### Abstract

Using conservation of energy-a fundamental property of closed classical and quantum mechanical systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol-1 for energies and 1 kcal mol-1 Å-1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods. 2017

Original language | English |
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Article number | e1603015 |

Journal | Science advances |

Volume | 3 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2017 May 1 |

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### ASJC Scopus subject areas

- Medicine(all)

### Cite this

*Science advances*,

*3*(5), [e1603015]. https://doi.org/10.1126/sciadv.1603015

**Machine learning of accurate energy-conserving molecular force fields.** / Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.; Poltavsky, Igor; Schütt, Kristof T.; Muller, Klaus.

Research output: Contribution to journal › Article

*Science advances*, vol. 3, no. 5, e1603015. https://doi.org/10.1126/sciadv.1603015

}

TY - JOUR

T1 - Machine learning of accurate energy-conserving molecular force fields

AU - Chmiela, Stefan

AU - Tkatchenko, Alexandre

AU - Sauceda, Huziel E.

AU - Poltavsky, Igor

AU - Schütt, Kristof T.

AU - Muller, Klaus

PY - 2017/5/1

Y1 - 2017/5/1

N2 - Using conservation of energy-a fundamental property of closed classical and quantum mechanical systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol-1 for energies and 1 kcal mol-1 Å-1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods. 2017

AB - Using conservation of energy-a fundamental property of closed classical and quantum mechanical systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol-1 for energies and 1 kcal mol-1 Å-1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods. 2017

UR - http://www.scopus.com/inward/record.url?scp=85041381183&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041381183&partnerID=8YFLogxK

U2 - 10.1126/sciadv.1603015

DO - 10.1126/sciadv.1603015

M3 - Article

AN - SCOPUS:85041381183

VL - 3

JO - Science advances

JF - Science advances

SN - 2375-2548

IS - 5

M1 - e1603015

ER -