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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 OSTI2024

Hierarchical Phased-Array Antennas Coupled to Al KIDs: A Scalable Architecture for Multi-band Millimeter/Submillimeter Focal Planes

We present the optical characterization of two-scale hierarchical phased-array antenna kinetic inductance detectors (KIDs) for millimeter/submillimeter wavelengths. Our KIDs have a lumped-element architecture with parallel plate capacitors and aluminum inductors. The incoming light is received with a hierarchical phased array of slot dipole antennas, split into 4 frequency bands (between 125 GHz and 365 GHz) with on-chip lumped-element band-pass filters, and routed to different KIDs using microstriplines. Individual pixels detect light for the 3 higher-frequency bands (190–365 GHz), and the signals from four individual pixels are coherently summed to create a larger pixel detecting light for the lowest frequency band (125–175 GHz). The spectral response of the band-pass filters was measured using Fourier transform spectroscopy (FTS), the far-field beam pattern of the phased-array antennas was obtained using an infrared source mounted on a 2-axis translating stage, and the optical efficiency of the KIDs was characterized by observing loads at 294 K and 77 K. We report on the results of these three measurements.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Synthesis of hierarchical graphene coated porous Si anode for lithium-ion batteries

The ultra-high capacity and widespread availability of Si materials have resulted in them being the focus of extensive studies to replace the graphite anode. However, the main barriers preventing the Si anodes from large-scale applications are their huge volume change and severe interface reactions in the lithiation/delithiation process, which pulverizes its structure and subsequently deteriorates its cycle life. Here, micrometer-scale porous Si coated with graphene coating (mpSi@G) has been synthesized by using SiO 2 nanoparticles and novel coal-derived humic acid as feedstocks through a magnesiothermic reduction, followed by spray drying and calcination techniques. SEM, Raman, and X-ray absorption analysis demonstrate that the hierarchical graphene shell and micrometer-sized porous Si structure effectively release the Si anode's mechanical stress upon lithiation to achieve good structural stability. Here, the synthesized mpSi@G anode delivers a high initial lithiation capacity of 2974.9 mAh g –1 at 0.1 A g –1 with an initial coulombic efficiency of 70.2 %. Furthermore, the conductive hierarchical graphene network, along with the tight contacts of porous-Si and the graphene shell, contribute to a high capacity of 1109.5 mAh g –1 at a high current density of 5.0 A g –1 , showing excellent rate capability.

25 ENERGY STORAGE↗

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↗

DOE OSTI2025

Coalescence-Induced Spontaneous Shedding of Microdroplets on Superhydrophobic Surfaces Featuring Enclosed Micropillars with Hierarchical Roughness

This study investigated water vapor condensation on superhydrophobic surfaces (SHSs) featuring micropillars enclosed by wall lattices and having three-tier hierarchical roughness. A total of five samples were created with three (NW-J, W200-J and W400-J samples) having large micropillar depth (~6 μm) and two (NW-S and W200-S samples) having small micropillar depth (~1 μm). Two distinct condensate removal modes were observed during condensation: coalescence-induced jumping on samples with large micropillar depth and coalescence-induced shedding on samples with small micropillar depth. The results showed that the diameter of the shedding droplet on the W200-S sample having small micropillar depth could be as small as 107 μm, as compared to the theoretical critical diameter of 267 μm for gravitational shedding on the same sample. The enhanced functionality of the three-tier nanotextures on the W200-S sample could effectively suppress localized pinning of the three-phase contact line and Wenzel neck formation during the growth of condensate droplets. Consequently, during multidroplet coalescence, the released surface energy easily overcomes the solid–liquid adhesion, leading to spontaneous shedding of merged droplets. The inclusion of the wall lattice aids condensate growth by the droplet self-alignment along the walls and promoting coalescence. As a result, the W200-S sample exhibited the highest condensate collection as well. In conclusion, the proposed surface design has great potential for scaling up and implementation in heating, ventilation, and air-conditioning equipment due to the simplicity of the surface morphology and the facile spray-coating method used to achieve hierarchical roughness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Hierarchical Resilience Planning for Networked Microgrids: A Case Study of Puerto Rico

Microgrids can be designed to enhance the energy resilience of communities and critical infrastructures, such as hospitals, data centers, and communication networks, which are vulnerable to frequent weather-related disruption. Coordinating multiple microgrids in a network can leverage the geographical diversity of load and generation resources while enabling resilient and cost-effective planning of the distribution system. Designing a networked microgrid is complex, involving intricate technical assessment, cost-benefit analysis, site-specific requirements, and the evaluation of existing resources. Therefore, this paper proposes a hierarchical resilience planning framework and performs an extensive techno-economic analysis for the design of a networked microgrid. Hierarchical resilience planning involves technology sizing at an individual community level to meet the critical load and satisfy resilience criteria, and resource optimization at networked microgrid level to provide a higher level of resilience and energy adequacy. A real-world case of Puerto Rico's cooperative microgrid “Microrred de la Montaña” is investigated considering localized electricity tariffs, site-specific demand profiles, solar generation, and existing hydro resources. Multiple optimization scenarios are developed based on the resiliency requirement to estimate the capacity of solar photovoltaic and battery energy storage (BES) to be installed at each substation. The results provide the optimal sizing for individual community and networked microgrid to withstand 1day and 3-day outages along with the criteria for critical load.

13 - HYDRO ENERGY↗

DOE OSTI2024

Hierarchically Structured Catalysts Toward Sustainable Hydrogen Economy: Electro‐ and Thermo‐Chemical Pathways

Abstract Hydrogen, as an important clean energy source, plays a more and more crucial role in decarbonizing the planet and meeting the global climate challenge due to its high energy density and zero‐emission. The demand for sustainable hydrogen is increasing drastically worldwide as driven by the global shift towards low‐carbon energy solutions. Thermochemical catalysis process dominates hydrogen production at scale given its relatively mature technology and commercialization status, as well as the established manufacturing infrastructure. While due to its environmentally friendly nature and growing abundant sources of renewable electricity, the electrochemical path for hydrogen production is rising as a major alternative to the thermochemical means. Nevertheless, hierarchically structured catalysts and devices have gradually taken the center stage toward replacing the traditional counterparts, especially with the rapid advancement of the design and manufacture of such ordered nanostructure assemblies toward high activity, efficient mass transport, and superb stability. In this review, the latest progress of the hierarchically structured catalysts for hydrogen production have been surveyed on electro‐ and thermo‐ chemical pathways comparatively. It covers the structure designs of atomic dispersion, nanoscale surfaces and interfaces for achieving highly active and durable catalysts, components, and devices. Both electrochemical and thermochemical approaches are reviewed in terms of the vast design details, engineered benefits, and understandings of various Pt‐group metal (PGM) and non‐PGM based transition metal catalysts for hydrogen production. As the growing trend, brief discussions are also presented toward the high‐level assembly and manufacture of complexly structured components and devices at scale in the electrochemical and thermochemical energy systems.

Deng, Chenxin↗

DOE OSTI2025

In Situ MOF Pyrolysis Construction of Hierarchical Porous Co‐Nanoparticles/Carbon Cloth Composites for Enhanced Electromagnetic Wave Shielding and Absorption

The development of high-performance electromagnetic protection materials integrating broadband absorption and effective shielding capabilities is hindered by challenges in simultaneously optimizing multiple electromagnetic properties through conventional material designs. This study pioneers a hierarchical porous Co nanoparticle/carbon cloth (Co/CC) composite via controlled annealing of a Co-MOF precursor on carbon cloth. The Co-MOF served a dual role as both magnetic source and pore-forming agent, enabling in situ generation of uniformly dispersed Co nanoparticles and creation of abundant pores/interfaces on the CC fibers during pyrolysis. This unique architecture synergistically enhanced dielectric loss (via interfacial/dipolar polarization) and magnetic loss (via natural resonance, exchange interactions, and eddy currents), significantly improving impedance matching. The hierarchical pores further functioned as integrated “absorption–reflection” units for efficient electromagnetic energy attenuation. Consequently, the Co/CC composite annealed at 800°C (Co/CC-800) achieves minimum reflection loss (−40.69 dB) and 120% effective absorption bandwidth extension (6.16 GHz) as a filler, and exhibits superior electromagnetic interference shielding effectiveness (46.66 dB) as an integrated component. Significantly, Co/CC-800 demonstrated robust photothermal and electrothermal conversion capabilities, ensuring operational stability in ice-covered and humid harsh environments. This work pioneers a pore-structure-mediated strategy to harmonize dielectric–magnetic synergy, providing a new paradigm for designing advanced multifunctional electromagnetic protection materials.

dielectric‐magnetic synergy↗

DOE OSTI2026

Emerging hierarchical dislocation structures: Insights from scanning electron microscopy-electron backscatter diffraction in situ tensile testing and multifractal analysis

Understanding the evolution of dislocation structures during plastic deformation is critical for predicting the mechanical performance of metallic materials. In this work, we applied in situ scanning electron microscopy/electron backscatter diffraction tensile testing combined with multifractal (MF) analysis to assess deformation-induced dislocation structure evolution in solution-annealed 304 L stainless steel, both in its as-received and neutron-irradiated states (5.4 displacements per atom). The analysis of kernel average misorientation patterns revealed the formation of hierarchical dislocation arrangements that exhibit clear MF scaling behavior. Despite pronounced visual differences between nonirradiated and irradiated specimens—most notably, the appearance of dislocation channels after irradiation—the singularity spectra suggest that both conditions give rise to similar underlying hierarchical structures. MF analysis provides a quantitative measure of the spatial complexity and self-organization of dislocation patterns, highlighting the accelerated emergence and evolution of the dislocation structures in irradiated polycrystalline materials, as well as the limitation of their spatial extent. The findings indicate that irradiation not only modifies microstructure but also alters correlation-driven dislocation organization. More generally, they demonstrate that MF analysis is a powerful tool for probing mesoscale deformation mechanisms.

Dislocation structures↗

DOE OSTI2024

Ab Initio-Based Bond Order Potential for Arsenene Polymorphs Developed via Hierarchical Reinforcement Learning

Arsenene, a less-explored two-dimensional material, holds the potential for applications in wearable electronics, memory devices, and quantum systems. This study introduces a bond-order potential model with Tersoff formalism, the ML-Tersoff, which leverages multireward hierarchical reinforcement learning (RL), trained on an ab initio data set. This data set covers a spectrum of properties for arsenene polymorphs, enhancing our understanding of its mechanical and thermal behaviors without the complexities of traditional models requiring multiple parameter sets. Our RL strategy utilizes decision trees coupled with a hierarchical reward strategy to accelerate convergence in high-dimensional continuous search spaces. Unlike the Stillinger-Weber approach, which demands separate formalisms for buckled and puckered forms, the ML-Tersoff model concurrently captures multiple properties of the two polymorphs by effectively representing the local environment, thereby avoiding the need for different atomic types. Here, we apply the ML model to understand the mechanical and thermal properties of the arsenene polymorphs and nanostructures. We observe an inverse relationship between the critical strain and temperature in arsenene. Thermal conductivity calculations in nanosheets show good agreement with ab initio data, reflecting a decrease in thermal conductivity attributable to increased anharmonic effects at higher temperatures. We also apply the model to predict the thermal behavior of arsenene nanotubes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Hierarchical Biogenic-Based Thermal Insulation Foam

Biogenic-based foam, renowned for its sustainable and eco-friendly properties, is emerging as a promising thermal insulating material with the potential to significantly enhance energy efficiency and sustainability in building applications. However, its relatively high thermal conductivity, large-pore configurations, and energy-intensive manufacturing processes hinder its widespread use. Here, we report on the scalable, one-pot synthesis of biogenic foams achieved by integrating recycled paper pulp and in situ nanoporous silica formation, resulting in a hierarchical structure comprising both micropores and nanopores. Ambient solvent-exchange drying can preserve the pore structure by reducing the capillary forces during the drying process. The resulting flame-retardant and hydrophobic foam exhibits low density (0.110 g/cm 3 ), ideal porosity (70.69%), excellent thermal conductivity (0.033 W/(m·K)), and impressive compressive strength (1.48 MPa at 80% strain). Furthermore, this recyclable biogenic foam, with its hierarchical pore structure and environmental durability, shows great potential for energy-efficient building applications.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Hierarchical Multi-agent Large Language Model Reasoning for Autonomous Heterogeneous Catalyst Discovery

Artificial intelligence is reshaping scientific exploration, but most methods automate procedural tasks without engaging in scientific reasoning, limiting autonomy in discovery. We demonstrate that hierarchical agentic large language model reasoning can efficiently drive simulation and scientific exploration. Across two chemical applications, CO adsorption on Cu surface transition metal adatoms and on M–N–C catalysts, reasoning-guided exploration reduces required atomistic simulations by up to 90% relative to heuristic or random selection. Comparisons across single-agent, multi-agent, and stochastic baselines show that hierarchical strategies yield more coherent and information-efficient search trajectories. Reasoning traces reveal chemically grounded decisions that cannot be explained by semantic bias or stochastic sampling. We realize these agentic reasoning strategies in Materials Agents for Simulation and Theory in Electronic-structure Reasoning (MASTER), a multimodal system that translates natural language into density functional theory workflows. Altogether, multi-agent collaboration accelerates heterogeneous catalyst discovery and marks a step toward more autonomous, reasoning-guided scientific exploration.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2026

Achieving strength-ductility synergy in hierarchical aluminum metal matrix composites via friction extrusion

We report the fabrication of aluminum metal matrix composites (Al-MMCs) with hierarchical architectures via friction extrusion (FE), a scalable, single-step, solid-phase processing technique. Precursor pucks containing 0–15 vol% Al₂O₃ particles were extruded into fully dense AA6061-based composite rods. The FE induced a tree-ring-like architecture of concentric particle-rich and particle-lean bands, yielding refined grains in particle-rich regions and coarser grains elsewhere. At the nanoscale, magnesium in AA6061 selectively reacted with Al₂O₃ particles to form virus-like nodes, improving particle–matrix bonding. This multi-scale design strategy, combining mesoscale architecture, microscale grain refinement, and nanoscale interface engineering overcome the conventional strength–ductility trade-off. Tensile testing showed substantial increases in yield and ultimate tensile strengths while retaining high ductility ( > 20%). Enhanced strain hardening, driven by the accumulation of geometrically necessary dislocations at interfaces, contributed to the performance. The hierarchical microstructure produced by FE demonstrates a promising pathway for scalable fabrication of lightweight MMCs for structural applications requiring a combined high strength and ductility.

Kalsar, Rajib [Pacific Northwest National Laborato↗

DOE OSTI2024

Macroscopic modeling of gas permeability in hierarchical micro/nanoporous media: A unified characterization of rarefaction using Klinkenberg theory and equivalent diameter

Estimating gas transport through a hierarchical micro/nanoporous system is challenging due to non-equilibrium gas dynamics. The primary difficulty lies in determining the rarefaction level, because identifying a representative flow dimension in a complex porous system with multiple pore scales is not straightforward. Our study performed a pore-level analysis for gas permeability in dual-scale porous media with varying porosity, throat size, and secondary pore size under different rarefaction conditions. We found that secondary porosity negatively affects permeability due to increased friction forces, with this influence growing as the secondary pore size and porosity increase until the secondary pore becomes comparable to the throat. However, rarefaction reduces the effects of secondary pores due to boundary slip. Traditional Knudsen number (Kn) calculations based on Darcy-defined height failed to accurately describe the rarefaction effects on gas permeability. Instead, we introduced an equivalent diameter to calculate the Kn, which provided an accurate normalization of apparent gas permeability independent of pore geometry. Furthermore, the extended Kozeny–Carman–Klinkenberg model developed in our previous study successfully yielded a macroscopic model for apparent gas permeability in hierarchical micro/nanoporous systems as a function of the traditional Darcy height and porosity.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2026

Hierarchical-embedding autoencoder with a predictor as efficient architecture for learning time-evolution in multi-scale turbulent flows

We introduce a scale-aware, data-driven deep learning modeling framework for accurately predicting the time evolution of multi-scale turbulent plasma and liquid flows. The approach is motivated by the idea of scale separation. Structures of vastly different length scales emerge in these systems, and interactions between these structures occur only locally. To exploit this structure, the flow state is transformed by a hierarchical, fully convolutional autoencoder, not into a single embedding layer as in conventional convolutional surrogate models, but into a series of embedding layers. A stepwise training strategy ensures that fine-scale features are encoded on a high-resolution grid, while larger structures are represented on progressively coarser layers. The time evolution predictor advances all embedding layers in sync, capturing local interactions between features at the same scale as well as between all scales. This approach enables efficient modeling of multi-scale systems since negligible interactions between distant, small-scale structures do not need to be directly modeled. Our hierarchical-embedding autoencoder with a predictor framework is evaluated on canonical examples of multi-scale turbulence: two-dimensional Kolmogorov flow and Hasegawa–Wakatani plasma turbulence. In both cases, the proposed framework significantly improves predictive accuracy relative to conventional convolutional network architectures. A significant improvement in prediction accuracy was observed for crucial statistical characteristics of the Hasegawa–Wakatani plasma as well as for individual trajectories of the Kolmogorov flow turbulence. Importantly, the model's rollout for the Hasegawa–Wakatani problem demonstrates a four-order-of-magnitude speedup compared to traditional numerical solvers.

Khrabry, Alexander I. [Princeton Univ., NJ (United↗

DOE OSTI2025

Statistical relationships across epigenomes using large-scale hierarchical clustering

Recent advances in genomics and sequencing platforms have revolutionized our ability to create immense data sets, particularly for studying epigenetic regulation of gene expression. However, the avalanche of epigenomic data is difficult to parse for biological interpretation given nonlinear complex patterns and relationships. This attractive challenge in epigenomic data lends itself to machine learning for discerning infectivity and susceptibility. In this study, we explore over 3000 epigenomes of uninfected individuals and provide a framework to characterize the relationships among epigenetic modifiers, their modifiers, genetic loci, and specific immune cell types across all chromosomes using hierarchical clustering. Hierarchical clustering of epigenomic data revealed consistent epigenetic patterns across chromosomes, demonstrating that variation due to epigenetic modifiers is greater than variation between cell types. Gene Ontology and KEGG pathway analyses indicated significant enrichment of genes involved in chromatin remodeling, mRNA splicing, immune responses, and the regulation of microRNAs and snoRNAs. Epigenetic modifiers frequently formed biologically relevant clusters, including the cohesin complex, RNA Polymerase II transcription factors, and PRC2 complex members. These clustering behaviors remained consistent across all chromosomes, supported by entropy analysis and high Adjusted Rand Index scores, indicating robust cross-chromosomal similarity. Co-occurrence analysis further revealed specific sets of modifiers that consistently appeared together within clusters, reflecting shared biological functions and interactions. Validation using another dataset confirmed the reproducibility of these clustering patterns and modifier co-occurrence relationships, underscoring the reliability and generalizability of the methodology.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗