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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

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 OSTI2021

In Situ Wood Delignification toward Sustainable Applications

As one of the most abundant and versatile natural materials on Earth, recently wood has attracted tremendous attention from scientists and engineers due to its outstanding advantages, including hierarchically porous microstructure, high mechanical strength, environmental friendliness, renewability, and biodegradability. Wood’s hierarchically porous structure and chemical components (e.g., cellulose, hemicelluloses, and lignin) enable its mechanical, ionic, optical, and thermal properties to be tuned via physical, chemical, and/or thermal modifications. Among these various approaches, the chemical delignification of bulk wood is the most fascinating, in which the majority of lignin and hemicelluloses is removed while leaving the cellulose intact, maintaining wood’s physical integrity and hierarchical structure. This delignified structure is unique, composed of hollow, aligned channels made up of cellulose microfibrils, and particularly attractive given its origin from a sustainable and renewable resource. As a result, delignified wood has attracted increasing attention for applications that go far beyond traditional wood utilization, such as lightweight yet strong structural materials, energy storage and conversion, environmental remediation, flexible electronics, and bioengineering. Here, we review recent developments in bulk wood delignification strategies toward the achievement of such advanced wood technologies for sustainable applications, with a focus on the research in our group. Similar to chemical pulping and bleaching, wood delignification involves a series of nucleophilic reactions based on alkaline Na 2 SO 3 or Na 2 S systems (i.e., chemical pulping) or electrophilic, radical, and oxidation reactions based on H 2 O 2 , ClO 2 , or NaClO systems (i.e., chemical bleaching) to deconstruct, fragment, and promote the hydrophilicity of lignin macromolecules, which finally make lignin easier to be removed. We discuss the structure and properties of partially and near-completely delignified wood, with a focus on process-structure–property relationships. The resulting delignified wood materials, with tunable structure and properties, demonstrate various advanced functions, in a wide range of advanced applications, such as building and construction, green energy, and electronics. Finally, the potential challenges and appealing perspectives of in situ wood delignification are discussed. In situ wood delignification, as a powerful modification strategy, has speeded up the development of advanced wood technologies and wood-based functional materials and products.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Modelica-based system modeling for studying control-related faults in chiller plants and boiler plants serving large office buildings

System modeling is critical when studying operation faults in chiller plants and boiler plants. However, current fault models have difficulties faithfully representing the operation of chiller plants and boiler plants under the effects of those faults, especially the control-related ones. In this study, we present a systematic method to develop high-fidelity models for approximating the behaviors of chiller plants and boiler plants under faulty conditions. Compared to existing ones, the resulting fault models have two advantages: first, they better characterize the dynamic patterns in the system operation. In those models, control architecture and control logic are faithfully implemented. Thus, they can be used to study control-related faults, such as incorrect staging control due to sensor bias and mistuned feedback control. Second, they are readily extensible and can support large-scale investigations to explore different faulty conditions/scenarios. Those models are established in a hierarchical structure while modules in each layer can be redeclared and parameterized at upper layers. In such a case, modifications to the models can be realized through model modifiers and the process can be easily streamlined with scripts. We applied the proposed models in a comprehensive fault impact evaluation of the 13 control-related faults of chiller and boiler plants. In this evaluation, the proposed plant model is coupled with the EnergyPlus thermal load model to study the impact of various faulty scenarios. Based on the evaluation results, we identified the faults that have the most significant impacts on the operation of the chiller and boiler plants, respectively. We also found that the relationship between the impacts of the studied faults and the severity level of the faults are highly non-linear

Huang, Sen↗
DOE OSTI2022

Multilayered Ordered Protein Arrays Self-Assembled from a Mixed Population of Virus-like Particles

Biology shows many examples of spatially controlled assembly of cells and biomacromolecules into hierarchically organized structures, to which many of the complex biological functions are attributed. While such biological structures have inspired the design of synthetic materials, it is still a great challenge to control the spatial arrangement of individual building blocks when assembling multiple types of components into bulk materials. Here, in this study, we report self-assembly of multilayered, ordered protein arrays from mixed populations of virus-like particles (VLPs). We systematically tuned the magnitude of the surface charge of the VLPs via mutagenesis to prepare four different types of VLPs for mixing. A mixture of up to four types of VLPs selectively assembled into higher-order structures in the presence of oppositely charged dendrimers during a gradual lowering of the ionic strength of the solution. The assembly resulted in the formation of three-dimensional ordered VLP arrays with up to four distinct layers including a central core, with each layer comprising a single type of VLP. A coarse-grained computational model was developed and simulated using molecular dynamics to probe the formation of the multilayered, core-shell structure. Our findings establish a simple and versatile bottom-up strategy to synthesize multilayered, ordered materials by controlling the spatial arrangement of multiple types of nanoscale building blocks in a one-pot fabrication.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Diversifying Composition Leads to Hierarchical Composites with Design Flexibility and Structural Fidelity

Although significant progress has been made in the self-assembly of nanostructures, present successes heavily rely on precision in building block design, composition, and pair interactions. These requirements fundamentally limit our ability to synthesize macroscopic materials where the likelihood of impurity inclusion escalates and, more importantly, to access molecular-to-nanoscopic-to-microscopic-to-macroscopic hierarchies, since the types and compositions of building blocks vary at each stage. Inspired by biological blends and high-entropy alloys, we hypothesize that diversifying the blend’s composition can overcome these limitations. Increasing the number of components increases mixing entropy, leading to the dispersion of different components and, as a result, enhances interphase miscibility, weakens the dependence on specific pair interactions, and enables long-range cooperativity. This hypothesis is validated in complex blends containing small molecules, block copolymer-based supramolecules, and nanoparticles/colloidal particles. Hierarchically structured composites can be obtained with formulation flexibility in the filler selection and blend composition. It is worth noting that, by adding small molecules, we can solve the size constraint that plagues traditional block copolymer/nanoparticle blends. Detailed characterization and simulation further confirm that each component is distributed to locally mediate unfavorable interactions, cooperatively mitigate composition fluctuations, and retain structural fidelity. Furthermore, the blends have sufficient mobility to access tunable microstructures without compromising the order of the nanostructure. Besides establishing a kinetically viable pathway to release current constraints in the composite design and to navigate uncertainties during structure formation over multiple length scales, the present study demonstrates that entropy-driven behaviors can be realized in systems beyond high-entropy alloys despite inherent differences between metal alloys and organic/inorganic hybrids.

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

Directed self-assembly of chiral liquid crystals into biomimetic bouligand structures in thin film

The Bouligand structure, renowned for its helicoidal arrangement and enhanced mechanical properties, has attracted significant research interest for its ability to impart enhanced strength to intrinsically soft materials. Biomimetic approaches have centered on fibrous structures in bulk materials, but translating this architecture into thin-film regime for miniaturized-wearable devices with programmable functions remains challenging. Here, we direct the self-assembly of cholesteric liquid crystals (CLCs) into hierarchical helical structures using chemically patterned surfaces. Alternating surface anchoring regions align uniform lying-down helices at the nanoscale, guiding a secondary microscale helical structure exhibiting both left- and right-handed twists. This mimetic Bouligand structure in CLCs enables optical modulation under applied field and strain with enhanced mechanical response. Simulations reveal the structural evolution from initial Bouligand configuration in LC layers to alternating twist helices. This research provides a basis for designing and manufacturing miniaturized or wearable devices with nanometer-scale precision in regulating electro-optical and mechanical properties. Bouligand structures, which offer strength in natural materials, are of interest but difficult to obtain. Here, the authors report the development of such structures by directed self-assembly of cholesteric single crystals into hierarchical helical structures, with the secondary structure having right and left-handed twists.

Bouligand structure↗
DOE OSTI2021

Structure–Property Correlation of Hierarchically Porous Carbons for Fluorocarbon Adsorption

Although traditional commercially available porous carbon-fluorocarbon working pairs have shown promising applicability for adsorption cooling, advancements in synthetic carbons may further improve performance. Moreover, insights into structure-property relationships that target higher sorption capacities within these synthesized carbons may guide such materials' future design. We utilized hierarchically porous synthetic carbons (HPCs) with colossal microporous and mesoporous characterized by high surface areas (up to 2689 m 2 /g) and pore volumes (up to 10.31 cm 3 /g) towards fluorocarbon R134a adsorption. This unique pore topology leads to exceptional R134a uptake, ~250 wt.%, outperforming the highest uptake carbon material to date, Maxsorb III (~220 wt.%). Additionally, material characterizations reveal that the outstanding R134a capacity may be attributed to textural properties and oxygen-terminated functional groups more than graphitization of the material. Most importantly, HPCs are efficiently utilized in a two-bed model chiller device, where the performance shows excellent working capacity (105 wt%, ~1.5 times the value of reported carbon materials/R134a). Fluorocarbons adsorption on HPCs also displays fast kinetics (equilibrium time: ~2 min) mainly driven by physical adsorption (Qst: ~27 kJ/mol), characteristic of swiftly reversible behavior adsorption-desorption behaviors. This work provides a fundamental understanding of the applicability of HPCs/R134a working pair for adsorption cooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Strain‐Driven Mixed‐Phase Domain Architectures and Topological Transitions in Pb 1− x Sr x TiO 3 Thin Films

Abstract The potential for creating hierarchical domain structures, or mixtures of energetically degenerate phases with distinct patterns that can be modified continually, in ferroelectric thin films offers a pathway to control their mesoscale structure beyond lattice‐mismatch strain with a substrate. Here, it is demonstrated that varying the strontium content provides deterministic strain‐driven control of hierarchical domain structures in Pb 1− x Sr x TiO 3 solid‐solution thin films wherein two types, c / a and a 1 / a 2 , of nanodomains can coexist. Combining phase‐field simulations, epitaxial thin‐film growth, detailed structural, domain, and physical‐property characterization, it is observed that the system undergoes a gradual transformation (with increasing strontium content) from droplet‐like a 1 / a 2 domains in a c / a domain matrix, to a connected‐labyrinth geometry of c / a domains, to a disconnected labyrinth structure of the same, and, finally, to droplet‐like c / a domains in an a 1 / a 2 domain matrix. A relationship between the different mixed‐phase modulation patterns and its topological nature is established. Annealing the connected‐labyrinth structure leads to domain coarsening forming distinctive regions of parallel c / a and a 1 / a 2 domain stripes, offering additional design flexibility. Finally, it is found that the connected‐labyrinth domain patterns exhibit the highest dielectric permittivity.

Kavle, Pravin↗
DOE OSTI2022

A novel hardmask-to-substrate pattern transfer method for creating 3D, multi-level, hierarchical, high aspect-ratio structures for applications in microfluidics and cooling technologies

Abstract This letter solves a major hurdle that mars photolithography-based fabrication of micro-mesoscale structures in silicon. Conventional photolithography is usually performed on smooth, flat wafer surfaces to lay a 2D design and subsequently etch it to create single-level features. It is, however, unable to process non-flat surfaces or already etched wafers and create more than one level in the structure. In this study, we have described a novel cleanroom-based process flow that allows for easy creation of such multi-level, hierarchical 3D structures in a substrate. This is achieved by introducing an ultra-thin sacrificial silicon dioxide hardmask layer on the substrate which is first 3D patterned via multiple rounds of lithography. This 3D pattern is then scaled vertically by a factor of 200–300 and transferred to the substrate underneath via a single shot deep etching step. The proposed method is also easily characterizable—using features of different topographies and dimensions, the etch rates and selectivities were quantified; this characterization information was later used while fabricating specific target structures. Furthermore, this study comprehensively compares the novel pattern transfer technique to already existing methods of creating multi-level structures, like grayscale lithography and chip stacking. The proposed process was found to be cheaper, faster, and easier to standardize compared to other methods—this made the overall process more reliable and repeatable. We hope it will encourage more research into hybrid structures that hold the key to dramatic performance improvements in several micro-mesoscale devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Mechanistic understanding of catalytic conversion of ethanol to 1-butene over 2D-pillared MFI zeolite

Ethanol is an important C2 platform molecule for producing value-added chemicals and distillate hydrocarbon fuels (e.g., jet and diesel). Among these, catalytic upgrading of ethanol to butenes can generate valuable commodity chemicals (e.g., 1-butene) and provide C4 olefin intermediates that can be further upgraded to jet/diesel fuels. 2D zeolites offer hierarchical mesoporous structures, leading to improved mass transport and reduced diffusion length, which can help to address the coking challenges faced by ethanol conversion to hydrocarbons over 3D zeolites. In this study, we investigate the acid-catalyzed conversion of ethanol to 1-butene over the Brønsted acid sites (BAS) in 2D-pillared MFI zeolite (2D-PMFI) using ab initio molecular dynamics (AIMD) simulations, in situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), and calorimetric measurements. A detailed thermodynamic analysis, using quasi-harmonic approximation (QHA), on the Gibbs free energy pathway of ethanol conversion shows that the consideration of entropy is critical to accurately capture the detailed thermodynamic profiles. The formation of bulky ethoxy-ethene complex is found to be a potential rate-determining step (RDS), proceeding via stepwise mechanism. The reactivity of 2D-PMFI can be further tuned by manipulating RDS through a careful control of number of BAS and operating temperatures. The accuracy of computational model is confirmed through the comparison of calculated vibrational density of states (VDOS) against the experimental DRIFTS measurements. Overall, our study provides mechanistic insights into ethanol upgrading over the 2D-PMFI and shows the importance of evaluating entropic effects in such confined system.

Ethanol conversion, 2D-pillared zeolite, MFI, Anha↗
DOE OSTI2026

Structural and compositional complexities of hierarchical self-assembly: A hypergraph approach

Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. In this work, we introduce a hypergraph-based formalism, Blocks & Bonds (B&B), which generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style structural complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the compositional complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based structural complexity and the compositional complexity across all examined systems. Owing to this agreement, the compositional complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol and glucose), DNA-origami lattices, and crystalline assemblies show that B&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Probing Condensed-Phase Structure and Dynamics in Hierarchical Zeolites and Nanosheets for Catalytic Upgradation of Biomass (Final Report)

Understanding complex reaction pathways in systems governed by multi-scale collective interactions across time and length scales remains a central scientific challenge. This project was guided by the hypothesis that the interplay among oligomers, solvents, and active sites can be tuned by a suitable choice of solvation environment and pore architecture in solid-acid catalysts to direct chemical transformations relevant to biomass conversion. Zeolites and zeolite nanosheets were used as model platforms, allowing for the interaction of macromolecules with the surface of the zeolite nanosheets and with smaller pores that host catalytically active sites. To investigate these coupled phenomena, we employ a multi-scale computational framework that integrates molecular-level descriptions with advanced sampling approaches to capture key physical and chemical interactions. Our work through this project improved fundamental understanding of how reactants and solid-acid catalysts interact in solvent-rich environments, thereby enabling the rational design of catalytic systems that upgrade biomass with enhanced selectivity and energy efficiency. In addition, the project developed advanced sampling methodologies critical for disentangling complex, reactive processes in multi-component catalytic environments.

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

Keratin-derived functional carbon with superior charge storage and transport for high-performance supercapacitors

In this work, we report a scalable method to synthesize hierarchically porous, hetero-atom doped activated carbon nanosheet from waste biomass-human hair, and demonstrates the use of this carbon as an ultra-high performance electrode material for supercapacitor applications. Microscopic analyses reveal that sheet size ranges from 50 to 200 nm having a thickness of 15–27 nm. As-synthesized, carbon nanosheets possess a hierarchical porous structure having a specific surface area of 1548 m 2 g -1 . Heteroatom concentration (nitrogen, oxygen, and sulfur) of around 25% is confirmed from XPS analysis. Therefore, the novel interconnected hierarchical porous nanosheets structure enables fast adsorption and transportation of ions during electrochemical processes. Also, the abundant chemically available electroactive heteroatom species in the material enhance the wettability of ions and contribute to pseudocapacitance. The electrochemical analyses through cyclic voltammetry and galvanostatic charge-discharge measurements in 6 M KOH reveal the quasi-EDLC behavior of the activated carbons due to the presence of heteroatoms. A reprensentative KOH activated carbon shows an excellent specific capacitance value of 999 F g -1 at a current density of 1 A g -1 . Furthermore, the symmetrically assembled two-electrode device also delivers a maximum energy density of 32 W h Kg -1 at a power density of 325 W Kg -1 . In addition, excellent cyclic stability of 98% capacitance retention is observed after 10,000 continuous GCD cycles even at a high current density of 5 A g -1 . Symmetric flexible supercapacitor device using KOH-PVA-K3FeCN6 as redox gel polymer electrolyte shows a synergistic specific capacitance of 145 mF cm -1 at a current density of 0.8 mA cm -1 exhibiting very less deviation in bending mode. Therefore, this waste biomass derived heteroatom doped hierarchical porous carbon nanosheets can be a promising material for cost-effective high- performance supercapacitor.

42 ENGINEERING↗
DOE OSTI2023

Radiative cooling textiles using industry-standard particle-free nonporous micro-structured fibers

Abstract Thermal radiation is a major dissipative pathway for heat generated by the human body and offers a significant thermoregulation mechanism over a wide range of conditions. We could use this in garment design to enhance personal cooling, which can improve the wearing comfort of garments or even result in energy savings in buildings. At present, however, radiative cooling has received insufficient attention in commercial design and production of textiles for wearable garments. Textiles that efficiently transmit the radiative heat were recently demonstrated, but either do not utilize standard weaving and knitting processes for wearable garments or require substantial process modifications. Here, we demonstrate the design and implementation of large-scale radiative cooling textiles for localized cooling management and enhanced thermal comfort using industry-standard particle-free nonporous micro-structured fibers that are fully compatible with standard textile materials and production methods. The micro-structured fibers, yarns and fabrics are part of a hierarchical photonic structure design that renders the textiles highly infrared transparent (up to > 0.8) while assuring visual opacity (up to 0.99). We design radiative cooling textiles with first-principles electromagnetic methods and fabricate them using commercial textile materials and formation facilities. Our “fabless” approach is confirmed by very good quantitative agreement between design and measurements. The resulting fabrics exhibit wearability properties expected of wearable textiles, and lower skin temperature by ≥ 3 °C compared to conventional textiles, which offers the potential for > 30 % energy savings in buildings and increases wearing comfort by significantly reducing the reliance on latent heat dissipation for thermoregulation.

Catrysse, Peter B.↗
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↗