Engineering PapersSearch

SEARCH · Engineering Papers

Results for “MATHEMATICS - BOUNDARY VALUES”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Scientific Discovery with Physics-Informed System Identification (Abbreviated Report)

My fellowship research focused on making physics-based simulations faster and more useful through machine learning. Many problems in science and engineering are governed by partial differential equations, but high-fidelity simulations are often too expensive to run repeatedly. I worked on improving Latent Space Dynamics Identification (LaSDI), a reduced-order modeling framework that compresses large simulation data sets into a smaller representation and then learns how that representation evolves over time. The motivation was to develop reduced models that remain accurate for more challenging systems, especially when predictions must remain reliable over long time intervals or when the underlying dynamics are more complicated than standard methods can easily handle. I also contributed to related work on Quandary, a high-performance software effort for simulation and control of open quantum systems, before focusing primarily on Latent Space Dynamics Identification methods. The main outcomes of the fellowship were two new algorithms (both of which were published), Rollout-LaSDI and Higher-Order LaSDI, together with supporting work on multi-stage Latent Space Dynamics Identification. Rollout-LaSDI improved long-term prediction by training the model to stay accurate over extended time horizons, and Higher-Order LaSDI broadened the method so it could model systems with higher-order time dynamics. My contributions to multistage Latent Space Dynamics Identification also helped show that its later training stages could be simplified without losing effectiveness, and that this behavior held across different model architectures and training strategies. Taken together, these advances improved the accuracy, flexibility, and practical value of reduced-order modeling tools for computational science.

97 MATHEMATICS AND COMPUTING

Weak Form Scientific Machine Learning: Test Function Construction for System Identification

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

FOS: Computer and information sciences

Estimation of intensity, footprint, and capacity of surface urban heat islands using a direction-enhanced adaptive synchronous extraction (DEASE) method

Here, the surface urban heat island (SUHI) effect, assessed through remotely sensed land surface temperature (LST), remains a focal point in urban climate research. Conventional indicators like SUHI intensity (SUHII) and footprint (SUHIF) capture peak values and spatial extent but fail to account for the cumulative thermal load—a critical dimension reflecting the total heat exposure imposed by spatially continuous warming, which directly limits a holistic assessment of ecological and societal impacts of the SUHI effect. Therefore, this study introduces an indicator termed SUHI capacity (SUHIC), designed to quantify the aggregated SUHI effect by integrating the magnitude of the warming signal across all affected areas, thereby enabling a more comprehensive evaluation of urban thermal environments. Furthermore, a direction-enhanced adaptive synchronous extraction (DEASE) method is proposed for the quantification of SUHIC. This method can dynamically identify the optimal background reference area based on the urban-rural LST gradients in various directions within the city, without relying on predefined mathematical models as previously. The results from 102 European cities first confirm that the directional variations in urban-rural LST gradients, and the DEASE method can effectively capture these distinctions for the simultaneous estimation of SUHII, SUHIF, and SUHIC. Secondly, the spatial patterns of absolute SUHIC values show strong associations with those of SUHIF (R2>0.86), while its relative values (normalized by the area of urban) align more closely with SUHII (R2 > 0.64). More importantly, SUHIC can serve as a crucial reference for assessing the urban thermal signal when SUHII and SUHIF diverge. The proposed method and framework contribute to standardizing the quantification of the SUHI effect.

Indicator

SENTRA: A Modular Computational Graph Framework for Critical Mineral and Materials Supply Chains: Part I: Network Construction Latent-Quantity Estimation, and Temporal Graph Forecasting

Global supply chains for critical minerals and materials are complex, evolving networks of countries, products, production stages, and trade relationships. Existing analytical approaches are limited by fragmented data and static network representations that do not capture the dynamic production dependencies linking raw materials, intermediate products, and final goods across multiple countries. Trade and production statistics provide only a partial view of domestic production, inventories, and material flows, making it difficult to identify indirect sourcing pathways, hidden dependencies, and embedded foreign exposures. This paper introduces the Supply Chain Exposure Network Tracking and Risk Assessment (SENTRA) framework, a modular graph-based computational framework for constructing, analyzing, and forecasting dynamic supply chain networks. As the first paper in a three-part methodological series, it establishes the computational foundation of SENTRA by constructing a temporal attributed multi-relational graph whose nodes represent product–country pairs and whose edges encode observed trade and within-country value-chain relationships. Statistical estimation and constrained optimization recover latent production, final demand, and product input dependency coefficients while enforcing economic accounting constraints. Graph-derived exposure measures quantify direct, transshipment, value-chain, and multi-hop supply chain dependencies independently of the forecasting model. A temporal graph forecasting architecture based on a relational graph neural network then forecasts the evolution of the graph under mass-balance constraints with distribution-free conformal uncertainty quantification. Validation on the global aluminum supply chain shows that the learned graph representations recover economically meaningful supply chain structure, accurately forecast out-of-sample trade relationships, and produce well-calibrated prediction intervals. Subsequent papers apply this computational foundation to exposure assessment, disruption analysis, and scenario-based policy analysis, and extend the framework to multimaterial supply chain modeling and decision support.

36 MATERIALS SCIENCE

Learning Topological Operations on Meshes with Application to Block Decomposition of Polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

97 MATHEMATICS AND COMPUTING

TeMPI Shim

This is the manual for the TeMPI Shim library, whose goal is to facilitate scientific apps being loosely coupled through MPI. TeMPI Shim can be used to create and manage Message Passing Interface (MPI, see [MPI]) Communicators for Single Program, Multiple Data (SPMD, see [SPMD]) and Multiple Programs, Multiple Data (MPMD, see [MPMD]) workflows. MPI provides the MPI_APPNUM command number to each of the processes within its context. This number, starting at 0, is the application number being executed. In a case where 3 applications are being run in MPMD mode, there would be MPI_APPNUM values of 0, 1, and 2. TeMPI Shim creates intra- and inter-communicators between each pair of MPI_APPNUM values. In the aforementioned case, application 0 would have intra- and inter-communicators to speak to itself, application 1, and application 2. This is replicated for each of the applications. Additionally, TeMPI Shim creates intra- and inter-communicators for the first MPI rank of each application to directly communicate only with each other. Finally, TeMPI Shim creates its own copy of the default world communicator, i.e., MPI_COMM_WORLD. In the case where there is only a single application, it will have the communicators to only speak with itself. TeMPI Shim is useful in this case since it is considered good practice for MPI applications to copy the default world communicator and reference this copy (see [Duplicate World]_) anyways. Ultimately, it provides value independent of the number of applications present.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION

Special Nuclear Geometric Modeling

This report is a summary of our summer interns project that focused on investigating the usefulness of the Gamma Detector Response and Analysis Software (GADRAS) into the Material Control & Accountability (MC&A) Measurements Team. The project's findings highlight the advantages of using GADRAS and demonstrate its value in improving the MC&A Measurements Team's analytical capabilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

High-Fidelity Modeling of a Type-5 Wind Turbine Gearbox (Intern Poster) [Poster]

Type-5 wind turbines are unique in their use of a permanent magnet synchronous generator, as well as their use of a hydraulic torque converter. This architecture presents an opportunity to provide steady and grid-ready energy without the need for a power converter. With infrastructure continuity and reliability being an important topic amongst renewable energies, researchers have been prompted to further investigate the benefits of type-5 turbines’ unique electromechanical configuration on stable electricity generation. Researchers involved in the WindSG project, SG standing for synchronous generator, are aiming to model a type-5 turbine using Real Time Digital Simulation (RTDS) to evaluate its efficacy in the grid. RSCAD, the software run on the RTDS, comes pre-loaded with electrical and electromechanical components to help simulate electrical generation and grid conditions. However, within this repertoire there is a lack of a component to represent a gearbox with high-fidelity. Within RSCAD’s case studies, the gearbox is often represented simply by a gear ratio value. This presented the task of developing a high-fidelity gearbox model in RSCAD for use in the larger RTDS type-5 wind turbine model. This poster describes a method of developing a lumped parameter mathematical model to represent a planetary-parallel-parallel gearbox in RSCAD for use in RTDS.

17 WIND ENERGY

High-Fidelity Modeling of a Type-5 Wind Turbine Gearbox (Intern Technical Presentation) (Poster)

Type-5 wind turbines are unique in their use of a permanent magnet synchronous generator, as well as their use of a hydraulic torque converter. This architecture presents an opportunity to provide steady and grid-ready energy without the need for a power converter. With infrastructure continuity and reliability being an important topic amongst renewable energies, researchers have been prompted to further investigate the benefits of type-5 turbines’ unique electromechanical configuration on stable electricity generation. Researchers involved in the WindSG project, SG standing for synchronous generator, are aiming to model a type-5 turbine using Real Time Digital Simulation (RTDS) to evaluate its efficacy in the grid. RSCAD, the software run on the RTDS, comes pre-loaded with electrical and electromechanical components to help simulate electrical generation and grid conditions. However, within this repertoire there is a lack of a component to represent a gearbox with high-fidelity. Within RSCAD’s case studies, the gearbox is often represented simply by a gear ratio value. This presented the task of developing a high-fidelity gearbox model in RSCAD for use in the larger RTDS type-5 wind turbine model. This presentation describes a method of developing a lumped parameter mathematical model to represent a planetary-parallel-parallel gearbox in RSCAD for use in RTDS.

17 WIND ENERGY

Using PyBioNetFit to leverage qualitative and quantitative data in biological model parameterization and uncertainty quantification

Data generated in studies of cellular regulatory systems are often qualitative. For example, measurements of signaling readouts in the presence and absence of mutations may reveal a rank ordering of responses across conditions but not the precise extents of mutation-induced differences. Qualitative data are often ignored by mathematical modelers or are considered in an ad hoc manner, as in the study of Kocieniewski and Lipniacki (2013) [Phys Biol 10: 035006], which was focused on the roles of MEK isoforms in ERK activation. In this earlier study, model parameter values were tuned manually to obtain consistency with a combination of qualitative and quantitative data. This approach is not reproducible, nor does it provide insights into parametric or prediction uncertainties. Here, starting from the same data and the same ordinary differential equation (ODE) model structure, we generate formalized statements of qualitative observations, making these observations more reusable, and we improve the model parameterization procedure by applying a systematic and automated approach enabled by the software package PyBioNetFit. We also demonstrate uncertainty quantification (UQ), which was absent in the original study. Our results show that PyBioNetFit enables qualitative data to be leveraged, together with quantitative data, in parameterization of systems biology models and facilitates UQ. These capabilities are important for reliable estimation of model parameters and model analyses in studies of cellular regulatory systems and reproducibility.

59 BASIC BIOLOGICAL SCIENCES

Omega-Limit Sets and Input-To-State Stability in Power Grids with Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields - or modes -, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of ..omega.. -limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION

Supporting Special Values in ZFP

This white paper outlines potential approaches to supporting special values in the ZFP numerical compressor without breaking backwards compatibility. Other than infinities and NaNs, special values are often used to indicate the absence of data, where no value is defined, for example by designating finite but extreme “fill values” as special. Such fill values are commonly used in earth system science, among other applications, but if left as is during compression lead to artifacts and loss of precision in nearby true values. Multiple candidate solutions that would allow ZFP to recognize special values are here proposed. Until such support is available, we also sketch available workarounds.

97 MATHEMATICS AND COMPUTING

Geothermal well testing pressure prediction by using a hybrid transformer model system: FORGE well use case

Geothermal has huge potential to become an indispensable component in achieving the goal of sustainable energy economy, given its capability to provide consistent baseload power to the electric grid. Injection tests are crucial in geothermal energy system as they naturally help to evaluate reservoir properties, understand fluid flow and even enhance reservoir performance. In this research, we developed a hybrid model system that integrates machine learning (ML) regression, a physics-based mathematical model, and transformer deep learning. Trained and validated using FORGE injection test dataset, this system can forecast the pressure variations both upward and downward over time. The pressure prediction achieved prediction accuracy within 3-6% variance of true pressure values. The system can significantly save time and reduce costs by testing only a few cycles and then using model predictions for further analysis, instead of conducting additional real injection cycle tests. The developed model system also holds promise for designing injection test processes and maintaining well production in geothermal energy. Presented at the IMAGE ‘25 Conference led by Shell.

FORGE

Coupled Cluster Theory for Nonadiabatic Dynamics: Nuclear Gradients and Nonadiabatic Couplings in Similarity Constrained Coupled Cluster Theory

Coupled cluster theory is one of the most accurate electronic structure methods for predicting ground and excited state chemistry. However, the presence of numerical artifacts at electronic degeneracies, such as complex energies, has made it difficult to apply the method in nonadiabatic dynamics simulations. While it has already been shown that such numerical artifacts can be fully removed by using similarity constrained coupled cluster (SCC) theory [J. Phys. Chem. Lett. 2017, 8(19), 4801–4807], simulating dynamics requires efficient implementations of gradients and nonadiabatic couplings. Here, we present an implementation of nuclear gradients and nonadiabatic derivative couplings at the similarity constrained coupled cluster singles and doubles (SCCSD) level of theory, thereby making possible nonadiabatic dynamics simulations using a coupled cluster theory that provides a correct description of conical intersections between excited states. We present a few numerical examples that show good agreement with literature values and discuss some limitations of the method.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA

DESI peculiar velocity survey – Fundamental Plane

The Dark Energy Spectroscopic Instrument (DESI) peculiar velocity survey aims to measure the peculiar velocities of early- and late-type galaxies within the DESI footprint using both the Fundamental Plane and optical Tully–Fisher relations. Direct measurements of peculiar velocities can significantly improve constraints on the growth rate of structure, reducing uncertainty by a factor of approximately 2.5 at redshift 0.1 compared to the DESI Bright Galaxy Survey’s redshift space distortion measurements alone. We assess the quality of stellar velocity dispersion measurements from DESI spectroscopic data. These measurements, along with photometric data from the Legacy Survey, establish the Fundamental Plane relation and determine distances and peculiar velocities of early-type galaxies. During survey validation, we obtain spectra for 6698 unique early-type galaxies, up to a photometric redshift of 0.15. 64 per cent of observed galaxies (4267) have relative velocity dispersion errors below 10 per cent. This percentage increases to 75 per cent if we restrict our sample to galaxies with spectroscopic redshifts below 0.1. We use the measured central velocity dispersion, along with photometry from the DESI Legacy Imaging Surveys, to fit the Fundamental Plane parameters using a 3D Gaussian maximum likelihood algorithm that accounts for measurement uncertainties and selection cuts. In addition, we conduct zero-point calibration using the absolute distance measurements to the Coma cluster, leading to a value of the Hubble constant, H 0 = 76.05 ± 0.35 (statistical) ±0.49 (systematic Fundamental Plane) ±4.86 (statistical due to calibration) km s –1 Mpc –1 ⁠. This H 0 value is within 2σ of Planck cosmic microwave background results and within 1σ of other low-redshift distance indicator-based measurements.

cosmological parameters

Quantifying the Operational Impacts of Cyber Events on Enterprise Network Environments

The "Quantifying the Operational Impacts of Cyber Events on Enterprise Network Environments" Feasibility Study addressed the question: Can an existing (novel) class of network characterization and change detection algorithms previously developed at LLNL for internal enterprise datasets, be effectively applied to assess and measure the analytic value of features derived from datasets composed of passively collected RF and wireless network data?

97 MATHEMATICS AND COMPUTING

Nanoindentation Stress Relaxation to Quantify Dislocation Velocity–Stress Exponent

This work reports a new methodology using indentation stress relaxation to characterize the dislocation velocity–stress exponent. Through the indentation stress relaxation process, the dislocation structure builds up at the rate governed by dislocation velocity, which is a function of the externally applied stress. The relationship between the dislocation velocity and stress can thus be derived from the indentation stress relaxation data of the stress as a function of time. In this study, instrumented nanoindentation stress relaxation experiments were performed on pure aluminum samples, following three different initial displacement rates of 100, 400, and 800 nm/s. Based on the scaling properties of dislocation kinetics, the data were interpreted to derive a dislocation velocity–stress exponent of 2.5 ± 0.5 for room-temperature aluminum. Crystal plasticity finite-element simulations were performed to illustrate the sensitivity of the proposed nanoindentation stress relaxation methodology to the dislocation velocity–stress exponent value.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Grey-Box System Identification of Grid-Forming Inverters

This paper demonstrates the use of grey-box system identification methods for simplifying and understanding the nonlinear power dynamics of grid-forming inverters (GFMs). The power and frequency outputs of complex high-order GFM models are fed into system identification software in order to fit them to a predetermined LTI system and learn system parameters such as (synthetic) inertia and droop constants. The same process is then run for a high-order synchronous generator model, and the outputs are fit to the same set of LTI equations. Simulation of a network of GFM inverters with diverse control architecture is also performed for the same process. The intent is threefold: first, to demonstrate the appropriateness of unified LTI models for describing the power and frequency dynamics of individual resources and connected networks, in order to facilitate analysis of larger heterogeneous networked systems; second, to discover the relationship between internal control parameters of GFMs and their externally observed values; and third, to validate that grey-box data-driven system identification techniques can be a valuable tool to discover the values of important parameters in the absence of explicit vendor models.

analytical models