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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.

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All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2022

A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via the momentum map. We numerically demonstrate this time invariance of the momentum map and its usefulness in establishing precise initial conditions with a desired initial electric field and fixed background charge. The restriction of this canonical, finite element Poisson structure to the 1X2P $1\frac {1}{2}$ -dimensional phase space is also considered and simulated numerically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

LayTracks3D: A new approach for meshing general solids using medial axis transform

This study presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex-dominant meshes of general solids. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D have no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the Results section. Work is underway to extend LayTracks3D to generate all-hex meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Engineering Privacy at the Edge: A Practical Guide to Differential Privacy in System Architectures

The rapid expansion of distributed and edge computing platforms—spanning autonomous vehicles, IoT sensors, and healthcare monitors—has heightened concerns about data privacy. Differential Privacy (DP) offers a rigorous mathematical framework to protect sensitive information while retaining analytical utility. This tutorial introduces the foundations of DP for both numerical and categorical datasets and extends the discussion to correlation-aware techniques tailored for structured and high-dimensional data. Hands-on demonstrations will begin with the PETINA (Privacy prEservaTIoN Algorithms) package for numerical data and continue with MIC-DP (Maximum Information Correlated Differential Privacy) for tabular data. Designed for researchers and practitioners in secure systems, embedded architectures, and AI accelerators, the tutorial emphasizes practical and scalable methods for integrating DP into real-world system designs.

Kotevska, Olivera [ORNL] (ORCID:0000000316772243)↗
DOE OSTI2022

A Privacy-Preserving Strategy for the Trust Layer of the Energy Grid of Things Distributed Energy Resource Management System

Emergent from the shadows of the traditional grid flaws, the Smart Grid (SG) idea was born and led by government mandates toward cleaner energy production. The SG represents the next generation of electricity distribution systems that subsume recent technological innovations. It uses digital communication between its components and entities to attain more automation, self-sufficiency, and reliability. Unfortunately, this relatively new concept is not flawless; the intrinsic reliance on increased digital communication spreads open attack paths for adversaries. Therefore, finding solutions that address information exchange vulnerabilities has become imperative. The Energy Grid of Things (EGoT) is Portland State University’s (PSU’s) implementation of a Distributed Energy Resource Management System (DERMS). The EGoT DERMS requires access to customers’ information to achieve operational objectives. The system’s access to customers’ information needs to be restricted such that it does not violate customers’ privacy. Applying privacy protection models such as K-anonymity to EGoT DERMS sub-components safeguards that privacy. This thesis work proposes a strategy to ensure communication in the EGoT DERMS is privacy-preserving and secure. Specifically, it provides an approach to applying the Mondrian Algorithm to ensure data within the system excludes Personally Identifiable Information (PII) and provides means for securing the communication according to industry standards (IEEE 2030.5). Results suggest that the generalization hierarchy derived for the EGoT DERMS exhibits an Identical Generalization Hierarchy structure. Guarantees of sameness manifested in the test feeder topology would not hold in real-world scenarios. This thesis work proposes a strategy to ensure communication in the EGoT DERMS is privacy-preserving and secure. Specifically, it provides an approach to applying the Mondrian Algorithm to ensure data within the system excludes Personally Identifiable Information (PII) and provides means for securing the communication according to industry standards (IEEE 2030.5). Results suggest that the generalization hierarchy derived for the EGoT DERMS exhibits an Identical Generalization Hierarchy structure. Guarantees of sameness manifested in the test feeder topology would not hold in real-world scenarios.

Alsiad, Mohammed↗
DOE OSTI2025

RLMolLM: Reinforcement Learning-Enhanced Language Model Framework for Inverse Molecular Design

Inverse molecular design faces significant challenges due to vast chemical space and complex property requirements. While language models show promise for molecular generation, they struggle with validity, multi-property optimization, and structural constraints. This work presents RLMolLM, a reinforcement learning framework combining Proximal Policy Optimization (PPO) with genetic algorithms to address these limitations. Our approach optimizes multiple user-specified properties including quantitative estimates of drug-likeness (QED), synthetic accessibility (SA), and ADMET (absorption, distribution, metabolism, excretion, and toxicity) endpoints without requiring complete model retraining, while maintaining capability for scaffold-constrained generation where specific substructures must be preserved. We outperform state-of-the-art methods for molecular optimization, achieving best QED scores across GDB13, Moses, and Zinc datasets with up to 31% improvement over previous methods while maintaining excellent validity, uniqueness, and novelty metrics. For simultaneous multi-property optimization, our framework achieves substantial improvements in ADMET properties including 4.5-fold reduction in hERG toxicity and enhanced Caco-2 permeability compared to Moses dataset. Under structural constraints, the framework significantly improves molecular validity while preserving scaffolds and effectively optimizing properties. In conclusion, this versatile solution advances pharmaceutical and materials molecular design through effective integration of reinforcement learning and genetic algorithms with multi-property optimization and scaffold preservation.

Genetic algorithms↗
DOE OSTI2015

Parallel seed-based approach to multiple protein structure similarities detection

Finding similarities between protein structures is a crucial task in molecular biology. Most of the existing tools require proteins to be aligned in order-preserving way and only find single alignments even when multiple similar regions exist. We propose a new seed-based approach that discovers multiple pairs of similar regions. Its computational complexity is polynomial and it comes with a quality guarantee—the returned alignments have both root mean squared deviations (coordinate-based as well as internal-distances based) lower than a given threshold, if such exist. We do not require the alignments to be order preserving (i.e., we consider nonsequential alignments), which makes our algorithm suitable for detecting similar domains when comparing multidomain proteins as well as to detect structural repetitions within a single protein. Because the search space for nonsequential alignments is much larger than for sequential ones, the computational burden is addressed by extensive use of parallel computing techniques: a coarse-grain level parallelism making use of available CPU cores for computation and a fine-grain level parallelism exploiting bit-level concurrency as well as vector instructions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Qualitative Analysis, Structure-Preserving Discretizations and Scalable Solvers for Multiphysics Problems. Final Technical Report

Many problems in physics, engineering, meteorology, computer science, and other fields involve a certain level of coupling between different physical quantities. With the development of advanced computational modeling, simulation, and hardware, simulations for many important multiphysics/multiscale coupling effects are now more tractable. In this project, we have developed robust, efficient, and practical numerical algorithms for such simulation software that are capable of tackling these complex mathematical models in many fundamental ways such as stability, wellposedness, and consistency. We expect that such an integrated theoretical and algorithmic framework will have a substantial impact on numerous multiscale and multiphysics modeling and simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2014

WE-G-BRF-05: Feasibility of Markerless Motion Tracking Using Dual Energy Cone Beam Computed Tomography (DE-CBCT) Projections

Purpose: To compare markerless template-based tracking of lung tumors using dual energy (DE) cone-beam computed tomography (CBCT) projections versus single energy (SE) CBCT projections. Methods: A RANDO chest phantom with a simulated tumor in the upper right lung was used to investigate the effectiveness of tumor tracking using DE and SE CBCT projections. Planar kV projections from CBCT acquisitions were captured at 60 kVp (4 mAs) and 120 kVp (1 mAs) using the Varian TrueBeam and non-commercial iTools Capture software. Projections were taken at approximately every 0.53° while the gantry rotated. Due to limitations of the phantom, angles for which the shoulders blocked the tumor were excluded from tracking analysis. DE images were constructed using a weighted logarithmic subtraction that removed bony anatomy while preserving soft tissue structures. The tumors were tracked separately on DE and SE (120 kVp) images using a template-based tracking algorithm. The tracking results were compared to ground truth coordinates designated by a physician. Matches with a distance of greater than 3 mm from ground truth were designated as failing to track. Results: 363 frames were analyzed. The algorithm successfully tracked the tumor on 89.8% (326/363) of DE frames compared to 54.3% (197/363) of SE frames (p<0.0001). Average distance between tracking and ground truth coordinates was 1.27 +/− 0.67 mm for DE versus 1.83+/−0.74 mm for SE (p<0.0001). Conclusion: This study demonstrates the effectiveness of markerless template-based tracking using DE CBCT. DE imaging resulted in better detectability with more accurate localization on average versus SE. Supported by a grant from Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Gauge properties of the guiding center variational symplectic integrator

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t{yields}0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the 'antisymmetric discretization gauge,' in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and {phi} are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law [J. Squire, H. Qin, and W. Tang (to be published)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Gauge properties of the guiding center variational symplectic integrator

Recently, variational symplectic algorithms have been developed for the long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms an instability arises because the discrete symplectic structure does not become the continuous structure in the t → 0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and Φ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

Quantum chemistry is a key application area for noisy-intermediate scale quantum (NISQ) devices, and therefore serves as an important benchmark for current and future quantum computer performance. Previous benchmarks in this field have focused on variational methods for computing ground and excited states of various molecules, including a benchmarking suite focused on the performance of computing ground states for alkali-hydrides under an array of error mitigation methods. State-of-the-art methods to reach chemical accuracy in hybrid quantum-classical electronic structure calculations of alkali hydride molecules on NISQ devices from IBM are outlined here. Here it is demonstrated how to extend the reach of variational eigensolvers with symmetry preserving Ansätze. Next, it is outlined how to use quantum imaginary time evolution and Lanczos as a complementary method to variational techniques, highlighting the advantages of each approach. Finally, a new error mitigation method is demonstrated which uses systematic error cancellation via hidden inverse gate constructions, improving the performance of typical variational algorithms. These results show that electronic structure calculations have advanced rapidly, to routine chemical accuracy for simple molecules, from their inception on quantum computers a few short years ago, and they point to further rapid progress to larger molecules as the power of NISQ devices grows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗