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At least 397 records · Page 22

Isoparametric finite element methods to estimate discontinuous coefficients in two-dimensional elliptic equations

A summary of findings is presented on the problem of estimating discontinuous coefficients, including the locations of interfaces at which discontinuities occur, for elliptic equations on a two-dimensional domain. Finite-element approximations are constructed that are based on an underlying grid that adaptively moves to follow locations of interfaces as they are iteratively updated in the numerical estimation process.

Lamm, Patricia K.↗

Software design as a problem in learning theory (a research overview)

Our interest in automating software design has come out of our research in automated reasoning, inductive inference, learnability, and algebraic machine theory. We have investigated these areas extensively, in connection with specific problems of language representation, acquisition, processing, and design. In the case of formal context-free (CF) languages we established existence of finite learnable models ('behavioral realizations') and procedures for constructing them effectively. We also determined techniques for automatic construction of the models, inductively inferring them from finite examples of how they should 'behave'. These results were obtainable due to appropriate representation of domain knowledge, and constraints on the domain that the representation defined. It was when we sought to generalize our results, and adapt or apply them, that we began investigating the possibility of determining similar procedures for constructing correct software. Discussions with other researchers led us to examine testing and verification processes, as they are related to inference, and due to their considerable importance in correct software design. Motivating papers by other researchers, led us to examine these processes in some depth. Here we present our approach to those software design issues raised by other researchers, within our own theoretical context. We describe our results, relative to those of the other researchers, and conclude that they do not compare unfavorably.

Fass, Leona F.↗

Onyx-Advanced Aeropropulsion Simulation Framework Created

The Numerical Propulsion System Simulation (NPSS) project at the NASA Glenn Research Center is developing a new software environment for analyzing and designing aircraft engines and, eventually, space transportation systems. Its purpose is to dramatically reduce the time, effort, and expense necessary to design and test jet engines by creating sophisticated computer simulations of an aerospace object or system (refs. 1 and 2). Through a university grant as part of that effort, researchers at the University of Toledo have developed Onyx, an extensible Java-based (Sun Micro-systems, Inc.), objectoriented simulation framework, to investigate how advanced software design techniques can be successfully applied to aeropropulsion system simulation (refs. 3 and 4). The design of Onyx's architecture enables users to customize and extend the framework to add new functionality or adapt simulation behavior as required. It exploits object-oriented technologies, such as design patterns, domain frameworks, and software components, to develop a modular system in which users can dynamically replace components with others having different functionality.

Reed, John A.↗

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate numerical schemes which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.

Barth, Timothy J.↗

Online Dectection and Modeling of Safety Boundaries for Aerospace Application Using Bayesian Statistics

The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.

Statistics↗

Measuring the robustness of predictive probability for early stopping in two-group comparisons

We report physical experiments are often expensive and time-consuming. Test engineers must certify the compatibility of aircraft and their weapon systems before they can be deployed in the field, but the testing required is time consuming, expensive, and resource limited. Adopting Bayesian adaptive designs is a promising way to borrow from the successes seen in the clinical trials domain. The use of predictive probability (PP) to stop testing early and make faster decisions is particularly appealing given the aforementioned constraints. Given the high-consequence nature of the tests performed in the national security space, a strong understanding of new methods is required before being deployed. Although PP has been thoroughly studied for binary data, there is less work with continuous data, where many reliability studies are interested in certifying the specification limits of components. A simulation study evaluating the robustness of this approach indicates early stopping based on PP is reasonably robust to minor assumption violations, especially when only a few interim analyses are conducted. The simulation study also compares PP to conditional power, showing its relative strengths and weaknesses. A post-hoc analysis exploring whether release requirements of a weapon system from an aircraft are within specification with desired reliability resulted in stopping the experiment early and saving 33% of the experimental runs.

97 MATHEMATICS AND COMPUTING↗

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scalable algorithms for domain decomposition of Monte Carlo neutral particle transport simulations on unstructured mesh

Monte Carlo simulations are the gold standard in particle transport simulations, for shielding and nuclear reactor simulations Full core simulations can require terabytes of memory for tracking pin-resolved (up to 50k pins), nuclide (200 tracked), axial (20-200 zones) reaction rates Domain decomposition, splitting the calculation and the memory storage, among several nodes is challenging as it involves communication of particles across domain boundaries We created a new MOOSE application, MaCaw, to study this problem Algorithms developed for ray tracing in MOOSE were adapted for simulating neutral particle transport Physics and tally routines in OpenMC, dynamically linked, are called from the application

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Towards Geospatial Knowledge Graph Infused Neuro-Symbolic AI for Remote Sensing Scene Understanding

Deep learning has proven its effectiveness in numerous tasks for remote sensing scene understanding. However there is an increasing interest to explore fusion of domain-specific background information to the deep neural network to further improve its performance. Remote sensing researchers are also working towards developing models that generalize and adapt to multiple applications. Generalization challenges coupled with the scarcity of large corpora of high-quality noise-free labelled data, have together fueled an interest for leveraging background information. Knowledge graphs serve as excellent choice to represent domain-specific information in a structured, standardized and extensible manner. Integrating symbolic knowledge representations in the form of Knowledge Graph Embedding (KGE) to perform neuro-symbolic reasoning is an emerging research direction promising significant impacts. This vision paper seeks to position ideas and provoke early thoughts toward advancing neuro-symbolic artificial intelligence in the context of geospatial challenges. Specifically, it conceptualizes and elaborates on an architecture for infusing geospatial knowledge from knowledge graph in a deep neural network pipeline. As guiding case studies - land-use land-cover classification, object detection and instance segmentation can benefit from infusing spatio-contextual information with remote sensing imagery. The discussion further reflects on and articulates the challenges and explainable AI opportunities anticipated when scaling and maintaining large-scale geospatial knowledge graphs.

Potnis, Abhishek↗

Manifold projection image segmentation for nano-XANES imaging

As spectral imaging techniques are becoming more prominent in science, advanced image segmentation algorithms are required to identify appropriate domains in these images. We present a version of image segmentation called manifold projection image segmentation (MPIS) that is generally applicable to a broad range of systems without the need for training because MPIS uses unsupervised machine learning with a few physically motivated hyperparameters. We apply MPIS to nanoscale x-ray absorption near edge structure (XANES) imaging, where XANES spectra are collected with nanometer spatial resolution. We show the superiority of manifold projection over linear transformations, such as the commonly used principal component analysis (PCA). Moreover, MPIS maintains accuracy while reducing computation time and sensitivity to noise compared to the standard nano-XANES imaging analysis procedure. Finally, we demonstrate how multimodal information, such as x-ray fluorescence data and spatial location of pixels, can be incorporated into the MPIS framework. We propose that MPIS is adaptable for any spectral imaging technique, including scanning transmission x-ray microscopy, where the length scale of domains is larger than the resolution of the experiment.

36 MATERIALS SCIENCE↗

An Integrated Design of a Polypseudorotaxane-Based Sea Cucumber Mimic

The development of integrated systems that mimic the multi-stage stiffness change of marine animals such as the sea cucumber requires the design of molecularly tailored structures. Herein, we used an integrated biomimicry design to fabricate a sea cucumber mimic using sidechain polypseudorotaxanes with tunable nano-to-macroscale properties. A series of polyethylene glycol (PEG)-based sidechain copolymers were synthesized to form sidechain polypseudorotaxanes with α-cyclodextrins (α-CDs). By tailoring the copolymers’ molecular weights and their PEG grafting densities, we rationally tuned the sizes of the formed polypseudorotaxanes crystalline domain and the physical crosslinking density of the hydrogels, which facilitated 3D printing and the mechanical adaptability to these hydrogels. After 3D printing and photo-crosslinking, the obtained hydrogels exhibited large tensile strain and broad elastic-to-plastic variations upon α-CD (de)threading. Finally, these discoveries enabled a successful fabrication of a sea cucumber mimic, demonstrating multi-stage stiffness changes.

36 MATERIALS SCIENCE↗

Design analysis and computer-aided performance evaluation of shuttle orbiter electrical power system. Volume 1: Summary

Studies were conducted to develop appropriate space shuttle electrical power distribution and control (EPDC) subsystem simulation models and to apply the computer simulations to systems analysis of the EPDC. A previously developed software program (SYSTID) was adapted for this purpose. The following objectives were attained: (1) significant enhancement of the SYSTID time domain simulation software, (2) generation of functionally useful shuttle EPDC element models, and (3) illustrative simulation results in the analysis of EPDC performance, under the conditions of fault, current pulse injection due to lightning, and circuit protection sizing and reaction times.

Source record↗

Blindness in designing intelligent systems

New investigations of the foundations of artificial intelligence are challenging the hypothesis that problem solving is the cornerstone of intelligence. New distinctions among three domains of concern for humans--description, action, and commitment--have revealed that the design process for programmable machines, such as expert systems, is based on descriptions of actions and induces blindness to nonanalytic action and commitment. Design processes focusing in the domain of description are likely to yield programs like burearcracies: rigid, obtuse, impersonal, and unable to adapt to changing circumstances. Systems that learn from their past actions, and systems that organize information for interpretation by human experts, are more likely to be successful in areas where expert systems have failed.

Denning, Peter J.↗

Time activities at the BIPM

The generation and dissemination of International Atomic Time, TAI, and of Coordinated Universal Time, UTC, are explicitly mentioned in the list of the principal tasks of the BIPM, recalled in the Comptes Rendus of the 18th Conference Generale des Poids et Mesures, in 1987. These tasks are fulfilled by the BIPM Time Section, thanks to international cooperation with national timing centers, which maintain, under metrological conditions, the clocks used to generate TAI. Besides the current work of data collection and processing, research activities are carried out in order to adapt the computation of TAI to the most recent improvements occurring in the time and frequency domains. Studies concerning the application of general relativity and pulsar timing to time metrology are also actively pursued. This paper summarizes the work done in all these fields and outlines future projects.

Thomas, Claudine↗

Investigation of finite element: ABC methods for electromagnetic field simulation

The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.

Chatterjee, A.↗

Cross Validation of the Network of Ground-Based Radar with GPM during the Remote Sensing of Electrification, Lightning, And Mesoscale/Microscale Processes with Adaptive Ground Observations (RELAMPAGO) Field Campaign

The cross-validation of radars in a network is important in making consistent retrievals across the domain and assuring the product quality. During the RELAMPAGO field campaign, two C-band radars, namely the Colorado State University C-band Hydrological Instrument for Volumetric Observations ( CSU-CHIVO) and the C-band Scanning ARM Precipitation Radar (CSAPR-2), were deployed near the Sierras de Cordoba in Argentina, a region known for having some of the most intense severe weather in the world. In addition to these two radars, the operational radar of the Cordoba City, the Radar Meteorologico Argentino 1 (RMA-1), adds another instrument to the RELAMPAGO network. This study presents an intercomparison between the RELAMPAGO C-band radars using the GPM spaceborne radar as a common reference ..A method to bring ground-based radars into better agreement is also proposed. Moreover, the attenuation correction for the C-band radar is studied in the context of intercomparing two radars. The attenuation coefficients are computed for the RELAMPAGO domain using the local disdrometers deployed. during the campaign. After the attenuation correction, CSU-CHIVO, CSAPR-2, and RMA-1 compare well with GPM-DPR with a high correlation and bias less than 1 dB.

54 ENVIRONMENTAL SCIENCES↗

Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

Here, we present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://doi.org/10.1016/j.cma.2024.117135), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.

97 MATHEMATICS AND COMPUTING↗