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At least 541 records · Page 30

Discovering new governing equations using ML

A hallmark of the scientific process since the time of Newton has been the derivation of mathematical equations meant to capture relationships between observables. As the field of mathematical modeling evolved, practitioners specifically emphasized mathematical formulations that were predictive, generalizable, and interpretable. Machine learning’s ability to interrogate complex processes is particularly useful for the analysis of highly heterogeneous, anisotropic materials where idealized descriptions often fail. As we move into this new era, we anticipate the need to leverage machine learning to aid scientists in extracting meaningful, but yet sometimes elusive, relationships between observed quantities.

97 MATHEMATICS AND COMPUTING↗

Gap Analysis of Supply Chain Cybersecurity for Distributed Energy Resources

A supply chain is the combination of the ecosystem of resources needed to design, manufacture, and distribute a product. In the context of supply chain cybersecurity, the resources that directly influence this ecosystem include software, data, and/or other digital components. Compromised equipment or software in the supply chain may lead to attacks such as financial loss; denial of service; a breach of confidential or proprietary information from a company, its customers, or its suppliers; ransomware that denies operation of automated equipment for payment; and malicious control actions that could damage equipment and endanger personnel. Currently 60.8% of US energy comes from fossil fuels, 18.9% comes from nuclear energy, and the last 20.1% comes from renewable sources. Federal Energy Regulatory Commission order FERC 2222 and Executive Order 14017 on America's Supply Chains are important milestones for safely expanding generation from renewable energy and achieving the goal of a decarbonized U.S. energy sector by 2035. This report analyzes gaps and opportunities in the supply chain currently available to the renewable energy sector, to help stakeholders formulate a coordinated response.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Root Cause Correlation Analysis of Software Failures via Orthogonal Defect Classification and Natural Language Processing

Systems theoretic process analysis (STPA) is becoming an increasingly popular technique to assess how complex digital software systems can fail. Rather than defining failures by their observable failure events, which may be sparse especially for safety rated nuclear digital instrumentation and control systems (DI&C), failures are defined as postulated unsafe actions under specific contextual conditions. This permits a top-down analysis of system hazards and identifies whether imposed constraints and requirements can sufficiently address undesirable hazards. However, STPA is a qualitative approach at identifying inadequacies in the development process and cannot currently be used to quantify unsafe action likelihoods for probabilistic risk assessment. Therefore, in this work, we examine the root causes of software failure and explore whether a consistent correlation can be linked to specific unsafe action classes. We implement Lbl2Vec, an unsupervised document classification and retrieval algorithm, on a database of 4,096 software defect reports acquired from various open-source software systems. By analyzing sentence structure, embedded labels, and word vectors, we show that certain defect types positively correlate to specific unsafe action classes over others. The correlations developed can be used to estimate the failure probability of safety intended DI&C systems which provides a licensing basis for nuclear plant modernization efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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↗

SCA Tools - SCRM Value Add or Lossy Noise Machines

Software supply chain risk management (SCRM) depends upon accurate information regarding the software components that comprise any given software system. The collection of components included in a software package can be organized within a software bill of materials, or SBOM. SBOMs are ideally generated when the software components are put together, such as at compile time, but for many reasons that has not and is not always possible. For example, legacy or proprietary software packages often do not have SBOMs available to downstream consumers of that software. It’s not just end users that are affected, manufacturers themselves also must deal with this problem. To answer these questions, the market has seen the rise of several commercial software composition analysis (SCA) tools. These tools aim to peer into completed software systems, automatically identifying hidden software dependencies and looking up known vulnerabilities associated with those dependencies to enable end-users to enhance their cyber supply chain risk management processes. These tools are potentially a huge boon to end users of legacy and proprietary software – and a potential bane, depending on how accurate they are. This research asks that question – how accurate are currently available binary SCA tools – and provides answers to several other questions: What does it mean to be “accurate”? What limitations do the tools have in identifying common edge cases that take place in modern software development? Can they help you avoid a devastating supply chain attack, or is it all just noise? After researching SCA tools on the market, we identified three vendors that fit our use case and would provide analysis on compiled binaries. Using these tools, we submitted firmware for critical infrastructure devices for analysis and SBOM generation. The SBOM outputs were then cross referenced with SBOMs generated through manual analysis for comparison. In addition to the firmware samples, we also submitted edge case samples based off a popular open-source library that were specifically crafted to evaluate each tools’ ability to accurately identify components. These samples were customized to be consistent with modifications we have seen in modern software development as well as a couple that are representative of supply chain attacks.

97 MATHEMATICS AND COMPUTING↗

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗

Topological Simplifications of Hypergraphs

Here we study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph into its graph representations, known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general and mathematically justifiable, and put vertex simplification and hyperedge simplification in a unifying framework.

97 MATHEMATICS AND COMPUTING↗

Patient-Specific Mathematical Model of the Clear Cell Renal Cell Carcinoma Microenvironment

The interactions between cells and molecules in the tumor microenvironment can give insight into the initiation and progression of tumors and their optimal treatment options. In this paper, we developed an ordinary differential equation (ODE) mathematical model of the interaction network of key players in the clear cell renal cell carcinoma (ccRCC) microenvironment. We then performed a global gradient-based sensitivity analysis to investigate the effects of the most sensitive parameters of the model on the number of cancer cells. The results indicate that parameters related to IL-6 have high a impact on cancer cell growth, such that decreasing the level of IL-6 can remarkably slow the tumor’s growth.

60 APPLIED LIFE SCIENCES↗

Robust error calibration for serial crystallography

Serial crystallography is an important technique with unique abilities to resolve enzymatic transition states, minimize radiation damage to sensitive metalloenzymes and perform de novo structure determination from micrometre-sized crystals. This technique requires the merging of data from thousands of crystals, making manual identification of errant crystals unfeasible. cctbx.xfel.merge uses filtering to remove problematic data. However, this process is imperfect, and data reduction must be robust to outliers. We add robustness to cctbx.xfel.merge at the step of uncertainty determination for reflection intensities. This step is a critical point for robustness because it is the first step where the data sets are considered as a whole, as opposed to individual lattices. Robustness is conferred by reformulating the error-calibration procedure to have fewer and less stringent statistical assumptions and incorporating the ability to down-weight low-quality lattices. We then apply this method to five macromolecular XFEL data sets and observe the improvements to each. The appropriateness of the intensity uncertainties is demonstrated through internal consistency. This is performed through theoretical CC 1/2 and I /σ relationships and by weighted second moments, which use Wilson's prior to connect intensity uncertainties with their expected distribution. This work presents new mathematical tools to analyze intensity statistics and demonstrates their effectiveness through the often underappreciated process of uncertainty analysis.

Mittan-Moreau, David W.↗

Ergodic Lagrangian dynamics in a superhero universe

We present a fictional scenario that, while undeniably whimsical, provides the foundation for a unique exercise in extended problem solving, physics analysis, and quantitative model development. Starting with the foundational premise of the Wild Cards shared-world superhero universe, we demonstrate how a variety of concepts appropriate to the advanced undergraduate level—ergodicity, functional analysis, Lagrangian mechanics, and the ever-important simplifying approximation—can be combined into a rich, coherent mathematical model. The goal of this case study is to develop a useful pedagogical exercise in exploring an open-ended research question that presents, at first glance, no clear path forward. Being both eclectic and lengthy, this exercise offers a unique way for students to apply their core physics and mathematics education. It is perhaps best used within a senior honors seminar or within a brief (e.g., January term) elective class.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Initial development of viscoplastic constitutive model of Alloy 800H in support of the use of inelastic analysis methods for ASME Section III, Division 5, Class A applications

This report describes the development of a preliminary inelastic constitutive model for the thermomechanical behavior of Alloy 800H. The objective is to develop a model suitable for incorporating into Nonmandatory Appendix Z to Section III, Division 5 of the ASME Boiler & Pressure Vessel Code, which provides guidance and reference constitutive models for the ASME design by inelastic analysis rules for Class A components. The report describes the process of collecting experimental data, developing a mathematical form for the model, and training the model against the test data. The initial version of the model captures most of the relevant material deformation mechanisms, including dynamic strain aging effects. However, further development of the model form will be required to develop a final model suitable for ASME use.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Data Driven Approach to Public Opinion Mining on Autonomous Vehicles: Sentiment Analysis of Social Media Comments Using Large Language Models

In the realm of online identity, social media has emerged as a rich and dynamic source of user-generated content, making it an invaluable resource for understanding public sentiment on a wide range of topics. Individuals often share their raw emotions and candid opinions on these platforms without fear of judgment or backlash. In this study, we conduct a sentiment analysis on user comments collected from various online platforms, with a specific focus on discussions surrounding autonomous vehicles. Leveraging the capabilities of large language models (LLMs), we classify each comment into one of five sentiment categories: Very Negative, Negative, Neutral, Positive, and Very Positive. Our approach demonstrates the effectiveness of LLMs in capturing nuanced contextual sentiment, offering a scalable and state-of-the-art alternative to traditional manual annotation methods. The results reveal key trends and insights into public perception, enabling a deeper understanding of how autonomous vehicle technologies are received by the online community. Our findings underscore the dynamic nature of public sentiment, which is shaped not only by advances in autonomous vehicle technology but also by contextual events such as regulatory developments, political adjustment and safety incidents.

24 POWER TRANSMISSION AND DISTRIBUTION↗

GrAMME: Semisupervised Learning Using Multilayered Graph Attention Models

Modern data analysis pipelines are becoming increasingly complex due to the presence of multiview information sources. While graphs are effective in modeling complex relationships, in many scenarios, a single graph is rarely sufficient to succinctly represent all interactions, and hence, multilayered graphs have become popular. Though this leads to richer representations, extending solutions from the single-graph case is not straightforward. Consequently, there is a strong need for novel solutions to solve classical problems, such as node classification, in the multilayered case. In this article, we consider the problem of semisupervised learning with multilayered graphs. Though deep network embeddings, e.g., DeepWalk, are widely adopted for community discovery, we argue that feature learning with random node attributes, using graph neural networks, can be more effective. To this end, we propose to use attention models for effective feature learning and develop two novel architectures, GrAMME-SG and GrAMME-Fusion, that exploit the interlayer dependences for building multilayered graph embeddings. Using empirical studies on several benchmark data sets, we evaluate the proposed approaches and demonstrate significant performance improvements in comparison with the state-of-the-art network embedding strategies. The results also show that using simple random features is an effective choice, even in cases where explicit node attributes are not available.

97 MATHEMATICS AND COMPUTING↗

Risk-Aware Measurement Synchronization and Recovery for DSSE With Heterogeneous Data Sources

Power distribution systems are increasingly integrating heterogeneous sensors with varying data reporting rates and types, which pose challenges to achieving observability at the desired temporal resolution of distribution system state estimation (DSSE). Multisensor failures caused by extreme events exacerbate these issues, introducing substantial uncertainties into DSSE. This article proposes a novel solution to these challenges by ensuring high-resolution system observability despite heterogeneous data sources and multisensor failures. First, a deep learning architecture combining long short-term memory (LSTM) and graph convolutional network (GCN) is employed to synchronize meters with different reporting rates, aiming to achieve system observability. A random-walk-model-based approach is introduced to generate pseudo-measurements while properly characterizing their uncertainties under multisensor failures. Finally, a disaster-risk-informed observability metric (RiOM) is defined to quantify the uncertainty associated with state estimation results. The proposed framework offers deeper insights into the system observability on the fly compared with conventional analysis. The effectiveness of the framework is demonstrated on an IEEE standard test case and a large-scale real-world distribution feeder in mid-Minnesota in the U.S.

97 MATHEMATICS AND COMPUTING↗

Re-evaluation of the TSL for Yttrium Hydride

Yttrium hydride (YH x ) is of interest as a high-temperature moderator material in advanced nuclear reactor systems because of its superior ability to retain hydrogen at elevated temperatures. Thermal neutron scattering laws (TSL) for hydrogen bound in yttrium hydride (H-YH 2 ) and yttrium bound in yttrium hydride (Y-YH 2 ) were previously evaluated by Naval Nuclear Laboratory using the ab initio approach and released in ENDF/B-VIII.0. In that work, density functional theory, incorporating the generalized gradient approximation (GGA) for the exchange-correlation energy, was used to simulate the face-centered cubic structure of YH 2 and calculate the interatomic Hellmann-Feynman forces for a 2×2×2 supercell containing 96 atoms. Lattice dynamics calculations using PHONON were used to determine the phonon density of states. The calculated phonon density of states for H and Y in YH 2 were then used to prepare H-YH 2 and Y-YH 2 TSL evaluations, in the incoherent approximation, using the LEAPR module of NJOY. In addition, elastic scattering was assumed to be incoherent for both H and Y. While the incoherent elastic scattering approximation is appropriate for H-YH 2 , it introduces an undesirable approximation for Y-YH 2 . In this work, we re-evaluate the TSL for Y-YH 2 using FLASSH (Full Law Analysis Scattering System Hub). Y-YH 2 is evaluated using the FLASSH generalized coherent elastic scattering capability in order to capture the Bragg peaks associated with the YH 2 crystal structure which were neglected in the prior NJOY-based evaluation due to limitations in LEAPR. An experimental approach to validate the Y-YH 2 TSL using neutron transmission measurements is discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Coupling SCALE with DAKOTA for Axial Burnup Profiles Assessment in Burnup Credit

This paper presents a computational study that demonstrates the application of the SCALE code system in conjunction with the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) for the analysis of key factors influencing the evaluation of burnup credit (BUC) in pressurized water reactors (PWRs). The primary objective of this analysis is to characterize the model by utilizing parameterization, uncertainty quantification, and optimization studies. Using this approach, we can comprehensively assess the system and conduct informed predictive studies. This study highlights the effectiveness of the SCALE code system integrated within the DAKOTA framework in terms of efficiency and capability. With the coupling of the burnup code ORIGAMI with the CSAS or TSUNAMI-3D sequence embedded in a DAKOTA analysis, we can characterize the factors that influence the k eff of PWR 17x17 spent nuclear fuel (SNF) in the GBC-32 computational benchmark cask for the assessment of BUC in criticality safety analysis. The coupling methodology used in this study is not exclusive to BUC analysis. However, the choice to apply this methodology to the BUC problem is particularly significant because of the diverse range of aspects it encompasses in nuclear criticality safety analyses. This problem presents a unique opportunity to explore and address multiple facets of such analyses related to BUC and illustrates the capability of the SCALE code system with DAKOTA. This analysis makes use of historical reference data for the axial burnup profile, where the entire space within the bounds is considered. Both SCALE and DAKOTA are currently integrated in the Nuclear Energy Advanced Modeling Simulation (NEAMS) Workbench code system, which has a user-friendly graphical interface that simplifies the setup of simulations and configuration of input parameters as well as the visualization of simulation results.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗