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At least 289 records · Page 16

Application of an efficient generator-coordinate subspace-selection algorithm to neutrinoless double- β decay

The generator coordinate method begins with the variational construction of a set of nonorthogonal mean-field states that span a subspace of the full many-body Hilbert space. These states are then often projected onto states with good quantum numbers to restore symmetries, leading to a set with members that can be similar to one another, and it is sometimes possible to reduce this set without greatly affecting results. Here, we propose a greedy algorithm that we call the energy-transition-orthogonality procedure (ENTROP) to select subsets of important states. As applied here, the approach selects on the basis of diagonal energy, orthogonality, and contribution to the matrix element that governs neutrinoless double-β decay. We present both shell-model and preliminary ab initio calculations of this matrix element for the decay of 76Ge, with quadrupole deformation parameters and the isoscalar pairing strength as generator coordinates. ENTROP converges quickly, reducing significantly the number of basis states needed for an accurate calculation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Evaluating Deception Detection Model Robustness To Linguistic Variation

With the increasing use of automated, machine learning-driven tools and the downstream impact that algorithmic judgements can have, it is critical to develop models that are robust to evolving or manipulated inputs. Evaluating the reliability of multimodal models across linguistic variations to understand model susceptibility to intentional linguistic adversarial attacks as well as natural linguistic variations is essential in this pursuit. We present extensive analysis of model robustness and susceptibility to linguistic variations in the setting of deceptive news detection, a difficult classification task that is an increasingly important problem to solve with the impact of misinformation spread online. We evaluate the effectiveness of incorporating adversarial defense strategies and measure model susceptibility to state-of-the-art adversarial attacks using two types of linguistic attacks — character and word perturbations. We consider two multiclass prediction tasks — a 3-way classification of tweets as trustworthy, propaganda, or disinformation; and a 4-way classification as clickbait, hoax, satire, or conspiracy — and compare the performance of three embeddings that have been state-of-the-art for several NLP tasks — GloVe, ELMo, and BERT — to highlight consistent trends in susceptibility, high confidence misclassifications, and high impact failures. We find that character or mixed ensemble models are the most effective defense mechanisms and that character perturbations are a more effective attack than word perturbations for deception classification.

adversarial evaluation↗

Joint Inversion of Body Wave Arrival Times, Surface Wave Dispersion Data and Receiver Functions: Method and Application to South China

In this work, we have developed a new joint inversion method that incorporates body wave arrival times, surface wave dispersion and receiver functions to simultaneously update earthquake locations and constrain three-dimensional P-wave (Vp) and S-wave velocity (Vs) models. Due to complementary sensitivities of the three types of data, the proposed joint inversion algorithm can reduce the intrinsic non-uniqueness of inversions using fewer types of data and better determine smooth velocity variations and velocity discontinuities. Synthetic tests demonstrate the advantages of this new joint inversion algorithm in resolving velocity structures, especially in constraining velocity gradients across the Moho interface. We have applied the proposed joint inversion algorithm to image the lithosphere velocity structure of south China. The inverted Vp and Vs models fit body wave arrival times, surface wave dispersion and receiver functions well. We further analyzed the distribution of Vs gradients across the Moho interface in detail, which helps us better understand tectonics in south China.

58 GEOSCIENCES↗

Development and Validation of Quantitative Model-Based Image Reconstruction for NDE of Reinforced Steel-Lined Concrete Structures: Kal-El FY 2020

This project studied the capabilities of Model-Based Image Reconstruction (MBIR) and Machine Learning (ML) algorithms in the imaging and estimation of rebar corrosion from ultrasound signals. The application was challenging due to the introduction of a steel liner between the sensor and the concrete containing the rebar. The study focused in a synthetic specimen with a 6.35 mm thick steel liner, and a 19.05 mm diameter rebar at a depth of 44.5 mm and with four levels of corrosion; 0%, 20%, 50%, and 100% corrosion level. The corrosion was applied uniformly around the rebar, generating a ring in the perimeter of the rebar with different acoustic density. In order to generate a realistic synthetic dataset, we added random texture to the concrete of the synthetic specimens. This texture will mimic the variations encountered in real concrete specimens.We adapted our MBIR algorithm for the application and enhanced the algorithm to integrate in the physical model known specimen features, such as the steel liner thickness. The new MBIR method was able to cancel out reverberation from the steel liner and properly image the rebar. In particular, corrosion for the 50% and 100% cases were easily visible and quantitative metrics showed a slight separation for the 0% and 20% levels. The quantitative results were in agreement with the qualitative assessment. We also developed a ML XGBoost model to estimate corrosion level from the ultrasound signals. By combining the ML method with MBIR, we can pinpoint in the ultrasound signals the section that corresponds to the echoes from the rebar. The extract signals are processed by the XGBoost model for prediction. From each system scan, we obtain 15 predictions. The median prediction value is used as the final prediction. The True Acceptance Rate for the method is over 99%.

36 MATERIALS SCIENCE↗

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

MAD using INRAD and Radiography [Slides]

We have previously evaluated Intrinsic Radiation Detection Algorithms from vendors for the Department of Homeland Security. These algorithms have limited spectra capability due to both the relatively low spectral content of the signal due to the use of PVT in the Radiation Portal detectors as well as relatively simple algorithms which are based on energy windowing and other simple algorithms to perform classification of Special Nuclear Material. Current detection algorithms are suceptible to nuissance alarms due to Naturally Occuring Radiation (NORM) and variations in background suppression. In this work, we propose to fuse the intrinsic radiation and radiographic data in conjunction with well-established machine learning algorithms to developed enhanced Threat Object detection capability.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Variational design principles for nonequilibrium colloidal assembly

Using large deviation theory and principles of stochastic optimal control, we show that rare molecular dynamics trajectories conditioned on assembling a specific target structure encode a set of interactions and external forces that lead to enhanced stability of that structure. Such a relationship can be formulated into a variational principle, for which we have developed an associated optimization algorithm and have used it to determine optimal forces for targeted self-assembly within nonequilibrium steady-states. We illustrate this perspective on inverse design in a model of colloidal cluster assembly within linear shear flow. We find that colloidal clusters can be assembled with high yield using specific short-range interactions of tunable complexity. Shear decreases the yields of rigid clusters, while small values of shear increase the yields of nonrigid clusters. The enhancement or suppression of the yield due to shear is rationalized with a generalized linear response theory. Furthermore, by studying 21 unique clusters made of six, seven, or eight particles, we uncover basic design principles for targeted assembly out of equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

KilonovaNet : Surrogate models of kilonova spectra with conditional variational autoencoders

ABSTRACT Detailed radiative transfer simulations of kilonova spectra play an essential role in multimessenger astrophysics. Using the simulation results in parameter inference studies requires building a surrogate model from the simulation outputs to use in algorithms requiring sampling. In this work, we present kilonovanet, an implementation of conditional variational autoencoders (cVAEs) for the construction of surrogate models of kilonova spectra. This method can be trained on spectra directly, removing overhead time of pre-processing spectra, and greatly speeds up parameter inference time. We build surrogate models of three state-of-the-art kilonova simulation data sets and present in-depth surrogate error evaluation methods, which can in general be applied to any surrogate construction method. By creating synthetic photometric observations from the spectral surrogate, we perform parameter inference for the observed light-curve data of GW170817 and compare the results with previous analyses. Given the speed with which kilonovanet performs during parameter inference, it will serve as a useful tool in future gravitational wave observing runs to quickly analyse potential kilonova candidates.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Attack-resilient algorithms and testbed federation for wide-area protection and control in smart grid

Today’s energy infrastructure is undergoing a massive transformation across all generation, transmission, and distribution systems to provide reliability, efficiency, and sustainability to the power system network. During the past 10 years, there has been a remarkable enhancement in developing close-loop wide-area protection and control (WAPAC) applications, such as automatic generation control (AGC), wide-area protection scheme (WAPS), synchrophasor-based wide-area voltage control system (WAVCS), etc., in the energy management system (EMS) to provide an adequate situational awareness to control center operators during physical disturbances and natural events. The rapid digitalization, unencrypted communication, and numerous data-sharing devices have increased digital access points that have exposed the grid network to countless cyberattacks pertinent to the WAPAC cybersecurity. Given the amount of complex grid network coupled with legacy infrastructures, it is untrustworthy to completely rely on information technology (IT)-based conventional security measures to defend against evolving cyberattacks. Hence, there is a compelling need to go beyond the traditional paradigm of ‘security by obscurity’ and ‘bolt-on’ security measures, and develop a suite of innovative security solutions at multiple layers to transform the current “fault-resilient” grid into “fault and attack-resilient” grid of the future. This dissertation specifically focuses on developing application-specific attack-resilient solutions for critical WAPAC applications in the smart grid. The first part of the study, Attack-Resilient Wide-Area Protection Scheme, presents a cyber-physical attack-resilient system (CPARS) for WAPS, where two anomaly detection methods are proposed to detect multi-level cyberattacks followed by the rules-based intrusion mitigation system (RIMS) to initiate effective mitigation strategies, tailored to these attacks, to restore the normal grid operation after disturbances. The first anomaly detection component, Machine learning-based Anomaly Detection for Centralized WAPS, discusses a novel architecture and methodology for developing a machine-learning-based anomaly detection system (ADS) for the centralized wide-area protection system (CWAPS) by applying the variational mode decomposition (VMD) technique and decision tree (DT) algorithms using cyber logs and synchrophasor measurements. The second component, Multi-Agent-based Anomaly Detection for Decentralized WAPS, presents a two-level hierarchical multi-agent-based decentralized WAPS against the system-aware stealthy cyber-attacks. Finally, for the RIMS, the state transition diagram-based mitigation measures are defined based on the grid operation states and experimental testing and evaluation are presented in a cyber-physical testbed environment. The second part of the study, Attack-Resilient Wide-Area Voltage Control System, addresses the existing vulnerabilities in the wide-area voltage control system (WAVCS), presents the methodology for performing an impact analysis during data integrity attacks, and proposes a data-driven attackresilient system (DARS) by incorporating machine learning-based ADS and rules-based anomaly mitigation system (RAMS) to detect these attacks and provide necessary mitigation actions to maintain the transient voltage stability after disturbances. Finally, the third part, Networked Federation Testbed (NEFTSec) for Smart Grid Cybersecurity, focuses on developing an interconnected federated testbed through a common network like the internet, describes its conceptual architectures, and also presents its design components for experimental testing, validation, and evaluation. Further, it presents the co-simulation interface algorithm (CIA) to facilitate the geographically-dispersed real-time distributed simulation (GD-RTDS) during the cyber-physical federation. In general, this dissertation presents innovative attack-resilient solutions for WAPAC applications that are experimentally tested and evaluated using the PowerCyber testbed and NEFTSec platform to accelerate the transition of state-of-the-art research works to the real-field deployments.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Evaluation of global terrestrial evapotranspiration using state-of-the-art approaches in remote sensing, machine learning and land surface modeling

Abstract. Evapotranspiration (ET) is critical in linking global water, carbon and energy cycles. However, direct measurement of global terrestrial ET is not feasible. Here, we first reviewed the basic theory and state-of-the-art approaches for estimating global terrestrial ET, including remote-sensing-based physical models, machine-learning algorithms and land surface models (LSMs). We then utilized 4 remote-sensing-based physical models, 2 machine-learning algorithms and 14 LSMs to analyze the spatial and temporal variations in global terrestrial ET. The results showed that the ensemble means of annual global terrestrial ET estimated by these three categories of approaches agreed well, with values ranging from 589.6 mm yr-1 (6.56×104 km3 yr-1) to 617.1 mm yr-1 (6.87×10 4 km3 yr -1 ). For the period from 1982 to 2011, both the ensembles of remote-sensing-based physical models and machine-learning algorithms suggested increasing trends in global terrestrial ET (0.62 mm yr -2 with a significance level of p<0.05 and 0.38 mm yr -2 with a significance level of p<0.05, respectively). In contrast, the ensemble mean of the LSMs showed no statistically significant change (0.23 mm yr -2 , p>0.05), although many of the individual LSMs reproduced an increasing trend. Nevertheless, all 20 models used in this study showed that anthropogenic Earth greening had a positive role in increasing terrestrial ET. The concurrent small interannual variability, i.e., relative stability, found in all estimates of global terrestrial ET, suggests that a potential planetary boundary exists in regulating global terrestrial ET, with the value of this boundary being around 600 mm yr -1 . Uncertainties among approaches were identified in specific regions, particularly in the Amazon Basin and arid/semiarid regions. Improvements in parameterizing water stress and canopy dynamics, the utilization of new available satellite retrievals and deep-learning methods, and model–data fusion will advance our predictive understanding of global terrestrial ET.

58 GEOSCIENCES↗

Assessing VQLS for Fluid Dynamics on a Hybrid Quantum-HPC Stack

Recent advances in quantum linear solvers offer a promising direction for accelerating extreme scientific computations such as fluid dynamics. However, the deep and complex circuits required by many quantum algorithms limit their practical use on current quantum hardware. The Variational Quantum Linear Solver (VQLS) presents a viable alternative for near-term quantum devices (NISQ), and initial efforts have explored its application to select fluid dynamics problems. In this work, we evaluate the use of VQLS for canonical fluid dynamics problems, aiming to identify pathways for generalizing its implementation across a broader class of systems. We analyze the impact of various circuit ansatz and classical optimizers on solution quality and convergence behavior. Furthermore, we assess the algorithm's feasibility within a hybrid quantum–high-performance computing (HPC) framework by porting it to QFw, a state-of-the-art quantum-HPC software stack. 11This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US DOE under Contract No. DE-AC05-00OR22725.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗

Predicting Intensive Care Unit Length of Stay and Mortality Using Patient Vital Signs: Machine Learning Model Development and Validation

Background: Patient monitoring is vital in all stages of care. In particular, intensive care unit (ICU) patient monitoring has the potential to reduce complications and morbidity, and to increase the quality of care by enabling hospitals to deliver higher-quality, cost-effective patient care, and improve the quality of medical services in the ICU. Objective: We here report the development and validation of ICU length of stay and mortality prediction models. The models will be used in an intelligent ICU patient monitoring module of an Intelligent Remote Patient Monitoring (IRPM) framework that monitors the health status of patients, and generates timely alerts, maneuver guidance, or reports when adverse medical conditions are predicted. Methods: We utilized the publicly available Medical Information Mart for Intensive Care (MIMIC) database to extract ICU stay data for adult patients to build two prediction models: one for mortality prediction and another for ICU length of stay. For the mortality model, we applied six commonly used machine learning (ML) binary classification algorithms for predicting the discharge status (survived or not). For the length of stay model, we applied the same six ML algorithms for binary classification using the median patient population ICU stay of 2.64 days. For the regression-based classification, we used two ML algorithms for predicting the number of days. We built two variations of each prediction model: one using 12 baseline demographic and vital sign features, and the other based on our proposed quantiles approach, in which we use 21 extra features engineered from the baseline vital sign features, including their modified means, standard deviations, and quantile percentages. Results: We could perform predictive modeling with minimal features while maintaining reasonable performance using the quantiles approach. The best accuracy achieved in the mortality model was approximately 89% using the random forest algorithm. The highest accuracy achieved in the length of stay model, based on the population median ICU stay (2.64 days), was approximately 65% using the random forest algorithm. Conclusions: The novelty in our approach is that we built models to predict ICU length of stay and mortality with reasonable accuracy based on a combination of ML and the quantiles approach that utilizes only vital signs available from the patient’s profile without the need to use any external features. This approach is based on feature engineering of the vital signs by including their modified means, standard deviations, and quantile percentages of the original features, which provided a richer dataset to achieve better predictive power in our models.

59 BASIC BIOLOGICAL SCIENCES↗

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of H2 and Li2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quantum computing, variational quantum solver, cou↗

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗

Calibrating uncertain parameters in melt pool simulations of additive manufacturing

Melt pool scale numerical modeling of additive manufacturing (AM) processes can provide predictive capabilities and theoretical insight into the process-property-structure-performance relationships for AM parts. Despite capabilities of numerical models to solve complex multi-physics problems, it is often important to consider a tradeoff between detailed physics and computational cost. Therefore, sources of uncertainty in both experimental conditions and the parameters needed for modeling require models to be validated against empirical evidence. Here, a method is proposed to calibrate uncertain parameters used in continuum-scale melt pool models for powder bed fusion (PBF) AM. Both a simplified heat transfer model and a heat transfer and fluid flow model were investigated. A surrogate model and Markov chain-based optimization algorithm calibrated melt pool geometry for models within experimental variation of the target melt pool width and depth from the NIST AM-Bench 2018-02 dataset. The melt pool temperature distributions, solidification parameters, and simulated multi-layer solidification microstructures were compared between the two models. Similar results from both models indicate that calibrated, lower fidelity numerical models may be used in place of higher fidelity models to generate melt pool solidification data. Finally, these calibrated models therefore enable lower computational cost melt pool simulations without a noticeable decrease in simulation accuracy for grain-scale microstructure simulations.

36 MATERIALS SCIENCE↗

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Remote Sensing of Tundra Ecosystems Using High Spectral Resolution Reflectance: Opportunities and Challenges

Abstract Observing the environment in the vast regions of Earth through remote sensing platforms provides the tools to measure ecological dynamics. The Arctic tundra biome, one of the largest inaccessible terrestrial biomes on Earth, requires remote sensing across multiple spatial and temporal scales, from towers to satellites, particularly those equipped for imaging spectroscopy (IS). We describe a rationale for using IS derived from advances in our understanding of Arctic tundra vegetation communities and their interaction with the environment. To best leverage ongoing and forthcoming IS resources, including National Aeronautics and Space Administration’s Surface Biology and Geology mission, we identify a series of opportunities and challenges based on intrinsic spectral dimensionality analysis and a review of current data and literature that illustrates the unique attributes of the Arctic tundra biome. These opportunities and challenges include thematic vegetation mapping, complicated by low‐stature plants and very fine‐scale surface composition heterogeneity; development of scalable algorithms for retrieval of canopy and leaf traits; nuanced variation in vegetation growth and composition that complicates detection of long‐term trends; and rapid phenological changes across brief growing seasons that may go undetected due to low revisit frequency or be obscured by snow cover and clouds. We recommend improvements to future field campaigns and satellite missions, advocating for research that combines multi‐scale spectroscopy, from lab studies to satellites that enable frequent and continuous long‐term monitoring, to inform statistical and biophysical approaches to model vegetation dynamics.

54 ENVIRONMENTAL SCIENCES↗

Unsupervised machine learning for unbiased chemical classification in X-ray absorption spectroscopy and X-ray emission spectroscopy

Here we report a comprehensive computational study of unsupervised machine learning for extraction of chemically relevant information in X-ray absorption near edge structure (XANES) and in valence-to-core X-ray emission spectra (VtC-XES) for classification of a broad ensemble of sulphorganic molecules. By progressively decreasing the constraining assumptions of the unsupervised machine learning algorithm, moving from principal component analysis (PCA) to a variational autoencoder (VAE) to t-distributed stochastic neighbour embedding (t-SNE), we find improved sensitivity to steadily more refined chemical information. Surprisingly, when embedding the ensemble of spectra in merely two dimensions, t-SNE distinguishes not just oxidation state and general sulphur bonding environment but also the aromaticity of the bonding radical group with 87% accuracy as well as identifying even finer details in electronic structure within aromatic or aliphatic sub-classes. We find that the chemical information in XANES and VtC-XES is very similar in character and content, although they unexpectedly have different sensitivity within a given molecular class. We also discuss likely benefits from further effort with unsupervised machine learning and from the interplay between supervised and unsupervised machine learning for X-ray spectroscopies. Our overall results, i.e., the ability to reliably classify without user bias and to discover unexpected chemical signatures for XANES and VtC-XES, likely generalize to other systems as well as to other one-dimensional chemical spectroscopies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗