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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Information and Statistics in Nuclear Experiment and Theory (ISNET)

As with all empirical sciences, nuclear physics operates in the virtuous cycle of the scientific method: observations inspire theoretical models; models lead to new predictions; predictions are tested in experiments; experiments lead to new observations; and so on. Evaluating what we are inferring, and how certain we are of it, is key to this process. These requirements, and a general interest in applying novel statistical, mathematical, and computational techniques, led to the formation of a dedicated research community entitled “Information and Statistics in Nuclear Experiment and Theory (ISNET)” (https://isnet-series.github.io/), which now includes more than 300 members. While the community’s interests lean toward nuclear theory, the unifying theme for this group is the inference of knowledge from data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A Hierarchical Gibbs Sampler for Spatially Varying Multi-Regularization Image Reconstructions

This is a presentation for SIAM's (Society for Industrial and Applied Mathematics) conference on computational science and engineering. This presentation describes research on novel techniques to deblur images under a Bayesian framework. The title of the conference is SIAM Conference on Computational Science and Engineering (CSE21). This is a VIRTUAL conference; it was originally scheduled in Fort Worth, TX. The conference dates are March 1-5, 2021. The link to the conference's website is https://www.siam.org/conferences/cm/conference/cse21

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling

The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.

58 GEOSCIENCES↗
DOE OSTI2025

Scalable Unit Commitment with Security Constrained AC Power Flow via ADMM and Hybrid Modeling Strategies

This research introduces a more efficient way to optimize power grid operations, breaking the problem into manageable steps and using advanced mathematical techniques to speed up calculations. By incorporating smart heuristics, improved preprocessing, and contingency analysis, the approach allows operators to make better decisions faster. These innovations enhance our understanding of how to optimize energy generation, making it possible to anticipate failures before they happen, reduce system costs, and improve overall grid performance. Ultimately, this research helps bridge the gap between theoretical models and real-world applications, paving the way for a smarter, more resilient power grid. This research directly benefits the public by making electricity more affordable, reliable, and sustainable. By improving how power grids schedule and distribute electricity, the project helps energy providers reduce operational costs, which can lead to lower electricity prices for consumers. Additionally, the ability to predict and prevent power system failures enhances grid reliability, reducing the likelihood of blackouts that can disrupt homes, businesses, and critical infrastructure such as hospitals. From an environmental perspective, optimizing power generation reduces energy waste and lowers carbon emissions, contributing to cleaner air and a more sustainable energy system. Furthermore, with extreme weather events becoming more frequent, these advancements make the power grid more resilient, ensuring communities are better prepared for emergencies and natural disasters. By strengthening the nation's energy infrastructure, this research plays a crucial role in improving economic stability, public safety, and environmental sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Developing ML/AI Methods for High-Throughput Characterization of Multiple-Sensor Streams of Tokamak Dynamics for High-Speed Control (Final Report)

This project evaluated and developed new mathematical and algorithmic techniques capable of handling (in real-time) the growing amounts of data generated by modern fusion research. While existing numerical linear algebra (NLA) methods provide the backbone to classical data analysis and algorithms, these methods fundamentally do not port to distributed architectures nor do they allow low-latency data reduction for control. Motivated by the needs for modern fusion reactors, this project explored and implemented new numerical methods to characterize plasma dynamics, respond in real-time to discharge evolution, and to process massive-scale data accurately and rapidly more fully. This project links expertise in multiple-sensor diagnostics of tokamak plasma dynamics from Columbia University’s Plasma Physics Laboratory with expertise in massive-scale data reduction and extreme data control algorithms at Columbia University’s Data Science Institute. This interdisciplinary project (i) applied machine learning methods, (ii) implemented a properly-trained neural-network for very fast processing of high-speed plasma videography, and (ii) developed the applied mathematical methods, based on randomized-NLA (rNLA) routines, for data analysis, reduction, and real-time control. The Columbia University High Beta Tokamak-Extended Pulse (HBT-EP) facility provided data to test new algorithms and partnership with Columbia University's Data Sciences Institute evaluated the broader use of new algorithms for many challenging control applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Review of multi-fidelity models

Multi-fidelity models provide a framework for integrating computational models of varying complexity, allowing for accurate predictions while optimizing computational resources. These models are especially beneficial when acquiring high-accuracy data is costly or computationally intensive. This review offers a comprehensive analysis of multi-fidelity models, focusing on their applications in scientific and engineering fields, particularly in optimization and uncertainty quantification. It classifies publications on multi-fidelity modeling according to several criteria, including application area, surrogate model selection, types of fidelity, combination methods and year of publication. The study investigates techniques for combining different fidelity levels, with an emphasis on multi-fidelity surrogate models. Here this work discusses reproducibility, open-sourcing methodologies and benchmarking procedures to promote transparency. The manuscript also includes educational toy problems to enhance understanding. Additionally, this paper outlines best practices for presenting multi-fidelity-related savings in a standardized, succinct and yet thorough manner. The review concludes by examining current trends in multi-fidelity modeling, including emerging techniques, recent advancements, and promising research directions.

42 ENGINEERING↗
DOE OSTI2022

A survey on processing-in-memory techniques: Advances and challenges

Processing-in-memory (PIM) techniques have gained much attention from computer architecture researchers, and significant research effort has been invested in exploring and developing such techniques. Increasing the research activity dedicated to improving PIM techniques will hopefully help deliver PIM’s promise to solve or significantly reduce memory access bottleneck problems for memory-intensive applications. We also believe it is imperative to track the advances made in PIM research to identify open challenges and enable the research community to make informed decisions and adjust future research directions. In this survey, we analyze recent studies that explored PIM techniques, summarize the advances made, compare recent PIM architectures, and identify target application domains and suitable memory technologies. We also discuss proposals that address unresolved issues of PIM designs (e.g., address translation/mapping of operands, workload analysis to identify application segments that can be accelerated with PIM, OS/runtime support, and coherency issues that must be resolved to incorporate PIM). We believe this work can serve as a useful reference for researchers exploring PIM techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A review of preserving privacy in data collected from buildings with differential privacy

Significant amounts of data are collected in buildings. While these data have great potential for maximizing the energy efficiency of buildings in general, only a small portion of the data are accessible to researchers, government, and industry for analyses. Concerns about privacy are one of the major barriers prohibiting access to these data. Privacy preservation techniques are generally applied to this problem not only to preserve underlying privacy but also to improve the usefulness of data. Among various privacy preserving techniques, differential privacy has become one of the more popular solutions since its introduction in 2006. Differential privacy is a mathematical measure for protecting privacy so that one's privacy cannot be incurred by participating in a database. Additionally, although significant research improvements have been made for more than a decade, applying differential privacy to data collected in buildings is still an immature field of study. Because implementing differential privacy on a certain use case is not straightforward and can be achieved with various configurations, it is important to understand variation of configurations with different use cases around data collected from buildings. This literature review aims to introduce what has been done to implement differential privacy in data collected in buildings, and to discuss associated challenges and potential future research opportunities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Deconvolution of dynamic heterogeneity in protein structure

Heterogeneity is intrinsic to the dynamic process of a chemical reaction. As reactants are converted to products via intermediates, the nature and extent of heterogeneity vary temporally throughout the duration of the reaction and spatially across the molecular ensemble. The goal of many biophysical techniques, including crystallography and spectroscopy, is to establish a reaction trajectory that follows an experimentally provoked dynamic process. It is essential to properly analyze and resolve heterogeneity inevitably embedded in experimental datasets. We have developed a deconvolution technique based on singular value decomposition (SVD), which we have rigorously practiced in diverse research projects. In this review, we recapitulate the motivation and challenges in addressing the heterogeneity problem and lay out the mathematical foundation of our methodology that enables isolation of chemically sensible structural signals. We also present a few case studies to demonstrate the concept and outcome of the SVD-based deconvolution. Finally, we highlight a few recent studies with mechanistic insights made possible by heterogeneity deconvolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

PAL Experimental Report Form

We constructed the first simultaneous dark- and bright-field X-ray microscope in this experiment, coupling it to simultaneous measurements of the wide-angle Xray diffraction, and the XFEL pulse intensity and energy spectrum on each shot. This experiment established proof of concept for this new advanced measurement technique and demonstrated DFXM at an XFEL for the first time. Within this complex experiment, we also acquired data that advanced our research goals within materials science and mathematics. These included: A preliminary study of how local effects reduce the X-ray damage threshold in diamond; A preliminary study of how X-ray radiation imparts heat into materials based on irreversible phase transitions that occur in boric acid with increasing temperature (based on hydration); A study of X-ray radiation damage from ultrafast thermal cycling and nonthermal melting in bismuth selenide; We also began developing software to automate alignment of compound refractive lenses (CRLs) using stochastic Nelder-Mead optimization methods. This work will expedite and improve the accuracy of alignments for many future experiments using CRLs.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Research Trends and Applications of PMUs

This work is a survey of current trends in applications of PMUs. PMUs have the potential to solve major problems in the areas of power system estimation, protection, and stability. A variety of methods are being used for these purposes, including statistical techniques, mathematical transformations, probability, and AI. The results produced by the techniques reviewed in this work are promising, but there is work to be performed in the context of implementation and standardization. As the smart grid initiative continues to advance, the number of intelligent devices monitoring the power grid continues to increase. PMUs are at the center of this initiative, and as a result, each year more PMUs are deployed across the grid. Since their introduction, myriad solutions based on PMU-technology have been suggested. The high sampling rates and synchronized measurements provided by PMUs are expected to drive significant advancements across multiple fields, such as the protection, estimation, and control of the power grid. This work offers a review of contemporary research trends and applications of PMU technology. Most solutions presented in this work were published in the last five years, and techniques showing potential for significant impact are highlighted in greater detail. Being a relatively new technology, there are several issues that must be addressed before PMU-based solutions can be successfully implemented. This survey found that key areas where improvements are needed include the establishment of PMU-observability, data processing algorithms, the handling of heterogeneous sampling rates, and the minimization of the investment in infrastructure for PMU communication. Solutions based on Bayesian estimation, as well as those having a distributed architectures, show great promise. The material presented in this document is tailored to both new researchers entering this field and experienced researchers wishing to become acquainted with emerging trends.

42 ENGINEERING↗
DOE OSTI2023

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗
DOE OSTI2025

Comparative Analysis of DNA LLM Classification Techniques Using Intra-Layer Feature Extraction with Autoencoder Stacks [Poster]

This project conducts a comparative analysis of DNA LLM classification techniques using Evo2, Grover, and UTRML, focusing on intra-layer feature extraction in Evo2. By extracting features from multiple layers of Evo2 and integrating them into an autoencoder stack with a binary classification head, we evaluate its effectiveness in classifying genomic sequences compared to smaller DNA language models. My findings demonstrate that Evo2 outperforms Grover and UTRML in classification accuracy on a dataset provided by department 08625, CAO2021, while UTRML offers competitive performance with lower computational costs. This study highlights the potential of advanced embedding techniques in enhancing genomic data analysis and informs future research in bioinformatics.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Applications of Federated Learning in Semiconductor Manufacturing [Poster]

As semiconductor manufacturers explore advanced data analytics and modeling techniques and data hungry machine learning models increase in popularity due to their accuracy in solving generalized problems and ability to learn complex relationships, federated learning emerges as a privacy preserving machine learning technique for preserving data privacy and ensuring intellectual property protection. Federated Learning is a machine learning technique focused on training models using distributed data that never needs to be centrally stored, allowing the use of advanced machine learning techniques without compromising data privacy, and in the semiconductor manufacturing industry advanced machine learning techniques can reduce cost and time, but maintaining data privacy is essential to maintaining a competitive advantage. This paper systematically reviews existing literature on applications of federated learning in the semiconductor manufacturing industry with a focus on identifying common themes, algorithms, and gaps within the literature to drive future research directions. The findings reveal five key themes, including improvements in quality assurance, virtual models, privacy preservation, reliable data practices, and emerging trends and developments. By identifying key themes in literature on federated learning and semiconductor manufacturing and analyzing gaps and discussed methodologies, this study highlights several potential future research directions to expand the application of federated learning techniques in the semiconductor manufacturing domain.

42 ENGINEERING↗
DOE OSTI2023

Multigrid Reduction in Time for Chaotic and Hyperbolic Problems (Final Report)

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallelin-time methods, with the most common method, parareal, diverging in many cases. The current state-of-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, this work shall continue researching the directions from the current collaboration with Dr. Falgout, which are laid out in the work Toward Parallel in Time for Chaotic Dynamical Systems and showed the first known results of a parallel-in-time speedup for a chaotic problem. This work outlines two key improvements to XBraid for chaotic problems, the so-called “theta” and “delta-correction” methods. Here, these two improvements will be implemented in a high-performance but general way in XBraid and explored for more complicated problems. We will additionally research, as time allows, improvements to these techniques, as well as multigrid relaxation techniques based on Least Squares Shadowing (LSS by Wang) and a nonintrusive block tridiagonal solver based on MGRIT, called TriMGRIT.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Comparative Study of Differentially Private Data Synthesis Methods

When sharing data among researchers or releasing data for public use, there is a risk of exposing sensitive information of individuals in the data set. Data synthesis is a statistical disclosure limitation technique for releasing synthetic data sets with pseudo individual records. Traditional data synthesis techniques often rely on strong assumptions of a data intruder’s behaviors and background knowledge to assess disclosure risk. Differential privacy (DP) formulates a theoretical approach for a strong and robust privacy guarantee in data release without having to model intruders’ behaviors. Efforts have been made aiming to incorporate the DP concept in the data synthesis process. Here, we examine current DIfferentially Private Data Synthesis (DIPS) techniques for releasing individual-level surrogate data for the original data, compare the techniques conceptually and evaluate the statistical utility and inferential properties of the synthetic data via each DIPS technique through extensive simulation studies. Our work sheds light on the practical feasibility and utility of the various DIPS approaches, and suggests future research directions for DIPS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Microchannel-based Membrane-less Extraction of Li from Unconventional Lithium Sources & the Separation of REE

This final report provides an overview of the Project's entire duration, covering July 1, 2021 to December 31, 2023. It primarily focuses on the achievements, technological developments, and unique challenges the team faced while working on separating and extracting Lithium from produced waters. The project's primary aim was to create an integrated, high-throughput, membrane-less, and modular microfluidic platform that could extract Lithium from unconventional sources. We have successfully met all goals and milestones envisioned in the SOPO document. The most critical primary milestones, including the Go-No-Go milestone (refer to the Gantt chart in the Appendices), were successfully accomplished. We demonstrated phase separation (>90%) and extraction (>85%) performance in the MPSE using synthetic, and representative produced water composition feed at 50 ml/min total flow through MPSE 36. We have also performed a parametric study of the MPSE operations, beyond the scope of SOPO, exploring operating conditions of current and broader interest. The extended investigation of operational parameters is concurrent with our efforts to seek further development of the MPSE technology beyond the scope of the Project. Along these lines of development, we have made efforts to be responsive to DOE calls for technological developments of other types of resources (beyond PW) for the recovery of Critical Materials and higher TRL development (beyond TRL 4). During the work on this Project, we developed and implemented three innovative technical approaches that emerged from our efforts to successfully meet the Project milestones. The innovative & original technical approaches developed and implemented in this Project are now the contributions to process engineering that could be clearly credited to the Project. First, Convergent Design Approach is a comprehensive feedforward & feedback loop of four design phases: i) design for functionality, ii) design for manufacturing, iii) design for sustainability, and iv) design for market. Next was Process Intensification. A major aim of this Project was to create an innovative phase separation & extraction microscale-based technology for Li separation – thus the words microchannel-based in the Project title. A microscale-based technology is intrinsically in the center of the Process Intensification domain as defined by its unique principles. Therefore, Process Intensification was implicitly envisioned in the Project’s SOPO. Lastly, Time Scale Analysis is a novel tool for discovering the needs and directions of Process Intensification implementations in any process technology. This Project is fully credited for developing and implementing the three novel technical approaches mentioned above. These are general contributions to process engineering that emerged from this Project. Beyond the original SOPO scope, the OSU-U.Pitt research group utilized a Convergent Design methodology, integrating first-principles mathematical modeling with experimental validation on the Minimum Development Vehicle. By creating these Digital Twins, the team rapidly assessed manufacturing iterations to support TEA analysis. This framework further enabled the development of advanced Surface Modification Techniques, where hydrophobic and oleophobic coating strategies were optimized via Digital Twin tools and validated through rigorous 100-hour longevity testing. TEA Analysis: The closing efforts of this Project were focused on the TEA analysis. TEA analysis had two primary functions: i) enabling critical assessments of design variations withing 10 the Concurrent Design Approach, thus enabling evolution of the MPSE design to reach faster- better-cheaper alternatives; and ii) to create a bridge between the accomplishments of this Project and future projects of higher TRL, beyond TRL 6 level. It is important to note that the TEA model created in the Project stirred the technological solutions for the recovery of critical materials toward a vision of a very profitable modular plant that has unique zero-waste water discharge signature. More importantly, thanks to our experimental performance data and conservative assumptions, the TEA model predicts minimal technological and investment risks. Low cost of a modular unit of a nominal capacity of [1000 tons of Li 2 CO 3 /year] positions the MPSE based technology within the reach of community investors, thus offering a paradigm shift in the development of critical technologies. The project successfully navigated two primary challenges: solvent selection and manufacturing adaptation. Restricted by the SOPO to existing literature for lithium recovery, the team identified a critical need for a "material excellence program" to develop next-generation solvents, eventually concluding with a preliminary investigation into promising Ionic Liquids (ILs). Simultaneously, COVID-19 supply chain disruptions forced a pivot from traditional manufacturing to advanced additive methods at ATAMI-OSU. By transitioning from stainless steel to 3D-printed polymer substrates, the team achieved a transformative three-order-of- magnitude reduction in manufacturing costs and compressed prototyping timelines from several months to just two days. The MPSE technology offers significant energy, environmental, and economic advantages by overcoming the traditional bottlenecks of phase-separation hardware and contactor size. Unlike conventional mixer-settlers or membrane-based systems, MPSE operates without moving parts or fouling-prone membranes, achieving robust performance even with challenging, viscous, or particulate-heavy feeds. Key performance metrics include an energy intensity reduction of 5–50x (3–40 kJ/m 3 ) compared to incumbent technologies and a dramatic reduction of processing time to under 60 seconds, which drastically reduces the physical plant footprint. These technical efficiencies translate into superior economic outcomes; for a 100 t/year Li 2 CO 3 facility, implementing MPSE is projected to nearly halve contactor CAPEX (from $\$$6.08M to $\$$3.01M) and significantly increase the project's Net Present Value (NPV), derisking new investment and enabling distributed critical-mineral processing configurations. The commercialization of MPSE technology is being spearheaded by Vigsur Dynamics Inc., which has adopted a structured, parallel approach to technical and business development since its formation in January 2026. Following extensive customer discovery and engagement with the Oregon State University accelerator, Vigsur Dynamics is working to establish a business model that transitions from pilot demonstrations to modular hardware sales, ultimately aiming for a "build-own-operate" service strategy. Current technical milestones—including 100 hours of continuous operation, superior energy efficiency, and successful 6-unit modular scale-up— provide a foundation for this transition. Backed by ongoing IP licensing and a growing network of industrial and venture advisors, the company is actively de-risking the platform to replace conventional mixer-settler systems in the critical minerals market.

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

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↗