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DOE OSTI2025

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization↗

DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Predicting Flow in Fracture Networks With Quantum Algorithms

Uncertainty quantification plays a crucial role in the modeling of subsurface flow. For instance, uncertainties in the properties of geologic fracture networks significantly impact flow, requiring numerous simulations to accurately estimate quantities of interest. However, each simulation is computationally expensive because it requires solving a large linear system to capture features that involve both small and large fractures. An example is in percolation, where the interaction of many small fractures (which cumulatively can have a large surface area) with the rock matrix must be modeled precisely. Quantum computing is an emerging tool with the potential to address this issue. Quantum algorithms offer a significant speedup in solving linear systems, achieving efficiencies that are challenging to match with classical approaches. These classical approaches include direct solvers, such as LU decomposition, and iterative methods, notably preconditioned conjugate gradient, commonly used in subsurface modeling to solve large sparse systems. However, applying quantum algorithms to geologic fracture flow requires careful attention to algorithmic and problem-specific constraints to fully realize this quantum advantage. In this work we describe a quantum algorithm for generalized Monte Carlo applications with a quadratic speedup over the classical approaches which can be combined with the quantum speedup, currently under investigation, for solving quantum linear systems for subsurface flow. We show that for quantum algorithms the computational cost of estimating a quantity of interest for a statistical ensemble of networks is roughly the same as that of a single realization, essentially implying that one can get uncertainty quantification for free.

58 GEOSCIENCES↗

DOE OSTI2025

Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable and general response results rely on path ensemble averaging. Furthermore, these techniques do not apply to perturbations that affect the diffusion tensor in a stochastic system. Here, we introduce an “effective” physical process that represents the diffusion perturbed dynamics and enables accurate calculations of responses to a change in the diffusion. Interestingly, the effective dynamics contain an additional drift involving the instantaneous “score” of the system, and we leverage score matching algorithms to carry out nonequilibrium response calculations on systems for which the exact stationary distribution is unknown.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Design Principles for Resonant Wave Energy Converters: Benchmarking Power Capture and Flow

Control co-design (CCD) in Wave Energy Converters (WECs) integrates the controller, power take-off (PTO), and buoy models during system design to optimize power output. Using the bi-conjugate impedance matching principle, this study models the PTO as a two-port network, revealing impedance matching conditions at the input and output ports as a function of the buoy, PTO, and controller. Here, this study examines the pairing of a flywheel-type pitch resonator PTO within a given buoy constrained by limited space and ballast capacity. The results show that physical constraints imposed by the buoy affect PTO performance. While controller tuning achieves optimal output impedance matching and flywheel inertia is maximized within the buoy's limitations, the PTO's input impedance remains smaller than the complex conjugate of the buoy's intrinsic impedance. This mismatch limits the PTO's ability to generate sufficient reaction torque, particularly outside the resonance frequency, resulting in narrow-band power transfer. The findings emphasize the need for PTO design modifications to improve input power transfer. Pendulum-based PTO mechanisms are proposed as alternatives to couple with multiple buoy motion modes and improve wave-to-wire efficiency while respecting system constraints.

Control Co-Design↗

DOE OSTI2024

NeuroFEM

SAND2025-00525O NeuroFEM is a software tool that demonstrates a neuromorphic algorithm for solving finite element problems. It sets up a 2D finite element problem for the Poisson equation on a disk, constructs synaptic matrices, and simulates neural dynamics to solve the resulting sparse linear system. The software illustrates how the algorithm converges to the solution and plots the results, showcasing a neuromorphic counterpart to traditional methods like Conjugate Gradient or GMRES. This tool is designed to highlight the potential of neuromorphic algorithms for solving sparse linear systems, which are prevalent in various computational applications. 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.

SciDAC↗

DOE OSTI2025

Topological protection in a Landau flat band at v = 7/11, a candidate filling factor for unconventional correlations

Strong interactions in Landau flat bands are known to stabilize correlated states that do not form in other types of flat bands. We report hallmarks of topological protection at the Landau level filling factor v = 7/11 in a 2D electron system. The v = 7/11 filling factor is the particle-hole conjugate of v = 4/11⁠, a filling factor intensely studied for the possibility of realizing unconventional electronic correlations. Our data establish a new instance for an unusual fractional quantum Hall state and opens up possibilities for the study of unconventional correlations in an enlarged parameter space. We report and discuss transport signatures developing at other filling factors of interest v = 7/11, 5/8⁠, and 8/13⁠, which however in our sample do not exhibit topological protection.

composite fermions↗

DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗

DOE OSTI2025

Highly Conjugated Porphyrin Arrays Enable Optical Resolution of Ferromagnetic and Antiferromagnetic Aligned States of the Triplet Exciton and an Incorporated Stable Radical

Well-defined photogenerated molecular spin systems have potential utility in spintronics and quantum information science (QIS). Because molecular magnetic, optical, and electronic properties can be controlled by design, diverse spin systems can be prepared at modest temperatures. Photogenerated molecular spin systems often involve states prepared from the interaction of excitons and charges. Resolving the nature of electron spin alignment in photogenerated spin states described by the coupling of a triplet exciton and a stable radical commonly relies on EPR spectroscopy. Here, we describe ethyne-bridged (porphinato)metal ( PM n ) oligomers that incorporate a macrocycle-bound Cu(II) radical center. Upon photoexcitation of such PM n arrays, a singdoublet ( 2 S 1 ) state is formed; ultrafast internal conversion (IC) then produces a tripdoublet ( 2 T 1 ) state, which undergoes intersystem crossing (ISC) to produce a tripquartet ( 4 T 1 ) state, before relaxation to the ground state ( 2 S 0 ). These highly conjugated Cu(II) radical-containing PMn arrays enable direct observation of copper porphyrin 2 T 1 → 4 T 1 ISC dynamics from the biexponential decay of the near-infrared (NIR) 2,4 T 1 → 2,4 T n transient absorption manifold. Multireference n-electron valence perturbation theory (NEVPT2) computations illuminate how PM n electronic structure controls the relaxation dynamics of these long-lived (>10 ns) electronically excited multiplet states. These studies show that highly conjugated and polarizable porphyrin arrays incorporating stable spin centers provide rare π-delocalized systems where the ferromagnetic and antiferromagnetic alignment between a triplet exciton and a stable radical are both spectrally resolved and addressable using transient optical spectroscopy at wavelengths exceeding 1 μm, providing new opportunities to QIS.

14 SOLAR ENERGY↗

DOE OSTI2025

Spin Dynamics of SCRPs in ZnO Quantum Dot–Organic Molecule Conjugates Studied with Pulsed EPR

Photogenerated spin-correlated radical pairs (SCRPs) are emerging as promising new candidates for Quantum Information Science applications, where they act as electron spin qubit pairs (SQPs). Historically, these pairs have been mostly investigated in natural photosynthesis and in molecular organic donor–(linker)–acceptor systems. Recently, we have shown that these spin pairs can also be observed by time-resolved electron-paramagnetic resonance (EPR) spectroscopy in hybrid inorganic–organic conjugates. The current study builds on recent work (ACS Nano, 2025, 19, 12194–12207), in which we systematically prepared hybrid inorganic–organic molecule systems with tunable geometries that can host SCRPs/SQPs. Here, we demonstrate using pulsed EPR spectroscopy that we can generate, study, and manipulate the spins in these photogenerated SCRPs hosted on highly tailorable inorganic–organic hybrid systems. Microwave pulse-based spin manipulation is the first step toward developing quantum computing and quantum sensing applications with these promising spin-based qubit materials, which can be reversibly photogenerated in highly spin-polarized states at moderate temperatures. An attractive feature of this new class of hybrid materials is that the g-factor of the unpaired electron spin in the ZnO QD (as part of the SCRP/SQP) can be adjusted using the quantum size effect in these QDs, which allows for the selective addressability of each spin in the SCRP using microwave pulses. Additionally, we also observed a difference between the g-values of the unpaired electron in the ZnO QD in the transient SCRP state and stable photoreduced state. We hypothesize that the unpaired electron in the SCRP is delocalized as a band-like conduction electron, while in the stable photoreduced state, the electron is delocalized in a shallow electron trap state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗

DOE OSTI2025

Manipulating Aromaticity to Redirect Topochemical Polymerization Pathways

Topochemical polymerization (TCP) represents an essential route to create regio- and stereoregular polymers through solid-state transformations. Herein, we present an innovative strategy for controlling topochemical polymerization pathways by tailoring the terminal group aromaticity in the para-azaquinodimethane (AQM) ring system. Substituting phenyl groups with less aromatic furyl units extends significant spin density delocalization across the conjugated core upon thermal activation, inducing significant diradicaloid characters at furyl positions and enabling unconventional reactivities in both solution and solid states. Thermal treatment in toluene yields a unique cyclophane dimer formed via furyl-methine C-C coupling, confirmed by X-ray crystallography, while solid-state reactions produce polymers formed via both intercolumnar furyl-methine coupling and intracolumnar methine-methine coupling. The spin-center-directed mechanism underlying these transformations is validated through theoretical modeling and isotopic labeling experiments. This study highlights the prowess of aromaticity modulation in functional pro-aromatic systems, which enables the synthesis of polymers with main chain structures that are otherwise difficult to access.

Zhang, Qingsong↗

DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool under development at Argonne National Laboratory for advanced non-LWR reactor safety analysis. It aims to provide fast-running, modest-fidelity, whole-plant transient analyses capabilities, which are essential for fast turnaround design scoping and engineering analyses of advanced reactor concepts. While SAM is being developed as a system-level modeling and simulation tool, advanced modeling techniques being implemented include a reduced-order three-dimensional module, pseudo 3-D conjugate heat transfer modeling in reactor core, flexible and multi-scale modeling of heat transfer between fluid and structures, in addition to the advances in software environments and design, and numerical methods. SAM aims to be a generic system-level safety analysis tool for advanced non-LWRs, including Liquid-Metal-cooled fast Reactors (LMR), Molten Salt Reactors (MSR), Fluoride-salt-cooled High-temperature Reactors (FHR), and High-Temperature Gas-cooled Reactors (HTGR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented computational framework (MOOSE), and its underlying meshing and finite-element library and linear and non-linear solvers, to leverage the modern advanced software environments and numerical methods. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As new code capabilities and features are added, the SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Four ppm measurement of the antihydrogen ground-state hyperfine splitting

The hydrogen atom is a touchstone for the foundations, evolution and frontiers of quantum theory. Key spectral lines of this atom have been determined to remarkable precision. Our research focuses on the study of antihydrogen, the antimatter counterpart of hydrogen. We test fundamental symmetries of nature (such as simultaneous charge conjugation, parity inversion, and time reversal or CPT symmetry) through precision comparisons of these atomic systems. Recent 1S–2S spectroscopic measurements on trapped antihydrogen have achieved relative precisions of parts per trillion. However, the ground-state hyperfine splitting, which is sensitive to the internal structure of the antiproton, has only been measured to 400 parts per million (ppm). Here we report a 4 ppm measurement of the antihydrogen ground-state hyperfine splitting energy a 1S , advancing the state-of-the-art precision by two orders of magnitude. From microwave spectroscopy experiments with roughly 24,000 anti-atoms, we determine ${a}_{1{\rm{S}}}/h=\mathrm{1,420,404.8}\pm 1.1(\mathrm{stat.})\pm 5.6\,(\mathrm{sys.})\,\text{kHz}$ in a 1-T magnetic field, consistent with expectations for hydrogen. At this level, our measurement is sensitive to the internal structure of the antiproton, which contributes at about 40 ppm and is approaching the limit of existing theoretical analyses. The gains we report are the product of marked advances in magnetic trap field control, stabilization and characterization; anti-atom spin-state manipulation; and improved antihydrogen accumulation rate.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Manipulation of intramolecular hydrogen bonds in conjugated pseudoladder polymer for semiconductivity and solution-processability

The conformational coplanarity and local rigidity of π-conjugated backbones are critical for the semiconducting performance of organic electronic materials. The conformational coplanarity and local rigidity of π-conjugated backbones are critical for the semiconducting performance of organic electronic materials. While fusing the aromatic system into a ladder-type structure effectively enhances these properties, it also often results in poor solution processability and hence limits their transition to device application. To address this challenge, an intramolecularly hydrogen-bonded pseudoladder polymer (HPLP) system based on alternating hydrogen bond donating benzobisimidazole (BBI) and hydrogen bond accepting benzodifuran (BDF) units, is designed and synthesized. A Boc-protected precursor of HPLP allows for feasible solution processing of the polymer into thin films. Subsequently, in situ thermal Boc-deprotection generates the HPLP polymer, in which intramolecular hydrogen bonds form between each pair of neighboring repeating units, inducing coplanarity and rigidity throughout the entire backbone. This process is accompanied by a significant red-shift of the absorption spectrum, reduced bandgap, and enhanced rigidity, as confirmed by NMR, UV-Vis, and density functional theory analyses. HPLP films exhibit a three-order-of-magnitude enhancement in charge carrier mobility compared to the Boc-protected precursor and demonstrate excellent solvent resistance in organic thin-film transistors.

Miranda, Octavio↗

DOE OSTI2025

Symmetry-projected spin-AGP methods applied to spin systems

Symmetry-projected wave function methods capture static correlation by breaking and restoring the symmetries of a system. In this article, we present the symmetry-projected spin antisymmetrized geminal power (spin-AGP) state projected onto space group symmetry as well as complex conjugation, spin-flip, and time-reversal symmetries. The method is benchmarked on the 1D XXZ model and the 2D J 1 − J 2 model with square and triangular lattices. Our results indicate that symmetry projection methods provide a powerful tool for frustrated spin systems.

Antisymmetrized geminal power↗

DOE OSTI2025

The UV Photoinduced Ring-Closing Reaction of Cyclopentadiene Probed with Ultrafast Electron Diffraction

Conjugated cyclic organic molecules are common across many fields such as pharmaceuticals, are naturally occurring in biological systems, and are used in synthetic materials. One particular area of interest from a photochemical point of view is the formation of highly strained cyclic organics. We investigate the photoinduced reaction of cyclopentadiene, a five-membered organic ring molecule which can form strained three and four carbon rings after photoexcitation with UV light, with the gas-phase ultrafast electron diffraction instrument at the SLAC MeV-UED facility. Electron diffraction offers a direct probe sensitive to the nuclear geometry during the reaction, allowing for the determination of the distribution of products formed following photoexcitation. We observe the simultaneous formation of the highly strained ring- closed bicyclo[2.1.0]pentene and vibrationally hot cyclopentadiene within the temporal resolution of the experiment, and determine the relative yield of all reaction products. Furthermore, the experimental results are in good agreement with the predictions of trajectory simulations.

Computational Chemistry↗