sGDML: Constructing Accurate and Data Efficient Molecular Force Fields Using Machine Learning

We present an optimized implementation of the recently proposed symmetric gradient domain machine learning (sGDML) model. The sGDML model is able to faithfully reproduce global potential energy surfaces (PES) for molecules with a few dozen atoms from a limited number of user-provided reference molecular conformations and the associated atomic forces. Here, we introduce a Python software package to reconstruct and evaluate custom sGDML force fields (FFs), without requiring in-depth knowledge about the details of the model. A user-friendly command-line interface offers assistance through the complete process of model creation, in an effort to make this novel machine learning approach accessible to broad practitioners. Our paper serves as a documentation, but also includes a practical application example of how to reconstruct and use a PBE0+MBD FF for paracetamol. Finally, we show how to interface sGDML with the FF simulation engines ASE (Larsen et al., J. Phys. Condens. Matter 29, 273002 (2017)) and i-PI (Kapil et al., Comput. Phys. Commun. 236, 214-223 (2019)) to run numerical experiments, including structure optimization, classical and path integral molecular dynamics and nudged elastic band calculations

Molecular Force Fields with Gradient-Domain Machine Learning: Construction and Application to Dynamics of Small Molecules with Coupled Cluster Forces

We present the construction of molecular force fields for small molecules (less than 25 atoms) using the recently developed symmetrized gradient-domain machine learning (sGDML) approach [Chmiela et al., Nat. Commun. 9, 3887 (2018); Sci. Adv. 3, e1603015 (2017)]. This approach is able to accurately reconstruct complex high-dimensional potential-energy surfaces from just a few 100s of molecular conformations extracted from ab initio molecular dynamics trajectories. The data efficiency of the sGDML approach implies that atomic forces for these conformations can be computed with high-level wavefunction-based approaches, such as the "gold standard" CCSD(T) method. We demonstrate that the flexible nature of the sGDML model recovers local and non-local electronic interactions (e.g. H-bonding, proton transfer, lone pairs, changes in hybridization states, steric repulsion and $n\to\pi^*$ interactions) without imposing any restriction on the nature of interatomic potentials. The analysis of sGDML molecular dynamics trajectories yields new qualitative insights into dynamics and spectroscopy of small molecules close to spectroscopic accuracy

By-passing the Kohn-Sham equations with machine learning

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to astrophysics. Machine learning holds the promise of learning the kinetic energy functional via examples, by-passing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing either larger systems or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. Both improved accuracy and lower computational cost with this method are demonstrated by reproducing DFT energies for a range of molecular geometries generated during molecular dynamics simulations. Moreover, the methodology could be applied directly to quantum chemical calculations, allowing construction of density functionals of quantum-chemical accuracy

SchNet: A continuous-filter convolutional neural network for modeling quantum interactions

Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential physical information, that would get lost if discretized. Thus, we propose to use continuous-filter convolutional layers to be able to model local correlations without requiring the data to lie on a grid. We apply those layers in SchNet: a novel deep learning architecture modeling quantum interactions in molecules. We obtain a joint model for the total energy and interatomic forces that follows fundamental quantum-chemical principles. This includes rotationally invariant energy predictions and a smooth, differentiable potential energy surface. Our architecture achieves state-of-the-art performance for benchmarks of equilibrium molecules and molecular dynamics trajectories. Finally, we introduce a more challenging benchmark with chemical and structural variations that suggests the path for further work

Ethnopädagogik. Ein propädeutischer Grundriss

Die Kenntnis der Erziehungspraxis einer Gesellschaft bietet immer eine besonders günstige Möglichkeit, nicht nur tiefere Einblicke in Struktur und Aufbau ihrer Kultur, sondern auch ein besseres Verständnis für die Menschen selbst, für ihre Probleme, Stärken und Schwächen zu gewinnen; sie besitzt einen schlechterdings optimalen Erkenntniswert für die Ethnologie. (DIPF/Orig.

Der sechste Sinn: Ethnologische Studien zu Phänomenen der außersinnlichen Wahrnehmung

Paranormale Erfahrungen wie Hellsehen, Telepathie, Geisterkontakte, Nahtodeserlebnisse und Präkognition sind seit alters bekannt und dokumentiert. In prämodernen, "traditionellen" Kulturen bildeten sie eine Selbstverständlichkeit. Das Buch geht den gängigsten Phänomenen nach und versucht auf ethnologischer Grundlage, kombiniert mit parapsychologischen und neueren naturwissenschaftlichen (physikalischen) Erkenntnissen, eine Erklärung dafür zu geben. Der Essay eröffnet durch seine interdisziplinäre Fundierung und seinen Materialreichtum faszinierende Einsichten in ein zugleich altes wie auch aktuelles Thema und regt zum Nach- und Weiterdenken über den "sechsten Sinn" an

Der sechste Sinn

Paranormale Erfahrungen wie Hellsehen, Telepathie, Geisterkontakte, Nahtodeserlebnisse und Präkognition sind seit alters bekannt und dokumentiert. In prämodernen, »traditionellen« Kulturen bildeten sie eine Selbstverständlichkeit. Das Buch geht den gängigsten Phänomenen nach und versucht auf ethnologischer Grundlage, kombiniert mit parapsychologischen und neueren naturwissenschaftlichen (physikalischen) Erkenntnissen, eine Erklärung dafür zu geben. Der Essay eröffnet durch seine interdisziplinäre Fundierung und seinen Materialreichtum faszinierende Einsichten in ein zugleich altes wie auch aktuelles Thema und regt zum Nach- und Weiterdenken über den »sechsten Sinn« an

Spinon excitations in the XX chain: spectra, transition rates, observability

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and periodic boundary conditions. Exact product formulas for the transition rates derived via Bethe ansatz are used to calculate asymptotic expressions of the 2-spinon and 4-spinon parts (for large even N) as well as of the 1-spinon and 3-spinon parts (for large odd N) of the dynamic spin structure factors. The observability of these spectral contributions is assessed for finite and infinite N.Comment: 19 pages, 10 figure

Towards Exact Molecular Dynamics Simulations with Machine-Learned Force Fields

Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as good as the underlying interatomic potential. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. Here we enable the direct construction of flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model in an automatic data-driven way. The developed sGDML approach faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged molecular dynamics simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations