Results for “Hierarchical control” — Page 14

DOE OSTI2021

High-Level Synthesis of Parallel Specifications Coupling Static and Dynamic Controllers

The increased need for efficient ways to implement domain-specific accelerators is driving design methodologies towards the use of abstractions higher than the Register Transfer Level (RTL). In this scenario, High Level Synthesis (HLS) plays a significant role by enabling the automatic generation of custom hardware accelerators starting from high level descriptions (e.g., C code). Conventional HLS tools exploit parallelism mostly at the Instruction Level (ILP). They statically schedule the input specifications, and build centralized Finite State Machine (FSM) controllers. However, aggressive exploitation of ILP in many applications has diminishing returns and, usually, centralized approaches do not efficiently exploit coarser parallelism because FSMs are inherently serial. In this paper we present a HLS framework able to synthesize applications that, beside ILP, also expose Task Level Parallelism (TLP). An application can expose TLP through annotations that identify the parallel functions (i.e., tasks). To generate accelerators that efficiently execute concur- rent tasks, we need to solve several issues: devise a mechanism to support concurrent execution flows, exploit memory parallelism, and manage synchronization. To support concurrent execution flows, we introduce a novel adaptive controller. The adaptive controller is composed of a set of interacting control elements that independently manage the execution of a single operation or function call. These control elements check dependencies and resource constraints at runtime, enabling as soon as possible execution. To support parallel access to shared memories and synchronization, we introduce a novel Hierarchical Memory Interface (HMI). With respect to previous solutions, the proposed interface supports multi-ported memories and atomic memory operations, which commonly occur in parallel programming. Our framework can generate the hardware implementation of C functions by employing two different approaches, depending on its characteristics. If a function exposes TLP, then the framework generates hardware implementations based on the adaptive controller. Otherwise, the framework implements the function by exploiting a more conventional FSM approach, which is optimized for ILP exploitation. We evaluate our framework on a set of parallel applications, and show substantial performance improvements (average speedup of 4.7) with limited area over- heads (average area increase of 5.48 times).

Castellana, Vito G.↗

DOE OSTI2021

High-Level Synthesis of Parallel Specifications Coupling Static and Dynamic Controllers

The increased need for efficient ways to implement domain-specific accelerators is driving design methodologies towards the use of abstractions higher than the Register Transfer Level (RTL). In this scenario, High Level Synthesis (HLS) plays a significant role by enabling the automatic generation of custom hardware accelerators starting from high level descriptions (e.g., C code). Conventional HLS tools exploit parallelism mostly at the Instruction Level (ILP). They statically schedule the input specifications, and build centralized Finite State Machine (FSM) controllers. However, aggressive exploitation of ILP in many applications has diminishing returns and, usually, centralized approaches do not efficiently exploit coarser parallelism because FSMs are inherently serial. In this paper we present a HLS framework able to synthesize applications that, beside ILP, also expose Task Level Parallelism (TLP). An application can expose TLP through annotations that identify the parallel functions (i.e., tasks). To generate accelerators that efficiently execute concur- rent tasks, we need to solve several issues: devise a mechanism to support concurrent execution flows, exploit memory parallelism, and manage synchronization. To support concurrent execution flows, we introduce a novel adaptive controller. The adaptive controller is composed of a set of interacting control elements that independently manage the execution of a single operation or function call. These control elements check dependencies and resource constraints at runtime, enabling as soon as possible execution. To support parallel access to shared memories and synchronization, we introduce a novel Hierarchical Memory Interface (HMI). With respect to previous solutions, the proposed interface supports multi-ported memories and atomic memory operations, which commonly occur in parallel programming. Our framework can generate the hardware implementation of C functions by employing two different approaches, depending on its characteristics. If a function exposes TLP, then the framework generates hardware implementations based on the adaptive controller. Otherwise, the framework implements the function by exploiting a more conventional FSM approach, which is optimized for ILP exploitation. We evaluate our framework on a set of parallel applications, and show substantial performance improvements (average speedup of 4.7) with limited area over- heads (average area increase of 5.48 times).

Castellana, Vito G.↗

DOE OSTI2020

Peptoid-based hierarchically-structured biomimetic nanomaterials: Synthesis, characterization and applications

Peptoids (or poly-N-substituted glycines) is a promising class of bioinspired sequence-defined polymers due to their highly efficient synthesis, high chemical stability, enzyme hydrolysis resistance, and biocompatibility. By tuning the side chain chemistry of peptoids, it allows for a precise control over sequences and achieving a large side-chain diversity. Due to these unique features, in the last several years, many amphiphilic peptoids were designed as highly tunable building blocks for the preparation of biomimetic nanomaterials with well-defined hierarchical structures and desired functionalities. In this paper, we provide an overview of the recent achievements in this area by dividing them into the following three aspects. First, mica- and silica-templated peptoid self-assembly was summarized. Here, the presence of inorganic substrates provides the guarantee of investigating their self-assembly mechanisms and interactions between peptoids and substrates using nanoscale characterization techniques, particularly in situ atomic force spectroscopy (AFM) and AFM-based dynamic force spectroscopy (AFM-DFS). Second, solution-phase self-assembly of peptoids into nanotubes and nanosheets was presented, as well as their self-repair properties. Third, the applications of peptoid based nanomaterials were outlined, including the construction of catalytic nanomaterials as a template and cytosolic delivery as cargoes.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Model-informed, Adaptive Physical Vapor Deposition to Fabricate Hierarchical Binary-alloy Thin-films

Designing next generation thin films, tailor-made for specific applications, relies on the availability of robust processing-structure-property relationships. Traditional structure zone diagrams are limited to low-dimensional mappings, with machine-learning methods only recently attempting to relate multiple processing parameters to the final microstructure. Despite this progress, structure-processing relationships are unknown for processing conditions that vary during thin-film deposition, limiting the range of microstructures and properties achievable. In this project, we employed a phase-field computational model combined with a genetic algorithm (GA) to identify and design time-dependent processing protocols that achieve tailor-made microstructures. We simulate the physical vapor deposition of a binary-alloy thin film by employing a phase-field model, where deposition rates and diffusivities are controlled via the genetic algorithm. Our GA-guided protocols achieve targeted microstructures with lateral and vertical concentration modulations, as well as more complex, hierarchical microstructures previously not described in simple structure zone diagrams. Our algorithm provides insight to experimentalists looking for additional avenues to design novel thin-film microstructures.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Catalytic Consequences of Hierarchical Pore Architectures within MFI and FAU Zeolites for Polyethylene Conversion

The benefits of hierarchical zeolites for the conversion of bulky molecules like polymeric waste have been reported in the literature; however, the impact of mesopore sizes and connectivities on rates, product selectivities, and catalyst deactivation in the context of plastic upcycling has not been systematically probed. Here, in this study, we synthesized a suite of hierarchical MFI and FAU zeolites via desilication under varying conditions for metal-free polyethylene conversion reactions under batch and flow conditions (473–523 K). Polyethylene (solid) conversion rates (normalized by Bro̷nsted acid site density) were higher on hierarchical than parent microporous MFI regardless of mesopore connectivities, i.e., open or constricted, suggesting that the incorporation of mesopores facilitates diffusion of intermediate products to access medium-pore protons for successive scission events. Furthermore, higher branched:linear gaseous product ratios were produced on hierarchical than parent MFI, since mesopores allow for egress of bulkier molecules without undergoing further secondary events, e.g., isomerization back to linear alkanes/alkenes or beta scission. Solid conversion rates on hierarchical FAU synthesized via desilication with cetyltrimethylammonium bromide (CTABr), however, were not higher than parent FAU, likely because the presence of CTABr facilitates recrystallization of leached species to form composites (hierarchical FAU and ordered mesoporous materials) with more isolated mesopores. The stagnation in rates, despite increased mesopore volumes (>0.22 cm 3 g –1 ), highlights the importance of confinement effects provided by micropores for cleaving C–C bonds at modest reaction conditions. In situ 1 H MAS NMR performed on polyethylene with MFI zeolite show that PE isomerizes (and potentially deconstructs) at temperatures near 450 K, highlighting the role of Bro̷nsted acid sites in activating C–C bonds under mild reaction conditions. Catalyst recyclability studies showed that all catalysts undergo deactivation during plastic upcycling reactions, but to varying extents. Overall, hierarchical materials have better catalyst stability than parent materials, although the differences in stability between hierarchical and parent FAU are smaller than those for MFI. Taken together, these findings demonstrate how rates, selectivities, and catalyst deactivation from plastic upcycling reactions can be controlled via fine-tuning the identity and connectivity of mesopores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Directing Assembly of Mesoscale Multi‐Shell Morphologies of DNA Origami Crystals

Nature builds hierarchically ordered materials, such as seashells, wood, and bones, through spatially and temporally regulated growth. Mimicking such a level of control in synthetic systems remains challenging, particularly in achieving multiscale organizations with prescribed nanoscale arrangements and desired material morphologies. In this study, we introduce a DNA-based self-assembly strategy for constructing diverse multi-shell mesoscale morphologies from nanoscale lattices, enabling prescribed structural, and compositional 3D material patterns. Using DNA origami frames as modular monomers, we direct anisotropic epitaxial growth through addressable DNA frame binding motifs and encapsulate nanoparticles (NPs) in desired 3D patterns. Sequential monomer addition under thermodynamically favorable conditions enables shell growth through heterogeneous nucleation while minimizing unwanted homogeneous nucleation. Here, we demonstrate that DNA-encoded addressability enables epitaxial shell growth along specific lattice directions, yielding crystals with multilayered mesoscale organization, including tube-like (sushi roll) and plate-like (macaron) morphologies. Shell-specific NP configurations and compositions are achieved through addressable and differentiated placement of NPs within each shell, as validated by small-angle x-ray scattering and cross-sectional scanning transmission electron microscopy. We further demonstrate addressable NP release and reveal that shells modulate release kinetics. Together, these findings establish a platform for fabricating DNA origami crystals with programmable mesoscale morphologies, nanoscale structure, composition, and transport properties.

3D patterning↗

DOE OSTI2024

On-demand nanoengineering of in-plane ferroelectric topologies

Hierarchical assemblies of ferroelectric nanodomains, so-called super-domains, can exhibit exotic morphologies that lead to distinct behaviours. Controlling these super-domains reliably is critical for realizing states with desired functional properties. Here we reveal the super-switching mechanism by using a biased atomic force microscopy tip, that is, the switching of the in-plane super-domains, of a model ferroelectric Pb 0.6 Sr 0.4 TiO 3 . We demonstrate that the writing process is dominated by a super-domain nucleation and stabilization process. A complex scanning-probe trajectory enables on-demand formation of intricate centre-divergent, centre-convergent and flux-closure polar structures. Correlative piezoresponse force microscopy and optical spectroscopy confirm the topological nature and tunability of the emergent structures. The precise and versatile nanolithography in a ferroic material and the stability of the generated structures, also validated by phase-field modelling, suggests potential for reliable multi-state nanodevice architectures and, thereby, an alternative route for the creation of tunable topological structures for applications in neuromorphic circuits.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2023

Understanding Dynamics and Thermodynamics of ENSO and Its Complexity Simulated by E3SM and Other Climate Models

Despite the seeming success of most state-of-the-art climate models in simulating the El Niño-Southern Oscillation (ENSO), there is strong evidence that models achieve realistic levels of ENSO activity do so often for wrong reasons. This is owing to an often occurred near cancelation of large errors in terms of contributions to ENSO growth rate from coupled dynamic and thermodynamic feedback processes. Climate models remain deficient in simulating the observed ENSO’s spatial and temporal complexity that involves interplays of coupled dynamic and thermodynamic feedbacks, interactions across multiple scales, nonlinear processes in the tropical atmosphere and ocean system, biases in mean sate and physical processes, and influences external to equatorial Pacific coupled ENSO dynamics. Our proposed research aims at advancing predictive and process-level understandings of ENSO simulated in E3SM and other climate models under current and future climate conditions with two main objectives: (i) better understanding the aforementioned broad range interactive processes and sources that control fundamental properties of ENSO in E3SM and CIMP6 outputs as well as in observational (reanalysis) data sets, using a hierarchical of coupled dynamical frameworks consisting of theoretical analysis, intermediate complexity modeling, and coupled dynamic diagnostics; (ii) to use this understanding to explore pathways towards improving E3SM’s capability of simulating ENSO and its complexity. More specifically, we will focus on four main thrusts of research: (1) ENSO’s dynamic and thermodynamic feedbacks; (2) the across-scale interactions of ENSO with annual cycle and MJO/WWB/TIW (Madden Julian Oscillation/Westerly Wind Burst/Tropical Instability Wave) activity; (3) key nonlinear processes of ENSO involving atmospheric convective thresholds, nonlinear ocean dynamic heating, and thermocline outcropping; and (4) the impacts of climate mean-state biases/changes and perturbed physical processes on simulated ENSO and its complexity.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM

Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.

ADMM↗

DOE OSTI2020

Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM

Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Precursor-mediated in situ growth of hierarchical N-doped graphene nanofibers confining nickel single atoms for CO 2 electroreduction

Despite the various strategies for achieving metal–nitrogen–carbon (M–N–C) single-atom catalysts (SACs) with different microenvironments for electrochemical carbon dioxide reduction reaction (CO 2 RR), the synthesis–structure–performance correlation remains elusive due to the lack of well-controlled synthetic approaches. Here, we employed Ni nanoparticles as starting materials for the direct synthesis of nickel (Ni) SACs in one spot through harvesting the interaction between metallic Ni and N atoms in the precursor during the chemical vapor deposition growth of hierarchical N-doped graphene fibers. By combining with first-principle calculations, we found that the Ni-N configuration is closely correlated to the N contents in the precursor, in which the acetonitrile with a high N/C ratio favors the formation of Ni-N 3 , while the pyridine with a low N/C ratio is more likely to promote the evolution of Ni-N 2 . Moreover, we revealed that the presence of N favors the formation of H-terminated edge of sp 2 carbon and consequently leads to the formation of graphene fibers consisting of vertically stacked graphene flakes, instead of the traditional growth of carbon nanotubes on Ni nanoparticles. With a high capability in balancing the *COOH formation and *CO desorption, the as-prepared hierarchical N-doped graphene nanofibers with Ni-N 3 sites exhibit a superior CO2RR performance compared to that with Ni-N 2 and Ni-N 4 ones.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM: Preprint

Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Harnessing emergent multiple scattering resonances in a photonic glass structure for photoelectrochemical energy conversion

Light trapping nanostructures are often necessary to improve carrier collection yields in semiconductor photoelectrodes with intrinsically poor electron transport. Photonic crystal templates can generate tailorable light trapping via periodic and precise nanostructure, though this is not a scalable strategy for photoelectrochemical (PEC) applications. It is therefore critical to identify alternative mechanisms for light trapping that tolerate disorder. Light trapping in disordered media is generated by the diffusive transport caused by multiple scattering. In some cases, multiple scattering can generate resonances that resemble those observed in photonic crystals. While resonant multiple scattering is a disorder tolerant light trapping mechanism, it is unclear if the effect is sufficiently adaptable, or even useful, for PEC applications. Here, we describe a photonic omission glass, a nanostructure that can controllably induce resonances in multiple scattering transport. We characterized the emergence of these resonances after coating a disordered SiO 2 colloidal structure with a layer of TiO 2 , which functions both as dielectric contrast and as a light absorbing semiconductor. We show in finite element simulations and spectroscopic characterization that the resonant multiple scattering effect improves light trapping near the interface between the structure and the bulk electrolyte. This effect, coupled with the increased electrochemically active surface area, results in a hierarchically structured TiO 2 photoanode with orders of magnitude higher photocurrents compared to an equivalent planar photoanode for PEC reactions such as alkaline water oxidation. We show that controlling this resonant multiple scattering effect can be advantageous for improving PEC energy conversion in disordered photoelectrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Matrimid substrates with bicontinuous surface and macrovoids in the bulk: A nearly ideal substrate for composite membranes in CO 2 capture

Scalable fabrication of thin-film composite (TFC) membrane for post-combustion carbon capture is often limited by the availability of high-performance nanoporous substrate. Ideally, the substrate should allow for fast gas transport at the selective layer/substrate interface as well as in the bulk of the substrate. In this study, highly permeable Matrimid substrates were prepared via vapor- and nonsolvent-induced phase separations. The phase separation mechanism of the Matrimid®/N-methyl-2-pyrrolidone casting solution was modulated by the addition of LiCl to control the solution thermodynamic stability, and nanoporous Matrimid substrates were formed with a bicontinuous surface and macrovoids in the bulk. This hierarchically optimized structure resulted in a CO 2 permeance of 2.60 × 10 5 GPU (1 GPU = 1 × 10 –6 cm 3 (STP) cm –2 s –1 cmHg –1 = 3.349 × 10 –10 mol m –2 s –1 Pa –1 ), which was ca. 11 times more permeable than a benchmark polyethersulfone substrate with cellular pores. The benefit of using this new substrate was demonstrated by coating a 170-nm amine-containing polymer to form a TFC facilitated transport membrane. The membrane exhibited a CO 2 permeance of 932 GPU at 57°C, which was 72 GPU higher than the counterpart coated on the benchmark substrate. Meanwhile, the CO 2 /N 2 selectivity was remained at 158. This permeance improvement could be well explained by the resistance-in-series model, where the improved permeance was attributed to the reductions in substrate and lateral diffusion mass transfer resistances. The upper bound (UB) analysis indicates that the Matrimid substrate is nearly ideal for the state-of-the-art polymers for CO 2 /N 2 separation. Here, the substrate improvement could also reduce the parasitic energy associated with the membrane process due to the reduced membrane cost and flue gas compression requirement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A Platform Technology for High-throughput Atomically Precise Manufacturing: Mechatronics at the Atomic Scale

The main objective of this project is to invent the necessary enabling technologies for high throughput atomically precise manufacturing (APM). APM is an emerging technology that refers to any manufacturing capability that enables fabrication of atomically precise structures, components, and devices under programmable control. APM will require positional assembly at the atomic and/or molecular scale, as well as at the nano and microscales using hierarchical assembly to create products ranging from nanoscale and quantum devices to macroscale systems and materials. This project builds on the expectation that commercial viability of APM will depend on a high level of parallelism to achieve the required throughput, a capability that currently does not exist. This project is the first attempt to address this key technological bottleneck.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Block Copolymer-Templated Synthesis of Fe–Ni–Co-Modified Nanoporous Alumina Films

Despite intense interest in the catalytic potential of transition metal oxide heterostructures, originating from their large surface area and tunable chemistry, the fabrication of well-defined multicomponent oxide coatings with controlled architectures remains challenging. Here, we demonstrate a simple and effective swelling-assisted sequential infiltration synthesis (SIS) strategy to fabricate hierarchically porous multicomponent metal-oxide electrocatalysts with tunable bimetallic composition. A combination of solution-based infiltration (SBI) of transition metals, iron (Fe), nickel (Ni), and cobalt (Co), into a block copolymer (PS73-b-P4VP28) template, followed by vapor-phase infiltration of alumina using sequential infiltration synthesis (SIS), was employed to synthesize porous, robust, conformal and transparent multicomponent metal-oxide coatings like Fe/AlO x , Fe+Ni/AlO x , and Fe+Co/AlO x . Electrochemical assessments for the oxygen evolution reaction (OER) in a 0.1 M KOH electrolyte demonstrated that the Fe+Ni/AlO x composite exhibited markedly superior catalytic activity, achieving an impressive onset potential of 1.41 V and a peak current density of 3.29 mA/cm 2 . This superior activity reflects the well-known synergistic effect of alloying transition metals with a trace of Fe, which facilitates OER kinetics. Overall, our approach offers a versatile and scalable path towards the design of stable and efficient catalysts with tunable nanostructures, opening new possibilities for a wide range of electrochemical energy applications.

conformal films↗

DOE OSTI2025

Stereochemical Control of Water Transport Properties in Thiol‐yne Polymers

Barrier polymers underpin almost every commercial sector, yet the needs of several emerging areas remain unmet by commercially‐available materials, including temporary orthopedic implants, transient health monitors, neural implants, and other long‐term implants. The ability to tune polymer composition independently of polymer structure positions thiol‐yne click chemistry as a promising platform to serve these emerging technologies. Here, this work describes the differences in the hierarchical structure of stoichiometrically identical materials which differ only in the proportion of the cis versus trans backbone alkene stereochemistry. Varying the isomer content in this way directs different temperature and rate dependent crystallization behavior, which affords control over micron‐scale structure. This investigation focuses on how these stereochemical features affect the water vapor permeation process by several methods and develops an understanding of how this unique structural regularity improves barrier performance relative to a commercially available water barrier polymer, poly(ethylene terephthalate).

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2024

Haar-Like Wavelets on Hierarchical Trees

Here, discrete wavelet methods, originally formulated in the setting of regularly sampled signals, can be adapted to data defined on a point cloud if some multiresolution structure is imposed on the cloud. A wide variety of hierarchical clustering algorithms can be used for this purpose, and the multiresolution structure obtained can be encoded by a hierarchical tree of subsets of the cloud. Prior work introduced the use of Haar-like bases defined with respect to such trees for approximation and learning tasks on unstructured data. This paper builds on that work in two directions. First, we present an algorithm for constructing Haar-like bases on general discrete hierarchical trees. Second, with an eye towards data compression, we present thresholding techniques for data defined on a point cloud with error controlled in the $L$ $\infty$ norm and in a Hölder-type norm. In a concluding trio of numerical examples, we apply our methods to compress a point cloud dataset, study the tightness of the $L$ $\infty$ error bound, and use thresholding to identify MNIST classifiers with good generalizability.

97 MATHEMATICS AND COMPUTING↗