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DOE OSTI2026

Spatially Accelerated Winding Numbers for Curved Geometry

The generalized winding number (GWN) is a scalar field that supports robust containment queries on curved geometry, including non-watertight, overlapping, and nested boundary representations. While queries can be easily parallelized over samples, direct evaluation on parametric curves and surfaces remains costly for large and complex models. Fast, state-of-the-art GWN approaches leverage a spatial index to approximate the GWN, typically coupled with a Taylor expansion which approximates the GWN contribution for far clusters of geometric primitives. However, such methods operate only on discrete inputs such as triangle meshes and point clouds, and would introduce containment errors near boundaries if applied to curved input. We extend support for fast GWN evaluation over arbitrary collections of NURBS curves in 2D and trimmed NURBS patches in 3D via a Bounding Volume Hierarchy that stores efficiently precomputed moment data in the hierarchy nodes. When querying the hierarchy, approximations for far clusters are used alongside direct evaluation for nearby NURBS primitives, achieving sub-linear complexity while preserving the geometric features in the vicinity of the query point. Central to our performance improvements is an adaptive subdivision strategy for NURBS primitives during a preprocessing phase, creating better spatial partitions while retaining the same accuracy for containment decisions as a direct evaluation. We demonstrate the performance and accuracy of our approach across a large collection of 2D and 3D datasets.

Computer science↗

DOE OSTI2026

Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution

The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.

Wu, Chenghao [Northeast Electric Power University]↗

DOE OSTI2024

On The Jacobian of the ECEF J2 Gravitation Model

An Earth-centered, Earth-fixed (ECEF) inertial navigation system must compute the Jacobian of its employed gravitation model with respect to position while time-propagating the error covariance of the system. One commonly used gravitation model is the ‘J2 model’ which is a second-order truncation of the Earth’s spherical harmonic gravitation model. The J2 model is popular because it can quickly and efficiently be evaluated, and the truncation error is small: The ‘J3 term’ --- the third term in the spherical harmonic expansion --- is approximately 1000 times smaller than the J2 term.

42 ENGINEERING↗

DOE OSTI2025

ExINP NSA Ice Nucleating Particle Concentrations

This data set comprises cumulative ambient ice-nucleating particle (INP) concentrations measured at the National Oceanic and Atmospheric Administration's (NOAA’s) Barrow Atmospheric Baseline Observatory (71.3230° N, 156.6114° W, “BRW” hereafter), next to the Atmospheric Radiation Measurement (ARM) North Slope of Alaska (NSA) site and ~ 6 km northeast of the town of Utqiaġvik. Our INP abundance data were generated using a combination of online instrument, the Portable Ice Nucleation Experiment chamber ver. 3 (PINE-03), and an offline cold stage, the West Texas Cryogenic Refrigerator Applied to Freezing Test system (WT-CRAFT). Our online INP data are all from the Examining the Ice-Nucleating Particles from NSA (ExINP-NSA) campaign conducted from October 19, 2021 to May 24, 2024. The offline INP concentration analysis was performed at West Texas A&M University for aerosol particle samples collected on polycarbonate filters (with 0.2-micron diameter pores). The PINE-03 measurements, as well as sampling activities for offline INP measurements, were conducted using the BRW site. An inset laminar sampling stack was mounted to the instrument platform, allowing PINE-03 to intake particle-laden air. For most of the campaign period, the semi-autonomous PINE-03 chamber was remotely controlled from West Texas A&M University using the LabView interface through the BeyondTrust remote-access console. PINE-03 was set to conduct an immersion freezing expansion experiment (i.e., simulated adiabatic cooling along with RHw at or above 100%). Except during the scheduled maintenance periods, the time resolution of each expansion experiment was approximately 12 minutes. PINE-03 continuously measured INP concentrations during the entire campaign without any substantial breaks. For most of the campaign period, PINE scanned its set-point vessel air temperatures from -14 °C to -31 °C and back to -14 °C about every 120 minutes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

ExINP NSA Ice Nucleating Particle Concentrations

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗

DOE OSTI2024

Taylor-Expansion-Based Robust Power Flow in Unbalanced Distribution Systems: A Hybrid Data-Aided Method

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. moreover, their computation accuracy and efficiency are heavily subject to unknown errors and bad data in measurements or prediction data of distributed energy resources (ders). to address these issues, this paper proposes a hybrid data-aided robust power flow algorithm in unbalanced distribution systems, which combines taylor series expansion knowledge with a data-driven regression technique. the proposed method initiates a linearization power flow model to derive an explicitly analytical solution by modified taylor expansion. to mitigate the approximation loss that surges due to the der integration and bad data, we further develop a data-aided robust support vector regression approach to estimate the errors efficiently. comparative analysis in the 13-bus and 123-bus ieee unbalanced feeders shows that the proposed hybrid algorithm achieves superior computational efficiency, with guaranteed accuracy and robustness against outliers.

data-driven↗

DOE OSTI2025

Gaussian Process Regression under Computational and Epistemic Misspecification

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Furthermore, our theory also accounts for epistemic misspecification in the choice of kernel parameters.

Gaussian process regression↗

DOE OSTI2026

A simple fourth order propagator based on the Magnus expansion in the Liouville space: Application to a Λ-system and assessment of the rotating wave approximation

A simple fourth-order propagator [Ture and Jang, J. Phys. Chem. A 128, 2871 (2024)] based on the Magnus expansion is extended to the Liouville space for both closed-system and Lindbladian open-system quantum dynamics. For both dynamics, commutator free versions of fourth-order propagators are provided as well. These propagators are then applied to the dynamics of a driven Λ-system, where Lindblad terms represent the effect of a photonic bath. For both dynamics, the accuracy of the rotating wave approximation (RWA) for the matter–radiation interaction is assessed. We confirmed reasonable performance of RWA for weak and resonant fields. However, small errors appear for moderate fields and substantial errors can be found for strong fields where coherent population trapping can still be expected. We also found that the presence of bath for open-system quantum dynamics consistently reduces the errors of the RWA. These results provide quantitative information on how the RWA breaks down beyond weak field or for non-resonant cases. Major results are benchmarked against results of our sixth-order ME-based propagator. Finally, we also provide numerical comparison of our algorithms with other fourth-order algorithms for the Λ-system. These confirm reasonable performance of our simple propagators and the improvement gained through commutator-free expressions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Comparison of DeePMD, MTP, GAP, ACE and MACE Machine‐Learned Potentials for Radiation‐Damage Simulations: A User Perspective

Accurate and efficient interatomic potentials are essential for molecular dynamics (MD) simulations of radiation damage, gas diffusion, and phase stability in complex ceramics such as LiAlO 2 , especially under extreme conditions relevant to tritium production. Here, we evaluate the performance of six machine-learned interatomic potentials (MLIPs), moment tensor potential (MTP), Gaussian approximation potential, deep potential (DeePMD), atomic cluster expansion (ACE), message-passing ACE (multilayer atomic cluster expansion (MACE) pretrained) and MACE (trained from-scratch), all trained on the same density functional theory dataset with inclusion of tritium. The MLIPs are benchmarked against traditional Buckingham and ReaxFF potentials in terms of energy accuracy, density predictions, thermal equilibration behavior, threshold displacement energy (E d ), tritium diffusivity, and computational cost. Among the models, MTP shows the best overall balance between efficiency and accuracy, with low force and energy errors and realistic E d values for Li and Al. The ACE and MACE (pretrained and trained from scratch) models exhibit high E d (>200 eV) and unphysical pair interactions. DeePMD underestimates Ed due to overly repulsive behavior even at equilibrium distances. All models over-estimate tritium diffusion but the pretrained MACE model behaves well during tritium-diffusion simulations up to 500 K, maintaining diffusivities in the physically consistent 10 −11 m 2 /s range. Finally, we quantify the computational cost of each potential in large-scale atomic/molecular massively parallel simulator, finding that only MTP is more efficient than traditional empirical potentials, while others are significantly more expensive. These findings explain the trade-offs between accuracy and computational cost in MLIP development and provide essential guidance for use in high-throughput radiation damage and gas diffusion simulations in nuclear ceramics.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

Loop series expansions for tensor networks

Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this article, we describe how a loop series expansion can be applied to systematically improve the accuracy of a BP approximation to a tensor network contraction, in principle converging arbitrarily close to the exact result. More generally, our result provides a framework for expanding a tensor network as a sum of component networks in a hierarchy of increasing complexity. We benchmark this proposal for the contraction of infinite projected entangled pair states, either representing the ground state of an Affleck-Kennedy-Lieb-Tasaki (AKLT) model or with randomly defined tensors, where it is shown to improve in accuracy over standard BP by several orders of magnitude while incurring only a minor increase in computational cost. These results indicate that the proposed series expansions could be a useful tool to accurately evaluate tensor networks in cases that otherwise exceed the limits of established contraction routines.

Evenbly, Glen [AWS Center for Quantum Computing, P↗

DOE OSTI2024

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Topochemical Oxidation of Ruddlesden–Popper Nickelates Reveals Distinct Structural Family: Oxygen-Intercalated Layered Perovskites

Layered perovskites─including the Dion–Jacobson, Ruddlesden–Popper, and Aurivillius families─exhibit a wide range of correlated electron phenomena, from high-temperature superconductivity to multiferroicity. Here, in this study, we report a new family of layered perovskites realized through topochemical oxidation of La n+1 Ni n O 3n+1+δ (n = 1–4) Ruddlesden–Popper nickelate thin films. Postgrowth ozone annealing induces a substantial c-axis expansion─17.8% for La 2 NiO 4+δ (n = 1)─that monotonically decreases with increasing n. Surface synchrotron X-ray diffraction and coherent Bragg rod analysis (COBRA) reveal that this structural expansion arises from the intercalation of approximately δ ≈ 0.7–1.0 oxygen atoms into interstitial sites within the rock salt spacer layers, far exceeding the previous record of δ ≈ 0.3 for any Ruddlesden–Popper oxide. These oxygen-intercalated phases form a new class of layered perovskites with a spacer layer composition intermediate between the Ruddlesden–Popper and Aurivillius phases. Furthermore, oxygen intercalation induces metallicity, enhances nickel–oxygen hybridization, and suppresses oxygen octahedral rotations, a feature associated with high-temperature superconductivity in Ruddlesden–Popper nickelates. Our work establishes topochemical oxidation as a powerful approach to accessing highly oxidized, metastable phases across a broad range of layered oxide systems, offering new platforms to engineer electronic properties via intercalation chemistry.

Ferenc Segedin, Dan [Harvard Univ., Cambridge, MA ↗

DOE OSTI2025

First-principles thermodynamics of Al 10 ⁢V: An analytical treatment of localized anharmonic modes

Many complex intermetallic structures possess cagelike environments that can host additional guest atoms. In Al 10 ⁢V, these atoms give rise to low-frequency, localized vibrations (Einstein modes) that dominate the thermodynamic response at low temperature. They become imaginary under volume expansion as temperature rises, invalidating the harmonic approximation. Here, we develop a framework to incorporate these strongly anharmonic vibrational modes into first-principles thermodynamic calculations. By explicitly modeling the cage potential and solving the associated Schrödinger equation numerically, we compute the full anharmonic free energy contribution and demonstrate its impact on the thermodynamic behavior of Al 10⁢ V. This allows us to examine structures with different cage fillings and construct the Al-V phase diagram in the relevant composition range. Our results reproduce key experimental signatures, including the anomalous rise in the thermal expansion coefficient and heat capacity at low temperatures, and reveal that the presence and the extent of cage filling by guest atoms is essential to stabilizing the Al 10 ⁢V phase at elevated temperatures.

anharmonic lattice dynamics↗

DOE OSTI2025

A parallel-kinetic-perpendicular-moment model for magnetised plasmas

We describe a new model for the study of weakly collisional, magnetised plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle dynamics parallel to the magnetic field while approximating the perpendicular dynamics through a spectral expansion in the perpendicular degrees of freedom, analogous to moment-based fluid approaches. In so doing, a hybrid approach is obtained that is computationally efficient enough to allow for larger-scale modelling of plasma systems while eliminating a source of difficulty in deriving fluid equations applicable to magnetised plasmas. We connect this system of equations to historical asymptotic models and discuss advantages and disadvantages of this approach, including the extension of this parallel-kinetic-perpendicular moment beyond the typical region of validity of these more traditional asymptotic models. This paper forms the first of a multi-part series on this new model, covering the theory and derivation, alongside demonstration benchmarks of this approach that include shocks and magnetic reconnection.

astrophysical plasmas↗

DOE OSTI2027

From zonal to nodal capacity expansion planning: Spatial aggregation impacts on a realistic test-case

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. Here, this work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8000 buses, we find that well-designed small spatial aggregations can yield good approximations but that coarser zonal models may result in large distortions of investment decisions, e.g., capacity under-investment of up to 41% for the lowest resolution model considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗

DOE OSTI2026

Glauber-theory analysis of nuclear reactions on a 12 C target with variational Monte Carlo wave functions

The application of Glauber theory has been playing an increasingly important role with the study of unstable or exotic nuclei. Its adaptation to medium and high-energy nucleus-nucleus collisions is severely limited because one has to evaluate the matrix elements of multiple-scattering operators. The extraction of physical observables has been done using ‘approximate’ Glauber theory whose validity is hard to evaluate. Here, we perform a full calculation of the matrix elements using Monte Carlo integration and analyze the elastic differential cross sections and the total reaction cross sections for p+¹²C, ⁴,⁶He+¹²C, and ¹²C+¹²C collisions. We use the variational Monte Carlo wave functions for ⁴,⁶He and ¹²C obtained by using realistic two- and three-nucleon potentials. We demonstrate the performance of the Glauber-theory calculations by comparing with available experimental data. We further discuss the accuracy of the conventional approximate methods in the light of the cumulant expansion for Glauber’s phase-shift function.

Horiuchi, W. [Osaka Metropolitan University (Japan↗