Convergent and structure preserving architectures for SciML.
Abstract not provided.
Trask, Nathaniel Albert↗
SEARCH · Engineering Papers
Results for “structure preservation”
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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Structure preserving machine learning for data-driven multiscale/multiphysics modeling.
Abstract not provided.
Trask, Nathaniel↗
Structure-preserving model reduction for marginally stable LTI systems.
Abstract not provided.
Peng, Liqian↗
State Space Reconstruction from Embeddings of Partial Observables in Structural Dynamic Systems for Structure-Preserving Data-Driven Methods.
Abstract not provided.
Najera-Flores, David↗
An Improved Approach to the Predictability & Reliability of the Onset of Turbulence With Shocks
The construction of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and for (b) obtaining correct propagation speed of discontinuities in the presence of stiff source terms share one important ingredient – minimization of numerical dissipation while maintaining numerical stability. The dual requirements to achieve both numerical stability and minimal numerical dissipation are often conflicting since existing shock capturing schemes were designed mainly to be robust for rapidly developed turbulence-free flows and for shock waves without stiff source term. For the past two decades, Yee and collaborators have focused on an improved understanding of the nonlinear behavior of different high order shock-capturing methods. It was found that even very high order methods without proper nonlinear stability and numerical dissipation control can either numerically smear the onset of turbulence due to excess numerical dissipation, or induce (onset) numerical turbulence that is not physical turbulence due to lack of proper numerical dissipation to improve nonlinear stability for long time integration. Our approach is to combine (I) and (II) below for obtaining the physically correct onset of turbulence with shocks, including problems with stiff source terms: (I) Nonlinear dynamics is utilized to complement the traditional linearized stability theory (Yee & Sweby, Yee et al., Griffiths et al., Lafon & Yee, Yee, Wang et al., Kotov et al. 1990- 2015) in order to (i) Minimize numerically induced false transition to turbulence, (ii) Minimize numerical instability due to long time integration of turbulent flows, (iii) Minimize numerically induced standing wave solutions, and (iv) Minimize wrong propagation of speed of discontinuities due to the presence of stiff source terms. (II) Our recently developed physical preserving (structural preserving) high order methods with improved nonlinear stability & accuracy that are essential in minimizing spurious numerics are used.
HECC↗
Data-driven reduced-order models for port-Hamiltonian systems with operator inference
Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.
97 MATHEMATICS AND COMPUTING↗
Phase-Field Modeling of Materials Interfaces and Nanostructures
Nanostructured materials offer unique properties for a wide range of energy applications. Among various known processing methods, liquid metal dealloying (LMD)—the selective dissolution of a base alloy element into a metallic melt—has emerged as a powerful technique to produce a new class of nano-/meso-scale open porous and bicontinuous composite structures with ultra-high interfacial area. LMD has recently been complemented by the advent of vapor phase dealloying (VPD), a novel technique that exploits the selective evaporation of one element from a parent alloy containing elements with very different vapor pressures, thereby enabling to fabricate open nanoporous structures of various elements from less-noble metals to inorganic elements regardless of their chemical activity without requiring high LMD temperatures and chemical etching. Together LMD and VPD have greatly expanded the scope of dealloying techniques, limited by traditional electrochemical means to noble metals, and boosted the design of new functional and structural materials that combine a wide variety of elements. Topologically-connected open porous structures with ultra-high surface area allow mass transport within the structure while preserving structural integrity, enabling them to serve as catalysts, fuel cells, supercapacitors, or high-capacity battery materials. Bicontinuous composite structures in turn can display high strength and high ductility or superior radiation-damage resistance due to the ultra-high interface area between interpenetrating solid phases. This research program makes use of state-of-the-art computational methods to understand at a basic level the self-organizing dealloying process with main focus on dealloying kinetics and interfacial pattern formation at the dealloying front controlling initial structure size, topology, and phase compositions. Phase-field simulation studies of LMD focus on solid solutions, line compounds, and intermetallic systems that can form ternary composites by nucleation and growth of a new phase. Studies of VPD employ phase-field modeling and a hybrid method combining a kinetic Monte Carlo (KMC) model of evaporation and surface diffusion with molecular dynamics for vapor-phase transport inside nanopores. Simulations explore mechanisms of interface- and diffusion-controlled dealloying kinetics, both observed in VPD but not fundamentally understood. In addition, our newly developed multi-physics phase-field approach of large-volume-change phase transformations is being used to model novel 3D anode geometries based on dealloyed nanoporous structures including novel sandwiched graphene/Si/silica for highrate Li ion battery. Those studies are aimed at elucidating geometric design principles that improve mechanical stability. We expect this research to enhance the capability to tailor nano-/mesoscale structures for a wide range of energy-related materials applications and to yield further advances in computational methodologies that benefit a broad materials research community.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Differential geometric approaches to momentum-based formulations for fluids [Slides]
This SAND report documents CIS Late Start LDRD Project 22-0311, "Differential geometric approaches to momentum-based formulations for fluids". The project primarily developed geometric mechanics formulations for momentum-based descriptions of nonrelativistic fluids, utilizing a differential geometry/exterior calculus treatment of momentum and a space+time splitting. Specifically, the full suite of geometric mechanics formulations (variational/Lagrangian, Lie-Poisson Hamiltonian and Curl-Form Hamiltonian) were developed in terms of exterior calculus using vector-bundle valued differential forms. This was done for a fairly general version of semi-direct product theory sufficient to cover a wide range of both neutral and charged fluid models, including compressible Euler, magnetohydrodynamics and Euler-Maxwell. As a secondary goal, this project also explored the connection between geometric mechanics formulations and the more traditional Godunov form (a hyperbolic system of conservation laws). Unfortunately, this stage did not produce anything particularly interesting, due to unforeseen technical difficulties. There are two publications related to this work currently in preparation, and this work will be presented at SIAM CSE 23, at which the PI is organizing a mini-symposium on geometric mechanics formulations and structure-preserving discretizations for fluids. The logical next step is to utilize the exterior calculus based understanding of momentum coupled with geometric mechanics formulations to develop (novel) structure-preserving discretizations of momentum. This is the main subject of a successful FY23 CIS LDRD "Structure-preserving discretizations for momentum-based formulations of fluids".
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Brilliant angle-independent structural colours preserved in weevil scales from the Swiss Pleistocene
Extant weevils exhibit a remarkable colour palette that ranges from muted monochromatic tones to rainbow-like iridescence, with the most vibrant colours produced by three-dimensional photonic nanostructures housed within cuticular scales. Although the optical properties of these nanostructures are well understood, their evolutionary history is not fully resolved, in part due to a poor knowledge of their fossil record. Here, we report three-dimensional photonic nanostructures preserved in brightly coloured scales of two weevils, belonging to the genus Phyllobius or Polydrusus , from the Pleistocene (16–10 ka) of Switzerland. The scales display vibrant blue, green and yellow hues that resemble those of extant Phyllobius/Polydrusus . Scanning electron microscopy and small-angle X-ray scattering analyses reveal that the subfossil scales possess a single-diamond photonic crystal nanostructure. In extant Phyllobius/Polydrusus , the near-angle-independent blue and green hues function primarily in crypsis. The preservation of far-field, angle-independent structural colours in the Swiss subfossil weevils and their likely function in substrate matching confirm the importance of investigating fossil and subfossil photonic nanostructures to understand the evolutionary origins and diversification of colours and associated behaviours (e.g. crypsis) in insects.
54 ENVIRONMENTAL SCIENCES↗
Microbial Preservation in Sulfates in the Haughton Impact Structure Suggests Target in Search for Life on Mars
Microbes in Haughton Crater Sulfates: Impact craters are of high interest in planetary exploration because they are viewed as possible sites for evidence of life [1]. Hydrothermal systems in craters are particularly regarded as sites where primitive life could evolve. Evidence from the Miocene Haughton impact structure shows that crater hydrothermal deposits may also be a preferred site for subsequent colonization and hence possible extant life: Hydrothermal sulfates at Haughton are colonized by viable cyanobacteria [2]. The Haughton impact structure, Devon Island, Canadian High Arctic, is a 24 km-diameter crater of mid-Tertiary age. The structure preserves an exceptional record of impact-induced hydrothermal activity, including sulfide, and sulfate mineralization [3]. The target rocks excavated at the site included massive gypsum-bearing carbonate rocks of Ordovician age. Impact-remobilized sulfates occur as metre-scale masses of intergrown crystals of the clear form of gypsum selenite in veins and cavity fillings within the crater s impact melt breccia deposits [4]. The selenite is part of the hydrothermal assemblage as it was precipitated by cooling hot waters that were circulating as a result of the impact. Remobilization of the sulfate continues to the present day, such that it occurs in soil crusts (Fig. 1) including sandy beds with a gypsum cement. The sulfate-cemented beds make an interesting comparison with the sulfate-bearing sandy beds encountered by the Opportunity MER [5]. The selenite crystals are up to 0.3 m in width, of high purity, and transparent. They locally exhibit frayed margins where cleavage surfaces have separated. This exfoliation may be a response to freeze-thaw weathering. The selenite contains traces of rock detritus, newly precipitated gypsum, and microbial colonies. The rock detritus consists of sediment particles which penetrated the opened cleavages by up to 2cm from the crystal margins. Some of the detritus is cemented into place by gypsum, which must have been dissolved and reprecipitated from the host selenite.
Parnell, J.↗
Early Life on Earth and the Search for Extraterrestrial Biosignatures
In the last 2 years, scientists within the ARES Directorate at JSC have applied the technology of Secondary Ion Mass Spectrometry (SIMS) to individual organic structures preserved in Archean (approximately 3 billion years old) sediments on Earth. These organic structures are among the oldest on Earth that may be microfossils - structurally preserved remnants of ancient microbes. The SIMS work was done to determine the microfossils' stable carbon isotopic composition (delta C-13 values). This is the first time that such ancient, potential microfossils have been successfully analyzed for their individual delta C-13 values. The results support the interpretation that these structures are remnants of early life on Earth and that they may represent planktonic organisms that were widely distributed in the Earth's earliest oceans. This study has been accepted for publication in the journal Geology.
Oehler, Dorothy Z.↗
Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems
Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.
Mathematics↗
Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm
Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. In this paper, we present a novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method. The numerical scheme is benchmarked by simulating the pitch angle scattering of a particle beam, and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable long time accuracy of the proposed algorithm.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm
Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. We present a novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method.
Zhang, Xin↗
Cognitive aging outcomes are related to both tau pathology and maintenance of cingulate cortex structure
Abstract INTRODUCTION Successful cognitive aging is related to both maintaining brain structure and avoiding Alzheimer's disease (AD) pathology, but how these factors interplay is unclear. METHODS A total of 109 cognitively normal older adults (70+ years old) underwent amyloid beta (Aβ) and tau positron emission tomography (PET) imaging, structural magnetic resonance imaging (MRI), and cognitive testing. Cognitive aging was quantified using the cognitive age gap (CAG), subtracting chronological age from predicted cognitive age. RESULTS Lower CAG (younger cognitive age) was related to slower decline in episodic memory, multi‐domain cognition, and atrophy of the midcingulate cortex (MCC). Lower entorhinal cortical tau was linked to slower decline in episodic memory, multi‐domain cognition, and hippocampal atrophy. DISCUSSION These results suggest that aging outcomes may be influenced by two independent pathways: one associated with tau accumulation, affecting primarily memory and hippocampal atrophy, and another involving tau‐independent structural preservation of the MCC, benefiting multi‐domain cognition over time. Highlights Younger cognitive age (lower cognitive age gap [CAG]) is related to slower cognitive decline. Lower CAG is linked to slower midcingulate cortex (MCC) atrophy. Reduced tau in the entorhinal cortex is related to less hippocampal atrophy and cognitive decline. Structural preservation of the MCC benefits multi‐domain cognition over time. Two independent pathways influence cognitive aging: tau accumulation and MCC preservation.
Neurosciences & Neurology↗
Xeropreservation of Functionalized Lipid Biomarkers in Hyperarid Soils in the Atacama Desert
Our understanding of long-term organic matter preservation comes mostly from studies in aquatic systems. In contrast, taphonomic processes in extremely dry environments are relatively understudied and are poorly understood. We investigated the accumulation and preservation of lipid biomarkers in hyperarid soils in the Yungay region of the Atacama Desert. Lipids from seven soil horizons in a 2.5 m vertical profile were extracted and analyzed using GC-MS and LC-MS. Diagnostic functionalized lipids and geolipids were detected and increased in abundance and diversity with depth. Deeper clay units contain fossil organic matter (radiocarbon dead) that has been protected from rainwater since the onset of hyperaridity. We show that these clay units contain lipids in an excellent state of structural preservation with functional groups and unsaturated bonds in carbon chains. This indicates that minimal degradation of lipids has occurred in these soils since the time of their deposition between greater than 40,000 and 2 million years ago. The exceptional structural preservation of biomarkers is likely due to the long-term hyperaridity that has minimized microbial and enzymatic activity, a taphonomic process we term xeropreservation (i.e., preservation by drying). The degree of biomarker preservation allowed us to reconstruct major changes in ecology in the Yungay region that reflect a shift in hydrological regime from wet to dry since the early Quaternary. Our results suggest that hyperarid environments, which comprise 7.5 percent of the continental landmass, could represent a rich and relatively unexplored source of paleobiological informationon Earth.
Hyperarid↗
Xeropreservation of Functionalized Lipid Biomarkers in Hyperarid Soils in the Atacama Desert
Our understanding of long-term organic matter preservation comes mostly from studies in aquatic systems. In contrast, taphonomic processes in extremely dry environments are relatively understudied and are poorly understood. We investigated the accumulation and preservation of lipid biomarkers in hyperarid soils in the Yungay region of the Atacama Desert. Lipids from seven soil horizons in a 2.5 meter vertical profile were extracted and analyzed using GC-MS ( Gas Chromatography-Mass Spectrometry) and LC-MS (Liquid Chromatography-Mass Spectrometry). Diagnostic functionalized lipids and geolipids were detected and increased in abundance and diversity with depth. Deeper clay units contain fossil organic matter (radiocarbon dead) that has been protected from rainwater since the onset of hyperaridity. We show that these clay units contain lipids in an excellent state of structural preservation with functional groups and unsaturated bonds in carbon chains. This indicates that minimal degradation of lipids has occurred in these soils since the time of their deposition between more than 40,000 and up to 2 million years ago. The exceptional structural preservation of biomarkers is likely due to the long-term hyperaridity that has minimized microbial and enzymatic activity, a taphonomic process we term xeropreservation (i.e. preservation by drying). The degree of biomarker preservation allowed us to reconstruct major changes in ecology in the Yungay region that reflect a shift in hydrological regime from wet to dry since the early Quaternary. Our results suggest that hyperarid environments, which comprise 7.5 percent of the continental landmass, could represent a rich and relatively unexplored source of paleobiological information on Earth.
Xeropreservation↗