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Uncertainty Analysis in Multi‐Sector Systems: Considerations for Risk Analysis, Projection, and Planning for Complex Systems

Abstract Simulation models of multi‐sector systems are increasingly used to understand societal resilience to climate and economic shocks and change. However, multi‐sector systems are also subject to numerous uncertainties that prevent the direct application of simulation models for prediction and planning, particularly when extrapolating past behavior to a nonstationary future. Recent studies have developed a combination of methods to characterize, attribute, and quantify these uncertainties for both single‐ and multi‐sector systems. Here, we review challenges and complications to the idealized goal of fully quantifying all uncertainties in a multi‐sector model and their interactions with policy design as they emerge at different stages of analysis: (a) inference and model calibration; (b) projecting future outcomes; and (c) scenario discovery and identification of risk regimes. We also identify potential methods and research opportunities to help navigate the tradeoffs inherent in uncertainty analyses for complex systems. During this discussion, we provide a classification of uncertainty types and discuss model coupling frameworks to support interdisciplinary collaboration on multi‐sector dynamics (MSD) research. Finally, we conclude with recommendations for best practices to ensure that MSD research can be properly contextualized with respect to the underlying uncertainties.

54 ENVIRONMENTAL SCIENCES↗

PlasmoData.jl — A Julia framework for modeling and analyzing complex data as graphs

Datasets encountered in scientific and engineering applications appear in complex formats (e.g., images, multivariate time series, molecules, video, text strings, networks). Graph theory provides a unifying framework to model such datasets and enables the use of powerful tools that can help analyze, visualize, and extract value from data. In this work, we present PlasmoData.jl, an open-source, Julia framework that uses concepts of graph theory to facilitate the modeling and analysis of complex datasets. The core of our framework is a general data modeling abstraction, which we call a DataGraph. We show how the abstraction and software implementation can be used to represent diverse data objects as graphs and to enable the use of tools from topology, graph theory, and machine learning (e.g., graph neural networks) to conduct a variety of tasks. We illustrate the versatility of the framework by using real datasets: (i) an image classification problem using topological data analysis to extract features from the graph model to train machine learning models; (ii) a disease outbreak problem where we model multivariate time series as graphs to detect abnormal events; and (iii) a technology pathway analysis problem where we highlight how we can use graphs to navigate connectivity. Further, our discussion also highlights how PlasmoData.jl leverages native Julia capabilities to enable compact syntax, scalable computations, and interfaces with diverse packages. Overall, we show that the DataGraph abstraction and PlasmoData.jl Julia package are able to model data within graphs and enable useful analysis.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

How Cooperatively Folding Are Homopolymer Molecular Knots?

Detailed thermodynamic analysis of complex systems with multiple stable configurational states allows for insight into the cooperativity of each individual transition. In this work, we derive a heat capacity decomposition comprising contributions from each individual configurational state, which together sum to a baseline heat capacity, and contributions from each state-to-state transition. We apply this analysis framework to a series of replica exchange molecular dynamics simulations of linear and 1-1 coarse-grained homo-oligomer models, which fold into stable, configurationally well-defined molecular knots, in order to better understand the parameters leading to stable and cooperative folding of these knots. We find that a stiff harmonic backbone bending angle potential is key to achieving knots with specific 3D structures. Tuning the backbone equilibrium angle in small increments yields a variety of knot topologies. Populations of different knotted states as a function of temperature can also be manipulated by tuning the backbone torsion stiffness or by adding side-chain beads. We find that sharp total heat capacity peaks for the homo-oligomer knots are largely due to a coil-to-globule transition rather than a cooperative knotting step. Furthermore, in some cases, the cooperativity of globule-to-knot and coil-to-globule transitions is comparable, suggesting that highly cooperative folding to knotted structures can be achieved by refining the model parameters or adding sequence specificity.

36 MATERIALS SCIENCE↗

IMPACTing Medical System Design with a Risk Analysis Tool [“IMPACT” sur la Conception du Système Médical avec un Outil d'Analyse des Risques]

Background: Following the success of Artemis I, NASA is preparing for human extended duration missions. Ongoing efforts are focused on mitigating mission-related risks, including those affecting crew health and performance. Communication latency, logistics of resupply and time frame of medical evacuation are barriers to provision of healthcare for these missions, especially with respect to constraints in mass, volume, and crew training. An in-depth assessment of medical risks, capabilities and resources for a specific mission design is necessary to determine an optimal balance that maximizes likelihood of mission success. Overview: IMPACT (Informed Mission Planning via Analysis of Complex Tradespaces) is a dynamic tool designed to estimate medical risk and outcomes for a specific mission design. In its current iteration, a list of medical conditions selected based on likelihood of occurrence and/or consequence was linked to a set of clinical capabilities and resources necessary for diagnosis and management. A probabilistic risk analysis tool was then used to identify and estimate the likelihood and consequence of risks through the following outcome metrics: loss of crew life (inflight mortality due to medical conditions), need for medical evacuation (return to definitive care), and crew disability (task time affected based on how medical conditions influence the ability to perform specific exploration mission crew tasks). Finally, the model’s optimization algorithm provides recommendations for medical capabilities that maximize risk mitigation relative to mass and volume constraints. In the Spring of 2023, IMPACT was utilized to estimate outcome metrics for a design reference mission that would be representative of an extended duration Artemis mission. Notional data generated were then used to determine a recommended set of medical capabilities and resources relative to user-defined mass and volume constraints. A multidisciplinary team has also been updating IMPACT to strengthen the model’s fidelity. Figure 1 shows how updates to outcome metric inputs for the conditions resulted in different capability and resource allocation recommendations. Discussion: This presentation will discuss the IMPACT tool and share the latest data generated for a representative extended duration Artemis mission. Efforts to improve the fidelity of data generated by the model’s algorithm will also be discussed.

K A Shair↗

IMPACTing Medical System Design with a Risk Analysis Tool

Background: Following the success of Artemis I, NASA is preparing for human extended duration missions. Ongoing efforts are focused on mitigating mission-related risks, including those affecting crew health and performance. Communication latency, logistics of resupply and time frame of medical evacuation are barriers to provision of healthcare for these missions, especially with respect to constraints in mass, volume, and crew training. An in-depth assessment of medical risks, capabilities and resources for a specific mission design is necessary to determine an optimal balance that maximizes likelihood of mission success. Overview: IMPACT (Informed Mission Planning via Analysis of Complex Tradespaces) is a dynamic tool designed to estimate medical risk and outcomes for a specific mission design. In its current iteration, a list of medical conditions selected based on likelihood of occurrence and/or consequence was linked to a set of clinical capabilities and resources necessary for diagnosis and management. A probabilistic risk analysis tool was then used to identify and estimate the likelihood and consequence of risks through the following outcome metrics: loss of crew life (inflight mortality due to medical conditions), need for medical evacuation (return to definitive care), and crew disability (task time affected based on how medical conditions influence the ability to perform specific exploration mission crew tasks). Finally, the model’s optimization algorithm provides recommendations for medical capabilities that maximize risk mitigation relative to mass and volume constraints. In the Spring of 2023, IMPACT was utilized to estimate outcome metrics for a design reference mission that would be representative of an extended duration Artemis mission. Notional data generated were then used to determine a recommended set of medical capabilities and resources relative to user-defined mass and volume constraints. A multidisciplinary team has also been updating IMPACT to strengthen the model’s fidelity. Figure 1 shows how updates to outcome metric inputs for the conditions resulted in different capability and resource allocation recommendations. Discussion: This presentation will discuss the IMPACT tool and share the latest data generated for a representative extended duration Artemis mission. Efforts to improve the fidelity of data generated by the model’s algorithm will also be discussed.

K A Shair↗

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

Polyelectrolyte Complex Coacervation across a Broad Range of Charge Densities

Polyelectrolyte complex coacervates of homologous (co)polyelectrolytes with a near-ideally random distribution of a charged and neutral ethylene oxide comonomer were synthesized. The unique platform provided by these building blocks enabled an investigation of the phase behavior across charge fractions 0.10 ≤ f ≤ 1.0. Experimental phase diagrams for f = 0.30–1.0 were obtained from thermogravimetric analysis of complex and supernatant phases and contrasted with molecular dynamics simulations and theoretical scaling laws. At intermediate to high f, a dependence of polymer weight fraction in the salt-free coacervate phase (w P,c ) of w P,c ~ f 0.37±0.01 was extracted; this trend was in good agreement with accompanying simulation predictions. Below f = 0.50, w P,c was found to decrease more dramatically, qualitatively in line with theory and simulations predicting an exponent of 2/3 at f ≤ 0.25. Preferential salt partitioning to either coacervate or supernatant was found to be dictated by the chemistry of the constituent (co)polyelectrolytes.

36 MATERIALS SCIENCE↗

Human Spaceflight Applications of Novel Miniature X-Ray Technologies

INTRODUCTION: Radiography (XR) has long been a cornerstone of terrestrial medical imaging, though it has not yet been used in the spaceflight environment. Medical systems for human spaceflight missions are constrained by mass, volume, and power, and until recently, XR systems have been considered too large and power-consuming for spaceflight diagnostic and therapeutic applications. However, the rise of commercial spaceflight and NASA’s refocused efforts on returning crews to the Moon for long-duration missions have introduced a higher degree of medical risk to human spaceflight and require a re-evaluation when optimizing medical system design. Over the last decade, XR devices have miniaturized while maintaining good diagnostic and therapeutic sensitivity and specificity, making new in-flight medical and non-medical XR applications a possibility. Initial research identified several medical conditions where miniature XR would be beneficial for the diagnosis and/or management of medical conditions arising in space, though a more in-depth analysis is required to identify whether XR may add value to the management of such conditions. With this presentation, we aim to introduce the potential utility of miniature XR, review prior work highlighting where XR may be beneficial, and evaluate how miniature XR may reduce medical risk in human spaceflight missions. METHODS: IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) is a risk assessment tool developed by NASA to advance exploration mission medical system design by quantitatively estimating mission medical risk. IMPACT v1.0 includes a novel evidence library baselined to exploration environments, an expanded list of 119 medical conditions, medical capabilities and resources critical for management of these medical conditions, and the ability for rapid and iterative analysis in the setting of modifiable design reference missions (DRMs). Our first analysis identified which of the 119 medical conditions XR had diagnostic or therapeutic utility for. Subject matter experts (SMEs) recorded which XR views would be performed under ideal terrestrial circumstances for diagnosis/management of each condition, as well as which views are pragmatic for spaceflight limitations. A second analysis utilized IMPACT to identify significant conditions that contribute greatest to medical risk during a notional long-duration Lunar orbit and Lunar surface DRM. Medical system risk estimates include loss of crew life (LOCL), need for return to definitive care (RTDC; medical evacuation), and an estimate of crew task time affected (TTA). Using a standardized semi-quantitative scoring methodology, a deeper evaluation of each of the most significant medical conditions was performed. Data from both of these separate analyses were used to hypothesize what ideal and pragmatic XR studies may impact clinical management of the most significant conditions predicted to lead to medical risk. RESULTS: Approximately 1/3 of the IMPACT conditions were identified as being more effectively or comprehensively assessed or treated with the addition of miniature XR technology. The resulting conditions benefitting diagnostically and therapeutically from XR are revealed, as well as the ideal and pragmatic XR views and medical procedures benefitting from XR. The conditions of clinical significance and those most contributing to risk are also displayed. Among the conditions that contribute greatest to LOCL, four conditions for which XR may improve the diagnosis and management of include: decompression sickness, traumatic shock, dental abscess, and respiratory failure. Among conditions that contributed to RTDC, the evaluation and management of wrist fracture is likely improved by XR. For conditions leading to crew TTA, evaluation and management of EVA shoulder injuries, upper and lower extremity strains, back strains, and EVA hand injuries are likely improved by XR. DISCUSSION: Miniature XR in spaceflight has the potential to improve the evaluation and management of a substantial portion of conditions that most contribute to medical risk. This presentation is an introduction to the possibilities miniature XR provides for future human spaceflight missions and subsequent presenters will expand on potential applications in more detail. LEARNING OBJECTIVES: 1) Understand the previous limitations of using radiography in the management of spaceflight medical conditions; 2) Evaluate the findings from the IMPACT tool analysis, which allows quantification of the benefit miniature XR could provide for managing high-risk medical conditions in long-duration lunar orbit and surface missions, focusing on improvements in crew health outcomes; 3) Analyze case studies where miniature XR technology could reduce the medical risks associated with spaceflight missions, specifically in diagnosing and managing conditions such as decompression sickness, traumatic shock, and EVA-related injuries.

A Anderson↗

Use of Fisher's Ratio assisted multivariate curve resolution- alternating least squares for discovery-based analysis using ultrahigh pressure liquid chromatography-high resolution mass spectrometry

Non-targeted analysis of complex chemical mixtures can be difficult considering the convoluted nature of the matrix and the potential unknown chemical differences between samples or classes of samples. Ultrahigh pressure liquid chromatography coupled to quadrupole time-of-flight mass spectrometry (UHPLC-QTOF) is an ideal technique to probe chemical differences for a wide variety of samples. While UHPLC-QTOF can discover minute chemical differences down to low part per billion (ppb) concentrations with a high degree of confidence, the application of high-resolution mass spectrometry can yield massive amounts of information (∼ 10 gb per sample) that cannot be analyzed manually. Therefore, the application of chemometric techniques is mandatory for the interrogation of complex samples. Fisher's ratio (FR) assisted multivariate curve resolution-alternating least squares (MCR-ALS) was used to the discover and identify the chemical differences between two classes of materials: 1) a pond water matrix and 2) the matrix spiked with a pharmaceutical standard mix containing 17 compounds. Thirteen of the seventeen spiked compounds were discovered using FR analysis, and then five were successfully deconvoluted using MCR-ALS wherein the number of curves chosen were automatically determined using singular value decomposition (SVD). In conclusion, the use of an automated FR assisted MCR-ALS will aid in discovering trace levels of chemical components without the need for the researcher to provide potentially biased input which will aid in non-targeted workflow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Introduction to Markov Modeling: Concepts and Uses

Kharkov modeling is a modeling technique that is widely useful for dependability analysis of complex fault tolerant systems. It is very flexible in the type of systems and system behavior it can model. It is not, however, the most appropriate modeling technique for every modeling situation. The first task in obtaining a reliability or availability estimate for a system is selecting which modeling technique is most appropriate to the situation at hand. A person performing a dependability analysis must confront the question: is Kharkov modeling most appropriate to the system under consideration, or should another technique be used instead? The need to answer this gives rise to other more basic questions regarding Kharkov modeling: what are the capabilities and limitations of Kharkov modeling as a modeling technique? How does it relate to other modeling techniques? What kind of system behavior can it model? What kinds of software tools are available for performing dependability analyses with Kharkov modeling techniques? These questions and others will be addressed in this tutorial.

Boyd, Mark A.↗

Synthesis, Structure, Characterization, and Decomposition of Nickel Dithiocarbamates: Effect of Precursor Structure and Processing Conditions on Solid-State Products

Single-crystal X-ray structures of four nickel dithiocarbamate complexes, the homoleptic mixed-organic bis-dithiocarbamates Ni[S2CN(isopropyl)(benzyl)]2, Ni[S2CN(ethyl)(n-butyl)]2, and Ni[S2CN(phenyl)(benzyl)]2, as well as the heteroleptic mixed-ligand complex NiCl[P(phenyl)3][(S2CN(phenyl)(benzyl)], were determined. Synthetic, spectroscopic, structural, thermal, and sulfide materials studies are discussed in light of prior literature. The spectroscopic results are routine. A slightly distorted square-planar nickel coordination environment was observed for all four complexes. The organic residues adopt conformations to minimize steric interactions. Steric effects also may determine puckering, if any, about the nickel and nitrogen atoms, both of which are planar or nearly so. A trans-influence affects the Ni-S bond distances. Nitrogen atoms interact with the CS2 carbons with a bond order of about 1.5, and the other substituents on nitrogen display transoid conformations. There are no strong intermolecular interactions, consistent with prior observations of the volatility of nickel dithiocarbamate complexes. Thermogravimetric analysis of the homoleptic species under inert atmosphere is consistent with production of 1:1 nickel sulfide phases. Thermolysis of nickel dithiocarbamates under flowing nitrogen produced hexagonal or -NiS as the major phase; thermolysis under flowing forming gas produced millerite (-NiS) at 300 C, godlevskite (Ni9S8) at 325 and 350 C, and heazlewoodite (Ni3S2) at 400 and 450 C. Failure to exclude oxygen results in production of nickel oxide. Nickel sulfide phases produced seem to be primarily influenced by processing conditions, in agreement with prior literature. Nickel dithiocarbamate complexes demonstrate significant promise to serve as single-source precursors to nickel sulfides, a quite interesting family of materials with numerous potential applications.

microscopy↗

A PC-Based Free Text DSS for Health Care

A free Decision Support System(DST) has been constructed for health care professional that allows the analysis of complex medical cases and the creation of diagnostic list of potential diseases for clinical evaluation.The system uses a PC-based text management system specifically designed for desktop operation. The texts employed in the decision support package include the Merck Manual (published by Merck Sharpe & Dohme) and Control of Communicable Diseas in Man (published by the American Public Health Association). The background and design of the database are discussed along with a structured analysis procedure for handling free text DSS system. A case study is presented to show the application of this technology and conclusions are drawn in the summary that point to expanded areas of professional intention and new frontiers yet to be explored in this rapidly progressing field.

Grams, Ralph R.↗

Reconstructing phase-resolved hysteresis loops from first-order reversal curves

The first order reversal curve (FORC) method is a magnetometry based technique used to capture nanoscale magnetic phase separation and interactions with macroscopic measurements using minor hysteresis loop analysis. This makes the FORC technique a powerful tool in the analysis of complex systems which cannot be effectively probed using localized techniques. However, recovering quantitative details about the identified phases which can be compared to traditionally measured metrics remains an enigmatic challenge. We demonstrate a technique to reconstruct phase-resolved magnetic hysteresis loops by selectively integrating the measured FORC distribution. From these minor loops, the traditional metrics—including the coercivity and saturation field, and the remanent and saturation magnetization—can be determined. In order to perform this analysis, special consideration must be paid to the accurate quantitative management of the so-called reversible features. This technique is demonstrated on three representative materials systems, high anisotropy FeCuPt thin-films, Fe nanodots, and SmCo/Fe exchange spring magnet films, and shows excellent agreement with the direct measured major loop, as well as the phase separated loops.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Newman, M.↗

Static Aeroelastic Analysis with an Inviscid Cartesian Method

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Aeroelastic↗

Development of technology for modeling of a 1/8-scale dynamic model of the shuttle Solid Rocket Booster (SRB)

A NASTRAN analysis of the solid rocket booster (SRB) substructure of the space shuttle 1/8-scale structural dynamics model. The NASTRAN finite element modeling capability was first used to formulate a model of a cylinder 10 in. radius by a 200 in. length to investigate the accuracy and adequacy of the proposed grid point spacing. Results were compared with a shell analysis and demonstrated relatively accurate results for NASTRAN for the lower modes, which were of primary interest. A finite element model of the full SRB was then formed using CQUAD2 plate elements containing membrane and bending stiffness and CBAR offset bar elements to represent the longerons and frames. Three layers of three-dimensional CHEXAI elements were used to model the propellant. This model, consisting of 4000 degrees of freedom (DOF) initially, was reduced to 176 DOF using Guyan reduction. The model was then submitted for complex Eigenvalue analysis. After experiencing considerable difficulty with attempts to run the complete model, it was split into two substructres. These were run separately and combined into a single 116 degree of freedom A set which was successfully run. Results are reported.

Levy, A.↗

Identification and quantification of lignin monomers and oligomers from reductive catalytic fractionation of pine wood with GC × GC – FID/MS

Thorough lignin characterization is vital to understand the physicochemical properties of lignin and to evaluate lignocellulose biorefinery processes. In this study, an in-depth characterization of lignin oil, obtained from reductive catalytic fractionation (RCF) of pine wood, was performed with quantitative GC × GC – FID analysis and qualitative GC × GC – MS. By utilizing high-temperature resistant column sets in the GC × GC system and by applying a derivatization step, unambiguous detection of lignin monomers, dimers, and trimers is enabled. In addition to confirm the identity of eleven monomers, corresponding to 34 wt% of the RCF lignin oil, thirty-six dimers (16 wt%) and twenty-one trimers (7 wt%) were comprehensively identified by analysis of their mass spectra and quantified by a FID, encompassing the identity of an additional 23 wt% of the RCF lignin oil. The proposed structures reveal the interlinkages present in the dimeric and trimeric oligomers, containing β-5, β-1, β–β, 5–5, and a minor fraction of β-O-4 and 4-O-5 bonds. Furthermore, aliphatic end-units in the dimeric and trimeric molecules were identified, consisting of various substituents at the C4 position, that have been previously observed in the RCF-derived lignin monomers. To reduce complexity for analysis, the RCF oil was separated into six fractions, prior to analysis. The structural motifs (inter-unit linkages and end-units) that are found in the different fractions vary significantly, such that the lignin fractions extracted in more polar solvents contained higher molecular weight fragments and more hydroxyl containing structural motifs. Additionally, the identified structures of individual dimer and trimer molecules by GC × GC align well with and further complement the recent findings from 1 H– 13 C HSQC NMR spectroscopy, demonstrating complementarity between both 2D techniques to obtain a holistic view on both the molecular structures and the distribution of bonds and end-units in RCF oil. The combination of these two techniques provides a powerful tool for future RCF and other lignin depolymerization research.

09 BIOMASS FUELS↗

Approaches for handling high-dimensional cluster expansions of ionic systems

Disordered multicomponent systems attract great interest due to their engineering design flexibility and subsequent rich space of properties. However, detailed characterization of the structure and atomic correlations remains challenging and hinders full navigation of these complex spaces. A lattice cluster expansion is one tool to obtain configurational and energetic resolution. While in theory a cluster expansion can be applied to any system of any dimensionality, the method has primarily been used in binary systems or ternary alloys. Here we apply cluster expansions in high-component ionic systems, setting up the largest cluster expansion ever attempted to our knowledge. In doing so, we address and discuss challenges specific to high-component ionic systems, namely charge state assignments, structural relaxations, and rank-deficient systems. We introduce practical procedures to make the fitting and analysis of complex systems tractable, providing guidance for future computational studies of disordered ionic systems.

25 ENERGY STORAGE↗