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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Slack, David C.↗
DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗
DOE OSTI2021

ExaSGD: 2021 Kernel Thrust Activities

The Kernel Thrust milestone ADSE22-214 covers the development of device-capable optimization algorithms and solvers technologies required by the ExaSGD project’s software stack in order to solve security-constrained alternating current optimal power flow (SC-ACOPF) problems on emerging exascale architectures. To this extent, in FY21 the main objective of the Kernel Thrust was (i) provide robust optimization solver(s) that run efficiently on hardware accelerator devices (i.e., NVIDIA and AMD GPUs) to perform intra-node computations and (ii) provide coarse-grain parallel optimization capabilities that exploit the decomposition opportunities present in the SC-ACOPF challenge problems to provide exascale-capable solvers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

A linguistic geometry for space applications

We develop a formal theory, the so-called Linguistic Geometry, in order to discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, and apply them to different systems. This research relies on the formalization of search heuristics of high-skilled human experts which allow for the decomposition of complex system into the hierarchy of subsystems, and thus solve intractable problems reducing the search. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. This paper includes a formal survey of the Linguistic Geometry, and new example of a solution of optimization problem for the space robotic vehicles. This example includes actual generation of the hierarchy of languages, some details of trajectory generation and demonstrates the drastic reduction of search in comparison with conventional search algorithms.

Stilman, Boris↗
NASA NTRS2004

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian↗
DOE OSTI2021

Constrained non-negative matrix factorization enabling real-time insights of in situ and high-throughput experiments

Non-negative matrix factorization (NMF) is an appealing class of methods for performing unsupervised learning on streaming spectral data, particularly in time-sensitive applications such as in situ characterization of materials. These methods seek to decompose a dataset into a small number of components and weights that can compactly represent the underlying signal while effectively reconstructing the observations with minimal error. However, canonical NMF methods have no underlying requirement that the reconstruction uses components or weights that are representative of the true physical processes. In this work, we demonstrate how constraining a subset of the NMF weights or components as rigid priors, provided as known or assumed values, can provide significant improvement in revealing true underlying phenomena. We present a PyTorch-based method for efficiently applying constrained NMF and demonstrate its application to several synthetic examples. Our implementation allows an expert researcher-in-the-loop to provide and dynamically adjust the constraints during a live experiment involving streaming spectral data. Such interactive priors allow researchers to specify known or identified independent components, as well as functional expectations about the mixing or transitions between the components. We further demonstrate the application of this method to measured synchrotron x-ray total scattering data from in situ beamline experiments. In such a context, constrained NMF can result in a more interpretive and scientifically relevant decomposition than canonical NMF or other decomposition techniques. As a result, the details of the method are provided, along with general guidance for employing constrained NMF in the extraction of critical information and insights during time-sensitive experimental applications.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Algorithmic considerations of integrated design for CSI on a hypercube architecture

An approach is presented to the integrated design problem for actively controlled large, flexible mechanical systems for which Control Structure Interaction (CSI) problems are of concern. The two coupled design problems were identified as the optimal Structural Design problem the optimal Controller Design problem. These two problems can be addressed within a decision making loop that would consider each separately, and then sequentially analyze the effects of one on the other. Embedded in such a loop would be the simulation and coordination tasks as part of the decision tools required in a total (software) package. All of the above are compute-intensive tasks. In any such task, possible decompositions and gains due to the inherent parallelism have to be exploited. The problems under consideration, as applied to large flexible mechanical structures, are particularly suited to be mapped onto multicomputer systems in a hypercube topology.

Oezguener, UE.↗
DOE OSTI2020

Space–time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing much accuracy, which results in a considerably more speed-up than the spatial reduction only. Recently, a novel space–time reduced order model for dynamical problems has been developed [17], where the space–time reduced order model shows an order of a hundred speed-up with a relative error of 10 –4 for small academic problems. However, in order for the method to be applicable to a large-scale problem, an efficient space–time reduced basis construction algorithm needs to be developed. Here we present the incremental space–time reduced basis construction algorithm. The incremental algorithm is fully parallel and scalable. Additionally, the block structure in the space–time reduced basis is exploited, which enables the avoidance of constructing the reduced space–time basis. These novel techniques are applied to a large-scale particle transport simulation with million and billion degrees of freedom. The numerical example shows that the algorithm is scalable and practical. Also, it achieves a tremendous speed-up, maintaining a good accuracy. Finally, error bounds for space-only and space–time reduced order models are derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1997

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗
NASA NTRS2006

MXER Simulation Study (Appendix B)

The task of prediction of the motion of a momentum exchange system with a 9-digit accuracy is extremely challenging, and it is relentlessly testing our ability to gain fundamental insights into the nature of the tether dynamics in this system. It has been show that the modal decomposition approach developed in the first part of this study is a very powerful and precise tool for the simulation of the dynamics of momentum exchange tethers. However, to get a prediction with required accuracy using this tool, one must have precise inputs, including the initial state, system parameters, and the environmental models. In simulations, the tether tip positioning has been observed to be quite sensitive to even small variations of the parameters involved in the calculations. It is therefore imperative that precise estimation and control algorithms be developed to compensate for the inevitable uncertainties and support high precision rendezvous.

Levin, E. M.↗
NASA NTRS1986

Two time scale output feedback regulation for ill-conditioned systems

Issues pertaining to the well-posedness of a two time scale approach to the output feedback regulator design problem are examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. It is shown that, under mild assumptions, minimization of this cost leads to feedback gains providing a second-order approximation of optimal full system performance. A simplified approach to two time scale feedback design is also developed, in which gains are separately calculated to stabilize the slow and fast subsystem models. By exploiting the notion of combined control and observation spillover suppression, conditions are derived assuring that these gains will stabilize the full-order system. A sequential numerical algorithm is described which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. It is shown that the algorithm converges to a local minimum under nonrestrictive assumptions. This procedure is adapted to and demonstrated for the two time scale design formulations.

Calise, A. J.↗
NASA NTRS2021

Validation of Satellite-Based Precipitation Products from TRMM to GPM

The global precipitation measurement mission (GPM) has been in operation for sevenyears and continues to provide a vast quantity of global precipitation data at finer temporospatialresolutions with improved accuracy and coverage. GPM’s signature algorithm, the integratedmultisatellite retrievals for GPM (IMERG) is a next-generation of precipitation product expectedfor wide variety of research and operational applications. This study evaluates the latest version(V06B) of IMERG and its predecessor, the tropical rainfall measuring mission (TRMM) multisatelliteprecipitation (TMPA) 3B42 (V7) using ground-based and gauge-corrected multiradar multisensorsystem (MRMS) precipitation products over the conterminous United States (CONUS). The spatialdistributions of all products are analyzed. The error characteristics are further examined for 3B42 andIMERG in winter and summer by an error decomposition approach, which partitions total bias intohit bias, biases due to missed precipitation and false precipitation. The volumetric and categoricalstatistical metrics are used to quantitatively evaluate the performance of the two satellite-basedproducts. All products show a similar precipitation climatology with some regional differences.The two satellite-based products perform better in the eastern CONUS than in the mountainousWestern CONUS. The evaluation demonstrates the clear improvement in IMERG precipitationproduct in comparison with its predecessor 3B42, especially in reducing missed precipitation inwinter and summer, and hit bias in winter, resulting in better performance in capturing lighter andheavier precipitation.

Jianxin Wang↗
NASA NTRS2021

Fast Near-Optimal Heterogeneous Task Allocation via Flow Decomposition

Multi-robot systems are uniquely well-suited to perform complex tasks such as patrolling and tracking, infor- mation gathering, and pick-up and delivery problems, offering significantly higher performance than single-robot systems. A fundamental building block in most multi-robot systems is dynamic task allocation: assigning robots to tasks (e.g., patrolling an area, or servicing a transportation request) as they appear based on the robots’ states to maximize reward. In many practical situations, the allocation must account for potentially heteroge- neous capabilities (e.g., availability of appropriate sensors or actuators) to ensure the feasibility of execution, and exploit predictive information concerning the likelihood of future tasks to promote a higher reward over a long time horizon. To this end, we present an efficient algorithm for predictive heterogeneous task- allocation achieving an approximation factor of at least 1/2 of the optimal reward. Our approach demonstrates that the problem can be decomposed into several homogeneous subproblems that can be solved efficiently using min-cost flow. Through simulation experiments, we show that our algorithm is faster by several orders of magnitude than a MILP-based approach.

Pavone, Marco↗
NASA NTRS1987

Parallel pivoting combined with parallel reduction

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

Alaghband, Gita↗
NASA NTRS1989

Parallel pivoting combined with parallel reduction and fill-in control

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generation of fill-ins and check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel pivoting technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

Alaghband, Gita↗
DOE OSTI2022

HiPACE++: A portable, 3D quasi-static particle-in-cell code

Modeling plasma accelerators is a computationally challenging task and the quasi-static particle-in-cell algorithm is a method of choice in a wide range of situations. In this work, we present the first performance-portable, quasi-static, three-dimensional particle-in-cell code HiPACE++. By decomposing all the computation of a 3D domain in successive 2D transverse operations and choosing appropriate memory management, HiPACE++ demonstrates orders-of-magnitude speedups on modern scientific GPUs over CPU-only implementations. The 2D transverse operations are performed on a single GPU, avoiding time-consuming communications. The longitudinal parallelization is done through temporal domain decomposition, enabling near-optimal strong scaling from 1 to 512 GPUs. HiPACE++ is a modular, open-source code enabling efficient modeling of plasma accelerators from laptops to state-of-the-art supercomputers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Detecting damage in composites using volume decomposition analysis of tomographic data

Detection of damage in a single tow ceramic matrix composite specimen has been achieved using orthogonal decomposition of volumetric tomographic datasets collected at four tensile loads. This decomposition approach has been applied at two different length scales: (i) individual fibres and (ii) bulk volumes containing fibres and matrix material. Volumes were first decomposed to feature vectors, orders of magnitude smaller than the original volume they describe, and then comparisons between datasets at different load levels were made in feature vector space. The results show quantitative measurements of damage location, damage morphology and the relative growth of this damage with increased load when compared with a dataset with less or no damage. No prior knowledge of the dataset or training of algorithms is required for damage to be detected, it is only necessary that at least two datasets are available for comparison, e.g. from in situ or repeated scanning measurements. Results are generated on significantly shorter timescales when compared with previous automated approaches to tomography data processing. This approach has the potential to be applied to damage detection in a range of materials through comparisons of volumetric datasets from a range of measurement or computational techniques.

Middleton, Ceri A.↗