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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Vapor-induced phase-separation-enabled versatile direct ink writing

Abstract Versatile printing of polymers, metals, and composites always calls for simple, economic approaches. Here we present an approach to three-dimensional (3D) printing of polymeric, metallic, and composite materials at room conditions, based on the polymeric vapor-induced phase separation (VIPS) process. During VIPS 3D printing (VIPS-3DP), a dissolved polymer-based ink is deposited in an environment where nebulized non-solvent is present, inducing the low-volatility solvent to be extracted from the filament in a controllable manner due to its higher chemical affinity with the non-solvent used. The polymeric phase is hardened in situ as a result of the induced phase separation process. The low volatility of the solvent enables its reclamation after the printing process, significantly reducing its environmental footprint. We first demonstrate the use of VIPS-3DP for polymer printing, showcasing its potential in printing intricate structures. We further extend VIPS-3DP to the deposition of polymer-based metallic inks or composite powder-laden polymeric inks, which become metallic parts or composites after a thermal cycle is applied. Furthermore, spatially tunable porous structures and functionally graded parts are printed by using the printing path to set the inter-filament porosity as well as an inorganic space-holder as an intra-filament porogen.

42 ENGINEERING↗
DOE OSTI2025

Crystal structure prediction with host-guided inpainting generation and foundation potentials

Unconditional crystal structure generation with diffusion models faces challenges in identifying symmetric crystals as the unit cell size increases. Here, we present the crystal host-guided generation (CHGGen) framework to address this challenge through conditional generation using an inpainting method, which optimizes a fraction of atomic positions within a predefined and symmetrized host structure to improve the success rate for symmetric structure generation. By integrating inpainting structure generation with a foundation potential for structure optimization, we demonstrate the method on the ZnS–P 2 S 5 and Li–Si chemical systems, where the inpainting method generates a higher fraction of symmetric structures than unconditional generation. The practical significance of CHGGen extends to enabling the structural modification of crystal structures, particularly for systems with partial occupancy or intercalation chemistry. The inpainting method also allows for seamless integration with other generative models, providing a versatile framework for accelerating materials discovery.

Zhong, Peichen [University of California, Berkeley↗
NASA NTRS2003

A 4 MPC X-Ray Filament Falling into the Cluster A85

We have completed a first paper confirming the ROSAT observation of a merging filamentary structure associated with the rich cluster A85. We detected a portion of the extended 4 Mpc filament first seen by the ROSAT PSPC. We confirm that there is an extended feature, aligned at the same position angle as the major axis of the central cD, the bright cluster galaxies, and nearby groups and clusters. We find that the X-ray emission from the filament is best described by thermal emission with a temperature of approx. 2 keV, which is significantly lower than the ambient cluster medium, but is significantly higher than anticipated for a gas in a weakly bound extended filament. It is not clear whether this is a filament of diffuse emission, a chain of several groups of galaxies, or stripped gas from the infalling south blob. In conclusion, the XMM-Newton observations confirmed that there really is a highly elongated filamentary like structure extending from the the merging south clump to the south east of Abell-85 along the direction defined by all the structures pointed out by Durret et al. (1998b). The fact that the spatial structure of the X-ray filament detected by XMM-Newton cannot be exactly superimposed to that obtained from ROSAT data shows that it is still difficult to determine exactly its nature. However, the X-ray spectrum from this structure is most likely thermal and its temperature is about 2.0 keV, consistent with that of groups. This value is notably cooler than that of the main cluster: the temperature map by Markevitch et al. (1998) shows the presence of gas at about 3-4 keV in the region at a distance from the cluster center at least as far as the northern part of the ellipse. So, we appear to be seeing cool gas as it enters the cluster core. Another possibility is that the filament is associated with the wake of cool stripped gas left behind by the south blob as it falls onto the cluster. In this case, the 'filament', whether it is diffuse or made of groups, would not really be a filament in the large scale structure formation sense. Besides X-ray observations with a much better signal to noise ratio, which probably will have to wait for the next generation of X-ray satellites, optical data can shed light on this question. With this purpose, we intend to perform wide field imaging in various bands to estimate galaxy photometric redshifts and determine how galaxies are distributed in the 'filament' area.

Forman, William↗
DOE OSTI2025

Review of Layered Transition Metal Oxide Materials for Cathodes in Sodium-Ion Batteries

The growing interest in sodium-ion batteries (SIBs) is driven by scarcity and the rising costs of lithium, coupled with the urgent need for scalable and sustainable energy storage solutions. Among various cathode materials, layered transition metal oxides have emerged as promising candidates due to their structural similarity to lithium-ion battery (LIB) counterparts and their potential to deliver high energy density at reduced costs. However, significant challenges remain, including limited capacity at high charge/discharge rates and structural instability during extended cycling. Addressing these issues is critical for advancing SIB technology toward industrial applications, particularly for large-scale energy storage systems. This review provides a comprehensive analysis of layered sodium transition metal oxides, focusing on their structural properties, electrochemical performance, and degradation mechanisms. Special attention is given to the intrinsic and extrinsic factors contributing to their instability, such as structural phase transitions, and cationic/anionic redox behavior. Additionally, recent advancements in material design strategies, including doping, surface modifications, and composite formation, are discussed to highlight the progress toward enhancing the stability and performance of these materials. This work aims to bridge the knowledge gaps and inspire further innovations in the development of high-performance cathodes for sodium-ion batteries.

Ahangari, Mehdi (ORCID:0000000345803969)↗
DOE OSTI2020

Resolving the Atomic Structure of Sequential Infiltration Synthesis Derived Inorganic Clusters

Sequential infiltration synthesis (SIS) is a route to the precision deposition of inorganic solids in analogy to atomic layer deposition but occurs within (vs upon) a soft material template. SIS has enabled exquisite nanoscale morphological complexity in various oxides through selective nucleation in block copolymers templates. However, the earliest stages of SIS growth remain unresolved, including the atomic structure of nuclei and the evolution of local coordination environments, before and after polymer template removal. We employed In K-edge extended X-ray absorption fine structure and atomic pair distribution function analysis of high-energy X-ray scattering to unravel (1) the structural evolution of InO x H y clusters inside a poly(methyl methacrylate) (PMMA) host matrix and (2) the formation of porous In 2 O 3 solids (obtained after annealing) as a function of SIS cycle number. Early SIS cycles result in InO x H y cluster growth with high aspect ratio, followed by the formation of a three-dimensional network with additional SIS cycles. That the atomic structures of the InO x H y clusters can be modeled as multinuclear clusters with bonding patterns related to those in In 2 O 3 and In(OH) 3 crystal structures suggests that SIS may be an efficient route to 3D arrays of discrete-atom-number clusters. As a result, annealing the mixed inorganic/polymer films in air removes the PMMA template and consolidates the as-grown clusters into cubic In 2 O 3 nanocrystals with structural details that also depend on SIS cycle number.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The Intermetallic Reactivity Database: Compiling Chemical Pressure and Electronic Metrics toward Materials Design and Discovery

Here, the advent of high-throughput Density Functional Theory (DFT) calculations has supported the creation of large databases containing the quantitative output necessary for constructing theoretical phase diagrams and predicting physical properties. In this Article, we present a complementary resource, the Intermetallic Reactivity Database (IRD), focused on the chemical bonding features of solid-state structures and indicators of potential structural transformations. Each IRD entry augments common features, such as band structures and density of states (DOS) distributions, with chemically motivated information including DFT-Chemical Pressure (CP) schemes and visualizable representations of the atomic charges. Together, these data types enable the rationalization and prediction of potential structural phenomena encountered in intermetallic chemistry, as we illustrate with four examples: the origins of the Y 2 Ni 2 Mg structure in terms of CP features of its parent structures, the anticipation of intergrowth phases from the net atomic CPs collected in Al-containing binary phases, the correlation between trends in the CP schemes of CaCu 5 -type phases and experimentally observed structural variations, and finally, the development of theoretical methodology with the testing of a streamlined method generating DFT-CP schemes. Altogether, these examples highlight how the IRD supports the creation of models of structural chemistry that extend beyond the bounds of its entries.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Calcium-Uranyl-Carbonato Species Kinetically Limit U(VI) Reduction by Fe(II) and Lead to U(V)-Bearing Ferrihydrite

Reaction conditions and mechanisms promoting or inhibiting U reduction exert a central control on U solubility and, therefore, U transport and its associated risks. Here, we vary and track common aqueous uranium species to show that a kinetic restriction inhibits homogeneous reduction of the calcium-uranyl-carbonato species (CaUO$_2$(CO$_3$)$_3$$^{2–}$ and Ca$_2$UO$_2$(CO$_3$)$_3$) by Fe(II)$_{(aq)}$, while ferrihydrite surface-catalyzed reduction of all aqueous uranyl by Fe(II) proceeds. Using U L$_3$ high energy resolution fluorescence detection (HERFD) X-ray absorption near edge structure (XANES) spectroscopy, U L$_3$ extended X-ray absorption fine structure (EXAFS) spectroscopy, and transmission electron microscopy (TEM), we also show that U(V) is generated and incorporated into ferrihydrite formed from homogeneous U(VI) reduction by Fe(II)(aq). Through elucidation of the mechanisms that inhibit reduction of the calcium-uranyl-carbonato species and promote stabilization of U(V), we advance our understanding of the controls on U solubility and thus improve prediction of U transport in surface and subsurface systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

Carbon/Carbon Panels Cooled By Heat Pipes

Durable and reusable high-temperature carbon/carbon heat-pipe structure operates at temperatures above 3,000 degree F (1,649 degree C) in vacuum or inert environment and up to 2,800 degree F (1,537 degree C) in oxidizing environment. New concept combines high-temperature heat-pipe and carbon/carbon technologies to extend both thermal structural capabilities of refractory-metal heat pipes and maximum heat-flux capability of carbon/carbon structures. Uses refractory-metal heat pipes embedded within carbon/carbon structure. Walls of heat pipes thin and contain working fluid (lithium or sodium) of heat pipe. Carbon/carbon acts as primary load-carrying part of structure. Heat pipes help to eliminate local hotspots and associated thermal gradients and stresses and to reduce peak surface temperatures of carbon/carbon to levels within capability of oxidation-resisting system.

Camarda, Charles J.↗
DOE OSTI2022

High manganese redox variability and manganate predominance in temperate soil profiles as determined by X-ray absorption spectroscopy

Manganese speciation is a key to understanding the fate of contaminants, nutrients, and organic matter in soils. To date, quantification of Mn species in bulk soils has been performed mainly by sequential extraction methods and rarely supported by spectroscopic analysis. In order to obtain quantitative information on the Mn species inventory of soils, we investigated 46 soil horizons (<2-mm fraction, 45.1–2,280 mg/kg Mn) of nine typical Central European soils (Cambisols, Chernozems, Luvisols, Podzol, Stagnosol) by chemical Mn analyses and Mn K-edge X-ray absorption spectroscopy, and related speciation results to major soil properties. Amounts of Mn 2+ , Mn 3+ , and Mn 4+ and the average oxidation state of Mn were evaluated by linear combination fitting (LCF) of X-ray absorption near edge structure (XANES) spectra. Additionally, we used extended X-ray absorption fine structure (EXAFS) spectroscopy to identify and quantify major Mn species. For this, EXAFS spectra of 20 organic and mineral soil samples from five soils (Cambisols, Chernozem, Luvisol) were analyzed by LCF and shell fitting. XANES analyses revealed a high Mn redox variability in organic surface layers, with Mn 2+ being most abundant (≤100%, $\overline{x}$ = 54%), followed by Mn 3+ (≤80%, $\overline{x}$ = 32%) and Mn 4+ (≤55%, $\overline{x}$ = 14%). Mineral soil horizons contained significantly less Mn 2+ (≤56%, $\overline{x}$ = 23%), about equal quantities of Mn 3+ (≤68%, $\overline{x}$ = 31%), and were enriched in Mn 4+ (≤89%, $\overline{x}$ = 46%). EXAFS analyses implied the presence of six major Mn species groups: manganates, organically complexed Mn, Mn(III) oxyhydroxides, silicate-bound Mn, Mn oxides without tunnel- or layer structure, and physisorbed Mn. In litter horizons, Mn was mainly present in organic complexes (58–91%, $\overline{x}$ = 78%) and as physisorbed Mn (≤15%), but individual horizons also comprised manganates, Mn(III) oxyhydroxides, and silicate-bound Mn. Manganates, likely mixtures of phyllomanganates with hexagonal layer symmetry and tectomanganates, dominated in all mineral soil horizons (37–94%, $\overline{x}$ = 67%). Correlation analysis showed that manganates dissolve completely during dithionite-citrate and acid ammonium oxalate extractions, and suggested that Mn 4+ -rich manganates preferentially form under less acidic soil conditions, partly by oxidation of organically complexed Mn(II), and that they are enriched in the soil clay fraction. Mineral soil horizons also contained minor quantities of organically complexed Mn (≤39%, $\overline{x}$ = 11%), silicate-bound Mn (≤30%, $\overline{x}$ = 8%), Mn(III) oxyhydroxides (≤37%, $\overline{x}$ = 7%), Mn oxides without tunnel- or layer structure (≤18%, $\overline{x}$ = 5%), and physisorbed Mn (≤14%, $\overline{x}$ <1%). The detection of Mn(III) oxyhydroxides such as feitknechtite (β-MnOOH) or groutite (α-MnOOH) as well as the spinel hausmannite (Mn 3 O 4 ) in acidic soils is remarkable, since their formation is normally linked to neutral or alkaline pH conditions. Minor contributions of silicate-bound Mn indicate the release of Mn from primary minerals already at early stages of soil formation, and low concentrations of physisorbed Mn suggest that exchangeable Mn is rapidly converted into manganates in oxic soils. In conclusion, the predominance of manganates in mineral soils has far-reaching implications for the functioning of soils and biogeochemical element cycles, as these minerals play an important role in metal binding, plant nutrition, and redox-related processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Ion Atmosphere of Wormlike Micelles Profiled by Contrast Variation Small-Angle Neutron Scattering

Structural studies of wormlike micelles have so far mostly focused on the conformational properties of surfactant aggregates. The diffuse ionic atmosphere, which has a profound influence on various micellization phenomena such as thermodynamic stability and structural polymorphism, remains largely unexplored experimentally. In this report a strategy of contrast variation small-angle neutron scattering for this crucial structural study is outlined. Underlined by a general criterion established for unbiasedly identifying the length scale relevant to charge association from the spectral evolution, our analytical framework can provide a quantitative description of counterion distribution in a mathematically tractable manner. Overall, our method can be conveniently extended to facilitate structural studies of complex multicomponent systems using contrast variation neutron scattering.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

Update on the Status of the FLUKA Monte Carlo Transport Code

The FLUKA Monte Carlo transport code is a well-known simulation tool in High Energy Physics. FLUKA is a dynamic tool in the sense that it is being continually updated and improved by the authors. Here we review the progresses achieved in the last year on the physics models. From the point of view of hadronic physics, most of the effort is still in the field of nucleus--nucleus interactions. The currently available version of FLUKA already includes the internal capability to simulate inelastic nuclear interactions beginning with lab kinetic energies of 100 MeV/A up the the highest accessible energies by means of the DPMJET-II.5 event generator to handle the interactions for greater than 5 GeV/A and rQMD for energies below that. The new developments concern, at high energy, the embedding of the DPMJET-III generator, which represent a major change with respect to the DPMJET-II structure. This will also allow to achieve a better consistency between the nucleus-nucleus section with the original FLUKA model for hadron-nucleus collisions. Work is also in progress to implement a third event generator model based on the Master Boltzmann Equation approach, in order to extend the energy capability from 100 MeV/A down to the threshold for these reactions. In addition to these extended physics capabilities, structural changes to the programs input and scoring capabilities are continually being upgraded. In particular we want to mention the upgrades in the geometry packages, now capable of reaching higher levels of abstraction. Work is also proceeding to provide direct import into ROOT of the FLUKA output files for analysis and to deploy a user-friendly GUI input interface.

Pinsky, L.↗
NASA NTRS2006

Elemental and Molecular Relative Abundances in the Ejecta of Eta Carinae

We are measuring relative elemental abundances for the ejecta in the line of sight from Eta Carinae using high dispersion spectroscopy with the HST/STIS and the VLT/UVES. While multiple velocity components have been identified, we focus on the -513 and -146 km/s components originating from the Homunculus and the Little Homunculus. Complicating factors are the complex nebular structures in the immediate vicinity of the bright, massive star: the very bright emission structures, Weigelt blobs B, C and D, the broad, clumpy structures of the extended wind apparently not photoionized by Eta Car B, and general scattered starlight from the extended wind and the dusty core of the circumstellar material. We have used the 3050 to 3160A region of overlap between STIS and UVES to intercompare equivalent widths of absorption lines to estimate the 'contributing factor', namely the amount of light originating from the star compared to nebular structures. While the extracted STIS spectra are from 0.1" wide aperture, the UVES spectra are limited by the 1" seeing conditions. Curiously we find that the scattering contribution in the UVES spectra changes with time, apparently with orbital phase of the 5.54-year period. This indicates that the dust may be modified by changes in the central source with phase. The noticeable drop in scattered light appears to occur about 1.7 years (phase 0.35) after the spectroscopic minimum. Relative abundances of iron peak elements and some molecules will be estimated. Observations in this study were accomplished with HST through STSci and with VLT through ESO and funded under STIS GTO resources.

Kober, G. V.↗
NASA NTRS1991

Large-scale solar and heliospheric magnetic fields

The magnetic structure of the extended solar corona varies with the changing photospheric field during the solar cycle. A simple potential model of the corona using solar surface observations from 1976 to the present shows how the large-scale coronal field evolves over more than a solar activity cycle. These predictions match well with large stable structures inferred from measurements of coronal electron density and the IMF, though dynamic changes are poorly modeled. The sun's polar field was about 25 stronger at solar minimum in 1986 than in 1976; the heliospheric current sheet was also flatter. In Cycle 21 the coronal and photospheric large-scale long-lived field patterns rotated every 26.9 days in the northern hemisphere; the southern field rotated every 28 days. Similar periods have been present in the IMF and in the occurrence of solar flares during the last several solar cycles.

Hoeksema, J. Todd↗
DOE OSTI2021

Scattering of lower hybrid radio frequency waves by cylindrical turbulent structures in the plasma edge in tokamaks

Lower hybrid (LH) radio frequency (RF) waves are used in fusion tokamak devices to generate non-inductively toroidal currents. LH waves are effective in imparting toroidal momentum to electrons in the core of the confined plasma. Since the LH waves are generated by wave guide structures near the wall of a tokamak, the waves have to propagate through a turbulent plasma in the edge region before coupling to the core. It is especially important to quantify the effect of this plasma region on the propagation characteristics of the LH waves, since fusion reactors like ITER will have an extended edge region. Structures in the plasma edge like filaments and blobs which have highly varying density fluctuations compared to the background density, span radial spatial scales that are comparable to the LH wavelength. We study the scattering of the LH waves by the filamentary structures using Maxwell's equations, in which the plasma permittivity is given by the cold plasma dispersion tensor. The collisional absorption of LH waves in the edge region is included by a modification to the elements of the dispersion tensor. The filaments are assumed to be cylindrical with the axis predominantly aligned along the direction of the toroidal magnetic field. Our studies are both analytical and numerical [1,2] and show that these structures can lead to reflection, refraction, diffraction, and side-scattering of both an incident LH plane wave and a Gaussian beam. We will present a variety of different density variations and collisional absorption rates in plasmas with filamentary structures of varying sizes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Blending Ionic and Coordinate Bonds in Hybrid Semiconductor Materials: A General Approach toward Robust and Solution-Processable Covalent/Coordinate Network Structures

Inorganic semiconductor materials are best known for their superior physical properties, as well as their structural rigidity and stability. However, the poor solubility and solution-processability of these covalently bonded network structures has long been a serious drawback that limits their use in many important applications. Here, we present a unique and general approach to synthesize robust, solution-processable, and highly luminescent hybrid materials built on periodic and infinite inorganic modules. Structure analysis confirms that all compounds are composed of one-dimensional anionic chains of copper iodide (Cu m I m+2 2- ) coordinated to cationic organic ligands via Cu-N bonds. The choice of ligands plays an important role in the coordination mode (μ 1 -MC or μ 2 -DC) and Cu-N bond strength. Greatly suppressed nonradiative decay is achieved for the μ 2 -DC structures. Record high quantum yields of 85% (λ ex = 360 nm) and 76% (λ ex = 450 nm) are obtained for an orange-emitting 1D-Cu 4 I 6 (L 6 ). Temperature dependent PL measurements suggest that both phosphorescence and thermally activated delayed fluorescence contribute to the emission of these 1D-AIO compounds, and that the extent of nonradiative decay of the μ 2 -DC structures is much less than that of the μ1 -DC structures. More significantly, all compounds are remarkably soluble in polar aprotic solvents, distinctly different from previously reported CuI based hybrid materials made of charge-neutral Cu m X m (X = Cl, Br, I), which are totally insoluble in all common solvents. Finally, the greatly enhanced solubility is a result of incorporation of ionic bonds into extended covalent/coordinate network structures, making it possible to fabricate large scale thin films by solution processes

36 MATERIALS SCIENCE↗
DOE OSTI2020

Prediction of chlorine and fluorine crystal structures at high pressure using symmetry driven structure search with geometric constraints

The high-pressure properties of fluorine and chlorine are not yet well understood because both are highly reactive and volatile elements, which have made conducting diamond anvil cell and x-ray diffraction experiments a challenge. Here, we use ab initio methods to search for stable crystal structures of both elements at megabar pressures. We demonstrate how symmetry and geometric constraints can be combined to efficiently generate crystal structures that are composed of diatomic molecules. Furthermore, our algorithm extends the symmetry driven structure search method by adding constraints for the bond length and the number of atoms in a molecule while still maintaining generality. As a method of validation, we have tested our approach for dense hydrogen and reproduced the known molecular structures of Cmca-12 and Cmca-4. We apply our algorithm to study chlorine and fluorine in the pressure range of 10 GPa–4000 GPa while considering crystal structures with up to 40 atoms per unit cell. We predict chlorine to follow the same series of phase transformations as elemental iodine from Cmca to Immm to Fm3¯m, but at substantially higher pressures. We predict fluorine to transition from a C2/c to Cmca structure at 70 GPa, to a novel orthorhombic and metallic structure with P42/mmc symmetry at 2500 GPa, and finally to its cubic analog form with Pm3¯n symmetry at 3000 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Structure of disordered TiO 2 phases from ab initio based deep neural network simulations

Amorphous TiO 2 (a-TiO 2 ) is widely used in many fields, ranging from photo-electrochemistry to bio-engineering, hence detailed knowledge of its atomic structure is of scientific and technological interest. Here we use an ab initio-based deep neural network potential (DP) to simulate large scale atomic models of crystalline and disordered TiO 2 with molecular dynamics. Our DP reproduces the structural properties of all (11) TiO 2 crystalline phases, predicts the densities and structure factors of molten and amorphous TiO 2 with only a few percent deviation from experiments, and describes the pressure dependence of the amorphous structure in agreement with recent observations. Furthermore, it can be extended to model additional structures and compositions and can be thus of great value in the study of TiO 2 -based (nano-)materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

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↗