firstprinciples data. The free energy calculated by the machinelearned potential is further corrected by using thermodynamic perturbation theory to provide the firstprinciples free energy. The calculated hydration free energies indicate that only the hydroxyl group adsorbed on the Pt(111) surface attains a hydration stabilization. The observed trend is attributed to differences in the adsorption site and surface morphology.  
2020 

Jinnouchi, Ryosuke; Miwa, Kazutoshi; Karsai, Ferenc; Kresse, Georg; Asahi, Ryoji OntheFly Active Learning of Interatomic Potentials for LargeScale Atomistic Simulations Journal Article The Journal of Physical Chemistry Letters, 11 (17), pp. 6946–6955, 2020. Abstract  Links  BibTeX  Tags: P03, preTACO @article{Jinnouchi2020, title = {OntheFly Active Learning of Interatomic Potentials for LargeScale Atomistic Simulations}, author = {Ryosuke Jinnouchi and Kazutoshi Miwa and Ferenc Karsai and Georg Kresse and Ryoji Asahi}, doi = {10.1021/acs.jpclett.0c01061}, year = {2020}, date = {20200731}, journal = {The Journal of Physical Chemistry Letters}, volume = {11}, number = {17}, pages = {69466955}, publisher = {American Chemical Society (ACS)}, abstract = {The onthefly generation of machinelearning force fields by activelearning schemes attracts a great deal of attention in the community of atomistic simulations. The algorithms allow the machine to selflearn an interatomic potential and construct machinelearned models on the fly during simulations. Stateoftheart query strategies allow the machine to judge whether new structures are out of the training data set or not. Only when the machine judges the necessity of updating the data set with the new structures are firstprinciples calculations carried out. Otherwise, the yet available machinelearned model is used to update the atomic positions. In this manner, most of the firstprinciples calculations are bypassed during training, and overall, simulations are accelerated by several orders of magnitude while retaining almost firstprinciples accuracy. In this Perspective, after describing essential components of the activelearning algorithms, we demonstrate the power of the schemes by presenting recent applications.}, keywords = {P03, preTACO}, pubstate = {published}, tppubtype = {article} } The onthefly generation of machinelearning force fields by activelearning schemes attracts a great deal of attention in the community of atomistic simulations. The algorithms allow the machine to selflearn an interatomic potential and construct machinelearned models on the fly during simulations. Stateoftheart query strategies allow the machine to judge whether new structures are out of the training data set or not. Only when the machine judges the necessity of updating the data set with the new structures are firstprinciples calculations carried out. Otherwise, the yet available machinelearned model is used to update the atomic positions. In this manner, most of the firstprinciples calculations are bypassed during training, and overall, simulations are accelerated by several orders of magnitude while retaining almost firstprinciples accuracy. In this Perspective, after describing essential components of the activelearning algorithms, we demonstrate the power of the schemes by presenting recent applications.  
2017 

Reticcioli, Michele; Setvin, Martin; Hao, Xianfeng; Flauger, Peter; Kresse, Georg; Schmid, Michael; Diebold, Ulrike; Franchini, Cesare PolaronDriven Surface Reconstructions Journal Article Physical Review X, 7 (3), pp. 031053, 2017. Abstract  Links  BibTeX  Tags: P02, P03, P07, preTACO @article{Reticcioli2017, title = {PolaronDriven Surface Reconstructions}, author = {Michele Reticcioli and Martin Setvin and Xianfeng Hao and Peter Flauger and Georg Kresse and Michael Schmid and Ulrike Diebold and Cesare Franchini}, doi = {10.1103/physrevx.7.031053}, year = {2017}, date = {20170925}, journal = {Physical Review X}, volume = {7}, number = {3}, pages = {031053}, publisher = {American Physical Society (APS)}, abstract = {Geometric and electronic surface reconstructions determine the physical and chemical properties of surfaces and, consequently, their functionality in applications. The reconstruction of a surface minimizes its surface free energy in otherwise thermodynamically unstable situations, typically caused by dangling bonds, lattice stress, or a divergent surface potential, and it is achieved by a cooperative modification of the atomic and electronic structure. Here, we combined firstprinciples calculations and surface techniques (scanning tunneling microscopy, noncontact atomic force microscopy, scanning tunneling spectroscopy) to report that the repulsion between negatively charged polaronic quasiparticles, formed by the interaction between excess electrons and the lattice phonon field, plays a key role in surface reconstructions. As a paradigmatic example, we explain the (1×1) to (1×2) transition in rutile TiO_{2}(110).}, keywords = {P02, P03, P07, preTACO}, pubstate = {published}, tppubtype = {article} } Geometric and electronic surface reconstructions determine the physical and chemical properties of surfaces and, consequently, their functionality in applications. The reconstruction of a surface minimizes its surface free energy in otherwise thermodynamically unstable situations, typically caused by dangling bonds, lattice stress, or a divergent surface potential, and it is achieved by a cooperative modification of the atomic and electronic structure. Here, we combined firstprinciples calculations and surface techniques (scanning tunneling microscopy, noncontact atomic force microscopy, scanning tunneling spectroscopy) to report that the repulsion between negatively charged polaronic quasiparticles, formed by the interaction between excess electrons and the lattice phonon field, plays a key role in surface reconstructions. As a paradigmatic example, we explain the (1×1) to (1×2) transition in rutile TiO_{2}(110). 