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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Improving Prediction of Surface Solar Irradiance Variability by Integrating Observed Cloud Characteristics and Machine Learning

A 5-year, 1-minute resolution observational dataset of clouds and solar radiation was produced that includes two metrics of the variability in surface solar irradiance due to cloud type and fractional sky cover. Multiple regression models were trained to fit observations of surface solar irradiance variability from those two cloud property predictors. We found that ensemble tree-based methods, Random Forest and Gradient Boosting Machine, have the least overfitting issues and showed the best performance with an R2 of 0.42. While the observational data trained in this study was only from one site, the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site in Oklahoma, initial comparisons of the seasonality of the statistics suggest that these results are relatively weather regime independent; the generality of such a finding across sites will be tested in future work. The observational data and developed machine learning model are being used to create a numerical weather prediction model parameterization to enable day-ahead solar variability prediction in a computationally efficient way. This is a first step towards creating a new paradigm of predicting day-ahead variability with the potential to provide a new tool to improve grid operation, planning, and resilience.

Riihimaki, Laura↗
DOE OSTI2014

In silico prediction of toxicity of non-congeneric industrial chemicals using ensemble learning based modeling approaches

Ensemble learning approach based decision treeboost (DTB) and decision tree forest (DTF) models are introduced in order to establish quantitative structure–toxicity relationship (QSTR) for the prediction of toxicity of 1450 diverse chemicals. Eight non-quantum mechanical molecular descriptors were derived. Structural diversity of the chemicals was evaluated using Tanimoto similarity index. Stochastic gradient boosting and bagging algorithms supplemented DTB and DTF models were constructed for classification and function optimization problems using the toxicity end-point in T. pyriformis. Special attention was drawn to prediction ability and robustness of the models, investigated both in external and 10-fold cross validation processes. In complete data, optimal DTB and DTF models rendered accuracies of 98.90%, 98.83% in two-category and 98.14%, 98.14% in four-category toxicity classifications. Both the models further yielded classification accuracies of 100% in external toxicity data of T. pyriformis. The constructed regression models (DTB and DTF) using five descriptors yielded correlation coefficients (R{sup 2}) of 0.945, 0.944 between the measured and predicted toxicities with mean squared errors (MSEs) of 0.059, and 0.064 in complete T. pyriformis data. The T. pyriformis regression models (DTB and DTF) applied to the external toxicity data sets yielded R{sup 2} and MSE values of 0.637, 0.655; 0.534, 0.507 (marine bacteria) and 0.741, 0.691; 0.155, 0.173 (algae). The results suggest for wide applicability of the inter-species models in predicting toxicity of new chemicals for regulatory purposes. These approaches provide useful strategy and robust tools in the screening of ecotoxicological risk or environmental hazard potential of chemicals. - Graphical abstract: Importance of input variables in DTB and DTF classification models for (a) two-category, and (b) four-category toxicity intervals in T. pyriformis data. Generalization and predictive abilities of the constructed (c) DTB and (d) DTF regression models to predict the T. pyriformis toxicity of diverse chemicals. - Highlights: • Ensemble learning (EL) based models constructed for toxicity prediction of chemicals • Predictive models used a few simple non-quantum mechanical molecular descriptors. • EL-based DTB/DTF models successfully discriminated toxic and non-toxic chemicals. • DTB/DTF regression models precisely predicted toxicity of chemicals in multi-species. • Proposed EL based models can be used as tool to predict toxicity of new chemicals.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Toward Machine Learning-Driven Mass Spectrometric Identification of Trichothecenes in the Absence of Standard Reference Materials

While a significant body of work exists on the detection of commonly known trichothecene toxins, biological, environmental, and other transformational processes can generate many under-characterized and unknown modified trichothecenes. Lacking both analytical reference standards and associated mass spectral databases, identification of these modified compounds reflects both a challenge and a critical gap from forensic and public health perspectives. Here we report here the application of machine learning (ML) techniques toward identification of discriminative fragment ions from mass spectrometric data that can be exploited to detect evidence of type A and B trichothecenes. The goal of this work is to establish a new method for the identification of unknown, though structurally similar trichothecenes, by leveraging objective ML techniques. Discriminative fragments derived from a series of gradient-boosted machine learners are then used to develop ML-driven precursor ion scan (PIS) methods on a triple quadrupole mass spectrometer (QQQ) for screening of “unknown unknown” trichothecenes. Specifically, we apply the PIS method to a laboratory-synthesized trichothecene, a first step in demonstrating the power of alternative, machine learning-driven mass spectrometric methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Evaluating Material Design Principles for Calcium-Ion Mobility in Intercalation Cathodes

Multivalent-ion batteries offer an alternative to Li-based technologies, with the potential for greater sustainability, improved safety, and higher energy density, primarily due to their rechargeable system featuring a passivating metal anode. Although a system based on the Ca 2+ /Ca couple is particularly attractive given the low electrochemical plating potential of Ca 2+ , the remaining challenge for a viable rechargeable Ca battery is to identify Ca cathodes with fast ion transport. In this work, a high-throughput computational pipeline is adapted to (1) discover novel Ca cathodes in a largely unexplored space of empty intercalation hosts and (2) develop material design rules for Ca-ion mobility. One candidate from the screening, W 2 O 3 (PO 4 ) 2 , is confirmed to have a low Nudged Elastic Band (NEB) barrier of 168 meV within a one-dimensional (1D) ion percolation topology. This candidate is subsequently synthesized and electrochemically tested, achieving reversible Ca cycling with a capacity of 25 mA h/g. To further accelerate the screening for promising Ca intercalation electrodes, machine learning (ML) Random Forest (RF) and Extreme Gradient Boosting (XGB) classification models are created with local environment descriptors based on a large, structurally and chemically diverse dataset of minimum energy pathways, spanning over 5,000 density functional theory (DFT) site energy calculations. Accuracies of 92% are achieved, material design metrics are quantified, ML force-fields are leveraged in an accelerated iteration of the screening, and a total of 27 novel Ca cathode materials are highlighted for further investigation.

25 ENERGY STORAGE↗
DOE OSTI2020

Operation and Optimization of Microwave-Heated Continuous-Flow Microfluidics

Microwave (MW) technology can be powerful for electrification and process intensification but limited fundamental understanding of scalability and design principles hinders its effective use. In this work, we build a continuous-flow microreactor inside a commercial single-mode MW applicator and the corresponding computational fluid dynamics model to simulate the temperature profile. The model is in good agreement with experiments for various microreactor dimensions and operating conditions. The model indicates that MW heating is greatly influenced by reactor geometry as well as the operating parameters. We observe a strong correlation between parameters and develop a gradient boost regression tree model to predict the outlet temperature accurately. This model is then applied to optimize the dimensions and operating conditions to maximize the outlet temperature and energy efficiency, resulting in a Pareto optimal. We demonstrate computationally and experimentally that it is possible to surpass the Pareto optimal and achieve an energy efficiency of ~90% or greater at temperatures relevant for liquid-phase chemistry via salting of the solvent. The present methodology can be applied to other complex MW reactors. Lastly, the combined numerical and experimental approach provides insights into and a framework for scale-up and optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Improving Data and Prediction Quality of High-Throughput Perovskite Synthesis with Model Fusion

Combinatorial fusion analysis (CFA) is an approach for combining multiple scoring systems using the rank-score characteristic function and cognitive diversity measure. One example is to combine diverse machine learning models to achieve better prediction quality. In this work, we apply CFA to the synthesis of metal halide perovskites containing organic ammonium cations via inverse temperature crystallization. Using a data set generated by high-throughput experimentation, four individual models (support vector machines, random forests, weighted logistic classifier, and gradient boosted trees) were developed. We characterize each of these scoring systems and explore 66 possible combinations of the models. When measured by the precision on predicting crystal formation, the majority of the combination models improves the individual model results. The best combination models outperform the best individual models by 3.9 percentage points in precision. In addition to improving prediction quality, we demonstrate how the fusion models can be used to identify mislabeled input data and address issues of data quality. In particular, we identify example cases where all single models and all fusion models do not give the correct prediction. Experimental replication of these syntheses reveals that these compositions are sensitive to modest temperature variations across the different locations of the heating element that can hinder or enhance the crystallization process. In summary, we demonstrate that model fusion using CFA can not only identify a previously unconsidered influence on reaction outcome but also be used as a form of quality control for high-throughput experimentation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Comparison of Machine Learning Approaches for Prediction of the Equivalent Alkane Carbon Number for Microemulsions Based on Molecular Properties

The chemical properties of oils are vital in the design of microemulsion systems. The hydrophilic–lipophilic difference equation used to predict microemulsions’ phase behavior expresses the oils’ physiochemical properties as the equivalent alkane carbon number (EACN). The experimental determination of EACN requires knowledge of the temperature dependence of the microemulsion system and the effects of different surfactant concentrations. Thus, the experimental determination is time-intensive and tedious, requiring days to months for proper separations. Furthermore, the experiments require high purity of chemicals because microemulsions are sensitive to impurities. Our work focuses on the quick and reliable predictions of the EACN with machine learning (ML) models. Due to the immaturity of ML chemical predictions, we compare three graph neural networks (GNNs) and a gradient-boosted tree algorithm, known as XGBoost. The GNNs use the molecular structures represented as simplified molecular-input line-entry system (SMILES) codes for the initial input, which allows us to assess whether geometry optimization is necessary for reliable results. The XGBoost model also begins with the SMILES representations of the molecules but uses molecular descriptors instead of geometry optimizations. As a result, the best model tested (crystal graph convolutional neural network with Merck molecular force field-94) has an error of 1.15 EACN units of the true EACN for unknown data with the errors skewed toward zero and an R² score of 0.9

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

PySIDT: Subgraph Isomorphic Decision Trees for Molecular Property Prediction

Accurate molecular property prediction is important across all fields of chemistry. Deep neural networks (DNNs) have become increasingly popular due to their ability to train automatically, avoiding the incredibly tedious process of constructing and extending traditional property estimation schemes. However, DNNs require large amounts of training data, are challenging to interpret, require large amounts of memory to load even during inference, and have severe difficulties incorporating qualitative chemical knowledge, which are often desired for molecular property prediction tasks. Here, in this study, we present PySIDT (https://github.com/zadorlab/PySIDT), a software for training and running inference on Subgraph Isomorphic Decision Trees (SIDTs). SIDTs are graph-based decision trees made of nodes associated with molecular substructures. Inference is done by descending target molecular structures down the decision tree to nodes with matching subgraph isomorphic substructures and making predictions based on the final (most specific) nodes matched. SIDTs scale down well to dataset sizes much smaller than is feasible for DNNs. As trees of molecular substructures, SIDTs are inherently readable and easy to visualize, making them easy to analyze. They are also straightforward to extend and retrain, facilitate uncertainty estimation, and enable easy integration of expert knowledge. We demonstrate the SIDT approach discussing its application to a diverse range of molecular prediction tasks: rate coefficient estimation, diffusion coefficient estimation, thermochemistry estimation, transition state bond stretch prediction, p K a prediction, stability of molecular structures, stability of surface structures, and prediction of surface lateral interaction energetics. Additionally, we demonstrate the power of the SIDT algorithms in two direct learning curve vanilla comparisons with the popular DNN-based software Chemprop and the popular gradient boosted trees-based software XGBoost on enthalpy of formation and rate coefficient prediction tasks. In particular, in the enthalpy of formation case, vanilla PySIDT is able to outperform vanilla Chemprop and XGBoost across the full range of training/validation set sizes out to 11,560 data points.

Johnson, Matthew Sean [Sandia National Laboratorie↗
DOE OSTI2020

Coupling High-Throughput Experiments and Regression Algorithms to Optimize PGM-Free ORR Electrocatalyst Synthesis

Over the past decades, significant improvement has been achieved in the performance of platinum group metal-free (PGM-free) materials as an alternative to Pt-based electrocatalysts for oxygen reduction reaction (ORR). However, further progress in ORR activity requires evaluation of precursors and synthesis approaches. In response to this challenge, we generated a first of its kind experimental data set of 36 samples using high-throughput synthesis and activity measurements. Several control parameters (e.g., Fe precursor identity, the precursor content, and pyrolysis temperature) were varied. We then developed several state-of-the-art machine learning (ML) based regression models to predict ORR activity, dependent on selected synthesis variables. Through an iterative algorithm, higher prediction accuracy (smaller root-mean-square error) was achieved. We identified that gradient boosting regression (GBR) and support vector regression (SVR), among several methods, work best for this data set. Aided by our ML-based surrogate models, we decided to alter catalyst synthesis conditions, which resulted in a 36% increase in measured ORR activity in comparison to the maximum ORR mass activity value of 21.9 A/g catalyst in the original data set. Overall, this combined experiment and machine learning approach represents a promising path forward toward developing highly efficient next-generation ORR electrocatalysts and, more generally, functional materials.

25 ENERGY STORAGE↗
DOE OSTI2023

Large Destabilization of (TiVNb)-Based Hydrides via (Al, Mo) Addition: Insights from Experiments and Data-Driven Models

High-entropy alloys (HEAs) represent an interesting alloying strategy that can yield exceptional performance properties needed across a variety of technology applications, including hydrogen storage. Examples include ultrahigh volumetric capacity materials (BCC alloys → FCC dihydrides) with improved thermodynamics relative to conventional high-capacity metal hydrides (like MgH 2 ), but still further destabilization is needed to reduce operating temperature and increase system-level capacity. Here, in this work, we demonstrate efficient hydride destabilization strategies by synthesizing two new Al 0.05 (TiVNb) 0.95–x Mo x (x = 0.05, 0.10) compositions. We specifically evaluate the effect of molybdenum (Mo) addition on the phase structure, microstructure, hydrogen absorption, and desorption properties. Both alloys crystallize in a bcc structure with decreasing lattice parameters as the Mo content increases. The alloys can rapidly absorb hydrogen at 25 °C with capacities of 1.78 H/M (2.79 wt %) and 1.79 H/M (2.75 wt %) with increasing Mo content. Pressure-composition isotherms suggest a two-step reaction for hydrogen absorption to a final fcc dihydride phase. The experiments demonstrate that increasing Mo content results in a significant hydride destabilization, which is consistent with predictions from a gradient boosting tree data-driven model for metal hydride thermodynamics. Furthermore, improved desorption properties with increasing Mo content and reversibility were observed by in situ synchrotron X-ray diffraction, in situ neutron diffraction, and thermal desorption spectroscopy.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine Learning Correlation of Electron Micrographs and ToF-SIMS for the Analysis of Organic Biomarkers in Mudstone

The spatial distribution of organics in geological samples can be used to determine when and how these organics were incorporated into the host rock. Mass spectrometry (MS) imaging can rapidly collect a large amount of data, but ions produced are mixed without discrimination, resulting in complex mass spectra that can be difficult to interpret. Here, we apply unsupervised and supervised machine learning (ML) to help interpret spectra from time-of-flight-secondary ion mass spectrometry (ToF-SIMS) of an organic-carbon-rich mudstone of the Middle Jurassic of England (UK). It was previously shown that the presence of sterane molecular biomarkers in this sample can be detected via ToF-SIMS (Pasterski, M. J. et al., Astrobiology 2023, 23, 936). We use unsupervised ML on scanning electron microscopy–electron dispersive spectroscopy (SEM-EDS) measurements to define compositional categories based on differences in elemental abundances. We then test the ability of four ML algorithms─k-nearest neighbors (KNN), recursive partitioning and regressive trees (RPART), eXtreme gradient boost (XGBoost), and random forest (RF)─to classify the ToF-SIM spectra using (1) the categories assigned via SEM-EDS, (2) organic and inorganic labels assigned via SEM-EDS, and (3) the presence or absence of detectable steranes in ToF-SIMS spectra. In terms of predictive accuracy and balanced accuracy, KNN was the best performing model and RPART the worst. The feature importance, or the specific features of the ToF-SIM spectra used by the models to make classifications, cannot be determined for KNN, preventing posthoc model interpretation. Nevertheless, the feature importance extracted from the other models was useful for interpreting spectra. In conclusion, we determined that some of the organic ions used to classify biomarker containing spectra may be fragment ions derived from kerogen which is abundant in this mudstone sample.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Machine Learning Predicts the Timing and Shear Stress Evolution of Lab Earthquakes Using Active Seismic Monitoring of Fault Zone Processes

Abstract Machine learning (ML) techniques have become increasingly important in seismology and earthquake science. Lab‐based studies have used acoustic emission data to predict time‐to‐failure and stress state, and in a few cases, the same approach has been used for field data. However, the underlying physical mechanisms that allow lab earthquake prediction and seismic forecasting remain poorly resolved. Here, we address this knowledge gap by coupling active‐source seismic data, which probe asperity‐scale processes, with ML methods. We show that elastic waves passing through the lab fault zone contain information that can predict the full spectrum of labquakes from slow slip instabilities to highly aperiodic events. The ML methods utilize systematic changes in P‐wave amplitude and velocity to accurately predict the timing and shear stress during labquakes. The ML predictions improve in accuracy closer to fault failure, demonstrating that the predictive power of the ultrasonic signals improves as the fault approaches failure. Our results demonstrate that the relationship between the ultrasonic parameters and fault slip rate, and in turn, the systematically evolving real area of contact and asperity stiffness allow the gradient boosting algorithm to “learn” about the state of the fault and its proximity to failure. Broadly, our results demonstrate the utility of physics‐informed ML in forecasting the imminence of fault slip at the laboratory scale, which may have important implications for earthquake mechanics in nature.

58 GEOSCIENCES↗
DOE OSTI2020

Medium Energy Electron Flux in Earth's Outer Radiation Belt (MERLIN): A Machine Learning Model

The radiation belts of the Earth, filled with energetic electrons, comprise complex and dynamic systems that pose a significant threat to satellite operation. While various models of electron flux both for low and relativistic energies have been developed, the behavior of medium energy (120–600 keV) electrons, especially in the MEO region, remains poorly quantified. At these energies, electrons are driven by both convective and diffusive transport, and their prediction usually requires sophisticated 4D modeling codes. In this paper, we present an alternative approach using the Light Gradient Boosting (LightGBM) machine learning algorithm. The Medium Energy electRon fLux In Earth's outer radiatioN belt (MERLIN) model takes as input the satellite position, a combination of geomagnetic indices and solar wind parameters including the time history of velocity, and does not use persistence. MERLIN is trained on >15 years of the GPS electron flux data and tested on more than 1.5 years of measurements. Tenfold cross validation yields that the model predicts the MEO radiation environment well, both in terms of dynamics and amplitudes o f flux. Evaluation on the test set shows high correlation between the predicted and observed electron flux (0.8) and low values of absolute error. The MERLIN model can have wide space weather applications, providing information for the scientific community in the form of radiation belts reconstructions, as well as industry for satellite mission design, nowcast of the MEO environment, and surface charging analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Learning the Low Frequency Earthquake Activity on the Central San Andreas Fault

Abstract Low frequency earthquakes (LFEs) originating below the central San Andreas Fault are associated with slow‐slip beneath the seismogenic zone within the more ductile portion of the crust. Monitoring efforts over 15 years detected >1 million LFEs. We train a gradient boosted tree model using statistical features describing the seismic waveforms to estimate the hourly LFE event count. The burst‐like LFE behavior is reproduced, while lower amplitudes are predicted during the most active periods. The hourly event counts are up to 18% greater than the catalog. The ability to continuously monitor LFE activity provides insight to when geodetic measurements of slow slip are possible, without the need for developing a computational‐intensive template‐matching catalog. Similar waveform statistical features are found between detecting LFEs and tremors, which provides additional evidence tremors are composed of LFEs. The approach extracts information contained in continuous seismic waveforms that might benefit detecting precursory signals.

58 GEOSCIENCES↗
DOE OSTI2023

Machine Learning of Key Variables Impacting Extreme Precipitation in Various Regions of the Contiguous United States

Abstract Amplification in extreme precipitation intensity and frequency can cause severe flooding and impose significant social and economic consequences. Variations in extreme precipitation intensity, frequencies, and return periods can be attributed to many physical variables across spatial and temporal scales. Here we employ ensemble machine learning (ML) methods, namely random forest (RF), eXtreme Gradient Boosting (XGB), and artificial neural networks (ANN), to explore key contributing variables to monthly extreme precipitation intensity and frequency in six regions over the United States. We further establish emulators for return periods. Results show that the ML models for intensity perform better in regions with obvious seasonality (i.e., Northern Great Plains, Southern Great Plains, and West Coast) than the other three regions (Northeast, Southwest, and Rocky Mountains), while for frequency the models perform well for most regions. The Shapley additive explanation is used to help explain the relationships between extreme precipitation characteristics and identify top variables for RF and XGB. We find that latent heat flux, relative humidity, soil moisture, and large‐scale subsidence are key common variables across the regions for both monthly intensity and frequency, and their compound effects are non‐negligible. The developed ML models capture the probability and return period of extreme precipitation well for all regions and may be used for decision making (e.g., infrastructure planning and design).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Mapping Glacier Basal Sliding Applying Machine Learning

During the RESOLVE project (“High-resolution imaging in subsurface geophysics: development of a multi-instrument platform for interdisciplinary research”), continuous surface displacement and seismic array observations were obtained on Glacier d’Argentière in the French Alps for 35 days in May 2018. The data set is used to perform a detailed study of targeted processes within the highly dynamic cryospheric environment. In particular, the physical processes controlling glacial basal motion are poorly understood and remain challenging to observe directly. Especially in the Alpine region for temperate based glaciers where the ice rapidly responds to changing climatic conditions and thus, processes are strongly intermittent in time and heterogeneous in space. Spatially dense seismic and Global Positioning System (GPS) measurements are analyzed applying machine learning to gain insight into the processes controlling glacial motions of Glacier d’Argentière. Using multiple bandpass-filtered copies of the continuous seismic waveforms, we compute energy-based features, develop a matched field beamforming catalog and include meteorological observations. Features describing the data are analyzed with a gradient boosting decision tree model to directly estimate the GPS displacements from the seismic noise. We posit that features of the seismic noise provide direct access to the dominant parameters that drive displacement on the highly variable and unsteady surface of the glacier. The machine learning model infers daily fluctuations and longer term trends. The results show on-ice displacement rates are strongly modulated by activity at the base of the glacier. The techniques presented provide a new approach to study glacial basal sliding and discover its full complexity.

58 GEOSCIENCES↗
DOE OSTI2024

Prediction of the SYM-H Index Using a Bayesian Deep Learning Method With Uncertainty Quantification

We propose a novel deep learning framework, named SYMHnet, which employs a graph neural network and a bidirectional long short-term memory network to cooperatively learn patterns from solar wind and interplanetary magnetic field parameters for short-term forecasts of the SYM-H index based on 1- and 5-min resolution data. SYMHnet takes, as input, the time series of the parameters' values provided by NASA's Space Science Data Coordinated Archive and predicts, as output, the SYM-H index value at time point t + w hours for a given time point t where w is 1 or 2. By incorporating Bayesian inference into the learning framework, SYMHnet can quantify both aleatoric (data) uncertainty and epistemic (model) uncertainty when predicting future SYM-H indices. Experimental results show that SYMHnet works well at quiet time and storm time, for both 1- and 5-min resolution data. The results also show that SYMHnet generally performs better than related machine learning methods. For example, SYMHnet achieves a forecast skill score (FSS) of 0.343 compared to the FSS of 0.074 of a recent gradient boosting machine (GBM) method when predicting SYM-H indices (1 hr in advance) in a large storm (SYM-H = -393 nT) using 5-min resolution data. When predicting the SYM-H indices (2 hr in advance) in the large storm, SYMHnet achieves an FSS of 0.553 compared to the FSS of 0.087 of the GBM method. In addition, SYMHnet can provide results for both data and model uncertainty quantification, whereas the related methods cannot.

79 ASTRONOMY AND ASTROPHYSICS↗