Atom-Density Representations for Machine Learning

The applications of machine learning techniques to chemistry and materials science become more numerous by the day. The main challenge is to devise representations of atomic systems that are at the same time complete and concise, so as to reduce the number of reference calculations that are needed to predict the properties of different types of materials reliably. This has led to a proliferation of alternative ways to convert an atomic structure into an input for a machine-learning model. We introduce an abstract definition of chemical environments that is based on a smoothed atomic density, using a bra-ket notation to emphasize basis set independence and to highlight the connections with some popular choices of representations for describing atomic systems. The correlations between the spatial distribution of atoms and their chemical identities are computed as inner products between these feature kets, which can be given an explicit representation in terms of the expansion of the atom density on orthogonal basis functions, that is equivalent to the smooth overlap of atomic positions (SOAP) power spectrum, but also in real space, corresponding to $n$-body correlations of the atom density. This formalism lays the foundations for a more systematic tuning of the behavior of the representations, by introducing operators that represent the correlations between structure, composition, and the target properties. It provides a unifying picture of recent developments in the field and indicates a way forward towards more effective and computationally affordable machine-learning schemes for molecules and materials

Feature Optimization for Atomistic Machine Learning Yields A Data-Driven Construction of the Periodic Table of the Elements

Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes it possible to improve the accuracy of the model for a given amount of reference data. When using a description of the structures that is transparent and well-principled, optimizing the representation might reveal insights into the chemistry of the data set. Here we show how one can generalize the SOAP kernel to introduce a distance-dependent weight that accounts for the multi-scale nature of the interactions, and a description of correlations between chemical species. We show that this improves substantially the performance of ML models of molecular and materials stability, while making it easier to work with complex, multi-component systems and to extend SOAP to coarse-grained intermolecular potentials. The element correlations that give the best performing model show striking similarities with the conventional periodic table of the elements, providing an inspiring example of how machine learning can rediscover, and generalize, intuitive concepts that constitute the foundations of chemistry.Comment: 9 pages, 4 figure

Loadcell supports for a dynamic force plate

An apparatus was developed to accurately measure components of force along three mutually perpendicular axes, torque, and the center of pressure imposed by the foot of a subject walking over its surface. The data obtained were used to supplement high-speed motion picture and electromyographic (EMG) data for in-depth studies of normal or abnormal human gait. Significant features of the design (in particular, the mechanisms used to support the loadcell transducers) are described. Results of the development program and typical data obtained with the device are presented and discussed

An analysis of etchant effects on penetrant performance

Etching welds prior to penetrant inspection for greater crack detectio

Study of expandable, terminal decelerators for Mars atmosphere entry, volume I Final summary report, Dec. 1965 - Oct. 1966

Expandable terminal decelerators studied for use in Mars atmosphere entr

Study of expandable, terminal decelerators for Mars atmosphere entry Interim summary report, Dec. 1965 - Jun. 1966

Design of expandable terminal decelerators for Mars atmosphere entry by Mars-lander capsul

T-28 data acquisition during COHMEX 1986

As part of the 1986 Cooperative Huntsville Meteorological Experiment (COHMEX) a cloud physics instrumented T-28 aircraft was used in conjunction with multiple ground based Doppler radars to characterize hydrometeors and updraft structure within developing summertime cumulus and cumulonimbus cloud systems near Huntsville, Alabama. Instrumentation aboard the aircraft included a Particle Measuring Systems (PMS) Forward Scattering Spectrometer Probe (FSSP), a PMS 2D Cloud Probe and a PMS 2D Precipitation Probe, as well as a hail spectrometer and a foil impactor. Hydrometeor spectra were obtained in the interior of mature thunderstorms over the size range from cloud droplets through hailstones. In addition, vertical wind speed, temperature, Johnson-Williams (JW) liquid water content and electric field measurements were made. Significant microphysical differences exist between these clouds and summertime cumulonimbus clouds which develop over the Central Plains. One notable difference in clouds displaying similar radar reflectivities is that COHMEX hydrometeors are typically smaller and more numerous than those observed in the Central Plains. The COHMEX cloud microphysical measurements represent ground truth values for the remote sensing instrumentation which was flown over the cloud tops at altitudes between 60,000 and 70,000 ft aboard NASA U-2 and ER-2 aircraft. They are also being used jointly with a numerical cloud model to assist in understanding the development of summertime subtropical clouds