Supplementary material to "Four-dimensional mesospheric and lower thermospheric wind fields using Gaussian process regression on multistatic specular meteor radar observations"

Author(s):  
Ryan Volz ◽  
Jorge L. Chau ◽  
Philip J. Erickson ◽  
Juha P. Vierinen ◽  
J. Miguel Urco ◽  
...  
2018 ◽  
Author(s):  
Gunter Stober ◽  
Jorge L. Chau ◽  
Juha Vierinen ◽  
Christoph Jacobi ◽  
Sven Wilhelm

2021 ◽  
Author(s):  
Ryan Volz ◽  
Jorge L. Chau ◽  
Philip J. Erickson ◽  
Juha P. Vierinen ◽  
J. Miguel Urco ◽  
...  

Abstract. Mesoscale dynamics in the mesosphere and lower thermosphere (MLT) region have been difficult to study from either ground- or satellite-based observations. For understanding of atmospheric coupling processes, important spatial scales at these altitudes range between tens to hundreds of kilometers in the horizontal plane. To date, this scale size is challenging observationally, and so structures are usually parameterized in global circulation models. The advent of multistatic specular meteor radar networks allows exploration of MLT mesocale dynamics on these scales using an increased number of detections and a diversity of viewing angles inherent to multistatic networks. In this work, we introduce a four dimensional wind field inversion method that makes use of Gaussian process regression (GPR), a non-parametric and Bayesian approach. The method takes measured projected wind velocities and prior distributions of the wind velocity as a function of space and time, specified by the user or estimated from the data, and produces posterior distributions for the wind velocity. Computation of the predictive posterior distribution is performed on sampled points of interest and is not necessarily regularly sampled. The main benefits of the GPR method include this non-gridded sampling, the built-in statistical uncertainty estimates, and the ability to horizontally-resolve winds on relatively small scales. The performance of the GPR implementation has been evaluated on Monte Carlo simulations with known distributions using the same spatial and temporal sampling as one day of real meteor measurements. Based on the simulation results we find that the GPR implementation is robust, providing wind fields that are statistically unbiased and with statistical variances that depend on the geometry and are proportional to the prior velocity variances. A conservative and fast approach can be straightforwardly implemented by employing overestimated prior variances and distances, while a more robust but computationally intensive approach can be implemented by employing training and fitting of model parameters. The latter GPR approach has been applied to a 24-hour data set and shown to compare well to previously used homogeneous and gradient methods. Small scale features have reasonably low statistical uncertainties, implying geophysical wind field horizontal structures as low as 20–50 km. We suggest that this GPR approach forms a suitable method for MLT regional and weather studies.


2021 ◽  
Vol 14 (11) ◽  
pp. 7199-7219
Author(s):  
Ryan Volz ◽  
Jorge L. Chau ◽  
Philip J. Erickson ◽  
Juha P. Vierinen ◽  
J. Miguel Urco ◽  
...  

Abstract. Mesoscale dynamics in the mesosphere and lower thermosphere (MLT) region have been difficult to study from either ground- or satellite-based observations. For understanding of atmospheric coupling processes, important spatial scales at these altitudes range between tens and hundreds of kilometers in the horizontal plane. To date, this scale size is challenging observationally, so structures are usually parameterized in global circulation models. The advent of multistatic specular meteor radar networks allows exploration of MLT mesoscale dynamics on these scales using an increased number of detections and a diversity of viewing angles inherent to multistatic networks. In this work, we introduce a four-dimensional wind field inversion method that makes use of Gaussian process regression (GPR), which is a nonparametric and Bayesian approach. The method takes measured projected wind velocities and prior distributions of the wind velocity as a function of space and time, specified by the user or estimated from the data, and produces posterior distributions for the wind velocity. Computation of the predictive posterior distribution is performed on sampled points of interest and is not necessarily regularly sampled. The main benefits of the GPR method include this non-gridded sampling, the built-in statistical uncertainty estimates, and the ability to horizontally resolve winds on relatively small scales. The performance of the GPR implementation has been evaluated on Monte Carlo simulations with known distributions using the same spatial and temporal sampling as 1 d of real meteor measurements. Based on the simulation results we find that the GPR implementation is robust, providing wind fields that are statistically unbiased with statistical variances that depend on the geometry and are proportional to the prior velocity variances. A conservative and fast approach can be straightforwardly implemented by employing overestimated prior variances and distances, while a more robust but computationally intensive approach can be implemented by employing training and fitting of model hyperparameters. The latter GPR approach has been applied to a 24 h dataset and shown to compare well to previously used homogeneous and gradient methods. Small-scale features have reasonably low statistical uncertainties, implying geophysical wind field horizontal structures as low as 20–50 km. We suggest that this GPR approach forms a suitable method for MLT regional and weather studies.


2020 ◽  
Author(s):  
Marc Philipp Bahlke ◽  
Natnael Mogos ◽  
Jonny Proppe ◽  
Carmen Herrmann

Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates (“error bars”) along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science.


2018 ◽  
Author(s):  
Caitlin C. Bannan ◽  
David Mobley ◽  
A. Geoff Skillman

<div>A variety of fields would benefit from accurate pK<sub>a</sub> predictions, especially drug design due to the affect a change in ionization state can have on a molecules physiochemical properties.</div><div>Participants in the recent SAMPL6 blind challenge were asked to submit predictions for microscopic and macroscopic pK<sub>a</sub>s of 24 drug like small molecules.</div><div>We recently built a general model for predicting pK<sub>a</sub>s using a Gaussian process regression trained using physical and chemical features of each ionizable group.</div><div>Our pipeline takes a molecular graph and uses the OpenEye Toolkits to calculate features describing the removal of a proton.</div><div>These features are fed into a Scikit-learn Gaussian process to predict microscopic pK<sub>a</sub>s which are then used to analytically determine macroscopic pK<sub>a</sub>s.</div><div>Our Gaussian process is trained on a set of 2,700 macroscopic pK<sub>a</sub>s from monoprotic and select diprotic molecules.</div><div>Here, we share our results for microscopic and macroscopic predictions in the SAMPL6 challenge.</div><div>Overall, we ranked in the middle of the pack compared to other participants, but our fairly good agreement with experiment is still promising considering the challenge molecules are chemically diverse and often polyprotic while our training set is predominately monoprotic.</div><div>Of particular importance to us when building this model was to include an uncertainty estimate based on the chemistry of the molecule that would reflect the likely accuracy of our prediction. </div><div>Our model reports large uncertainties for the molecules that appear to have chemistry outside our domain of applicability, along with good agreement in quantile-quantile plots, indicating it can predict its own accuracy.</div><div>The challenge highlighted a variety of means to improve our model, including adding more polyprotic molecules to our training set and more carefully considering what functional groups we do or do not identify as ionizable. </div>


2019 ◽  
Vol 150 (4) ◽  
pp. 041101 ◽  
Author(s):  
Iakov Polyak ◽  
Gareth W. Richings ◽  
Scott Habershon ◽  
Peter J. Knowles

Sign in / Sign up

Export Citation Format

Share Document