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DOE OSTI2025

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗

DOE OSTI2023

Data-Driven Smoothers for Extreme-Scale Computing

Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational domain. The two most common families of patch-based methods are block-Jacobi and Schwarz methods, where the former typically corresponds to non-overlapping domains and the later implies some overlap. We focus on cases where each patch consists of the degrees of freedom on a finite element method mesh cell. Patch methods often capture complex local physics much more effectively than simpler point-smoothers such as Jacobi; however, forming, inverting, and applying each patch can be prohibitively expensive in terms of both storage and computation time. To this end, we propose several approaches for performing analysis on these patches and constructing a reduced representation. The compression techniques rely on either matrix norm comparisons or unsupervised learning via a clustering approach. We illustrate how it is frequently possible to retain/factor less than 5% of all patches and still develop a method that converges only a little slower than when all patches are stored/factored.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Concurrent Enhancement of Acetylene Uptake Capacity and Selectivity by Progressive Core Expansion and Extra–Framework Anions in Pore–Space–Partitioned Metal–Organic Frameworks

A multi-stage core-expansion method is proposed here as one component of the integrative binding-site/extender/core-expansion (BEC) strategy. The conceptual deconstruction of the partitioning ligand into three editable parts draws our focus onto progressive core expansion and allows the optimization of both acetylene uptake and selectivity. Herein the effectiveness of this strategy is shown through a family of eight cationic pore-partitioned materials containing three different partitioning ligands and various counter anions. The optimized structure, Co 3 -cpt-tph-Cl (Hcpt=4-(p-carboxyphenyl)-1,2,4-triazole, H-tph=(2,5,8-tri-(4-pyridyl)-1,3,4,6,7,9-hexaazaphenalene) with the largest surface area and highest C 2 H 2 uptake capacity (200 cm 3 /g at 298 K), also exhibits (desirably) the lowest CO 2 uptake and hence the highest C 2 H 2 /CO 2 selectivity. The successful boost in both C 2 H 2 capacity and IAST selectivity allows Co 3 -cpt-tph-Cl to rank among the best crystalline porous materials, ionic MOFs in particular, for C 2 H 2 uptake and C 2 H 2 /CO 2 experimental breakthrough separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Multi–Modular Design of Stable Pore–Space–Partitioned Metal–Organic Frameworks for Gas Separation Applications

Pore space partition (PSP) is an effective materials design method for developing high-performance small-pore materials for storage and separation of gas molecules. The continued success of PSP depends on broad availability and judicious choice of pore-partition ligands and better understanding of each structural module on stability and sorption properties. Here, by using substructural bioisosteric strategy (sub-BIS), a dramatic expansion of pore-partitioned materials is targeted by using ditopic dipyridyl ligands with non-aromatic cores or extenders, as well as by expanding heterometallic clusters to uncommon nickel–vanadium and nickel–indium clusters rarely known before in porous materials. The dual-module iterative refinement of pore-partition ligands and trimers leads to remarkable enhancement of chemical stability and porosity. Here a family of 23 pore-partitioned materials synthesized from five pore-partition ligands and seven types of trimeric clusters is reported. New materials with such compositionally and structurally diverse framework modules reveal key factors that dictate stability, porosity, and gas separation properties. Among these, materials based on heterometallic vanadium–nickel trimeric clusters give rise to the highest long-term hydrolytic stability and remarkable uptake capacity for CO 2 , C 2 H 2 /C 2 H 4 /C 2 H 6 , and C 3 H 6 /C 3 H 8 hydrocarbon gases. Here, the breakthrough experiment shows the potential application of new materials for separating gas mixtures such as C 2 H 2 /CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0

SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This article overviews several significant improvements and new features added over the last 3 years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge–Kutta, symplectic partitioned Runge–Kutta, and operator splitting. In addition, we describe new timestep adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge–Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.

Computer science↗

DOE OSTI2020

Solvent Selection for the Separation of Lignin-Derived Monomers Using the Conductor-like Screening Model for Real Solvents

The separation of desired monomers from a liquid-phase mixture of lignin depolymerization products is necessary to facilitate their upscaling and upgrading for industrial applications. One effective method to separate multiple liquid-phase products is countercurrent chromatography (CCC), which is a common liquid chromatography technique that separates target solutes based on differences in their partitioning in a biphasic solvent system. Effective CCC separation requires the selection of solvent compositions to tune solute partition coefficients. Here, to alleviate the experimental burden of selecting optimal solvent systems, we apply the conductor-like screening model for real solvents (COSMO-RS) method to compute partition coefficients of representative lignin monomers from four currently used depolymerization strategies in standard solvent systems. We further design new ternary and quaternary solvent systems that are predicted to further improve separation efficacy. On the basis of these predicted partition coefficients and empirical solvent selection criteria for CCC measurements, we suggest a range of solvent systems that would be suitable for the effective separation of aromatic lignin-derived products via CCC or similar liquid–liquid extraction methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

BTZ one-loop determinants via the Selberg zeta function for general spin

We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with H 3 /Z, extending (arXiv:1811.08433) [1]. Previously, Perry and Williams [2] showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers. We extend the integer relabeling to the case of general spin, and discuss its relationship to the removal of non-square-integrable Euclidean zero modes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Fast and Invertible Simplicial Approximation of Magnetic‐Following Interpolation for Visualizing Fusion Plasma Simulation Data

We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root-finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X-Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7-X (W7-X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet.

Ren, Congrong [The Ohio State Univ., Columbus, OH ↗

DOE OSTI2023

BARC Element Classifier (barc)

SAND2024-02120O This program enumerates and classifies all possible functional elements in several different categories within the Ballistic Asynchronous Reversible Computing (barc) model of computation. barc software is a research tool that is being used to help document the possible digital behaviors of primitive functional elements in the ABRC a.k.a. BARC model of computation. The method of operation of this software leverages elementary concepts and methods from discrete mathematics: combinatorics (permutations), partitions and equivalence classes, symmetry transformations, and the theory of finite groups. Implementation is in Python programming language. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Frank, Michael↗

DOE OSTI2024

Off-shell Partition Functions in 3d Gravity

We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of PSL(2,R) Chern-Simons theory and is simpler to treat in canonical quantization. Its phase space for an initial value surface Σ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form Σ×S 1 , where Σ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of n asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{M}$ g,n , which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces Σ. As a result, there is a scaling limit in which the model reduces to JT gravity and our methods give a novel way to compute JT partition functions via equivariant localization.

Classical and Quantum Gravity↗

DOE OSTI2021

Projector-Based Quantum Embedding for Molecular Systems: An Investigation of Three Partitioning Approaches

Projector-based embedding is a relatively recent addition to the collection of methods that seek to utilize chemical locality to provide improved computational efficiency. This work considers the interactions between the different proposed procedures for this method and their effects on the accuracy of the results. The interplay between the embedded background, projector type, partitioning scheme, and level of atomic orbital (AO) truncation are investigated on a selection of reactions from the literature. The Huzinaga projection approach proves to be more reliable than the level-shift projection when paired with other procedural options. Active subsystem partitioning from the subsystem projected AO decomposition (SPADE) procedure proves slightly better than the combination of Pipek-Mezey localization and Mulliken population screening (PMM). Along with these two options, a new partitioning criteria is proposed based on subsystem von Neumann entropy and the related subsystem orbital occupancy. This new method overlaps with the previous PMM method, but the screening process is computationally simpler. Finally, AO truncation proves to be a robust option for the tested systems when paired with the Huzinaga projection, with satisfactory results being acquired at even the most severe truncation level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Automating methods for estimating metabolite volatility

The volatility of metabolites can influence their biological roles and inform optimal methods for their detection. Yet, volatility information is not readily available for the large number of described metabolites, limiting the exploration of volatility as a fundamental trait of metabolites. Here, we adapted methods to estimate vapor pressure from the functional group composition of individual molecules (SIMPOL.1) to predict the gas-phase partitioning of compounds in different environments. We implemented these methods in a new open pipeline called volcalc that uses chemoinformatic tools to automate these volatility estimates for all metabolites in an extensive and continuously updated pathway database: the Kyoto Encyclopedia of Genes and Genomes (KEGG) that connects metabolites, organisms, and reactions. We first benchmark the automated pipeline against a manually curated data set and show that the same category of volatility (e.g., nonvolatile, low, moderate, high) is predicted for 93% of compounds. We then demonstrate how volcalc might be used to generate and test hypotheses about the role of volatility in biological systems and organisms. Specifically, we estimate that 3.4 and 26.6% of compounds in KEGG have high volatility depending on the environment (soil vs. clean atmosphere, respectively) and that a core set of volatiles is shared among all domains of life (30%) with the largest proportion of kingdom-specific volatiles identified in bacteria. With volcalc , we lay a foundation for uncovering the role of the volatilome using an approach that is easily integrated with other bioinformatic pipelines and can be continually refined to consider additional dimensions to volatility. The volcalc package is an accessible tool to help design and test hypotheses on volatile metabolites and their unique roles in biological systems.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Seismic strain energy partitioning: estimating the strain energy of seismic body waves.

This report details a method to estimate the energy content of various types of seismic body waves. The method is based on the strain energy of an elastic wavefield and Hooke’s Law. We present a detailed derivation of a set of equations that explicitly partition the seismic strain energy into two parts: one for compressional (P) waves and one for shear (S) waves. We posit that the ratio of these two quantities can be used to determine the relative contribution of seismic P and S waves, possibly as a method to discriminate between earthquakes and buried explosions. We demonstrate the efficacy of our method by using it to compute the strain energy of synthetic seismograms with differing source characteristics. Specifically, we find that explosion-generated seismograms contain a preponderance of P wave strain energy when compared to earthquake-generated synthetic seismograms. Conversely, earthquake-generated synthetic seismograms contain a much greater degree of S wave strain energy when compared to explosion-generated seismograms.

58 GEOSCIENCES↗

DOE OSTI2024

Improving modular bootstrap bounds with integrality

We propose methods that efficiently impose integrality — i.e., the condition that the coefficients of characters in the partition function must be integers — into numerical modular bootstrap. We demonstrate the method with a number of examples where it can be used to strengthen modular bootstrap results. First, we show that, with a mild extra assumption, imposing integrality improves the bound on the maximal allowed gap in dimensions of operators in theories with a U(1) c symmetry at c = 3, and reduces it to the value saturated by the SU(4) 1 WZW model point of c = 3 Narain lattices moduli space. Second, we show that our method can be used to eliminate all but a discrete set of points saturating the bound from previous Virasoro modular bootstrap results. Finally, when central charge is close to 1, we can slightly improve the upper bound on the scaling dimension gap.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Electrochemical Salt Wasteform Development: A Review of Salt Treatment and Immobilization Options

Electrochemical reprocessing, also referred to as pyroprocessing, is a technique for recycling actinides from used nuclear fuel (UNF) to produce fuel for future reactors. Here, UNF is dissolved in a molten salt (e.g., LiCl-KCl eutectic) within an electrorefiner. After UNF dissolution, fission products are released into the electrolyte salt and converted to chlorides. This paper discusses wasteform options for processing the base electrolyte salt with the fission product salts as well as just the rare-earth fission products (as RECl 3 , REOCl, or REO x ) with the intent of finding optimal methods for reducing total waste salt volumes or partitioning the salt for alternate wasteform options. Furthermore, two of the more detailed partitioning options discussed herein include halide removal from the salt (dehalogenation), which accounts for more than half of the salt on a molar basis, and RE fission product removal for wasteforms with high-RE loadings. Wasteform properties are compared with emphasis on wasteform volume starting from a given amount of (1) total salt cations or (2) RE cations. Comparisons are also made of wasteform chemical durabilities, with the data available from like testing methods. A main conclusion from this work is the justification of subsequent salt processing after electrorefiner operations for achieving significant wasteform volume reduction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Machine learning method for enforcing variable independence in background estimation with LHC data: ABCDisCoTEC

A novel solution is presented for the problem of estimating the backgrounds of a signal search using observed data while simultaneously maximizing the sensitivity of the search to the signal. The 'ABCD method' provides a reliable framework for background estimation by partitioning events into one signal-enhanced region (A) and three background-enhanced control regions (B, C, and D) via two smoothly varying, statistically independent variables. In practice, even slight correlations between the two variables can significantly undermine the method's performance. Thus, choosing appropriate variables by hand can present a formidable challenge, especially when background and signal differ only subtly. To address this issue, the ABCD with distance correlation (ABCDisCo) method was developed to construct two learned variables via a neural network trained to provide strong signal-background discrimination with small values of the distance correlation (DisCo) measure between the two learned variables. However, relying solely on minimizing the DisCo can result in learned variables that may not have distributions of background events that are smoothly varying and localized at extreme values, as necessary for the validity of the background estimation. The ABCDisCo training enhanced with closure (ABCDisCoTEC) method is introduced to solve this issue by directly minimizing the nonclosure, expressed as a dedicated differentiable loss term. This extended method is applied to a data set of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the CMS detector at the CERN Large Hadron Collider. Additionally, given the complexity of the minimization problem with constraints on multiple loss terms, the modified differential method of multipliers is applied and shown to greatly improve the stability and robustness of the ABCDisCoTEC method, compared to grid search hyperparameter optimization procedures.

Hayrapetyan, Aram [Yerevan Phys. Inst.]↗

DOE OSTI2020

Learning-Accelerated ADMM for Distributed DC Optimal Power Flow

We suggest a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118-and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this paper, the ideas presented are naturally extended to other distributed optimization problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗