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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗
DOE OSTI2025

The hierarchical growth of bright central galaxies and intracluster light as traced by the magnitude gap

Using a sample of 2800 galaxy clusters identified in the Dark Energy Survey across the redshift range 0.20 < z < 0.60, we characterize the hierarchical assembly of bright central galaxies (BCGs) and the surrounding intracluster light (ICL). To quantify hierarchical formation we use the stellar mass–halo mass (SMHM) relation, comparing the halo mass, estimated via the mass–richness relation, to the stellar mass within the BCG + ICL system. Moreover, we incorporate the magnitude gap (M14), the difference in brightness between the BCG (measured within 30 kpc) and fourth brightest cluster member galaxy within 0.5 $R_{200,c}$, as a third parameter in this linear relation. The inclusion of M14, which traces BCG hierarchical growth, increases the slope and decreases the intrinsic scatter, highlighting that it is a latent variable within the BCG + ICL SMHM relation. Moreover, the correlation with M14 decreases at large radii. However, the stellar light within the BCG + ICL transition region (30 –80 kpc) most strongly correlates with halo mass and has a statistically significant correlation with M14. Since the transition region and M14 are independent measurements, the transition region may grow due to the BCG’s hierarchical formation. Additionally, as M14 and ICL result from hierarchical growth, we use a stacked sample and find that clusters with large M14 values are characterized by larger ICL and BCG + ICL fractions, which illustrates that the merger processes that build the BCG stellar mass also grow the ICL. Furthermore, this may suggest that M14 combined with the ICL fraction can identify dynamically relaxed clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Hierarchical Bayesian modeling for Inverse Uncertainty Quantification of system thermal-hydraulics code using critical flow experimental data

The best estimate plus uncertainty methodology in nuclear system thermal-hydraulic studies necessitates a comprehensive understanding of uncertainties in system code predictions. The forward uncertainty quantification (UQ) process involves the propagation of input uncertainties through the computational models to obtain uncertainties in the outputs. To this end, achieving an accurate estimation of input uncertainties is important, which is the focus of inverse UQ (IUQ). Traditionally, research in Bayesian IUQ within the nuclear engineering domain has largely relied on single-level Bayesian inference. While being effective for relatively small datasets, this approach encounters limitations for cases with large datasets. The use of a single-level model may prove inefficient, as the resultant posterior distributions can significantly differ when distinct subsets of data are employed. To address this issue, we employ an hierarchical Bayesian model for IUQ. Furthermore, this approach involves organizing observations into different groups based on the test conditions, thereby accommodating varying calibration parameters across these distinct groups. In this study, we developed and implemented a hierarchical Bayesian IUQ method to consider the grouping effect of critical flow measurement data from various geometries. Comparing the outcomes of IUQ under different selections of test data using hierarchical Bayesian IUQ against those obtained from single-level Bayesian IUQ, the forward propagation of hierarchical Bayesian IUQ results demonstrates a notably improved agreement with the experimental data.

42 ENGINEERING↗
DOE OSTI2025

Tailoring multi-dimensional hierarchical self-assembly of metallacages through balancing non-covalent interactions

Despite advances in non-covalent interactions and complex self-assembly, precise control of multi-dimensional hierarchical self-assembly (HSA) from the molecular level to larger scales remains challenging. Herein, we designed and synthesized two rigid tetratopic ligands with multiple preset driving forces, and assembled them with Zn(II) ions to obtain metallacages SC6 and SC12 . Through balancing multiple non-covalent interactions, including metal–organic coordination, hydrophobic, and π–π interactions, SC6 can hierarchically self-assemble driven by a poor solvent, from one-dimensional nanowires to super-helical nanostructures via non-equilibrium self-assembly, progressing continuously with time and the increasing proportion of the poor solvent. However, for SC12 with enhanced hydrophobic interactions, two-dimensional monolayer nanogrids were formed by hierarchical self-assembly. Notably, these structures can be recycled back to primary metallacages through simple dissolution, highlighting their potential for efficient recycling and reuse. These results demonstrate that multi-dimensional hierarchical structures enable precise construction by balancing non-covalent interactions through a bottom-up self-assembly approach. This study provides deeper insight into the mechanisms of HSA and a promising strategy for the tailored creation of complex structures and sustainable porous materials.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Hierarchical Truncations for Many-Body Expansion Potentials

In this work, a new strategy to truncate high-order terms in the many-body expansion (MBE) is proposed. This new approach, which we call a hierarchical many-body expansion (HMBE), is based on a hierarchical partition of the system into multitier fragments and can in principle be applied to any large molecular system. Numerical tests on a series of (H 2 O) 64 structures are presented, demonstrating satisfactory relative energies between the clusters and binding energies of individual clusters compared with full-cluster calculations, with significantly fewer high-order terms computed than conventional MBE. The hierarchical truncation can be augmented by certain many-body terms for fragments at the interface between the partitions (called “Schengen terms”) to further improve accuracy. This work establishes the HMBE scheme as a promising framework to model very large systems (e.g., proteins), which are naturally built on a hierarchical structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Strong, ductile, and hierarchical hetero-lamellar-structured alloys through microstructural inheritance and refinement

The strength−ductility trade-off exists ubiquitously, especially in brittle intermetallic-containing multiple principal element alloys (MPEAs), where the intermetallic phases often induce premature failure leading to severe ductility reduction. Hierarchical heterogeneities represent a promising microstructural solution to achieve simultaneous strength−ductility enhancement. However, it remains fundamentally challenging to tailor hierarchical heterostructures using conventional methods, which often rely on costly and time-consuming processing. Here, we report a multiscale microstructural inheritance and refinement strategy to process “structural hierarchy precursors” in as-cast heterogeneous Al 0.7 CoCrFeNi MPEAs, which lead directly to a hierarchical hetero-lamellar structure (HLS) after simple rolling and annealing. Interestingly, it takes only 10 min of annealing time, two orders of magnitude less than that required to render the state-of-the-art properties during conventional processing of Al 0.7 CoCrFeNi, for us to achieve record-high strength−ductility combinations via the hierarchical HLS design that sequentially stimulates multiple unusual deformation and reinforcement mechanisms. In particular, the HLS-enabled high hetero-deformation-induced (HDI) internal stress triggers profuse <111>-type dislocations on over five independent slip systems in the supposedly brittle intermetallic phase and activates extensive stacking faults (SFs) and nanotwinning in the adjoining soft phase with a rather high SF energy. These unexpected, dynamically reinforcing hetero-deformation mechanisms across multiple length scales facilitate high sustained HDI strain hardening, along with a salient microcrack-mediated extrinsic ductilization effect, suggesting that the proposed microstructural inheritance and refinement strategy provides an efficient, fast, and low-cost approach to overcome the strength−ductility trade-off in a broad range of structural materials.

Science & Technology - Other Topics↗
DOE OSTI2025

Multi-Label Classification with Constraint-Based Learning for Hierarchical Consistency

We explore the limitations of traditional crossentropy loss in a hierarchical multi-label classification setting and introduce a novel loss function. This function is designed to integrate hierarchical constraints directly into the training process. By incorporating such constraints into the loss, our approach slightly improves the logical consistency of predictions in structured domains. We demonstrate the efficacy of our approach through experiments on primary site and histology classification by using electronic pathology reports. These results show that our proposed hierarchical loss function enhances the model's ability to produce predictions that are logically consistent with the natural data hierarchies, and it slightly improves predictive accuracy. Our framework may be extended to other hierarchical domains, however the performance gains are context specific.

Shivanna, Abhishek [ORNL] (ORCID:0009000665228593)↗
DOE OSTI2025

Hierarchical Bayesian Modeling for Cosmology: Can NPE reliably replace MCMC?

Hierarchical neural posterior estimation has its place Hierarchical Bayesian Modeling (HBM) combined with MCMC algorithms has been shown to provide more robust and accurate inference for real-world phenomena in which nature takes a nested form. However, MCMC-based inference can be computationally expensive, and its performance often suffers for complex posterior geometries. These costs are especially pertinent for HBM. Studies have recently demonstrated the potential for a flexible, expressive, and amortized hierarchical neural posterior estimator (HNPE) built on Normalizing Flows. These studies have mostly been performed on simple datasets, or they focus on a single parameter from each level of the hierarchy. A systematic study analyzing how both hierarchical methods compare for more complex and realistic datasets is necessary before applying HNPE for scientific measurements. Here, we re-explore the theory behind HNPE and conduct comparative numerical experiments of HNPE and MCMC-based HBM methods on real and synthetic data, including strong gravitational lensing simulations. In particular, we use a suite of diagnostics to show trade-offs in terms of accuracy, precision, time to train or sample, reproducibility, and the need for expert domain knowledge. Especially for higher dimensional and complex posteriors, HNPE is expected to drastically improve on time for inference, accuracy, and precision with an upfront training time cost.

Hur, Rachel [Chicago U.] (ORCID:000900089890445X)↗
DOE OSTI2026

Compositional Reasoning for Hierarchical State Machines

Harel statecharts and its derivatives are popular graphical languages for specifying discrete control systems via hierarchical state machines. Separately, there has been a long line of work on specifying concurrent systems with process calculi which come equipped with an algebraic theory, the ability reason compositionally about various temporal properties, and strong type systems. While these two approaches to modeling systems are tantalizingly similar, the integrated reasoning principles that exist for process calculi have not been demonstrated in hierarchical state machines. A key issue is that operational theories for process calculi do not behave like control systems, and thus, there is virtually no tool support for modeling control systems with such languages. For a control system designer, bringing the integrated, more scalable reasoning from the process calculi to state-machine languages would enable the specification of more complex systems and a more modular systems development process. Our insight is that we can recover many important results from the process calculi in hierarchical state machines with local scope. We employ a structural operational semantics, which is ubiquitous in process and 𝜆-calculi but uncommon in hierarchical statemachine formalizations, to enable inductive reasoning about behavior. Taking inspiration from the structure of process calculi metatheories, we define a calculus of refinement and equivalence that we prove sound with respect to local notion of (bi)simulation. Furthermore, we prove that the calculus preserves the behavioral properties of reactivity, observational determinism, traces, and linear temporal properties. Our results are mechanized in the Rocq proof assistant.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Graph-Based Modeling and Decomposition of Hierarchical Optimization Problems

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex hierarchical connectivity that arises from decision-making over multiple spatial and temporal scales (e.g., integration of planning, scheduling, and operations in manufacturing and infrastructures). We also show that the graph abstraction facilitates the conceptualization and implementation of decomposition and approximation schemes. Specifically, we propose a graph-based Benders decomposition (gBD) framework that enables the exploitation of hierarchical (nested) structures and that uses graph aggregation/partitioning procedures to discover such structures. In addition, we provide a Julia implementation of gBD, which we call PlasmoBenders.jl. We illustrate the capabilities using examples arising in the context of energy and power systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

This paper analyzes hierarchical Bayesian inverse problems using techniques from highdimensional statistics. Furthermore, our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.

MAP estimation↗
DOE OSTI2025

Modular Assembly of FTO|Chromophore-Catalyst Hierarchical Films Based on Strong Dipole Interactions

Here, we have designed and characterized modular self-assembled hierarchical films containing a molecular catalyst tethered to an anchoring molecule by means of dipole-induced dipole interactions. In order to do so, two new Co III -based molecular catalyst candidates were designed, namely, [Co III L 1 (pyrr) 2 ]ClO 4 (Co1) and [Co III L 2 (pyrr) 2 ]ClO 4 (Co2), where L 1 and L 2 are the respective deprotonated forms of N,N′-[4,5-bis(dodecyloxy)-1,2-phenylene]dipicolinamide and N,N′-[4,5-bis(methoxyethoxy)-1,2-phenylene]dipicolinamide and were characterized by electrochemical, electronic, and film formation properties. Species Co1 and Co2 were deposited onto an anchor molecule such as octylphosphonic acid (OPA) or the chromophoric [Ru II (bpy PO3H ) 2 (bpy C7 )]Cl 2 (Ru) previously attached onto conductive fluorine-doped tin oxide (FTO). Four hierarchical films of the form substrate|anchor-catalyst were obtained, namely, FTO|OPA-Co1, FTO|OPA-Co2, FTO|Ru-Co1, and FTO|Ru-Co2, and the role of dipole-dipole interactions between anchor and catalyst modules was assessed. These newly synthesized hierarchical films were characterized by a host of surface-specific methods that include X-ray photoelectron spectroscopy, ellipsometry, X-ray fluorescence, and water contact angle, thus enabling an unprecedented level of analysis. Compared to the weak C-H van der Waals interactions exhibited by Co1, the presence of alkoxy chains in Co2 ensures stronger dipole-dipole interactions with the alkyl chain of the anchors due to O···H formation. The persistence of their redox properties, which include metal oxidation, and directionality of electron transport were probed suggesting direct relevance to catalytic processes such as water oxidation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Hierarchical Chiral Self-Assembly of Nanocylinders Composed of Sequence-Defined Mesogenic Dimers

Chiral ensembles can arise through supramolecular curvature that resolves geometric frustrations in the packing of bent, achiral molecular or colloidal building blocks. Here, we leverage orthogonal protection−deprotection click chemistry to create sequence-defined mesogenic heterodimers exhibiting emergent chirality. We compare the hierarchical self-assembly of the synthesized asymmetric, achiral heterodimers, which differ only in the position of a methyl substituent. Both dimers form chiral spherulites composed of nanocylinders. However, the detailed arrangement of nanocylinders depends on the position of the methyl substituent and the crystallization conditions. Despite the chemical similarity, in one dimer, two crystalline forms are optically active. They form conglomerates of dextrorotatory and levorotatory spherulites. The other dimer forms more highly anisotropic spherulites that mask circular birefringence arising from the misorientation of nanocylinders, while mapping of nanocylinder directors reveals a sense at the spherulite surface. We propose that differences in nanocylinder arrangements may arise from changes in nanocylinder curvature and dimensions dictated by the methyl substituent position, inducing chirality. These results demonstrate multiscale hierarchical assembly relevant to dense systems of tubular structures and highlight the role of sequence and molecular design in directing the bottom-up hierarchical self-assembly and chirality of mesogenic systems.

Alkyls↗
DOE OSTI2026

Hierarchical microstructure of Yb-filled skutterudites through ultrasonically atomized spherical powders for enhanced thermoelectric performance

Hierarchical microstructures are widely explored as a strategy to reduce lattice thermal conductivity in thermoelectric materials while preserving favorable electronic transport. Here we demonstrate that ultrasonic atomization of precursor powders provides an intrinsic pathway to generate such architectures in n-type Yb0.3Co4Sb12 skutterudites. Materials were synthesized by both conventional sealed-ampoule and ultrasonic atomization routes, each yielding essentially single-phase skutterudite after densification. However, the atomized spherical powders undergo a distinct reaction-driven microstructural evolution during thermal treatment prior to densification. Electron microscopy reveals that the skutterudite phase within the particles induces swelling, cracking, and fragmentation of the droplets before consolidation. Multimodal structural and microstructural characterizations show that densification of these fragmented powders produces a hierarchical microstructure consisting of submicron grains, micrometer-scale faceted crystallites, and powder-derived domains separated by oxide-decorated boundaries. Comprehensive thermoelectric transport measurements evidence that this multiscale architecture lowers the lattice thermal conductivity while maintaining favorable electronic transport, leading to an average ~10% enhancement in the thermoelectric figure of merit. Complementary 121Sb Mössbauer spectroscopy further indicates lattice softening in the atomized material. These results demonstrate that ultrasonic atomization provides an effective route to engineer hierarchical microstructures in skutterudite thermoelectrics and offers a promising strategy for tailoring thermal transport in energy-conversion materials.

Bouteiller, Hugo [ORNL] (ORCID:0009000421322962)↗
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↗
DOE OSTI2025

Theoretical and methodological challenges in hierarchical Bayesian inference for model-form uncertainty

This report describes challenges associated with the hierarchical Bayesian approach to inform model-form uncertainty (MFU) representations, which are parameterized modifications to a mathematical models’ governing equations to express uncertainty in form of the equations. To inform model-form uncertainties, hierarchical Bayesian inference is often employed. Here, the MFU parameters are distributed parametrically, and the hyperparameters of the parametric distribution are informed through Bayesian inference, with the aim of determining the MFU parameter distribution that best agrees with calibration data. In practice, however, we have found the hierarchical Bayesian approach falls short of this aim. We discuss theoretical and methodological challenges of the approach, and we present several numerical demonstrations of these challenges. To conclude, we suggest promising alternative approaches for future investigation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SHF: Symmetrical Hierarchical Forest with Pretrained Vision Transformer Encoder for High-Resolution Medical Segmentation

This paper presents a novel approach to addressing the long-sequence problem in high-resolution medical images for Vision Transformers (ViTs). Using smaller patches as tokens can enhance ViT performance, but quadratically increases computation and memory requirements. Therefore, the common practice for applying ViTs to high-resolution images is either to: (a) employ complex sub-quadratic attention schemes or (b) use large to medium-sized patches and rely on additional mechanisms within the model to capture the spatial hierarchy of details. We propose Symmetrical Hierarchical Forest (SHF), a lightweight approach that adaptively patches the input image to increase token information density and encode hierarchical spatial structures into the input embedding. We then apply a reverse depatching scheme to the output embeddings of the transformer encoder, eliminating the need for convolution-based decoders. Unlike previous methods that modify attention mechanisms or use a complex hierarchy of interacting models, SHF can be retrofitted to any ViT model to allow it to learn the hierarchical structure of details in high-resolution images without requiring architectural changes. Experimental results demonstrate significant gains in computational efficiency and performance: on the PAIP WSI dataset, we achieved a 3∼32×speedup or a 2.95%∼7.03% increase in accuracy (measured by Dice score) at a 64K2 resolution with the same computational budget, compared to state-of-the-art production models. On the 3D medical datasets BTCV and KiTS, training was 6×faster, with accuracy gains of 6.93% and 5.9%, respectively, compared to models without SHF.

Zhang, Enzhi [Hokkaido University, Japan]↗
DOE OSTI2026

Curvilinear Magnonic Crystal Based on 3D Hierarchical Nanotemplates

Curvilinear magnetic nanostructures enable control of magnetization dynamics through geometry-induced anisotropy and chiral interactions, as well as magnetic field modulation. In this work, we report a curvilinear magnonic crystal based on large-area square arrays of truncated nanospikes fabricated by conformal coating of 3D hierarchical templates with permalloy thin films. Brillouin light scattering spectroscopy reveals an anisotropic band structure with multiple dispersive and folded Bloch-type dispersive spin-wave modes as well as nondispersive modes exhibiting direction-dependent frequency shifts and intensity asymmetries along lattice principal axes. Finite element micromagnetic simulations indicate that curvature-induced variations of the demagnetizing field govern the magnonic response, enabling the identification of modes propagating in nanochannels and others localized on nanospike apexes or along the ridges connecting adjacent nanospikes. The combination of geometric curvature and optical probing asymmetry produces directional dependence of magnonic bands, establishing 3D hierarchical templates as a versatile platform for curvature-engineered magnonics.

3D hierarchical templates↗