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Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Fast Catalysis at Low Overpotential: Designing Efficient Dicationic Re(bpy 2+ )(CO) 3 I Electrocatalysts for CO 2 Reduction

Here we report a series of isomeric, dicationic Re(bpy 2+ )(CO) 3 I com-plexes with bpy (2,2'-bipyridine) modified by two phenyl-CH 2 -(NMe 3 )+ pendants with cations located at variable distances from the active site for electrocatalytic CO 2 reduction in CH 3 CN/2.8 M H 2 O. The position of the cationic groups dramatically increases the rate of catalysis by 800-fold, from 1.2 to 950 s -1 , with a minor increase in overpotential. Acceleration is due to stabilization of the initial CO 2 adduct and lowering of ΔG ‡ for C-OH bond cleavage by Coulombic stabilization of anionic charges. Performance may be enhanced by accumulation in the electrochemical double layer. Transition state stabilization in the optimized isomer unlocks the low overpotential "protonation-first" pathway, highlighting the sizable effects of subtle structural optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Data Structure Alchemy

In an increasingly more data-driven world, the project set out to uncover the first principles of data-structure design, chart the immense design space they form, and build automation that can synthesize an optimal structure, or even a whole storage engine, for any given workload, hardware platform, and cost target. Data structures are at the center of every computational system and are directly responsible for its performance. Two core technical thrusts were defined: 1) Mapping design spaces for key data-centric abstractions (filters, hash functions, storage-engine layouts, neural-network topologies, blockchain protocols, image layouts, etc.). 2) Developing search & synthesis algorithms, initially analytical cost models, later neural-guided bi-level optimisers that navigate sextillions of candidate designs in seconds and materialise the best one as ready‐to-run code. This report distills the key insights, accomplishments, and impact.

97 MATHEMATICS AND COMPUTING

Manufacturing Full-Scale High Gradient Copper Accelerators: Electron Beam Welding and Allied Processes

This DOE ARDAP-funded study examines the technical and business feasibility of manufacturing high-gradient normal conducting RF (NCRF) copper accelerating structures using electron beam welding (EBW) instead of conventional high-temperature brazing. The core motivation is material performance: brazing softens copper significantly, while hard copper alloys have demonstrated ~75% higher operational gradients in SLAC tests, making cold-joining techniques highly attractive. EBW, applied to split-cell (half or quadrant) structure designs, preserves copper hardness away from the weld joint and simplifies machining — but industrial process optimization remains immature and a substantial learning curve is expected. The business case was modeled for two scenarios: a greenfield EBW linac company (> $10M upfront costs, viable above ~30 units/year) and an EBW division added to an existing accelerator firm to reduce risk and upfront costs, at the expense of being less optimal structure for the higher volume production. The study concludes that without a significant increase in demand, private investment alone cannot sustain this capability, and recommends federal support through R&D grants, procurement incentives, and CAPEX cost-sharing to incubate domestic EBW-NCRF manufacturing — with the existing-company model.

43 PARTICLE ACCELERATORS

An innovative radial gradient material design using hot isostatic pressing for applications in extreme environments

Functionally graded materials (FGMs) are highly advanced continuous or discontinuous structures whose structural and material properties vary along a singular geometric dimension either in the axial or radial direction. Here, the radial gradient FGM design makes for an optimal structural design to incorporate a bi-metallic structure with a copper-based high entropy alloy (Cu-HEA) with good mechanical properties and high irradiation resistance, and Chromium (Cr) with great corrosion resistance. This study focuses on the experimental design of a metal powder loading mechanism to fabricate a bi-metallic radial gradient structure using Cu-HEA and 99.9 % pure Cr metal powders. The powder loading strategy uses custom-designed concentric cylindrical dividers to separate the individual compositions. Two benchtop trial runs were performed for design optimization. The optimized design was then implemented to eventually load the HEA and Cr powders for consolidation via powder metallurgy hot isostatic pressing (PM-HIP). The electron microscopy analysis reveals the successful fabrication of the radial gradient structure with the chemical mapping analysis, demonstrating the gradual composition shift from the HEA at the center to the pure-Cr at the periphery via a three-step gradient.

High Entropy Alloys (HEAs)

Multinuclear Solid-State NMR and NMR Crystallography of Solid Forms of Creatine and Creatinine

Creatine is a performance-enhancing supplement with two widely available commercial solid forms, namely, creatine monohydrate (creatine·H 2 O) and creatine HCl, the latter of which does not have a reported crystal structure. Moreover, commercial formulations of creatine may contain creatinine, an undesired impurity phase resulting from the self-cyclization of creatine during manufacturing. Therefore, reliable methods for characterizing the different solid forms of creatine and detecting the presence of creatinine are essential. Herein, we address these challenges using 13 C, 15 N, and 35 Cl solid-state NMR (SSNMR) spectroscopy to obtain distinct spectral fingerprints for creatine·H 2 O and creatine HCl, along with creatinine and creatinine HCl. The acquisition of these SSNMR spectra offers a robust approach for both the rapid characterization of each solid form and the detection of the impurity phases. Additionally, quadrupolar NMR crystallography-guided crystal structure prediction (QNMRX-CSP) was applied for the de novo crystal structure determination of creatine HCl, which was validated by the subsequently determined single-crystal X-ray diffraction (SCXRD) structure. Finally, to investigate the relationship between NMR parameters and structural features, 13 C and 15 N chemical shifts and 35 Cl electric field gradient (EFG) tensors were computed from geometry-optimized structures of the four solid forms by using dispersion-corrected DFT-D2* methods. Finally, this integrative approach offers a powerful framework for advancing the structural understanding and quality control of creatine-based supplements and next-generation formulations, as well as a wide range of other solid pharmaceuticals and nutraceuticals.

NMR

Graphene oxide precursor effects on 3D-printed carbon scaffolds

Manganese oxide (MnO 2 ), an earth-abundant material, is a promising component for energy storage devices, with uses in both pseudocapacitors and batteries. However, high MnO 2 loading often leads to reduced performance due to poor ion diffusion. 3D printing, particularly using the direct ink writing (DIW) technique, offers a solution by enabling the fabrication of electrodes with hierarchical porous structures and open channels that enhance mass transport and ion diffusion. Previous work demonstrated that 3D-printed graphene aerogels with MnO 2 coatings exhibited excellent electrochemical performance, even with thick electrodes, due to their optimized structure. Building on this work, the current study investigates the performance differences between aerogels developed using graphene oxide (GO) and reduced graphene oxide (rGO) as carbon precursors. Both materials were incorporated into thixotropic inks, 3D-printed into lattice structures, and carbonized. Despite expected similarities between the final graphene aerogel, rGO-based aerogels exhibited superior areal capacitance, compared to GO-based aerogels. These differences are attributed to the lower oxygen content and defect density of rGO, which influence its interaction with cellulose viscosifiers in the ink formulation. Brunauer–Emmett–Teller (BET) surface area analysis revealed that rGO aerogels exhibit a larger surface area and mesoporous structure, further enhancing their performance. When coated with MnO 2 , rGO-based aerogels maintained their superior capacitive behavior over GO-based aerogels. This study highlights the effect of carbon precursor on the end performance of graphene aerogels.

Materials science

Cooperative Education

Los Alamos National Laboratory (LANL) is a multidisciplinary national laboratory that conducts research and development in national security, engineering, materials science, computational modeling, and advanced manufacturing. The laboratory develops innovative technologies to address complex scientific and engineering challenges. This project focuses on the development and evaluation of high-performance absorbing structures through computational design, simulation, and engineering analysis. Absorbing structures are used in applications where damage mitigation, structural protection, and material efficiency are critical performance requirements. The increasing demand for lightweight, high-strength, and highly efficient structural systems has created a need for improved design methodologies capable of maximizing absorption while minimizing weight and material usage. The project utilizes advanced engineering software, including 3D CAD software and FEA, to generate and optimize structural concepts. Computational simulations are performed to evaluate structural behavior under loading conditions, while mathematical analyses are conducted using Python-based tools as well as established analytical equations from material and structural mechanics. The project benefits LANL by supporting the development of advanced design methodologies and improving the understanding of material and structural performance. During the internship term, a significant portion of the design development, simulation, and data analysis activities will be completed. Success of the project depends on collaboration among engineering mentors and technical staff members. Work will be conducted at Los Alamos National Laboratory using laboratory computing resources and engineering software.

42 ENGINEERING

Higher-order factorization machine for accurate surrogate modeling in material design

Efficient and robust optimization is important in material science for identifying optimal structural parameters and enhancing material performance. Surrogate-based active learning algorithms have recently gained great attention for their ability to efficiently navigate large, high-dimensional design spaces. Among surrogate models, 2 nd -order factorization machine (FM) models are widely employed as the surrogate model in active learning algorithms due to their balance between simplicity and effectiveness. However, their quadratic nature limits their capacity to capture complex, higher-order interactions among variables, often leading to suboptimal solutions. To overcome this limitation, we propose an active learning scheme integrating a 3 rd -order FM model, capable of modeling three-variable interactions and more intricate relationships in material systems. We comprehensively evaluate the surrogate modeling performance of the 3 rd -order FM case using various objective functions. Furthermore, we examine the optimization reliability and efficiency of the 3 rd -order FM-based active learning in a real-world material design task (e.g., nanophotonic structures for transparent radiative cooling). Our study shows that the 3 rd -order FM outperforms the 2 nd -order model in both surrogate accuracy and optimization performance, highlighting higher-order models’ promises for material design and optimization problems.

Factorization machine

Elucidation of a Metastable p(2 × 1) O Atom Adlayer Structure on Cu(111)

Cu-based catalysts are ubiquitous in many industrial reactions, including methanol synthesis. Under partially oxidizing conditions, Cu catalysts can have dynamic surface structures that greatly influence their reactivities. Therefore, elucidating the surface structures that are present on Cu, and looking for metastable structures, aids in the long term goal of understanding and controlling their catalytic behavior. Thin-film copper oxides such as the “29” and “44” structures have been described at length in the literature, but precursors to these thin-film oxides can be challenging to study because they exist only under certain conditions. Using a combination of experimental and computational surface science techniques, we discovered, modeled, and quantified a previously unreported O atom adlayer structure on Cu(111) with a p(2 × 1) unit cell. Here, we used scanning tunneling microscopy to visualize the striped 2 × 1 structure and density functional theory (DFT) structure optimizations to identify the thermodynamically most favorable positions of Cu and O atoms in a p(2 × 1) unit cell. Using X-ray photoelectron spectroscopy and temperature-programmed desorption, we determined the stoichiometry of the structure to be 2:1 for surface Cu atoms to O adatoms, the same stoichiometry as that modeled by DFT. This work reports a new metastable structure formed on Cu(111) at the very initial stages of oxidation and is therefore worth considering in models of catalytically relevant redox processes at Cu surfaces.

36 MATERIALS SCIENCE

Charge-induced atomic strain as a predictor of structural phase transformation in rare-earth intermetallics

We present a descriptor based on charge-induced atomic strain in crystalline lattices for predicting structural phase transformations in rare-earth intermetallic compounds containing lanthanides and transition metals. The charge-induced local atomic strain was obtained from structural optimization of experimentally known crystalline phases using state of the art density-functional theory methods. The predictive power of the descriptor was evaluated on 𝑅⁢𝐸 2 ⁢In (𝑅𝐸 = rare earth) compounds, a class known for diverse phase transformations. We show that incorporating quantum-mechanical effects—such as local charge distribution, bonding, symmetry, and electronic structure—enhances the robustness of the descriptor. To gain further insight, we analyzed phononic and electronic behavior in Y 2 ⁢In and demonstrated that experimental phase transformations are captured only when atomic strain effects are included. The descriptor was further used to predict structural phase changes in (Y⁢b 1–𝑥 ⁢E⁢r 𝑥 ) 2 ⁢In and G⁡d 2 ⁡(I⁢n 1–𝑥⁢ A⁢l 𝑥 ), with predictions confirmed by x-ray powder diffraction. Here, while the current study is focused on lanthanide-based intermetallics, the underlying principles of the descriptor suggest potential applicability to other closely related classes of rare-earth intermetallics.

Density functional theory

Multilayer Architecture Barriers for High Temperature Nuclear Applications

Innovative thin film multilayer metal/ceramic barrier coatings have been developed by Argonne National Laboratory to protect fuel cladding against different phenomena that can be encountered under the harsh operating conditions of advanced nuclear reactors. One phenomenon is Fuel-Cladding Chemical Interaction (FCCI), which can represent a challenge to the performance of steel-clad metallic fuels in sodium-cooled fast reactors (SFRs), especially when operating to high burnups at elevated cladding temperatures, and long fuel residence time. Another phenomenon is the corrosion of zirconium-based cladding under prototypic boiling water reactor (BWR) conditions and associated cladding during off normal conditions, including loss of coolant accidents (LOCA). This work provides details of the development and testing of a thin film (few microns) multilayer metal/ceramic (CrY/Y 2 O 3 ) coatings on steel cladding and its performance against FCCI. The coating architecture evolved through systematic mechanical testing, radiation tolerance assessments, and high-temperature diffusion studies from a preliminary multilayer concept to an optimized high-performance design. The optimized structure leverages stoichiometric Y 2 O 3 for its exceptional radiation stability, chemical inertness, and ultra-low fission product diffusivity (e.g., Ce diffusivity ~10 -20 m 2 /s in irradiated Y 2 O 3 at 650 °C). This is paired with ductile chromium-rich interlayers (Cr 95 Y 5 ), which significantly enhance fracture toughness and mechanical resilience. Design refinements, including increased ceramic layer thickness and optimized Cr–Y interlayer composition, eliminated fracture propagation and preserved coating integrity under extreme mechanical stress (>10× typical reactor conditions) and prolonged radiation exposure (~300 dpa). Those conditions are well beyond expected conditions during normal operations in SFR, and cover some of the transient conditions as well. In addition, the coating deposition was demonstrated to be applied uniformly to the inner surface of steel tubes representing prototypic SFR cladding. Another phenomenon under consideration in this work is the corrosion of zirconium-based cladding under prototypic boiling water reactor (BWR) conditions and associated off normal conditions including loss of coolant accident (LOCA). Another multilayer thin film coating is considered for mitigation of this phenomenon, where a coating of yttrium aluminum and yttrium aluminum ceramic/metal thin film coating. Preliminary results on the coating performance during high temperature thermal cycling (up to 1000 C) have shown promising performance of the coating. On-going optimization of the coating will continue in FY26.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Interface Evolutionand Long-Term Performance of NegativeCarbon Fiber Structural Electrodes

Abstract Laminated structural batteries present a transformative solution to reducing weight constraints in electric vehicles. These structural batteries are based on a multifunctional material that incorporates an energy storage function within a carbon fiber-reinforced polymer. Despite the potential of this technology, the intricate morphology of fiber–matrix or electrode–electrolyte interfaces and the impact of long-term cycling at low current rates (C-rates) on these interfaces remain insufficiently understood. This study addresses these critical knowledge gaps by examining the influence of matrix composition on the long-term electrochemical performance of structural battery electrodes and exploring advanced techniques to investigate carbon fiber–matrix interfaces. Localized imaging and X-ray scattering techniques were used to characterize morphological changes at the electrode–electrolyte interfaces by analyzing negative structural electrodes. The findings revealed that the matrix composition influences long-term electrochemical behavior and fiber–matrix interface formation. While the intrinsic properties of carbon fibers largely remain unaffected by long-term cycling, cycling promotes debonding at fiber–matrix interfaces. Nonetheless, residual regions of adhesion persist, underscoring the potential for preserving multifunctionality even under prolonged cycling conditions. These insights advance the understanding of interface dynamics, which is critical for optimizing structural battery technologies.

Chemistry

Maximizing dynamic range and performance of anatase TiO 2 ECRAM through structure and programming

Here, in this study, we investigate the structure-dependent modulation characteristics of all-solid-state three-terminal electrochemical random-access memory (ECRAM) based on an anatase Li x TiO 2 channel. By directly comparing “asymmetric” and “symmetric” ECRAM device architectures, we reveal significant insight into the impact of a non-zero gate-drain open-circuit voltage and its influence on voltage vs. current-controlled gating. We also explore the impact of potentiation/depression write parameters on the symmetry, linearity, and dynamic range of the device response. Together, initial results from optimizing structure and programming approaches yielded unprecedented G max /G min ratios of >1,000 for ECRAM and hundreds of tunable memory states with excellent linearity and symmetry. Simulations based on these ECRAM devices further illustrate the promise of this analog memory technology, achieving near 2% classification error in the MNIST digit recognition benchmark for a range of training parameters compared to a theoretical best of 1.66% and outperforming other device models extracted from the literature.

AIHWKit

Order–Disorder Phase Stabilization by Pressure‐Induced Charge Transfer Enhances the Ferroelectric Photovoltaic Effect in Multiferroic BaFe 4 O 7

Abstract Multiferroic ferroelectric photovoltaic (FPV) materials, combining magnetic and ferroelectric properties, are of paramount importance for optoelectronic and photovoltaic applications. However, optimizing both the remanent polarization and the optical bandgap—key factors for enhanced FPV performance—presents a significant challenge due to their trade‐off. This work shows that pressure‐induced charge transfer between different metal sites can break this trade‐off. Above ≈20 GPa, charge transfer between different trivalent iron (Fe) sites in the multiferroic material BaFe 4 O 7 leads to Fe valence disproportionation, FeO 4 tetrahedra disorder, and Jahn–Teller distortion of FeO 6 octahedra. These changes reduce the bandgap, lower resistivity, and enhance ferroelectric polarization, resulting in a 2.5‐fold increase in photocurrent. Upon decompression, BaFe 4 O 7 retains an order–disorder structure, optimal ferroelectric and optical properties at ambient conditions. This work provides a novel pathway to simultaneously optimizing ferroelectricity and bandgap via pressure‐induced charge transfer, overcoming the traditional trade‐off in FPV materials, and offers a promising approach for developing high polarization performance, narrow‐bandgap FPV materials.

Chemistry

Targeted Adaptive Design

Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. Here, we abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated expected log-predictive probability density of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.

97 MATHEMATICS AND COMPUTING

Understanding the structural mechanics of ligated DNA crystals via molecular dynamics simulation

DNA self-assembly is a highly programmable method to construct arbitrary architectures based on sequence complementarity. Among various constructs, DNA crystals are macroscopic crystalline materials formed by assembling motifs via sticky end association. Due to their high structural integrity and size ranging from tens to hundreds of micrometers, DNA crystals offer unique opportunities to study the structural properties and deformation behaviors of DNA assemblies. For example, enzymatic ligation of sticky ends can selectively seal nicks resulting in more robust structures with enhanced mechanical properties. However, the research efforts have been mostly on experiments involving different motif designs, structural optimization, or new synthesis methods, while their mechanics are not yet fully understood. The complex properties of DNA crystals are difficult to study via experiments alone, and numerical simulation can complement and aid the experiments. The coarse-grained molecular dynamics (MD) simulation is a powerful tool that can probe the mechanics of DNA assemblies. Here, we investigate DNA crystals made of four different motif lengths with various ligation patterns (full ligation, major directions, connectors, and in-plane) using oxDNA, an open-source, coarse-grained MD platform. We found that several distinct deformation stages emerge in response to mechanical loading and that the number and the location of ligated nucleotides can significantly modulate structural behaviors. These findings should be useful for predicting crystal properties and thus improving the design.

DNA crystal

Enhancing durability and activity toward oxygen evolution reaction using single-site Re-doped NiFeO x catalysts at ampere-level

NiFeO x materials are known as among the most active catalysts toward oxygen evolution reaction (OER) for hydrogen generation in alkaline media. Nevertheless, the long-term durability of NiFeO x catalysts for OER is still too far to the industrial application. Herein, we prepared a NiFeReO x catalyst with single-site Re dopants and observed that the single-site Re dopants could significantly enhance the durability without compromising the activity. A cell voltage of 1.82 V without iR correction is noted at the current density of 3000 mA cm –2 in anion-exchange membrane water electrolyzer (AEMWE) with NiFeReO x catalyst, and a very small degradation is observed under 2000 and 1000 mA cm –2 , which remarkably outperforms the pristine NiFeO x . Additionally, the overpotential of 305 mV at 10 mA cm –2 is achieved with the NiFeReO x catalyst, which is lower than 50 mV compared with the pristine NiFeO x catalyst, together with a smaller Tafel slope of 54.3 mV dec -1 . The boosted OER durability and activity of the NiFeReO x catalyst could be attributed to the strong electron-withdrawing property of Re 7+ single atoms leading to the electronic structure optimization and stabilization of Ni/Fe active sites. Our insights propose a new path for designing NiFeO x catalysts with high durability and activity toward OER.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH