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At least 703 records · Page 39

AUTONOMOUS GAUSSIAN DECOMPOSITION

We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗

Predictive Big Data Analytics: A Study of Parkinson’s Disease Using Large, Complex, Heterogeneous, Incongruent, Multi-Source and Incomplete Observations

Background A unique archive of Big Data on Parkinson’s Disease is collected, managed and disseminated by the Parkinson’s Progression Markers Initiative (PPMI). The integration of such complex and heterogeneous Big Data from multiple sources offers unparalleled opportunities to study the early stages of prevalent neurodegenerative processes, track their progression and quickly identify the efficacies of alternative treatments. Many previous human and animal studies have examined the relationship of Parkinson’s disease (PD) risk to trauma, genetics, environment, co-morbidities, or life style. The defining characteristics of Big Data–large size, incongruency, incompleteness, complexity, multiplicity of scales, and heterogeneity of information-generating sources–all pose challenges to the classical techniques for data management, processing, visualization and interpretation. We propose, implement, test and validate complementary model-based and model-free approaches for PD classification and prediction. To explore PD risk using Big Data methodology, we jointly processed complex PPMI imaging, genetics, clinical and demographic data. Methods and Findings Collective representation of the multi-source data facilitates the aggregation and harmonization of complex data elements. This enables joint modeling of the complete data, leading to the development of Big Data analytics, predictive synthesis, and statistical validation. Using heterogeneous PPMI data, we developed a comprehensive protocol for end-to-end data characterization, manipulation, processing, cleaning, analysis and validation. Specifically, we (i) introduce methods for rebalancing imbalanced cohorts, (ii) utilize a wide spectrum of classification methods to generate consistent and powerful phenotypic predictions, and (iii) generate reproducible machine-learning based classification that enables the reporting of model parameters and diagnostic forecasting based on new data. We evaluated several complementary model-based predictive approaches, which failed to generate accurate and reliable diagnostic predictions. However, the results of several machine-learning based classification methods indicated significant power to predict Parkinson’s disease in the PPMI subjects (consistent accuracy, sensitivity, and specificity exceeding 96%, confirmed using statistical n-fold cross-validation). Clinical (e.g., Unified Parkinson's Disease Rating Scale (UPDRS) scores), demographic (e.g., age), genetics (e.g., rs34637584, chr12), and derived neuroimaging biomarker (e.g., cerebellum shape index) data all contributed to the predictive analytics and diagnostic forecasting. Conclusions Model-free Big Data machine learning-based classification methods (e.g., adaptive boosting, support vector machines) can outperform model-based techniques in terms of predictive precision and reliability (e.g., forecasting patient diagnosis). We observed that statistical rebalancing of cohort sizes yields better discrimination of group differences, specifically for predictive analytics based on heterogeneous and incomplete PPMI data. UPDRS scores play a critical role in predicting diagnosis, which is expected based on the clinical definition of Parkinson’s disease. Even without longitudinal UPDRS data, however, the accuracy of model-free machine learning based classification is over 80%. The methods, software and protocols developed here are openly shared and can be employed to study other neurodegenerative disorders (e.g., Alzheimer’s, Huntington’s, amyotrophic lateral sclerosis), as well as for other predictive Big Data analytics applications.

Science & Technology - Other Topics↗

Machine Learning an Ab-Initio Based Bond-Order Potential for Bismuthene

Bismuthene is a heavy 2D material whose strong spin–orbit coupling and recently observed single-element ferroelectricity have intensified interest in its structural, vibrational, and transport properties. Accurate modeling of these behaviors requires a short-range interatomic potential that can reproduce the underlying bonding physics at a fraction of the computational cost of first-principles methods. However, such a potential is currently unavailable. Here, in this work, we construct a Tersoff bond-order potential for β-bismuthene using a reinforcement-learning framework that integrates a continuous Monte Carlo Tree Search with a simplex-based local optimizer. The optimized parameter sets reproduce first-principles lattice constants, cohesive energy, the equation of state, elastic constants, and phonon dispersion. We validate the models by performing thermal-conductivity calculations and uniaxial fracture simulations our findings confirm the reliability of the resulting models across multiple thermomechanical regimes. Comparison of the three best solutions reveals how differences in pairwise interactions, angular terms, and bond-order behavior govern phonon features and mechanical responses. We demonstrate an interpretable and computationally efficient potential for bismuthene and demonstrate a general reinforcement-learning strategy for developing bond-order models in emerging 2D materials.

deformation↗

Investigation of hydrometeorological influences on reservoir releases using explainable machine learning methods

Long short-term memory (LSTM) networks have demonstrated successful applications in accurately and efficiently predicting reservoir releases from hydrometeorological drivers including reservoir storage, inflow, precipitation, and temperature. However, due to its black-box nature and lack of process-based implementation, we are unsure whether LSTM makes good predictions for the right reasons. In this work, we use an explainable machine learning (ML) method, called SHapley Additive exPlanations (SHAP), to evaluate the variable importance and variable-wise temporal importance in the LSTM model prediction. In application to 30 reservoirs over the Upper Colorado River Basin, United States, we show that LSTM can accurately predict the reservoir releases with NSE ≥ 0.69 for all the considered reservoirs despite of their diverse storage sizes, functionality, elevations, etc. Additionally, SHAP indicates that storage and inflow are more influential than precipitation and temperature. Moreover, the storage and inflow show a relatively long-term influence on the release up to 7 days and this influence decreases as the lag time increases for most reservoirs. These findings from SHAP are consistent with our physical understanding. However, in a few reservoirs, SHAP gives some temporal importances that are difficult to interpret from a hydrological point of view, probably because of its ignorance of the variable interactions. SHAP is a useful tool for black-box ML model explanations, but the hydrological processes inferred from its results should be interpreted cautiously. More investigations of SHAP and its applications in hydrological modeling is needed and will be pursued in our future study.

54 ENVIRONMENTAL SCIENCES↗

Operator inference with roll outs for learning reduced models from scarce and low-quality data

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. Here, in this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.

97 MATHEMATICS AND COMPUTING↗

Machine Learning Framework for Characterizing Processing–Structure Relationship in Block Copolymer Thin Films

The morphology of block copolymers (BCPs) critically influences material properties and applications. This work introduces a machine learning (ML)-enabled, high-throughput framework for analyzing grazing incidence small-angle X-ray scattering (GISAXS) data and atomic force microscopy (AFM) images to characterize BCP thin film morphology. A convolutional neural network was trained to classify AFM images by surface features, achieving 97% testing accuracy. Classified images were then analyzed to extract 2D grain size measurements from the samples in a high-throughput manner. ML models were trained to predict domain orientation based on processing parameters such as solvent ratio, additive type, and additive ratio. GISAXS-based properties were predicted with strong performances (R 2 > 0.75), while AFM-based property predictions were less accurate (R 2 < 0.60), likely due to the localized nature of AFM measurements compared to the bulk information captured by GISAXS. Beyond model performance, interpretability was addressed using SHapley Additive exPlanations (SHAP). SHAP analysis revealed that the additive ratio had the largest impact on morphological predictions, where additive provides the BCP chains with increased volume to rearrange into thermodynamically favorable morphologies. This interpretability helps validate model predictions and offers insight into parameter importance. Altogether, the presented framework combining high-throughput characterization and interpretable ML offers an approach to exploring and optimizing BCP thin film morphology across a broad processing landscape.

36 MATERIALS SCIENCE↗

What drives the scatter of local star-forming galaxies in the BPT diagrams? A Machine Learning based analysis

ABSTRACT We investigate which physical properties are most predictive of the position of local star forming galaxies on the BPT diagrams, by means of different Machine Learning (ML) algorithms. Exploiting the large statistics from the Sloan Digital Sky Survey (SDSS), we define a framework in which the deviation of star-forming galaxies from their median sequence can be described in terms of the relative variations in a variety of observational parameters. We train artificial neural networks (ANN) and random forest (RF) trees to predict whether galaxies are offset above or below the sequence (via classification), and to estimate the exact magnitude of the offset itself (via regression). We find, with high significance, that parameters primarily associated to variations in the nitrogen-over-oxygen abundance ratio (N/O) are the most predictive for the [N ii]-BPT diagram, whereas properties related to star formation (like variations in SFR or EW(H α)) perform better in the [S ii]-BPT diagram. We interpret the former as a reflection of the N/O–O/H relationship for local galaxies, while the latter as primarily tracing the variation in the effective size of the S+ emitting region, which directly impacts the [S ii] emission lines. This analysis paves the way to assess to what extent the physics shaping local BPT diagrams is also responsible for the offsets seen in high redshift galaxies or, instead, whether a different framework or even different mechanisms need to be invoked.

79 ASTRONOMY AND ASTROPHYSICS↗

Learning from learning machines: improving the predictive power of energy-water-land nexus models with insights from complex measured and simulated data

Focal Area(s): Insights gleaned from complex data (observed and simulated) using AI; Predictive modeling through the use of AI techniques and AI-derived model components, including physics- and knowledge-informed models; Energy-water-land nexus and integrated energy systems – models of MultiSector dynamics. Science Challenge: Scientific communities are in need of tools for the computational integration of physics-based models, experimental data, and empirical/observational studies across a broad range of temporal and spatial scales to explore and meet EESSD grand challenges. We require AI algorithms for the discovery of process-drivers in the Earth-energy-human system and to link them with complex measured and simulated data. We aim to understand the energy-water-land nexus, particularly under extreme forcing scenarios and rare events, leveraging scale-aware AI process models, including probabilistic uncertainties, and benefiting from the emerging 5G-enabled landscape-scale sensing and edge computing capabilities. These models are needed to identify instabilities and tipping points that manifest extreme system behaviors with consequences for integrated energy systems and the environment. This work requires fundamental advances in uncertainty quantification, in particular, to identify and model unlikely but catastrophic outliers. Specifically, we need models that are interpretable to domain scientists and, essentially, explainable to public and private stake holders.

54 ENVIRONMENTAL SCIENCES↗

Los Alamos works on a biologically realistic computer network

Brain neuroscientists and computer scientists call this field neuromimetic computing—building computers inspired by how the cerebral cortex of the brain works. Its cortical processes rely on billions of small biological “switches,” called neurons. To learn, they store and process information. Using an approach called neural networks, researchers are developing computers that simulate neurons and their interconnections. Then computers can learn about their surroundings, interpret data, and make predictions based on it. In practice, however, researchers attempting to simulate neural processing at anything close to the scale and complexity of the brain’s cortical circuits have been stymied by limitations on computer memory and computational power. All that has changed with the new Trinity supercomputer at Los Alamos, which became fully operational in mid-2017. Trinity has unique capabilities designed for the stockpile stewardship mission, which includes highly complex nuclear simulations that have replaced the testing of nuclear weapons. All this capability means Trinity allows a fundamentally different approach to large-scale cortical simulations, enabling an unprecedented leap in the ability to model neural processing. To test that capability on a limited-scale problem, computer scientists and neuroscientists at Los Alamos created a “sparse prediction machine” that runs on a neural network on Trinity. A sparse prediction machine is designed to work like the brain: researchers expose it to data—in this case, various videos of a car driving down a road—without labeling the data in any way. Then the program sorts through that data frame by frame, focuses on the important information, and develops a prediction about the car’s motion. With Trinity’s power, the Los Alamos team simulates the way a brain handles information in its neurons but uses the fewest neurons at any given moment to explain the information at hand. That’s the “sparse” part, and it makes the brain very efficient—and, hopefully, a computer more efficient, too.

97 MATHEMATICS AND COMPUTING↗

High‐Resolution National‐Scale Water Modeling Is Enhanced by Multiscale Differentiable Physics‐Informed Machine Learning

Abstract The National Water Model (NWM) is a key tool for flood forecasting, planning, and water management. Key challenges facing the NWM include calibration and parameter regionalization when confronted with big data. We present two novel versions of high‐resolution (∼37 km 2 ) differentiable models (a type of hybrid model): one with implicit, unit‐hydrograph‐style routing and another with explicit Muskingum‐Cunge routing in the river network. The former predicts streamflow at basin outlets whereas the latter presents a discretized product that seamlessly covers rivers in the conterminous United States (CONUS). Both versions use neural networks to provide a multiscale parameterization and process‐based equations to provide a structural backbone, which were trained simultaneously (“end‐to‐end”) on 2,807 basins across the CONUS and evaluated on 4,997 basins. Both versions show great potential to elevate future NWM performance for extensively calibrated as well as ungauged sites: the median daily Nash‐Sutcliffe efficiency of all 4,997 basins is improved to around 0.68 from 0.48 of NWM3.0. As they resolve spatial heterogeneity, both versions greatly improved simulations in the western CONUS and also in the Prairie Pothole Region, a long‐standing modeling challenge. The Muskingum‐Cunge version further improved performance for basins >10,000 km 2 . Overall, our results show how neural‐network‐based parameterizations can improve NWM performance for providing operational flood predictions while maintaining interpretability and multivariate outputs. The modeling system supports the Basic Model Interface (BMI), which allows seamless integration with the next‐generation NWM. We also provide a CONUS‐scale hydrologic data set for further evaluation and use.

Song, Yalan [Civil and Environmental Engineering T↗

Paleo-Megadroughts and Abrupt Climate Changes in the Speleothem Records. Final report

This project is motivated by the speleothem isotope records in Asia, which show regional responses in the hydrologic cycle to different climate forcings. Speleothem isotopic records are typically interpreted in terms of local precipitation variations or monsoon intensity. Our study demonstrates that non-local processes also play an important role. We started this project to understand the regional difference in speleothem isotopic composition between the Last Glacial Maximum (LGM) and the present-day. The record in Southwest China showed greater depletion during the LGM compared to those in East China. Our modeling and analysis showed that speleothems record, in addition, large scale changes in atmospheric circulation and moisture transport and their subsequent impact on precipitation. We developed an algorithm to partition total precipitation according to their formation dynamics, namely into frontal and non-frontal precipitation, and showed that the two have different trends and hence different causal mechanism. We then focused our subsequent attention on circulation impacts on precipitation changes. We applied a machine learning algorithm to detect rainbands in the ERA-Interim reanalysis product, and showed that the seasonal migrations of the rainbands are tied to the seasonal migrations of the jet stream, in particular the northerlies of the jet meanders. These northerlies, in turn, are partly topographic Rossby waves excited as the upstream westerlies impinge on the Tibetan Plateau. The seasonal variations of these upstream westerlies thus contribute to the seasonal movements of the rainbands and regional precipitation changes. Our analysis of the modern precipitation isotope record further confirms the importance of jet stream changes in the isotopic variations and shows that isotope-enriched years have reduced summer seasonality, with less pronounced northward migration of the jet.

54 ENVIRONMENTAL SCIENCES↗

Cloud Fusion of Big Data and Multi-Physics Models using Machine Learning for Discovery, Exploration, and Development of Hidden Geothermal Resources

The primary goals of this project are identifying hidden geothermal resources in the USA and designing profitable enhanced geothermal systems (EGS). Many non-obvious processes and parameters could characterize geothermal resources and could control the ultimate energy potential of geothermal fields. Diverse datasets (e.g., geology, geochemistry, geophysics, satellite, airborne geophysics) are available to help characterize geothermal resources, but this data is sparse and multi-scale. This has hindered attempts to leverage the datasets for geothermal exploration and profitable EGS design. Recent advancements in machine learning (ML) give promise to overcome these issues. Modern ML methods and tools can (1) analyze large datasets, (2) assimilate model ensembles that include a multitude of inputs and outputs, (3) process sparse datasets, (4) perform transfer learning between sites with different data quality, (5) extract hidden geothermal signatures from field and simulation data, (6) label geothermal resources and processes, (7) identify high-value data acquisition targets, and (8) guide geothermal exploration and production by selecting optimal exploration, production, and drilling strategies. In this work, we implement ML-based geothermal exploration and an enhanced geothermal systems (EGS) design tool to achieve the above goals. Our exploration tool is GeoThermalCloud (GTC) EGS design tool is GeoDT-ML. GTC (github.com/SmartTensors/GeoThermalCloud.jl) utilizes a LANL unsupervised ML platform called SmartTensors (https://tensors.lanl.gov/) to automate data analyses and interpretations by extracting hidden signatures to identify geothermal prospects. It enables the identification of critical measurements needed to identify geothermal resource signatures. GeoDT-ML (github.com/SmartTensors/GeoThermalCloud.jl/tree/master/) adds coupling to GeoDT (https://github.com/GeoDesignTool/GeoDT.git) for stochastic EGS design optimization and performance prediction. GeoDT-ML leverages recent advances in deep learning and high-performance computing. Contributors to this effort include LANL, PNNL, Google, Stanford, and Julia Computing.

15 GEOTHERMAL ENERGY↗

Landscaper v1

Understanding the inner workings of machine learning models through their loss landscapes offers crucial insights into model properties, optimization dynamics, and generalizability. However, accessing these insights has traditionally required specialized mathematical expertise, limiting broader adoption. Landscaper is an open-source Python package designed to bridge this gap. Landscaper seamlessly integrates a suite of multi-dimensional loss landscape analyses with cutting-edge topological data analysis (TDA) methods. This powerful combination makes both fundamental loss landscape analysis and advanced TDA techniques accessible to the broader scientific ML community, without requiring deep pre-existing mathematical knowledge. Landscaper offers three key functionalities: * Construction: Builds detailed loss landscape representations through versatile low and high-dimensional sampling techniques. * Quantification: Applies advanced metrics, including a novel topological data analysis (TDA) based smoothness metric, enabling new perspectives on model behavior. * Visualization: Offers intuitive tools to visualize and interpret loss landscapes, providing actionable insights beyond traditional performance metrics.

Weber, Gunther [Lawrence Berkeley National Laborat↗

Discovering CO Adsorption and Desorption Pathways from Chemical Reaction Neural Network Modeling of Transient Kinetics Spectroscopy

Here, we demonstrate a data-driven approach to interpreting surface reactions by combining time-resolved gas pulsing infrared spectroscopy with chemical reaction neural networks (CRNNs). Using CO adsorption and desorption on Pd(111) at 460–490 K as a model system, we show how transient kinetic data can reveal detailed reaction mechanisms. Starting with a simple one-species model, we systematically evaluate increasingly complex mechanisms involving hollow and bridge site adsorption. Despite the similar goodness of fit to the same experimental absorbance data, our models predict distinct coverage dynamics for different adsorption sites. Through analysis of spectral peak stability and predicted dynamics, we identify a mechanism in which CO primarily adsorbs on bridge sites followed by rapid conversion to hollow sites as being the most physically consistent with experimental observations. This work provides a framework for extracting mechanistic insights from limited experimental data, demonstrating how machine learning can bridge the gap between transient kinetic measurements and a molecular-level understanding of surface reactions.

36 MATERIALS SCIENCE↗

Uncertain of uncertainties? A comparison of uncertainty quantification metrics for chemical data sets

Abstract With the increasingly more important role of machine learning (ML) models in chemical research, the need for putting a level of confidence to the model predictions naturally arises. Several methods for obtaining uncertainty estimates have been proposed in recent years but consensus on the evaluation of these have yet to be established and different studies on uncertainties generally uses different metrics to evaluate them. We compare three of the most popular validation metrics (Spearman’s rank correlation coefficient, the negative log likelihood (NLL) and the miscalibration area) to the error-based calibration introduced by Levi et al. ( Sensors 2022 , 22 , 5540). Importantly, metrics such as the negative log likelihood (NLL) and Spearman’s rank correlation coefficient bear little information in themselves. We therefore introduce reference values obtained through errors simulated directly from the uncertainty distribution. The different metrics target different properties and we show how to interpret them, but we generally find the best overall validation to be done based on the error-based calibration plot introduced by Levi et al. Finally, we illustrate the sensitivity of ranking-based methods (e.g. Spearman’s rank correlation coefficient) towards test set design by using the same toy model ferent test sets and obtaining vastly different metrics (0.05 vs. 0.65).

Rasmussen, Maria H.↗

Prediction of Dielectric Constant in Series of Polymers by Quantitative Structure-Property Relationship (QSPR)

This work is devoted to the investigation of dielectric permittivity which is influenced by electronic, ionic, and dipolar polarization mechanisms, contributing to the material’s capacity to store electrical energy. In this study, an extended dataset of 86 polymers was analyzed, and two quantitative structure–property relationship (QSPR) models were developed to predict dielectric permittivity. From an initial set of 1273 descriptors, the most relevant ones were selected using a genetic algorithm, and machine learning models were built using the Gradient Boosting Regressor (GBR). In contrast to Multiple Linear Regression (MLR)- and Partial Least Squares (PLS)-based models, the gradient boosting models excel in handling nonlinear relationships and multicollinearity, iteratively optimizing decision trees to improve accuracy without overfitting. The developed GBR models showed high R2 coefficients of 0.938 and 0.822, for the training and test sets, respectively. An Accumulated Local Effect (ALE) technique was applied to assess the relationship between the selected descriptors—eight for the GB_A model and six for the GB_B model, and their impact on target property. ALE analysis revealed that descriptors such as TDB09m had a strong positive effect on permittivity, while MLOGP2 showed a negative effect. These results highlight the effectiveness of the GBR approach in predicting the dielectric properties of polymers, offering improved accuracy and interpretability.

Ascencio-Medina, Estefania↗

Joint Modeling of Quasar Variability and Accretion Disk Reprocessing Using Latent Stochastic Differential Equations

Quasars are bright active galactic nuclei powered by the accretion of matter around supermassive black holes at the center of galaxies. Their stochastic brightness variability depends on the physical properties of the accretion disk and black hole. The upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to observe tens of millions of quasars, so there is a need for efficient techniques like machine learning that can handle the large volume of data. Quasar variability is believed to be driven by an X-ray corona, which is reprocessed by the accretion disk and emitted as UV/optical variability. We are the first to introduce an auto-differentiable simulation of the accretion disk and reprocessing. We use the simulation as a direct component of our neural network to jointly model the driving variability and reprocessing, trained with supervised learning on simulated LSST-like 10 yr quasar light curves. We encode the light curves using a transformer encoder, and the driving variability is reconstructed using latent stochastic differential equations, a physically motivated generative deep learning method that can model continuous-time stochastic dynamics. By embedding the physical processes of the driving signal and reprocessing into our network, we achieve a model that is more robust and interpretable. We demonstrate that our model outperforms a Gaussian process regression baseline and can infer accretion disk parameters and time delays between wave bands, even for out-of-distribution driving signals. Our approach provides a powerful framework that can be adapted to solve other inverse problems in multivariate time series.

Fagin, Joshua [City Univ. of New York (CUNY), NY (↗

A Confidence-Guided Technique for Tracking Time-Varying Features

Application scientists often employ feature tracking algorithms to capture the temporal evolution of various features in their simulation data. However, as the complexity of the scientific features is increasing with the advanced simulation modeling techniques, quantification of reliability of the feature tracking algorithms is becoming important. One of the desired requirements for any robust feature tracking algorithm is to estimate its confidence during each tracking step so that the results obtained can be interpreted without any ambiguity. To address this, we develop a confidence-guided feature tracking algorithm that allows reliable tracking of user-selected features and presents the tracking dynamics using a graph-based visualization along with the spatial visualization of the tracked feature. Here, the efficacy of the proposed method is demonstrated by applying it to two scientific datasets containing different types of time-varying features.

97 MATHEMATICS AND COMPUTING↗