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Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws
We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the flux function and a corresponding entropy, NESCFN promotes conservation and entropy dissipation, which is critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Furthermore, numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.
Fast dynamic aperture optimization with forward-reversal integration
A fast dynamic aperture (DA) optimization method for storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symmetry, a numerical forward integration differs from its reversal. For a chaotic trajectory, cumulative round-off errors are scaled, which results in an exponential growth on the difference. The exponential effect is a generic chaos indicator which represents the sensitivity of the chaotic motion to its initial condition. The chaos indicator of the charged particle motion can be obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. “backward integrations.” The indicator is observable even through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. Finally, the DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.
Fast Dynamic Aperture Optimization with Reversal Integration
A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symme- try, a numerical forward integration di ers from its reversal. For chaotic trajectories, cumulative round-o errors are scaled, which results in an exponential growth in the di erence. The exponential e ect, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. \backward integrations." The indicator was con rmed to be ob- servable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test di raction-limited light source ring, were optimized using this method for the purpose of demonstration.
Self-Consistent Relativistic Electron Scattering using the Sherlock Scattering Model for X-ray Diagnostics
We present on a new, self-consistent, arbitrary-temperature Romberg integration scheme for modeling electron scattering in materials in a LANL Lagrangian Shock Hydro (LSH) code. Electron beam-target interactions are fundamental to a wide range of scientific and technological applications. When high-energy electron beams hit their target, they may scatter, deposit energy, or ionize the source. These processes govern the behavior and outcomes in nanotechnology manufacturing, electron microscopy, and modern X-ray diagnostics. Simulating these interactions is essential for interpreting experimental results, predicting material responses, and designing efficient tools and experiments. At Los Alamos, this is done using a LSH code, which is a multi-dimension, multi-material, massively parallel, multi-physics code used to simulate applications from asteroid impacts to electron beam interactions. By effectively and efficiently modeling the way that electrons scatter from the beam we can bolster these simulations and more accurately predict experimental outcomes. The model currently implemented in the LSH of interest is based on work by Papp and does not self-consistently preserve momentum in the slightly relativistic regime; here we adopt a model proposed by Braams and Karney and implement a Romberg integration scheme to compute the diffusion tensor. In this paper we will provide background on the Braams-Karney diffusion tensor as well as the Romberg integration scheme we employed to numerically solve for it. We will show that our integration scheme is accurate in solving for the set of scalar potentials used to re-express the diffusion tensor in differential form, and in solving for the diffusion coefficients in the larger LSH code. By using this diffusion tensor rather than the existing Papp one, and numerically integrating it with a Romberg method, we produce much more accurate, self-consistent results.
A Knowledge Graph Approach to Analyze Systems and Assets Health
Nuclear power plants collect large amounts of equipment reliability data elements that contain information on the statuses of component, assets, and systems. All these data elements precisely record asset and system performance and health throughout the lifecycle of those assets and systems. However, several challenges have proved to be roadblocks to this process. While some of these challenges are technical in nature (i.e., data are often distributed over several physical servers or databases), others are conceptual in nature (i.e., data elements come in different formats, numeric or textual), and measured values have different scales (e.g., vibration spectra and oil temperature). This paper directly focuses on the integration of numeric and textual data elements in order to assist plant system engineers in analyzing equipment reliability data. This task begins with preprocessing the data by extracting knowledge from textual data via natural language processing methods and quantifying system, asset, and component health based on numeric data. We then employed model-based system engineering (MBSE) models of systems and assets to identify their architecture and functional (i.e., cause and effect) relations. Data elements were then associated with a single MBSE graph element, based on their nature. This bonding of MBSE models and data elements constitutes a first-of-its-kind knowledge graph of a nuclear power plants system, with data elements being organized in a structured manner that enables system engineers to identify cause-effect trends in data elements and carry out appropriate actions in response.
LiAISON (Life-cycle Assessment Integration into Scalable Open-source Numerical models) [SWR-24-01]
We introduce an open source prospective LCA framework, the Life-cycle Assessment Integration into Scalable Open-source Numerical models (LiAISON), to analyze the non-linear relationships between technology foreground and the future energy system background across a series of midpoint and resource use metrics The integration of LCA and IAM data is achieved using prospective environmental Impact assessment (PREMISE)7. We showcase it by assessing two Power-to-Hydrogen (PtH2) processes, namely Solid Oxide Electrolysis (SOE) and Polymer Electrolyte Membrane Electrolysis (PEME). We compare the technologies to a baseline of hydrogen production via natural gas-based Steam Methane Reforming (SMR) in a US context of multiple energy system and climate change mitigation futures. Besides providing an analysis that specifies the LCA results ranges with temporal and geospatial explicitness across the two technologies, metrics, and impact assessment methods, this research also aims to establish a base framework that can be expanded to use other IAM generated scenarios and US open-source life cycle inventory (LCI) databases. We find that the temporal environmental performance of either technology or their difference to SMR is directly influenced by the underlying background dynamics. Under baseline projections (i.e., no decarbonization goals), neither process reaches parity with the incumbent technology across several environmental metrics. Under the decarbonization scenarios, the underlying sectoral shifts result in declining impacts over time, compared to 2020 levels, except for metal depletion levels, which increase. The background shifts postulate a heavily decarbonized economy and energy system, which help technologies reach parity with SMR between 2040-2050 (RCP2.6) and 2030-2040 (RCP1.9) for global warming. Despite declines across several other metrics over time, neither PtH2 technology break even with SMR by 2100 besides for global warming. Scientific publication available here: https://pubs.acs.org/doi/full/10.1021/acs.est.2c04246
Integrated Methane Monitoring Platform Design (Final Report)
As the urgency for understanding methane emissions and the number of methane monitoring technologies being deployed have increased in the last two decades, there is an opportunity and a need to integrate the numerous disparate data sources to enable the detection, quantification, contextualization, and reporting of methane emissions along the oil and gas supply chain. Such an integration would enable emissions reductions through early detection of super emitters, data-driven mitigation strategies, and improved greenhouse gas inventories. The GTI Energy (“GTI”) project team (“the team”) worked with a multitude of industry experts, stakeholders, and subject matter experts (SMEs) to collect guidance, insights, and information to inform the requirements and subsequent engineering, design, deployment, and operations of an integrated methane monitoring platform (IMMP). This final report describes the results of the team’s effort to execute the Integrated Methane Monitoring Platform Design project, ultimately providing an engineering, design, deployment, and operating plan (EDDOP) for the IMMP. This final report summarizes and integrates the project tasks' results and outputs.
Supporting Information for the Integrated Methane Monitoring Platform Design (Final Report)
As the urgency for understanding methane emissions and the number of methane monitoring technologies being deployed have increased in the last two decades, there is an opportunity and a need to integrate the numerous disparate data sources to enable the detection, quantification, contextualization, and reporting of methane emissions along the oil and gas supply chain. Such an integration would enable emissions reductions through early detection of super emitters, data-driven mitigation strategies, and improvedgreenhouse gas inventories. The GTI Energy (“GTI”)project team (“the team”) worked with a multitude of industry experts, stakeholders, and subject matter experts (SMEs) to collect guidance, insights, and information to inform the requirements and subsequent engineering, design, deployment, and operations of an integrated methane monitoring platform (IMMP). This final report describes the results of the team’s effort to execute the Integrated Methane Monitoring Platform Design project, ultimately providing an engineering, design, deployment, and operating plan (EDDOP) for the IMMP. This document provides additional information supporting the findings in the final report.
Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories
This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.
MadNIS - Neural multi-channel importance sampling
Theory predictions for the LHC require precise numerical phase-space integration and generation of unweighted events. We combine machine-learned multi-channel weights with a normalizing flow for importance sampling, to improve classical methods for numerical integration. We develop an efficient bi-directional setup based on an invertible network, combining online and buffered training for potentially expensive integrands. We illustrate our method for the Drell-Yan process with an additional narrow resonance.
A novel green hydrogen production using water-energy nexus framework
The transformation of electrical energy to hydrogen via water electrolysis consumes considerable amount of fresh water and a productive use of nontraditional water sources enhances the reliability and resilience of energy and water systems. In this study, we have designed a solid oxide electrolysis cell (SOEC) system which is an evolving hydrogen production technology at high temperatures for water electrolysis. Here, the SOEC uses steam generated from flue gas as its feedstock and is fully integrated with numerous power production units, including coal and natural gas-fired power plants as its energy feedstock. While there is a hasten global shift away from fossil fuel, integrating its asset into this technology helps limit the risk and future losses of stranded assets and reduce the cost of investment in the new technologies. But high capital expenditures and doubt concerning the future cost and efficiency upgrade are obstacles to investing in water electrolysis. Such a detailed Levelized cost of hydrogen and techno-economic analysis is conducted to show the viability and environmental impacts of this novel technology. The results show SOEC efficiency of 97.4 % and 56.3 % as thermal-to-hydrogen efficiency of the system with a daily hydrogen production of 242,400 kg at $2.9–3.5/kg H 2 . The estimates show a positive gain prospect in this technology and techno-economic challenges.
Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation
With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.
From Machine Learning to Machine Reasoning: A Model-based Approach to Analyze Equipment Reliability Data
In current nuclear power plants (NPPs) a large amount of condition-based data which can be used to assess and monitor component health and performance. Assessing component health from such data can be performed with a large variety of methods. While the analysis of numeric data can be performed with several methods, the extraction of information from textual data remains a challenge. Currently employed natural language processing (NLP) methods do not really provide quantitative information that might be contained in IRs. In addition, the integration of numeric and textual data to identify possible causal relationships between data elements is still an unresolved challenge. This paper presents an approach to extract information from textual (e.g., incident or maintenance reports) and numeric data that relies on model based system engineer (MBSE) models. MBSE are diagrams designed to represent system and component dependencies (from both a form and functional point of view). In our approach, MBSE models emulate system engineer knowledge about component/system architecture. NLP methods are employed to perform syntactic and semantic analyses. Syntactic analysis analyzes the grammatical structure of a sentence while semantic analysis is designed to analyze the logic structure of a sentence. An innovative element of our approach is that semantic analysis uses MBSE models to identify links between textual elements. Similarly, numeric data is directly linked to elements of the MBSE models in order to map which functions are being monitored.
Lattice Green’s Functions for High-Order Finite Difference Stencils
Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of existing numerical solvers that make use of LGFs rely on a second-order discretization and operate on domains with free-space boundary conditions in all directions. Under these conditions, fast expansion methods are available that enable precomputation of 2D or 3D LGFs in linear time, avoiding the need for brute-force multi-dimensional quadrature of numerically unstable integrals. Here we focus on higher-order discretizations of the Laplace operator on domains with more general boundary conditions, by (1) providing an algorithm for fast and accurate evaluation of the LGFs associated with high-order dimension-split centered finite differences on unbounded domains, and (2) deriving closed-form expressions for the LGFs associated with both dimension-split and Mehrstellen discretizations on domains with one unbounded dimension. Through numerical experiments we demonstrate that these techniques provide LGF evaluations with near machine-precision accuracy, and that the resulting LGFs allow for numerically consistent solutions to high-order discretizations of the Poisson's equation on fully or partially unbounded 3D domains.
Implicit–explicit multirate infinitesimal stage-restart methods
Implicit–Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is split into stiff and nonstiff processes with the goal of lower computational costs than a purely implicit or explicit approach. A complementary form of flexible IVP solvers are multirate infinitesimal methods for problems split into fast- and slow-changing dynamics, that solve a multirate IVP by evolving a sequence of “fast” IVPs using any suitably accurate algorithm. This article introduces a new class of high-order implicit–explicit multirate methods that are designed for multirate IVPs in which the slow-changing dynamics are further split in an IMEX fashion. This new class, which we call implicit–explicit multirate infinitesimal stage-restart (IMEX-MRI-SR), both improves upon the previous implicit–explicit multirate infinitesimal generalized-structure additive Runge Kutta (IMEX-MRI-GARK) methods by allowing for far easier creation of new embedded methods, and extends multirate exponential Runge Kutta (MERK) methods by allowing the fast-changing dynamics to be nonlinear and the methods to be implicit. We leverage GARK theory to derive conditions for orders of accuracy up to four, and we provide second- and third-order accurate example methods, which are the first known embedded MRI methods with IMEX structure. We then perform numerical simulations demonstrating convergence rates and computational performance in both fixed-step and adaptive-step settings.
Quantifying the effect of tow architecture variability on the performance of biaxially braided composite tubes
Targeted experiments are performed with stereoscopic digital image correlation to quantify the effect of irregular braid structure on the local surface mechanical response of carbon-fiber reinforced epoxy composite tubes. Virtual models comparing both nonuniform and uniform tow structure of the outer braid of each specimen are integrated into numerical simulations similar to experiments. Experimental and numerical results agree well. Statistical tests are used to support correlations between as-manufactured braid variation ranges to local increases in stress up to 18% compared to an ideal, uniform structure in the elastic regime. Results support improved manufacturing and modeling efforts of defect sensitive braided composites.