# Neural-network based simulation of rare event processes at the water/oxide interface

### Subproject P12

Atomistic computer simulations of processes occurring at the water/oxide interface are challenging in several ways. The calculation of atomic forces based on *ab initio* methods is computationally very demanding, and barrier crossing events may lead to long computation times. Both these aspects severely limit accessible system sizes and simulation times.

In project P12, we will address these challenges using a combination of machine learning and advanced rare event sampling methods. In particular, using software developed in our group and collaborating with P03 Kresse, we will train neural network potentials based on the Behler-Parrinello approach for oxide/water interfaces, starting with the Fe_{3}O_{4}/water system studied in P11 Backus. We will pay special attention to error estimation and the correct treatment of long-range interactions. With the new potential, we will study the structure and dynamics of water near the oxide surface to provide the atomistic information necessary to rationalize the spectroscopy experiments of P11 Backus. Another important goal of P12 is to explore how deep generative models can be used to enhance rare event simulations. For this purpose, we will apply normalizing flows, represented by deep neural networks, to trajectory space. The resulting improved transition path sampling simulations will be used to study reactive processes investigated experimentally in other subprojects of TACO.

## Expertise

Our research efforts focus on the development of simulation algorithms and their application to investigate dynamical processes in condensed matter systems based on the principles of equilibrium and non-equilibrium statistical mechanics. In particular, we have helped to create the transition path sampling methodology for the simulation of rare but important events, such as nucleation aprocesses, chemical reactions and biomolecular reorganizations. More recently, we have worked on applying machine learning methods to molecular structure recognition and the representation of potential and free energy surfaces.

Recent research topics include:

- Self-assembly of nanocrystals
- Folding and unfolding of biopolymers
- Interfaces in aqueous systems
- Phase separation in alloys
- Thermo-polarisation
- Structure and dynamics of water and ice
- Cavitation
- Crystallization
- Non-equilibrium work fluctuations

## Team

#### Associates

## Publications

### 2023

Hijes, Pablo Montero; Romano, Salvatore; Gorfer, Alexander; Dellago, Christoph

The kinetics of the ice–water interface from *ab initio* machine learning simulations

In: The Journal of Chemical Physics, vol. 158, no. 20, pp. 204706, 2023.

Abstract | Links | BibTeX | Tags: P12

@article{Hijes2023a,

title = {The kinetics of the ice–water interface from \textit{ab initio} machine learning simulations},

author = {Pablo Montero Hijes and Salvatore Romano and Alexander Gorfer and Christoph Dellago},

doi = {10.1063/5.0151011},

year = {2023},

date = {2023-05-24},

urldate = {2023-05-24},

journal = {The Journal of Chemical Physics},

volume = {158},

number = {20},

pages = {204706},

publisher = {AIP Publishing},

abstract = {Molecular simulations employing empirical force fields have provided valuable knowledge about the ice growth process in the past decade. The development of novel computational techniques allows us to study this process, which requires long simulations of relatively large systems, with ab initio accuracy. In this work, we use a neural-network potential for water trained on the revised Perdew–Burke–Ernzerhof functional to describe the kinetics of the ice–water interface. We study both ice melting and growth processes. Our results for the ice growth rate are in reasonable agreement with previous experiments and simulations. We find that the kinetics of ice melting presents a different behavior (monotonic) than that of ice growth (non-monotonic). In particular, a maximum ice growth rate of 6.5 Å/ns is found at 14 K of supercooling. The effect of the surface structure is explored by investigating the basal and primary and secondary prismatic facets. We use the Wilson–Frenkel relation to explain these results in terms of the mobility of molecules and the thermodynamic driving force. Moreover, we study the effect of pressure by complementing the standard isobar with simulations at a negative pressure (−1000 bar) and at a high pressure (2000 bar). We find that prismatic facets grow faster than the basal one and that pressure does not play an important role when the speed of the interface is considered as a function of the difference between the melting temperature and the actual one, i.e., to the degree of either supercooling or overheating.},

keywords = {P12},

pubstate = {published},

tppubtype = {article}

}

Falkner, Sebastian; Coretti, Alessandro; Romano, Salvatore; Geissler, Phillip; Dellago, Christoph

Conditioning Normalizing Flows for Rare Event Sampling

Journal ArticleOpen AccessSubmittedarXivIn: arXiv, 2023.

Abstract | Links | BibTeX | Tags: P12

@article{Falkner2023a,

title = {Conditioning Normalizing Flows for Rare Event Sampling},

author = {Sebastian Falkner and Alessandro Coretti and Salvatore Romano and Phillip Geissler and Christoph Dellago},

url = {https://arxiv.org/abs/2207.14530},

year = {2023},

date = {2023-05-19},

urldate = {2023-05-19},

journal = {arXiv},

abstract = {Understanding the dynamics of complex molecular processes is often linked to the study of infrequent transitions between long-lived stable states. The standard approach to the sampling of such rare events is to generate an ensemble of transition paths using a random walk in trajectory space. This, however, comes with the drawback of strong correlations between subsequently sampled paths and with an intrinsic difficulty in parallelizing the sampling process. We propose a transition path sampling scheme based on neural-network generated configurations. These are obtained employing normalizing flows, a neural network class able to generate statistically independent samples from a given distribution. With this approach, not only are correlations between visited paths removed, but the sampling process becomes easily parallelizable. Moreover, by conditioning the normalizing flow, the sampling of configurations can be steered towards regions of interest. We show that this approach enables the resolution of both the thermodynamics and kinetics of the transition region. },

keywords = {P12},

pubstate = {published},

tppubtype = {article}

}

Jung, Hendrik; Covino, Roberto; Arjun, A.; Leitold, Christian; Dellago, Christoph; Bolhuis, Peter G.; Hummer, Gerhard

Machine-guided path sampling to discover mechanisms of molecular self-organization

Journal ArticleOpen AccessIn: Nature Computational Science, vol. 3, no. 4, pp. 334–345, 2023.

Abstract | Links | BibTeX | Tags: P12

@article{Jung2023,

title = {Machine-guided path sampling to discover mechanisms of molecular self-organization},

author = {Hendrik Jung and Roberto Covino and A. Arjun and Christian Leitold and Christoph Dellago and Peter G. Bolhuis and Gerhard Hummer},

doi = {10.1038/s43588-023-00428-z},

year = {2023},

date = {2023-04-24},

journal = {Nature Computational Science},

volume = {3},

number = {4},

pages = {334--345},

publisher = {Springer Science and Business Media LLC},

abstract = {Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and—if needed—update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.},

keywords = {P12},

pubstate = {published},

tppubtype = {article}

}

Hijes, Pablo Montero; Espinosa, Jorge R; Vega, Carlos; Dellago, Christoph

Minimum in the pressure dependence of the interfacial free energy between ice Ih and water

Journal ArticleOpen AccessIn: The Journal of Chemical Physics, vol. 158, no. 12, pp. 124503, 2023.

Abstract | Links | BibTeX | Tags: P12

@article{Hijes2023,

title = {Minimum in the pressure dependence of the interfacial free energy between ice Ih and water},

author = {Pablo Montero Hijes and Jorge R Espinosa and Carlos Vega and Christoph Dellago},

doi = {10.1063/5.0140814},

year = {2023},

date = {2023-03-23},

urldate = {2023-03-23},

journal = {The Journal of Chemical Physics},

volume = {158},

number = {12},

pages = {124503},

publisher = {AIP Publishing},

abstract = {Despite the importance of ice nucleation, this process has been barely explored at negative pressures. Here, we study homogeneous ice nucleation in stretched water by means of molecular dynamics seeding simulations using the TIP4P/Ice model. We observe that the critical nucleus size, interfacial free energy, free energy barrier, and nucleation rate barely change between isobars from −2600 to 500 bars when they are represented as a function of supercooling. This allows us to identify universal empirical expressions for homogeneous ice nucleation in the pressure range from −2600 to 500 bars. We show that this universal behavior arises from the pressure dependence of the interfacial free energy, which we compute by means of the mold integration technique, finding a shallow minimum around −2000 bars. Likewise, we show that the change in the interfacial free energy with pressure is proportional to the excess entropy and the slope of the melting line, exhibiting in the latter a reentrant behavior also at the same negative pressure. Finally, we estimate the excess internal energy and the excess entropy of the ice Ih–water interface.},

keywords = {P12},

pubstate = {published},

tppubtype = {article}

}

Falkner, Sebastian; Coretti, Alessandro; Dellago, Christoph

Journal ArticleOpen AccessarXivIn: arXiv, 2023.

Abstract | Links | BibTeX | Tags: P12

@article{Falkner2023,

title = {Enhanced Sampling of Configuration and Path Space in a Generalized Ensemble by Shooting Point Exchange},

author = {Sebastian Falkner and Alessandro Coretti and Christoph Dellago},

url = {https://arxiv.org/abs/2302.08757},

year = {2023},

date = {2023-03-22},

urldate = {2023-03-22},

journal = {arXiv},

abstract = {The computer simulation of many molecular processes is complicated by long time scales caused by rare transitions between long-lived states. Here, we propose a new approach to simulate such rare events, which combines transition path sampling with enhanced exploration of configuration space. The method relies on exchange moves between configuration and trajectory space, carried out based on a generalized ensemble. This scheme substantially enhances the efficiency of the transition path sampling simulations, particularly for systems with multiple transition channels, and yields information on thermodynamics, kinetics and reaction coordinates of molecular processes without distorting their dynamics. The method is illustrated using the isomerization of proline in the KPTP tetrapeptide.},

keywords = {P12},

pubstate = {published},

tppubtype = {article}

}

### 2022

Tröster, Andreas; Verdi, Carla; Dellago, Christoph; Rychetsky, Ivan; Kresse, Georg; Schranz, Wilfried

Hard antiphase domain boundaries in strontium titanate unravelled using machine-learned force fields

Journal ArticleIn: Physical Review Materials, vol. 6, no. 9, pp. 094408, 2022.

Abstract | Links | BibTeX | Tags: P03, P12

@article{Troester2022,

title = {Hard antiphase domain boundaries in strontium titanate unravelled using machine-learned force fields},

author = {Andreas Tröster and Carla Verdi and Christoph Dellago and Ivan Rychetsky and Georg Kresse and Wilfried Schranz},

doi = {10.1103/physrevmaterials.6.094408},

year = {2022},

date = {2022-09-16},

urldate = {2022-09-16},

journal = {Physical Review Materials},

volume = {6},

number = {9},

pages = {094408},

publisher = {American Physical Society (APS)},

abstract = {We investigate the properties of hard antiphase boundaries in SrTiO_{3} using machine-learned force fields. In contrast to earlier findings based on standard \textit{ab initio} methods, for all pressures up to 120kbar the observed domain wall pattern maintains an almost perfect Néel character in quantitative agreement with Landau-Ginzburg-Devonshire theory, and the in-plane polarization P_{3} shows no tendency to decay to zero. Together with the switching properties of P_{3} under reversal of the Néel order parameter component, this provides hard evidence for the presence of rotopolar couplings. The present approach overcomes the severe limitations of \textit{ab initio} simulations of wide domain walls and opens avenues toward concise atomistic predictions of domain-wall properties even at finite temperatures.},

keywords = {P03, P12},

pubstate = {published},

tppubtype = {article}

}

_{3}using machine-learned force fields. In contrast to earlier findings based on standard

*ab initio*methods, for all pressures up to 120kbar the observed domain wall pattern maintains an almost perfect Néel character in quantitative agreement with Landau-Ginzburg-Devonshire theory, and the in-plane polarization P

_{3}shows no tendency to decay to zero. Together with the switching properties of P

_{3}under reversal of the Néel order parameter component, this provides hard evidence for the presence of rotopolar couplings. The present approach overcomes the severe limitations of

*ab initio*simulations of wide domain walls and opens avenues toward concise atomistic predictions of domain-wall properties even at finite temperatures.

Coretti, Alessandro; Falkner, Sebastian; Geissler, Phillip; Dellago, Christoph

Learning Mappings between Equilibrium States of Liquid Systems Using Normalizing Flows

Journal ArticleOpen AccessarXivIn: arXiv, 2022.

Abstract | Links | BibTeX | Tags: P12

@article{Coretti2022,

title = {Learning Mappings between Equilibrium States of Liquid Systems Using Normalizing Flows},

author = {Alessandro Coretti and Sebastian Falkner and Phillip Geissler and Christoph Dellago},

url = {https://arxiv.org/abs/2208.10420},

year = {2022},

date = {2022-08-22},

urldate = {2022-08-22},

journal = {arXiv},

abstract = { Generative models are a promising tool to address the sampling problem in multi-body and condensed-matter systems in the framework of statistical mechanics. In this work, we show that normalizing flows can be used to learn a transformation to map different liquid systems into each other allowing at the same time to obtain an unbiased equilibrium distribution through a reweighting process. Two proof-of-principles calculations are presented for the transformation between Lennard-Jones systems of particles with different depths of the potential well and for the transformation between a Lennard-Jones and a system of repulsive particles. In both numerical experiments, systems are in the liquid state. In future applications, this approach could lead to efficient methods to simulate liquid systems at ab-initio accuracy with the computational cost of less accurate models, such as force field or coarse-grained simulations.},

keywords = {P12},

pubstate = {published},

tppubtype = {article}

}

### 2021

Bircher, Martin P; Singraber, Andreas; Dellago, Christoph

Improved description of atomic environments using low-cost polynomial functions with compact support

Journal ArticleOpen AccessIn: Machine Learning: Science and Technology, vol. 2, no. 3, pp. 035026, 2021.

Abstract | Links | BibTeX | Tags: P12, pre-TACO

@article{Bircher2021,

title = {Improved description of atomic environments using low-cost polynomial functions with compact support},

author = {Martin P Bircher and Andreas Singraber and Christoph Dellago},

doi = {10.1088/2632-2153/abf817},

year = {2021},

date = {2021-06-16},

urldate = {2021-06-16},

journal = {Machine Learning: Science and Technology},

volume = {2},

number = {3},

pages = {035026},

publisher = {IOP Publishing},

abstract = {The prediction of chemical properties using machine learning techniques calls for a set of appropriate descriptors that accurately describe atomic and, on a larger scale, molecular environments. A mapping of conformational information on a space spanned by atom-centred symmetry functions (SF) has become a standard technique for energy and force predictions using high-dimensional neural network potentials (HDNNP). An appropriate choice of SFs is particularly crucial for accurate force predictions. Established atom-centred SFs, however, are limited in their flexibility, since their functional form restricts the angular domain that can be sampled without introducing problematic derivative discontinuities. Here, we introduce a class of atom-centred SFs based on polynomials with compact support called polynomial symmetry functions (PSF), which enable a free choice of both, the angular and the radial domain covered. We demonstrate that the accuracy of PSFs is either on par or considerably better than that of conventional, atom-centred SFs. In particular, a generic set of PSFs with an intuitive choice of the angular domain inspired by organic chemistry considerably improves prediction accuracy for organic molecules in the gaseous and liquid phase, with reductions in force prediction errors over a test set approaching 50% for certain systems. Contrary to established atom-centred SFs, computation of PSF does not involve any exponentials, and their intrinsic compact support supersedes use of separate cutoff functions, facilitating the choice of their free parameters. Most importantly, the number of floating point operations required to compute polynomial SFs introduced here is considerably lower than that of other state-of-the-art SFs, enabling their efficient implementation without the need of highly optimised code structures or caching, with speedups with respect to other state-of-the-art SFs reaching a factor of 4.5 to 5. This low-effort performance benefit substantially simplifies their use in new programs and emerging platforms such as graphical processing units. Overall, polynomial SFs with compact support improve accuracy of both, energy and force predictions with HDNNPs while enabling significant speedups compared to their well-established counterparts.},

keywords = {P12, pre-TACO},

pubstate = {published},

tppubtype = {article}

}

### 2020

Wohlfahrt, Oliver; Dellago, Christoph; Sega, Marcello

Journal ArticleOpen AccessIn: The Journal of Chemical Physics, vol. 153, no. 14, pp. 144710, 2020.

Abstract | Links | BibTeX | Tags: P12, pre-TACO

@article{Wohlfahrt2020,

title = {Ab initio structure and thermodynamics of the RPBE-D3 water/vapor interface by neural-network molecular dynamics},

author = {Oliver Wohlfahrt and Christoph Dellago and Marcello Sega},

doi = {10.1063/5.0021852},

year = {2020},

date = {2020-10-14},

urldate = {2020-10-14},

journal = {The Journal of Chemical Physics},

volume = {153},

number = {14},

pages = {144710},

publisher = {AIP Publishing},

abstract = {Aided by a neural network representation of the density functional theory potential energy landscape of water in the Revised Perdew–Burke–Ernzerhof approximation corrected for dispersion, we calculate several structural and thermodynamic properties of its liquid/vapor interface. The neural network speed allows us to bridge the size and time scale gaps required to sample the properties of water along its liquid/vapor coexistence line with unprecedented precision.},

keywords = {P12, pre-TACO},

pubstate = {published},

tppubtype = {article}

}

### 2019

Michl, Jakob; Sega, Marcello; Dellago, Christoph

Phase stability of the ice XVII-based CO_{2} chiral hydrate from molecular dynamics simulations

In: The Journal of Chemical Physics, vol. 151, no. 10, pp. 104502, 2019.

Abstract | Links | BibTeX | Tags: P12, pre-TACO

@article{Michl2019,

title = {Phase stability of the ice XVII-based CO_{2} chiral hydrate from molecular dynamics simulations},

author = {Jakob Michl and Marcello Sega and Christoph Dellago},

doi = {10.1063/1.5116540},

year = {2019},

date = {2019-09-12},

urldate = {2019-09-12},

journal = {The Journal of Chemical Physics},

volume = {151},

number = {10},

pages = {104502},

publisher = {AIP Publishing},

abstract = {We computed the phase diagram of CO_{2} hydrates at high pressure (HP), from 0.3 to 20 kbar, by means of molecular dynamics simulations. The two CO_{2} hydrates known to occur in this pressure range are the cubic structure I (sI) clathrate and the HP hydrate, whose water framework is the recently discovered ice XVII. We investigated the stability of both hydrates upon heating (melting) as well as the phase changes upon compression. The CO_{2}-filled ice XVII is found to be more stable than the sI clathrate and than the mixture of ice VI and dry ice at pressure values ranging from 6 to 18 kbar and in a wide temperature range, although a phenomenological correction suggests that the stability should more realistically range from 6.5 to 13.5 kbar. Our simulation results support the current hypothesis that the HP hydrate is stable at temperatures above the melting curve of ice VI.},

keywords = {P12, pre-TACO},

pubstate = {published},

tppubtype = {article}

}

_{2}hydrates at high pressure (HP), from 0.3 to 20 kbar, by means of molecular dynamics simulations. The two CO

_{2}hydrates known to occur in this pressure range are the cubic structure I (sI) clathrate and the HP hydrate, whose water framework is the recently discovered ice XVII. We investigated the stability of both hydrates upon heating (melting) as well as the phase changes upon compression. The CO

_{2}-filled ice XVII is found to be more stable than the sI clathrate and than the mixture of ice VI and dry ice at pressure values ranging from 6 to 18 kbar and in a wide temperature range, although a phenomenological correction suggests that the stability should more realistically range from 6.5 to 13.5 kbar. Our simulation results support the current hypothesis that the HP hydrate is stable at temperatures above the melting curve of ice VI.