Search NASA⌕ Search

SEARCH · Search NASA

Results for “Structure preserving algorithms”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Thermodynamically consistent algorithms for models of incompressible multiphase polymer solutions with a variable mobility

Here we present a general strategy for developing structure and property preserving numerical algorithms for thermodynamically consistent models of incompressible multiphase polymer solutions with a variable mobility. We first present a formalism to derive thermodynamically consistent, incompressible, multiphase polymer models. Then, we develop the general strategy, known as the supplementary variable method, to devise thermodynamically consistent numerical approximations to the models. We illustrate the numerical strategy using newly developed models of incompressible diblock copolymer solutions coupled with an electric and a magnetic field, respectively. Mesh refinement is conducted to verify convergence rates of the developed schemes. Some numerical examples are given to exhibit underlying dynamics absent from and driven by the external fields, respectively, highlighting differences between models with the variable and constant mobilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Low rank approximation in simulations of quantum algorithms

Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low rank tensors. Here, in this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms. Two rank reduction algorithms are used to enable efficient simulation. We show that some of the algorithms preserve the low rank structure of the input state and can thus be efficiently simulated on a classical computer. However, the rank of the intermediate states in other quantum algorithms can increase rapidly, making efficient simulation more difficult. To some extent, such difficulty reflects the advantage or superiority of a quantum computer over a classical computer. As a result, understanding the low rank structure of a quantum algorithm allows us to identify algorithms that can benefit significantly from quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems

Here, an explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as discrete differential form fields on a fixed mesh. With the assistance of Whitney interpolating forms, this scheme preserves the gauge symmetry of the electromagnetic field, and the pressure field is naturally derived from the discrete internal energy. The whole system is solved using the Hamiltonian splitting method discovered by He et al. [Phys. Plasmas 22, 124503 (2015)], which was been successfully adopted in constructing symplectic particle-in-cell schemes. Because of its structure preserving and explicit nature, this algorithm is especially suitable for large-scale simulations for physics problems that are multi-scale and require long-term fidelity and accuracy. The algorithm is verified via two tests: studies of the dispersion relation of waves in a two-fluid plasma system and the oscillating two-stream instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Counting topological interface modes using simplicial characteristic classes

A computational approach for predicting the number of topological interface modes (TIMs) in hermitian systems using the spectral flow—monopole correspondence is presented. The number of TIMs is determined by calculating the Chern number of a complex line bundle of local polarisation vectors over a phase space sphere surrounding a Weyl point. The Chern number is computed by constructing the simplicial first Chern class of a discrete vector bundle on a simplicial mesh. This approach is gauge invariant, derivative free, structure preserving, and robust to noise. The algorithm is shown to reproduce the expected number of TIMs for the case of equatorial fluid waves and the topological Langmuir cyclotron wave. The possibility of using this algorithm to analyse experimental measurements of bulk wave polarisations and predict the associated number of TIMs is explored in a synthetic example.

discrete vector bundles↗
DOE OSTI2024

Uncertainty-Aware, Structure-Preserving Machine Learning Approach for Domain Shift Detection From Nonlinear Dynamic Responses of Structural Systems

Complex structural systems deployed for aerospace, civil, or mechanical applications must operate reliably under varying operational conditions. Structural health monitoring (SHM) systems help ensure the reliability of these systems by providing continuous monitoring of the state of the structure. SHM relies on synthesizing measured data with a predictive model to make informed decisions about structural states. However, these models—which may be thought of as a form of a digital twin—need to be updated continuously as structural changes (e.g., due to damage) arise. We propose an uncertainty-aware machine learning model that enforces distance preservation of the original input state space and then encodes a distance-aware mechanism via a Gaussian process (GP) kernel. The proposed approach leverages the spectral-normalized neural GP algorithm to combine the flexibility of neural networks with the advantages of GP, subjected to structure-preserving constraints, to produce an uncertainty-aware model. This model is used to detect domain shift due to structural changes that cannot be observed directly because they may be spatially isolated (e.g., inside a joint or localized damage). This work leverages detection theory to detect domain shift systematically given statistical features of the prediction variance produced by the model. The proposed approach is demonstrated on a nonlinear structure being subjected to damage conditions. In conclusion, it is shown that the proposed approach is able to rely on distances of the transformed input state space to predict increased variance in shifted domains while being robust to normative changes.

Algorithms↗
DOE OSTI2026

A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.

65M75, 70H05, 70G65↗
DOE OSTI2020

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗
DOE OSTI2022

Augmenting Graph Convolution with Distance Preserving Embedding for Improved Learning

Graph convolution incorporates topological information of a graph into learning. Message passing corresponds to traversal of a local neighborhood in classical graph algorithms. We show that incorporating additional global structures, such as shortest paths, through distance preserving embedding can improve performance. Our approach, Gavotte, significantly improves the performance of a range of popular graph neu-ral networks such as GCN, GA T,Graph SAGE, and GCNII for transductive learning. Gavotte also improves the performance of graph neural networks for full-supervised tasks, albeit to a smaller degree. As high-quality embeddings are generated by Gavotte as a by-product, we leverage clustering algorithms on these embed dings to augment the training set and introduce Gavotte+. Our results of Gavotte+ on datasets with very few labels demonstrate the advantage of augmenting graph convolution with distance preserving embedding.

Cong, Guojing↗
DOE OSTI2016

Iterative metal artifact reduction for x-ray computed tomography using unmatched projector/backprojector pairs

Purpose: Metal artifact reduction (MAR) is a major problem and a challenging issue in x-ray computed tomography (CT) examinations. Iterative reconstruction from sinograms unaffected by metals shows promising potential in detail recovery. This reconstruction has been the subject of much research in recent years. However, conventional iterative reconstruction methods easily introduce new artifacts around metal implants because of incomplete data reconstruction and inconsistencies in practical data acquisition. Hence, this work aims at developing a method to suppress newly introduced artifacts and improve the image quality around metal implants for the iterative MAR scheme. Methods: The proposed method consists of two steps based on the general iterative MAR framework. An uncorrected image is initially reconstructed, and the corresponding metal trace is obtained. The iterative reconstruction method is then used to reconstruct images from the unaffected sinogram. In the reconstruction step of this work, an iterative strategy utilizing unmatched projector/backprojector pairs is used. A ramp filter is introduced into the back-projection procedure to restrain the inconsistency components in low frequencies and generate more reliable images of the regions around metals. Furthermore, a constrained total variation (TV) minimization model is also incorporated to enhance efficiency. The proposed strategy is implemented based on an iterative FBP and an alternating direction minimization (ADM) scheme, respectively. The developed algorithms are referred to as “iFBP-TV” and “TV-FADM,” respectively. Two projection-completion-based MAR methods and three iterative MAR methods are performed simultaneously for comparison. Results: The proposed method performs reasonably on both simulation and real CT-scanned datasets. This approach could reduce streak metal artifacts effectively and avoid the mentioned effects in the vicinity of the metals. The improvements are evaluated by inspecting regions of interest and by comparing the root-mean-square errors, normalized mean absolute distance, and universal quality index metrics of the images. Both iFBP-TV and TV-FADM methods outperform other counterparts in all cases. Unlike the conventional iterative methods, the proposed strategy utilizing unmatched projector/backprojector pairs shows excellent performance in detail preservation and prevention of the introduction of new artifacts. Conclusions: Qualitative and quantitative evaluations of experimental results indicate that the developed method outperforms classical MAR algorithms in suppressing streak artifacts and preserving the edge structural information of the object. In particular, structures lying close to metals can be gradually recovered because of the reduction of artifacts caused by inconsistency effects.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Coupled cluster Green function: Model involving single and double excitations

In this paper, we report on the development of a parallel implementation of the coupled-cluster (CC) Green function formulation (GFCC) employing single and double excitations in the cluster operator (GFCCSD). A key aspect of this work is the determination of the frequency dependent self-energy, Σ(ω). The detailed description of the underlying algorithm is provided, including approximations used that preserve the pole structure of the full GFCCSD method, thereby reducing the computational costs while maintaining an accurate character of methodology. Furthermore, for systems with strong local correlation, our formulation reveals a diagonally dominate block structure where as the non-local correlation increases, the block size increases proportionally. Here, to demonstrate the accuracy of our approach, several examples including calculations of ionization potentials for benchmark systems are presented and compared against experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Prediction of novel high-pressure H 2 O -NaCl and carbon oxide compounds with a symmetry-driven structure search algorithm

Crystal structure prediction with theoretical methods is particularly challenging when unit cells with many atoms need to be considered. Here we employ a symmetry-driven structure search (SYDSS) method and combine it with density functional theory (DFT) to predict novel crystal structures at high pressure. We sample randomly from all 1,506 Wyckoff positions of the 230 space groups to generate a set of initial structures. During the subsequent structural relaxation with DFT, existing symmetries are preserved, but the symmetries and the space group may change as atoms move to more symmetric positions. By construction, our algorithm generates symmetric structures with high probability without excluding any configurations. This improves the search efficiency, especially for large cells with 20 atoms or more. We apply our SYDSS algorithm to identify stoichiometric (H 2 O) n -(NaCl) m and C n O m compounds at high pressure. We predict a novel H 2 O-NaCl structure with Pnma symmetry to form at 3.4 Mbar, which is within the range of diamond anvil experiments. In addition, we predict a novel C 2 O structure at 19.8 Mbar and C4O structure at 44.0 Mbar with Pbca and C2/m symmetry respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Low-Memory, Discrete Ordinates, Discontinuous Galerkin Methods for Radiative Transport

The discrete ordinates discontinuous Galerkin (SN-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind SN-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original SN-DG method, the low-memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in the scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. Finally, for both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Degenerate variational integrators for magnetic field line flow and guiding center trajectories

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem “degenerate variational integration.” Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Lastly, numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part II: linesweep ALE rezoning for nonconformal block-structured AMR meshes

The simulation of flows presenting contact discontinuities, vorticity, and large variations in spatial scales can be performed in a framework coupling Arbitrary Lagrangian Eulerian (ALE) algorithms and Adaptive Mesh Refinement (AMR). This coupling requires adaptation of ALE rezoning techniques to meshes containing nonconformal nodes arising from both the AMR topology and the junction of mesh blocks. Here, in this paper, we present an ALE rezoning strategy that is compatible with such meshes, and that can also act as a disentangling algorithm. Emphasis is put on an algorithm that respects intrinsic Lagrangian mesh properties in order to preserve accuracy around discontinuities. To that end, we adapt the weighted linesweep algorithm to nonconformal block-structured AMR meshes. Then, we present control parameters introduced in the method for it to be applicable in practical situations. Notably, the method is coupled to a specific metric optimization in order to palliate some shortcomings of the linesweep method. Finally, numerical test cases are presented that feature the capabilities of the ALE-AMR algorithm for flows that present discontinuities, vorticity, and a variety of scales. Notably, we show that our ALE-AMR algorithm gives results at least similar to Euler-AMR, but provides better accuracy in cases where discontinuities are involved, thanks to a method that respects the Lagrangian features of the mesh. Additionally, it enables Euler-AMR-like computations on domains with temporally varying domain boundaries.

Adaptive mesh refinement↗
DOE OSTI2015

SU-D-207-04: GPU-Based 4D Cone-Beam CT Reconstruction Using Adaptive Meshing Method

Purpose: Due to the limited number of projections at each phase, the image quality of a four-dimensional cone-beam CT (4D-CBCT) is often degraded, which decreases the accuracy of subsequent motion modeling. One of the promising methods is the simultaneous motion estimation and image reconstruction (SMEIR) approach. The objective of this work is to enhance the computational speed of the SMEIR algorithm using adaptive feature-based tetrahedral meshing and GPU-based parallelization. Methods: The first step is to generate the tetrahedral mesh based on the features of a reference phase 4D-CBCT, so that the deformation can be well captured and accurately diffused from the mesh vertices to voxels of the image volume. After the mesh generation, the updated motion model and other phases of 4D-CBCT can be obtained by matching the 4D-CBCT projection images at each phase with the corresponding forward projections of the deformed reference phase of 4D-CBCT. The entire process of this 4D-CBCT reconstruction method is implemented on GPU, resulting in significantly increasing the computational efficiency due to its tremendous parallel computing ability. Results: A 4D XCAT digital phantom was used to test the proposed mesh-based image reconstruction algorithm. The image Result shows both bone structures and inside of the lung are well-preserved and the tumor position can be well captured. Compared to the previous voxel-based CPU implementation of SMEIR, the proposed method is about 157 times faster for reconstructing a 10 -phase 4D-CBCT with dimension 256×256×150. Conclusion: The GPU-based parallel 4D CBCT reconstruction method uses the feature-based mesh for estimating motion model and demonstrates equivalent image Result with previous voxel-based SMEIR approach, with significantly improved computational speed.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

An extended/generalized phase-field finite element method for crack growth with global-local enrichment

In this paper, an extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction-correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two- and three-dimensional quasistatic fracture are provided to demonstrate the approach.

multiscale↗
DOE OSTI2018

Graph-Based Approach to Systematic Molecular Coarse-Graining

A novel methodology is introduced here to generate coarse-grained (CG) representations of molecular models for simulations. The proposed strategy relies on basic graph-theoretic principles and is referred to as graph-based coarse-graining (GBCG). It treats a given system as a molecular graph and derives a corresponding CG representation by using edge contractions to combine nodes in the graph, which correspond to atoms in the molecule, into CG sites. A key element of this methodology is that the nodes are combined according to well-defined protocols that rank-order nodes based on the underlying chemical connectivity. By iteratively performing these operations, successively coarser representations of the original atomic system can be produced to yield a systematic set of CG mappings with hierarchical resolution in an automated fashion. These capabilities are demonstrated in the context of several test systems, including toluene, pentadecane, a polysaccharide dimer, and a rhodopsin protein. In these examples, GBCG yields multiple, intuitive structures that naturally preserve the chemical topology of the system. Importantly, these representations are rendered from algorithmic implementation rather than an arbitrary ansatz, which, until now, has been the conventional approach for defining CG mapping schemes. Overall, the results presented here indicate that GBCG is efficient, robust, and unambiguous in its application, making it a valuable tool for future CG modeling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗