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At least 505 records · Page 28

Application of Data Science and Engineering

Metal additive manufacturing (AM) processes exhibit significant variability in the quality and properties of components that are produced. This variability has prevented the widespread adoption of AM in industry. The need for more advanced and descriptive process monitoring, part qualification, and process control has led to an increasing number of sensors on machines and subsequent data to analyze. Increasingly, data science principles are being leveraged in each of these domains in order to process this data and better understand the causes of variability and the corresponding quality inconsistencies that occur in additive manufacturing.

Halsey, William↗

Stochastic simulations of temporally and spatially variable Fe cycling within a floodplain aquifer

This data package contains model input and output files for local and global sensitivity analysis (SA) of a reactive transport model simulating redox cycling within a floodplain aquifer. The reaction network is implemented in CrunchFlow and focuses on spatially and temporally heterogeneous Fe cycling, though it contains several other species and redox pathways (37 aqueous species and 7 minerals in total). The package contains data from 600 Monte Carlo simulations (for global SA) and 104 one-at-a-time simulations (for local SA). It includes all input files required to run the CrunchFlow model, as well as limited model output – .csv files containing time series of primary species concentrations at 21 grid cells within the domain. These time series files contain the following species: H+, CO32-, SO42-, Cl-, Ca2+, Mg2+, Na+, K+, Fe(II), Fe(III), HS-, CH3COO-, O2(aq), S(aq), and Br-.These data were used to demonstrate the application of a novel form of global SA, distance-based generalized sensitivity analysis (DGSA) to a reactive transport model. The 2D model simulates the export of reduced species from pockets of fine-grained, organic-rich sediments embedded in a coarse sand aquifer. Stochastic simulations jointly varied 17 key model input parameters across several orders of magnitude, including the spatial variability of each parameter. DGSA on the model results reveal that the amplitude and variability of exported Fe(II) are most sensitive to the interaction between sand permeability and individual reaction rates. By contrast, the propagation of reducing conditions downgradient from the fine-grained lenses depends most heavily on the rate of dissolved organic carbon and sulfate release from the fines.

54 ENVIRONMENTAL SCIENCES↗

Attribution of the record-high 2023 SST using a deep-learning framework

Abstract The global-mean sea surface temperature (SST) reached a record high in 2023, exceeding the 2016 record by 0.14 °C. This unprecedented change in global-mean SST has major implications for our understanding of internal variability and the forced response in our changing climate. In this work, we use neural networks trained on simulated climate data to separate the contributions of internal variability and the forced response within observations. Performing attribution reveals that internal variability was responsible for +0.07 °C of the 2023 global mean SST, due to anomalously warm conditions in the Pacific, Atlantic, and Indian Ocean basins. Furthermore, these results provide a line of evidence for accelerated forced warming in recent years. Continued monitoring of the climate will be critical for understanding the drivers behind this unprecedented SST record.

Rader, Jamin K. (ORCID:0000000222045977)↗

Understanding the structural and morphological effects of synthesis route on NpO 2

The availability of actinide standard materials for use in nuclear safeguard applications is critical, as is thorough characterization thereof. Although accurate trace element compositions and isotopic considerations are paramount for deployment of reference standards, structural characterization is also essential towards accurately describing the chemical form and potential matrix effects in candidate materials. Here, to this end, samples of NpO 2 were synthesized via a direct denitration (DD) method and probed with powder X-ray diffraction (PXRD), Raman spectroscopy, and scanning electron microscopy (SEM) for structural and morphological characterization and comparison with NpO 2 materials produced via modified direct denitration (MDD). PXRD confirmed the bulk identity of NpO 2 , and no additional phases were identified using this method. Analysis of Raman data collected using a 532 nm excitation wavelength indicates that samples are mostly phase pure; however, some variability in spectral features is observed. Analysis of additional spectroscopic data collected with a 785 nm excitation wavelength revealed variability in the relative intensity of spectral features. Raman spectroscopy indicates that the sample is primarily NpO 2 ; however, additional signals indicate possible structural disorder, oxidized species, or potential contributions from other Np phases. To further investigate the possibility of additional phase contributions within the sample of NpO 2 , Raman spectroscopic mapping was employed to examine the homogeneity of the sample produced via DD. From this analysis, we determined that despite variability in the intensity of Raman-active vibrational modes, consistent spectra are obtained throughout the area of the sample investigated. SEM images show aggregates with variable sizes and shapes, with rounded, primary particles possessing an average diameter of approximately 100 nm. Comparison of the results of these multimodal analyses to the literature indicates that the crystal chemical, spectroscopic, and microstructural properties of NpO 2 vary based on synthesis method, even if X-ray diffraction data indicate that the bulk phase is NpO 2 .

Direct denitration↗

Multifidelity validation of digital surrogates using variable-density turbulent mixing models

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable-density (Atwood = 0.22), compressible turbulent mixing. Though models of this kind (Reynolds averaged NavierStokes and large-eddy simulations) have been validated extensively with more canonical flows in previous studies, here the present approach offers novelty in the complexity of the geometry, the ensemble-based validation, and the uniformity of the computational framework on which the models are tested. Moreover, all experimental and computational tasks were completed by the authors which has led to a tightly coupled experimental configuration with its “digital twin.” The experimental divergent-shock-tube facility and its data acquisition methods are described and replicated in simulation space. A 2D Euler model which neglects the turbulent mixing at the interface is optimized to experimental data using a Gaussian process. This model then serves as the basis for both the 2D RANS and 3D LES studies that make comparisons to the mixing-layer data from the experiment. A relatively simple RANS model is shown to produce good agreement with experimental data only at late flow development times. The LES ensembles generally show good agreement with experimental data but display sensitivity to the characterization of initial conditions. Resolution-dependent behavior is also observed for certain higher-order statistics of interest. Overall, the LES model successfully captures the effects of divergent geometry, compressibility, and combined nonlinear instabilities inherent to the problem. The successful prediction of mixing width and its growth rate highlight the existence of three distinct regimes in the development of the instability, each with similarities to previously studied instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Leveraging observed soil heterotrophic respiration fluxes as a novel constraint on global-scale models

Microbially-explicit models may improve understanding and projections of carbon dynamics in response to future climate change, but their fidelity in simulating global-scale soil heterotrophic respiration (RH), a stringent test for soil biogeochemical models, has never been evaluated. We used statistical global RH products, as well as 7,821 daily site-scale RH measurements, to evaluate the spatio-temporal performance of one first-order decay model (CASA-CNP) and two microbially-explicit biogeochemical models (CORPSE and MIMICS) that were forced by two different climate datasets. CORPSE and MIMICS did not provide any measurable performance improvement; instead, the models were highly sensitive to the meteorological input data used to drive them. Spatial RH variability was generally well simulated except in the northern middle latitudes (~50°N) and arid regions; models captured the seasonal variability of RH well, but showed more divergence in tropic and arctic regions. Our results demonstrate that the next generation of biogeochemical models shows promise, but also needs to be improved for realistic spatio-temporal variability of RH. Finally, we emphasize the importance of net primary production, soil moisture, and soil temperature inputs, and that jointly evaluating soil models for their spatial (global scale) and temporal (site scale) performance provides crucial benchmarks for improving biogeochemical models.

Jian, Jinshi↗

A Probabilistic Approach to Load Modeling for Central HVAC Systems in Large Commercial Buildings for Retrofit Decisions Under Uncertainty

Retrofitting central HVAC systems in large commercial buildings with advanced technologies like heat recovery chillers (HRCs) offers a significant opportunity to enhance energy efficiency. However, analyzing these retrofits is challenging with traditional whole-building simulation tools, which require intensive calibration and struggle to model innovative system configurations and controls. To overcome these limitations, this study proposes a load profilebased retrofit analysis framework that provides better decisions under uncertainty. The main focus of this paper is the development of a probabilistic load profile model that can be used in the framework by using exploratory data analysis (EDA) of measured building data to properly quantify its inherent variability. A non-parametric Gaussian Process (GP) model was employed to capture the time- and weather-dependent characteristics of the heating load while explicitly modeling its uncertainty. The model's effectiveness is demonstrated through strong predictive performance on unseen data and physically interpretable insights into load behavior. This data-driven, probabilistic load profile serves as a robust and flexible input for subsequent system simulations, enabling a more confident and statistically sound analysis of retrofit potential.

Ham, S W↗

Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events

This paper is the basis for a presentation help at the 2026 Georgia Tech Fault & Disturbance Analysis Conference, which can be found at OSTI # 3168287 Paper Abstract—Phasor Measurement Units (PMUs) stream time synchronized, high-resolution measurements from the grid, enabling data-driven techniques for event detection and classification. Accurate event classification improves grid reliability and stability. Events can be detected by varying numbers of PMUs and exhibit different durations depending on the event type. This variability challenges standard classifiers that require uniform input sizes. Moreover, multiple events may coincide, which increases classification complexity. Standard classifiers assign each instance to the class with the highest predicted probability, whereas overlapping events may exhibit comparable probabilities across multiple classes. In this study, to handle data size variability, we extract a wide range of time–frequency domain features from all available PMUs for each event into a fixed-length vector, facilitating the application of standard machine learning classifiers, including Random Forest, XGBoost, LightGBM, Support Vector Machine, and Multilayer Perceptron. To account for overlapping events, a probabilistic post-processing step is applied. For a given data instance, if multiple predicted class probabilities exceed 30% and the differences between them are less than 10%, the event is assigned to multiple classes. Experiments using real-world PMU data demonstrate that the Random Forest and XGBoost models achieve the highest accuracy, while the proposed post-processing method yields perfect classification performance on external unseen test sets.

Nematirad, Reza [Danovo Energy Solutions]↗

Duke Forest FACE (FACTS-I): Meteorological and Soil Data

This dataset, collected from Duke Forest Free Air CO2 Enrichment (FACE) – Forest-Atmosphere Carbon Transfer and Storage (FACTS-I) experiment, includes variables describing the meteorological conditions above canopy, within canopy, and soil depending on the variable. The Duke FACE experiment was located in a loblolly pine (Pinus taeda L.) plantation established in 1983. Naturally regenerated broadleaved species including sweetgum (Liquidambar styraciflua L.) and tulip poplar (Liriodendron tulipifera L.), mostly in the overstory, and winged elm (Ulmus alata Michx.) and red maple (Acer rubrum L.) were common in the understory. The FACE experiment commenced with two plots (plots 7-8) in 1994 (Oren et al. 2001), with six additional plots (plots 1-6) coming online on 27 August 1996. The CO2 enrichment was terminated on 31 October 2010 and post-enrichment data collection continued through 2012. Complete fertilization was applied annually to half of plots 7-8 from 1998 to 2004. The nutrient addition experiment expanded to half of plot 1-6 with a common protocol of N-fertilization in 2005. N-fertilization continued until 2012. The data range varied by sensor availability. A summary of information about variable name and data range can be found in the ‘FileDescription_[variable_name].txt’ files.

54 ENVIRONMENTAL SCIENCES↗

Simultaneous Millimeter-wave, Gamma-Ray, and Optical Monitoring of the Blazar PKS 2326-502 during a Flaring State

Including millimeter-wave data in multiwavelength studies of the variability of active galactic nuclei (AGN) can provide insights into AGN physics that are not easily accessible at other wavelengths. We demonstrate in this work the potential of cosmic microwave background (CMB) telescopes to provide long-term, high-cadence millimeter-wave AGN monitoring over large fractions of sky. We report on a pilot study using data from the SPTpol instrument on the South Pole Telescope (SPT), which was designed to observe the CMB at arcminute and larger angular scales. Between 2013 and 2016, SPTpol was used primarily to observe a single 500 deg2 field, covering the entire field several times per day with detectors sensitive to radiation in bands centered at 95 and 150 GHz. We use SPT 150 GHz observations to create AGN light curves, and we compare these millimeter-wave light curves to those at other wavelengths, in particular γ-ray and optical. In this Letter, we focus on a single source, PKS 2326-502, which has extensive, day-timescale monitoring data in gamma-ray, optical, and now millimeter-wave between 2013 and 2016. We find PKS 2326-502 to be in a flaring state in the first 2 yr of this monitoring, and we present a search for evidence of correlated variability between millimeter-wave, optical R-band, and γ-ray observations. This pilot study is paving the way for AGN monitoring with current and upcoming CMB experiments such as SPT-3G, Simons Observatory, and CMB-S4, including multiwavelength studies with facilities such as Vera C. Rubin Observatories Large Synoptic Survey Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

Perfecting Our Set of Spectrophotometric Standard DA White Dwarfs

We verified for photometric stability a set of DA white dwarfs with Hubble Space Telescope magnitudes from the near-ultraviolet to the near-infrared and ground-based spectroscopy by using time-spaced observations from the Las Cumbres Observatory network of telescopes. The initial list of 38 stars was whittled to 32 final ones, which comprise a high-quality set of spectrophotometric standards. These stars are homogeneously distributed around the sky and are all fainter than r ~ 16.5 mag. Their distribution is such that at least two of them would be available to be observed from any observatory on the ground at any time at airmass less than 2. Light curves and different variability indices from the Las Cumbres Observatory data were used to determine the stability of the candidate standards. When available, Pan-STARRS1, Zwicky Transient Facility, and TESS data were also used to confirm the star classification. Our analysis showed that four DA white dwarfs may exhibit evidence of photometric variability, while a fifth is cooler than our established lower temperature limit, and a sixth star might be a binary. In some instances, due to the presence of faint nearby red sources, care should be used when observing a few of the spectrophotometric standards with ground-based telescopes. Light curves and finding charts for all the stars are provided.

79 ASTRONOMY AND ASTROPHYSICS↗

Post-fire time series photos from five sites across the Oak Creek watershed, Washington

This dataset supports a broader study examining wildfire impacts on hydrologic connectivity across 5 sites within the Oak Creek watershed and the resulting biogeochemical impacts. Sites were selected using the Advanced Terrestrial Simulator (ATS) hydrologic model to identify locations with varying groundwater contributions and hydrologic responses across different burn severity scenarios. The Retreat Fire burned from July 23 to August 2, 2024, affecting all five sites. This dataset provides time series game camera photos, while the broader study includes continuous water quality monitoring, biogeochemical sampling of water and soils, precipitation data, and organic matter analysis. The other data types and additional metadata (include site environmental information) can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3018020. Because this study is ongoing, this data package will be updated regularly to include newly collected photos. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) file-level metadata; (2) data dictionary; (3) field metadata; (4) readme; (5) field protocol; and (6) folders of game camera photos. The game camera photos are organized by site with subfolders by month of collection. The field metadata contains a subset of the information collected that is most relevant to photo-processing. The full set of field metadata can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3018020. All files are .csv, .pdf, or .jpg.

Burn severity↗

Surface water nitrogen and sediment potential nitrate reduction rates, nutrient stocks, and stable isotopes from nine wetlands at the Tanglewood Biological Station, Alabama

This dataset supports a broader study investigating wetland hydrologic and biogeochemical responses to inundation disturbances. Bimonthly surface water and sediment sampling events were conducted at nine wetland sites situated within the Tanglewood Biological Station in Alabama from April 2023 to February 2024. The contents included in the data package include surface water nitrogen (nitrogen oxides and ammonium) and sediment potential nitrate reduction rates (measured as potential denitrification and dissimilatory nitrate reduction to ammonium processing), nutrient stocks (total carbon, total nitrogen, and organic matter), and stable isotopes (carbon and nitrogen). Water level data related to each wetland location can be found at https://data.ess-dive.lbl.gov/view/doi:10.15485/2530253 (Kirker et al., 2024) and related water geochemistry data can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3001967 (Forbes et al., 2025). In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) file-level metadata; (2) data dictionary; (3) field metadata and international generic sample numbers (IGSNs); (4) readme; (5) the field protocol; and (6) a subfolder with sample data. The sample data subfolder contains (1) sediment potential denitrification rate, (2) sediment potential dissimilatory nitrate reduction to ammonium (DNRA) rate, (3) sediment total carbon and nitrogen content, (4) sediment stable isotopes (delta nitrogen-15 and delta carbon-13), (5) sediment percent organic matter, (6) surface water nitrous oxides, (7) surface water ammonium, and (8) methods codes. All files are .csv or .pdf.

Ammonium↗

Soil nitrogen mineralization rates, nutrient stocks, stable isotopes, and water volumetric measurements across terrestrial-aquatic interfaces from three wetlands at the Tanglewood Biological Station, Alabama

This dataset supports a broader study investigating wetland hydrologic and biogeochemical responses to inundation events. Soil samples were collected across four sampling events along terrestrial-aquatic gradients at three wetland sites located within the Tanglewood Biological Station in Alabama from April 2024 to June 2025. The contents in this data package include soil in-situ nitrogen mineralization rates (measurements of net nitrification, net ammonification, and net mineralization), nutrient stocks (total carbon, total nitrogen, and organic matter), stable isotopes (carbon and nitrogen), and water volumetric measurements (water-filled pore space). Water level data related to each wetland location can be found at https://data.ess-dive.lbl.gov/view/doi:10.15485/2530253 (Kirker et al., 2024), related water geochemistry data can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3001967 (Forbes et al., 2025), and related surface water sediment chemistry data can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/3377325 (Molina Serpas et al., 2026). In addition to this readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) file-level metadata; (2) data dictionary; (3) field metadata and international generic sample numbers (IGSNs); (4) readme; (5) the field protocol; and (6) a subfolder with sample data. The sample data subfolder contains (1) net nitrification rate, (2) net ammonification rate, (3) areal net mineralization rate, (4) percent organic matter, (5) water-filled pore space, (6) total carbon content, (7) total nitrogen content, (8) stable carbon isotope (delta carbon-13), and (9) stable nitrogen isotope (delta nitrogen-15), and (10) methods codes. All files are .csv or .pdf.

13-C↗

Automatic Search of Cataclysmic Variables Based on LightGBM in LAMOST-DR7

The search for special and rare celestial objects has always played an important role in astronomy. Cataclysmic Variables (CVs) are special and rare binary systems with accretion disks. Most CVs are in the quiescent period, and their spectra have the emission lines of Balmer series, HeI, and HeII. A few CVs in the outburst period have the absorption lines of Balmer series. Owing to the scarcity of numbers, expanding the spectral data of CVs is of positive significance for studying the formation of accretion disks and the evolution of binary star system models. At present, the research for astronomical spectra has entered the era of Big Data. The Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST) has produced more than tens of millions of spectral data. the latest released LAMOST-DR7 includes 10.6 million low-resolution spectral data in 4926 sky regions, providing ideal data support for searching CV candidates. To process and analyze the massive amounts of spectral data, this study employed the Light Gradient Boosting Machine (LightGBM) algorithm, which is based on the ensemble tree model to automatically conduct the search in LAMOST-DR7. Finally, 225 CV candidates were found and four new CV candidates were verified by SIMBAD and published catalogs. This study also built the Gradient Boosting Decision Tree (GBDT), Adaptive Boosting (AdaBoost), and eXtreme Gradient Boosting (XGBoost) models and used Accuracy, Precision, Recall, the F1-score, and the ROC curve to compare the four models comprehensively. Experimental results showed that LightGBM is more efficient. The search for CVs based on LightGBM not only enriches the existing CV spectral library, but also provides a reference for the data mining of other rare celestial objects in massive spectral data.

79 ASTRONOMY AND ASTROPHYSICS↗

Subseasonal Variability of U.S. Coastal Sea Level from MJO and ENSO Teleconnection Interference

Abstract Climate variability affects sea levels as certain climate modes can accelerate or decelerate the rising sea level trend, but subseasonal variability of coastal sea levels is underexplored. This study is the first to investigate how remote tropical forcing from the MJO and ENSO impact subseasonal U.S. coastal sea level variability. Here, composite analyses using tide gauge data from six coastal regions along the U.S. East and West Coasts reveal influences on sea level anomalies from both the MJO and ENSO. Tropical MJO deep convection forces a signal that results in U.S. coastal sea level anomalies that vary based on MJO phase. Further, ENSO is shown to modulate both the MJO sea level response and background state of the teleconnections. The sea level anomalies can be significantly enhanced or weakened by the MJO-associated anomaly along the East Coast due to constructive or destructive interference with the ENSO-associated anomaly, respectively. The West Coast anomaly is found to be dominated by ENSO. We examine physical mechanisms by which MJO and ENSO teleconnections impact coastal sea levels and find consistent relationships between low-level winds and sea level pressure that are spatially varying drivers of the variability. Two case studies reveal how MJO and ENSO teleconnection interference played a role in notable coastal flooding events. Much of the focus on sea level rise concerns the long-term trend associated with anthropogenic warming, but on shorter time scales, we find subseasonal climate variability has the potential to exacerbate the regional coastal flooding impacts. Significance Statement Coastal flooding due to sea level rise is increasingly threatening communities, but natural fluctuations of coastal sea levels can exacerbate the human-caused sea level rise trend. This study assesses the role of tropical influences on coastal subseasonal (2 weeks–3 months) sea level heights. Further, we explore the mechanisms responsible, particularly for constructive interference of signals contributing to coastal flooding events. Subseasonal signals amplify or suppress the lower-frequency signals, resulting in higher or lower sea level heights than those expected from known climate modes (e.g., ENSO). Low-level onshore winds and reduced sea level pressure connected to the tropical phenomena are shown to be indicators of increased U.S. coastal sea levels, and vice versa. Two case studies reveal how MJO and ENSO teleconnection interference played a role in notable coastal flooding events. Much of the focus on sea level rise concerns the long-term trend associated with anthropogenic warming, but on shorter time scales, we find subseasonal climate variability has the potential to exacerbate the regional coastal flooding impacts.

Meteorology & Atmospheric Sciences↗

Soil biogeochemical properties and metrics of tree-mycorrhizal dominance for a 25-Ha forest in South Central Indiana, USA.

This data package contains a dataset used in the papers “Seeing the forest for all the trees: Mycorrhizal-associated nutrient economies are modulated by stem density and the synchrony between overstory and understory communities” and “Mycorrhizal associations of tree species influence soil nitrogen dynamics via effects on soil acid–base chemistry”. Four csv files are included along with a dataset. The dataset features chemical soil properties for a single sampling campaign within the 25 Ha Lilly-Dickey Woods Smithsonian Forest Global Earth Observatory (ForestGEO) plot in South Central Indiana, USA (ldw_dat_raw.csv). Also included are separate files focused on pH (pH_data.csv), carbon and nitrogen (CN_data.csv), and nitrification rates (Nitrification_data.csv). These variables are commonly associated with the tree-mycorrhizal dominance of forest stands. In these data subsets, each soil variable was matched to a 10 meter radius neighborhood wherein metrics of tree-mycorrhizal dominance (basal area, stem count, importance value, etc.) were calculated. Models between these soil variables and dominance metrics were used to investigate how different assessments of mycorrhizal associated nutrient economies (MANE) capture these relationships. This research was performed as a part of the Smithsonian ForestGEO project. This data package can be used to explore spatial variability in soil chemistry within a mature hardwood forest, or it can be combined with the included tree data, other fine-scale spatial information, or other tree inventory data for the site to evaluate how soil chemistry varies with tree community composition or edaphic or topographic properties.

Craig, Matthew [ORNL] (ORCID:0000000288907920)↗

Reliable and Efficient Machine Learning (Final Technical Report)

Modern scientific experiments generate massive amounts of data at a pace much faster than humans can manually analyze. While machine learning has revolutionized commercial data analysis (such as recommending movies or recognizing faces), applying these tools to complex scientific discovery is challenging because scientific answers must be precise, interpretable, and adhere to physical laws. The research under this project aims to develop new mathematical tools and computer algorithms specifically designed for scientific applications. Major progress has been made in automatically cleaning and deconstructing messy experimental data, analyzing the visual information of physical phenomena, determining the underlying physical variables, and providing rig orous mathematical analysis of interesting algorithms and concepts widely used in machine learning. This project addressed the critical gap between our ability to generate massive scientific data and our ability to extract interpretable information from it. We established mathematical foundations for Scientific Machine Learning (SciML) aimed at effective data analytics and automated discovery. Our work focused on three core objectives: (1) developing reliable feature extraction methods for dynamic high-dimensional data, (2) establishing mathematical foundations for discovering dynamics via neural networks, and (3) creating rigorous optimization techniques for these models. Key outcomes come from two fronts. On the practical side, they include the development of algorithms that significantly enhance the extraction of signals from field data, as well as the capability to handle situations that exhibit smooth variations or physical stretching due to temperature changes. They also include the creation of an automated framework for discovering fundamental state variables from raw experimental data, demonstrating the ability to identify intrinsic physical dimensions without prior knowledge of the governing laws. On the theoretical front, the research results in theoretical advances in Optimal Transport, a widely used notion in SciML, specifically regarding functions with fixed-size nodal sets, provide sharp bounds relevant to uncertainty quantification. Meanwhile, the outcomes also include the establishment of convergence theories for nonlocal gradient descent methods, enabling robust optimization with noisy data in high-dimensional settings commonly encountered in scientific modeling. The project also helps creating opportunities to train the next generation of researchers, equipping them with the necessary technical skills for today’s workplace and preparing them for future advances.

97 MATHEMATICS AND COMPUTING↗