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At least 217 records · Page 12

Multiphysics simulation of TRISO fuel compacts and the effects of homogenization on silver release predictions

This work studies the impact of explicit and homogenized modeling approaches on the multiphysics simulation of TRistructural ISOtropic (TRISO) fuel compacts in prismatic High Temperature Gas Reactors (HTGRs) and the silver release predictions. TRISO fuel compacts exhibit complex double heterogeneity that significantly affects heat conduction, neutron transport, and fission products release. In this work, we use Cardinal, a multiphysics tool based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, to couple neutron transport and heat conduction. OpenMC is used for neutron transport and the MOOSE heat transfer module is used for the heat conduction. Then, we use BISON for the silver release predictions. Two different modeling approaches—explicit modeling of individual TRISO particles and homogenized representation using effective thermal properties—are compared at high TRISO packing fractions (20% and 40%) across varying power densities. Results demonstrate that homogenization significantly under-predicts peak temperatures, for the case of high power/TRISO, there is a difference of 83.73 K in the maximum temperature. Additionally, homogenization underestimates the silver release predictions compared to explicit modeling. Specifically, the temperature and power density differences lead to significant differences in silver release predictions. This work demonstrates the importance of accurately modeling heterogeneity of the TRISO particles to reliably predict fission product release and assess reactor safety margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spinor-helicity formalism for massive and massless amplitudes in five dimensions

Five-dimensional gauge and gravity theories are known to exhibit striking properties. D = 5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor theories. Five-dimensional supergravities are highly constrained and admit elegant geometric and algebraic formulations, with global symmetries manifest at the Lagrangian level. In this paper, we take a step towards the systematic investigation of amplitudes in five dimensions, and present a five-dimensional version of the spinor-helicity formalism, applicable to massless, massive and supersymmetric states. We give explicit representations for on-shell spinor and polarization variables such that the little-group symmetry and gauge redundancy are manifest. Massive self-dual tensor states are discussed in some detail, as well as all the on-shell supermultiplets that can appear in matter-coupled gauge and supergravity theories. As a byproduct of considering supersymmetry in the presence of central charge, we obtain massless ten-dimensional Majorana-Weyl spinors as products of five-dimensional massive spinors. We present compact expressions for superamplitudes at multiplicity three and four, including several novel superamplitudes that either do not straightforwardly uplift to six dimensions, or have not appeared in the six-dimensional literature. We discuss several examples of five-dimensional double-copy constructions in the context of gravitational theories with massive vectors and tensors, illustrating that the formalism we construct can also be used to considerably streamline the double-copy construction of $\mathcal{N}$ = 2 Maxwell-Einstein supergravities.

79 ASTRONOMY AND ASTROPHYSICS↗

Evaluating the impact of peat soils and snow schemes on simulated active layer thickness at pan-Arctic permafrost sites

Abstract Permafrost stability is significantly influenced by the thermal buffering effects of snow and active-layer peat soils. In the warm season, peat soils act as a barrier to downward heat transfer mainly due to their low thermal conductivity. In the cold season, the snowpack serves as a thermal insulator, retarding the release of heat from the soil to the atmosphere. Currently, many global land models overestimate permafrost soil temperature and active layer thickness (ALT), partially due to inaccurate representations of soil organic matter (SOM) density profiles and snow thermal insulation. In this study, we evaluated the impacts of SOM and snow schemes on ALT simulations at pan-Arctic permafrost sites using the Energy Exascale Earth System Model (E3SM) land model (ELM). We conducted simulations at the Circumpolar Active Layer Monitoring (CALM) sites across the pan-Arctic domain. We improved ELM-simulated site-level ALT using a knowledge-based hierarchical optimization procedure and examined the effects of precipitation-phase partitioning methods (PPMs), snow compaction schemes, and snow thermal conductivity schemes on simulated snow depth, soil temperature, ALT, and CO 2 fluxes. Results showed that the optimized ELM significantly improved agreement with observed ALT (e.g. RMSE decreased from 0.83 m to 0.15 m). Our sensitivity analysis revealed that snow-related schemes significantly impact simulated snow thermal insulation levels, soil temperature, and ALT. For example, one of the commonly used snow thermal conductivity schemes (quadratic Sturm or SturmQua) generally produced warmer soil temperatures and larger ALT compared to the other two tested schemes. The SturmQua scheme also amplified the model’s sensitivity to PPMs and predicted deeper ALTs than the other two snow schemes under both current and future climates. The study highlights the importance of accurately representing snow-related processes and peat soils in land models to enhance permafrost dynamics simulations.

54 ENVIRONMENTAL SCIENCES↗

Lieb-Schultz-Mattis, Luttinger, and 't Hooft - anomaly matching in lattice systems

We analyze lattice Hamiltonian systems whose global symmetries have ’t Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field strength), the nonzero spatial components of the gauge fields can be thought of as twisted boundary conditions, or equivalently, as topological defects. The symmetries of the twisted Hilbert space and their representations capture the anomalies. We demonstrate this approach with a number of examples. In some of them, the anomalous symmetries are internal symmetries of the lattice system, but they do not act on-site. (We clarify the notion of “on-site action.”) In other cases, the anomalous symmetries involve lattice translations. Using this approach we frame many known and new results in a unified fashion. In this work, we limit ourselves to 1+1d systems with a spatial lattice. In particular, we present a lattice system that flows to the c=1 c = 1 compact boson system with any radius (no BKT transition) with the full internal symmetry of the continuum theory, with its anomalies and its T-duality. As another application, we analyze various spin chain models and phrase their Lieb-Shultz-Mattis theorem as an ’t Hooft anomaly matching condition. We also show in what sense filling constraints like Luttinger theorem can and cannot be viewed as reflecting an anomaly. As a by-product, our understanding allows us to use information from the continuum theory to derive some exact results in lattice model of interest, such as the lattice momenta of the low-energy states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Data reduction through optimized scalar quantization for more compact neural networks

Raw data generation for several existing and planned large physics experiments now exceeds TB/s rates, generating untenable data sets in very little time. Those data often demonstrate high dimensionality while containing limited information. Meanwhile, Machine Learning algorithms are now becoming an essential part of data processing and data analysis. Those algorithms can be used offline for post processing and post data analysis, or they can be used online for real time processing providing ultra low latency experiment monitoring. Both use cases would benefit from data throughput reduction while preserving relevant information: one by reducing the offline storage requirements by several orders of magnitude and the other by allowing ultra fast online inferencing with low complexity Machine Learning models. Moreover, reducing the data source throughput also reduces material cost, power and data management requirements. In this work we demonstrate optimized nonuniform scalar quantization for data source reduction. This data reduction allows lower dimensional representations while preserving the relevant information of the data, thus enabling high accuracy Tiny Machine Learning classifier models for online fast inferences. We demonstrate this approach with an initial proof of concept targeting the CookieBox, an array of electron spectrometers used for angular streaking, that was developed for LCLS-II as an online beam diagnostic tool. We used the Lloyd-Max algorithm with the CookieBox dataset to design an optimized nonuniform scalar quantizer. Optimized quantization lets us reduce input data volume by 69% with no significant impact on inference accuracy. When we tolerate a 2% loss on inference accuracy, we achieved 81% of input data reduction. Finally, the change from a 7-bit to a 3-bit input data quantization reduces our neural network size by 38%.

97 MATHEMATICS AND COMPUTING↗

Learning Latent Representations to Bridge Coarse-Grained and Atomistic Resolutions in Polymer Simulations

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning−physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators

The linear collisionless damping of zonal flows is calculated for quasi-symmetric stellarator equilibria in flux-tube, flux-surface, and full-volume geometry. Equilibria are studied from the quasi-helical symmetry configuration of the Helically Symmetric eXperiment (HSX), a broken symmetry configuration of HSX, and the quasi-axial symmetry geometry of the National Compact Stellarator eXperiment (NCSX). Zonal flow oscillations and long-time damping affect the zonal flow evolution, and the zonal flow residual goes to zero for small radial wavenumber. The oscillation frequency and damping rate depend on the bounce-averaged radial particle drift in accordance with theory. While each flux tube on a flux surface is unique, several different flux tubes in HSX or NCSX can reproduce the zonal flow damping from a flux-surface calculation given an adequate parallel extent. The flux-surface or flux-tube calculations can accurately reproduce the full-volume long-time residual for moderate kx, but the oscillation and damping time scales are longer in local representations, particularly for small kx approaching the system size.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Millimeter- and Submillimeter-Wave Remote Sensing Using Small Satellites

Cloud ice properties and processes play fundamental roles in atmospheric radiation and precipitation. Limited knowledge and poor representation of clouds in global climate models have led to large uncertainties about cloud feedback processes under climate change. Ice clouds have been used as a tuning parameter in the models to force agreement with observations of the radiation budget at the top of the atmosphere, and precipitation at the bottom. The lack of ice cloud measurements has left the cloud processes at intermediate altitudes unconstrained. Millimeter (mm) and submillimeter (submm)-wave radiometry is widely recognized for its potential to fill the cloud measurement gap in the middle and upper troposphere. Analyses have shown that channels from 183900 GHz offer good sensitivity to ice cloud scattering and can provide ice water path (IWP) products to an accuracy of 25 by simultaneously retrieving ice particle size (Dme) and IWP. Therefore, it is highly desirable to develop a cost-effective, compact mm/submm-wave instrument for cloud observations that can be deployed on future small satellites.This paper presents a conceptual study for a mm/submm-wave instrument for multispectral measurements of ice clouds. It discusses previous work at these frequencies by NASA Goddard Space Flight Center (GSFC) and the current instrument study, as well as receiver architectures and their anticipated performance. And finally, it describes a microsatellite prototype intended for use with this mm/submm-wave instrument.

small satellites↗

Efficient high-fidelity TRISO statistical failure analysis using Bison: Applications to AGR-2 irradiation testing

The ability of tri-structural isotropic (TRISO) fuel to contain fission products is largely dictated by the quality of the manufacturing process, since most of the fission product release is expected to occur due to coating layer failure in a small number of particles containing defects. The Bison fuel performance code has capabilities to predict failure in individual particles, accounting for the presence of defects, and to apply statistical analysis methods to compute the probability of failure in a set of fuel particles. Bison has recently undergone significant development both to improve its physical representations of fuel particle behavior and to improve the efficiency of its statistical failure calculations. Physical model improvements include new capabilities to account for the pressure generated by fission gases on inner pyrolytic carbon (IPyC) crack surfaces and to use local material coordinate orientation to accurately incorporate the anisotropy in the material properties in aspherical particles. To improve statistical modeling efficiency, a direct integration approach which involves directly integrating the failure probability function associated with statistically varying parameters has been developed. The direct integration approach is much more efficient than the Monte Carlo (MC) schemes commonly employed, and allows Bison to directly run high-dimensional fuel performance models, which improves the accuracy of failure probability calculations. Finally, a set of benchmark problems is considered here to compare the MC and direct integration approaches, and a statistical failure analysis of compacts in the Advanced Gas Reactor (AGR)-2 experiments is performed using the direct integration approach.

36 MATERIALS SCIENCE↗

Prediction of sound radiation from different practical jet engine inlets

Computer codes which were based upon a special integral representation of the external solutions of the Helmholtz equation were upgraded so that they would yield accurate results for the acoustic radiation patterns in the field surrounding an axisymmetric body for nondimensional wave numbers, based on duct radius, of up to twenty. The accuracy of these computer programs was checked by the use of the point source method for the generation of exact solutions and then by comparison with the results of other experimental and theoretical studies. These computer codes were used in a parametric study of the dependence of the radiated sound field on input modal distribution, wave number, and inlet lip shape. The results of this study show that: (1) as the wave number (i.e., cut off ratio) is increased for a given input modal distribution that the acoustic radiation peak moves towards the inlet centerline and becomes more compact (i.e., narrows); (2) as the input mode number is increased for a given cut off ratio the acoustic radiation peak moves away from the inlet centerline and becomes more compact.

Meyer, W. L.↗

Permutation invariant polynomial neural network based diabatic ansatz for the ( E + A ) × ( e + a ) Jahn–Teller and Pseudo-Jahn–Teller systems

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of $H^3_+$ is studied, which is an (E + A) × (e + a) Jahn–Teller and Pseudo-Jahn–Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. Further, the adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers

RUSHMAPS is a new onboard data reduction scheme that gives real-time access to key science parameters (e.g. moments) of a class of heliophysics science and/or solar system exploration investigation that includes plasma particle spectrometers (PPS), but requires moments reporting (density, bulk-velocity, temperature, pressure, etc.) of higher-level quality, and tolerates a lowpass (variable quality) spectral representation of the corresponding particle velocity distributions, such that telemetry use is minimized. The proposed methodology trades access to the full-resolution velocity distribution data, saving on telemetry, for real-time access to both the moments and an adjustable-quality (increasing quality increases volume) spectral representation of distribution functions. Traditional onboard data storage and downlink bandwidth constraints severely limit PPS system functionality and drive cost, which, as a consequence, drives a limited data collection and lower angular energy and time resolution. This prototypical system exploit, using high-performance processing technology at GSFC (Goddard Space Flight Center), uses a SpaceCube and/or Maestro-type platform for processing. These processing platforms are currently being used on the International Space Station as a technology demonstration, and work is currently ongoing in a new onboard computation system for the Earth Science missions, but they have never been implemented in heliospheric science or solar system exploration missions. Preliminary analysis confirms that the targeted processor platforms possess the processing resources required for realtime application of these algorithms to the spectrometer data. SpaceCube platforms demonstrate that the target architecture possesses the sort of compact, low-mass/power, radiation-tolerant characteristics needed for flight. These high-performing hybrid systems embed unprecedented amounts of onboard processing power in the CPU (central processing unit), FPGAs (field programmable gate arrays), and DSP (digital signal processing) elements. The fundamental computational algorithm de constructs 3D velocity distributions in terms of spherical harmonic spectral coefficients (which are analogous to a Fourier sine-cosine decomposition), but uses instead spherical harmonics Legendre polynomial orthogonal functions as a basis for the expansion, portraying each 2D angular distribution at every energy or, geometrically, spherical speed-shell swept by the particle spectrometer. Optionally, these spherical harmonic spectral coefficients may be telemetered to the ground. These will provide a smoothed description of the velocity distribution function whose quality will depend on the number of coefficients determined. Successfully implemented on the GSFC-developed processor, the capability to integrate the proposed methodology with both heritage and anticipated future plasma particle spectrometer designs is demonstrated (with sufficiently detailed design analysis to advance TRL) to show specific science relevancy with future HSD (Heliophysics Science Division) solar-interplanetary, planetary missions, sounding rockets and/or CubeSat missions.

Figueroa-Vinas, Adolfo↗

Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation

Abstract An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H 4 , H 2 O, and BeH 2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolving radon diffusion through earthen barriers at uranium waste disposal sites

Field measurements of Rn-222 fluxes from the tops and bottoms of compacted clay radon barriers were used to calculate effective Rn diffusion coefficients (D Rn ) at four uranium waste disposal sites in the western United States to assess cover performance after more than 20 years of service. Values of D Rn ranged from 7.4 × 10 -7 to 6.0 × 10 -9 m 2 /s, averaging 1.42 × 10 -7 . Water saturation (S W ) from soil cores indicated that there was relatively little control of D Rn by S W , especially at higher moisture levels, in contrast to estimates from most steady-state diffusion models. Further, this is attributed to preferential pathways intrinsic to construction of the barriers or to natural process that have developed over time including desiccation cracks, root channels, and insect burrows in the engineered earthen barriers. A modification to some models in which fast and slow pathway D Rn values are partitioned appears to give a good representation of the data; 4% of the fast pathway was needed to fit the data regression. For locations with high S w and highest D Rn (and fluxes) at each site, the proportion of fast pathway ranged from 1.7% to 34%, but for many locations with lower fluxes, little if any fast pathway was needed.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A new method for operating a continuous-flow diffusion chamber to investigate immersion freezing: assessment and performance study

Abstract. Glaciation in mixed-phase clouds predominantly occurs through the immersion-freezing mode where ice-nucleating particles (INPs) immersed within supercooled droplets induce the nucleation of ice. Model representations of this process currently are a large source of uncertainty in simulating cloud radiative properties, so to constrain these estimates, continuous-flow diffusion chamber (CFDC)-style INP devices are commonly used to assess the immersion-freezing efficiencies of INPs. This study explored a new approach to operating such an ice chamber that provides maximum activation of particles without droplet breakthrough and correction factor ambiguity to obtain high-quality INP measurements in a manner that previously had not been demonstrated to be possible. The conditioning section of the chamber was maintained at −20 ∘C and water relative humidity (RHw) conditions of 113 % to maximize the droplet activation, and the droplets were supercooled with an independently temperature-controlled nucleation section at a steady cooling rate (0.5 ∘C min−1) to induce the freezing of droplets and evaporation of unfrozen droplets. The performance of the modified compact ice chamber (MCIC) was evaluated using four INP species: K-feldspar, illite-NX, Argentinian soil dust, and airborne soil dusts from an arable region that had shown ice nucleation over a wide span of supercooled temperatures. Dry-dispersed and size-selected K-feldspar particles were generated in the laboratory. Illite-NX and soil dust particles were sampled during the second phase of the Fifth International Ice Nucleation Workshop (FIN-02) campaign, and airborne soil dust particles were sampled from an ambient aerosol inlet. The measured ice nucleation efficiencies of model aerosols that had a surface active site density (ns) metric were higher but mostly agreed within 1 order of magnitude compared to results reported in the literature.

54 ENVIRONMENTAL SCIENCES↗

Stereo Vision Based Terrain Mapping for Off-Road Autonomous Navigation

Successful off-road autonomous navigation by an unmanned ground vehicle (UGV) requires reliable perception and representation of natural terrain. While perception algorithms are used to detect driving hazards, terrain mapping algorithms are used to represent the detected hazards in a world model a UGV can use to plan safe paths. There are two primary ways to detect driving hazards with perception sensors mounted to a UGV: binary obstacle detection and traversability cost analysis. Binary obstacle detectors label terrain as either traversable or non-traversable, whereas, traversability cost analysis assigns a cost to driving over a discrete patch of terrain. In uncluttered environments where the non-obstacle terrain is equally traversable, binary obstacle detection is sufficient. However, in cluttered environments, some form of traversability cost analysis is necessary. The Jet Propulsion Laboratory (JPL) has explored both approaches using stereo vision systems. A set of binary detectors has been implemented that detect positive obstacles, negative obstacles, tree trunks, tree lines, excessive slope, low overhangs, and water bodies. A compact terrain map is built from each frame of stereo images. The mapping algorithm labels cells that contain obstacles as no-go regions, and encodes terrain elevation, terrain classification, terrain roughness, traversability cost, and a confidence value. The single frame maps are merged into a world map where temporal filtering is applied. In previous papers, we have described our perception algorithms that perform binary obstacle detection. In this paper, we summarize the terrain mapping capabilities that JPL has implemented during several UGV programs over the last decade and discuss some challenges to building terrain maps with stereo range data.

passive perception↗

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↗