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DOE OSTI2025

Towards Full ‘Galilei General Relativity’: Gravitational Kinematics in Bargmann Spacetimes

Because of the strict separation of mass and energy in Galilei physics, a Galilei-invariant tensor formalism is most at home in a 5-dimensional extended spacetime associated with the Bargmann-Galilei (traditionally ‘Bargmann’) group, a central extension of the Galilei group that explicitly exhibits the transformation properties of kinetic energy. While not necessary for a tensor formalism fully embodying Poincaré physics, a similar central extension of the Poincaré group to the Bargmann-Poincaré group may illuminate a path towards a strong-field ‘Galilei general relativity’. Here the Bargmann metric is generalized to curved spacetime by extending the usual 1+3 (traditionally ‘3+1’) formalism of general relativity on 4-dimensional spacetime to a 1+3+1 formalism, whose spacetime kinematics is shown to be consistent with that of the usual 1+3 formalism. On Bargmann spacetime, tensor laws governing the motion of an elementary classical material particle and the dynamics of a simple fluid reference the foliation of spacetime in a manner that partially reverts the Einstein perspective (accelerated fiducial observers, and geodesic material particles and fluid elements) to a Newton-like perspective (geodesic fiducial observers, and accelerated material particles and fluid elements subject to a gravitational force).

Cardall, Christian [ORNL] (ORCID:000000020086105X)↗

DOE OSTI2026

Supercurrents and (partial) supersymmetry in adjoint QCD 2 and its generalizations

1 + 1-dimensional SU(N) gauge theory coupled to an adjoint Majorana fermion, also known as adjoint QCD 2 , has the surprising feature that at fermion mass $\sqrt{\frac{g^2N}{2\pi }}$ it exhibits supersymmetry. In this paper, we obtain a deeper insight into how the supersymmetry works by constructing the gauge invariant, Lorentz covariant supercurrent j μA . Its conservation relies crucially on the presence of a quantum anomaly. We generalize this construction to a class of models where, in addition to an adjoint Majorana fermion of an appropriate mass, the gauge theory is coupled to some collection of massless fermions (SU(N) may be replaced by a more general gauge group). In general, these models have a supersymmetric massive sector and a non-supersymmetric CFT sector [1], but there are cases in which both sectors are supersymmetric. An example of such a gapless, fully supersymmetric model is SU(N) gauge theory coupled to three adjoint Majorana fermions, of which two are massless and the third has mass $\sqrt{\frac{3{g}^2N}{2\pi }}$.

anomalies in field and string theories↗

DOE OSTI2025

Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory

We develop a gauge invariant, Loop-String-Hadron (LSH) based representation of SU(2) Yang-Mills theory defined on a general graph consisting of vertices and half-links. Inspired by weak coupling studies, we apply this technique to maximal tree gauge fixing. This allows us to develop a fully gauge-fixed representation of the theory in terms of LSH quantum numbers. We explicitly show how the quantum numbers in this formulation directly relate to the variables in the magnetic description. In doing so, we will also explain in detail how the Kogut-Susskind formulation, prepotentials, and point splitting work for general graphs. In the appendix of this work, we provide a self-contained exposition of the mathematical details of Hamiltonian pure gauge theories defined on general graphs.

Algorithms and Theoretical Developments↗

DOE OSTI2025

Generalized fiducial inference on differentiable manifolds

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer graphics, and geology. Here, this new approach uses generalized fiducial inference (GFI) to obtain a posterior-like distribution on the manifold, without needing to know local parameterizations that map to the constrained space from an unconstrained Euclidean space. Using mathematical tools from Riemannian geometry, we construct a constrained generalized fiducial distribution (CGFD). A Bernstein-von Mises-type result for the CGFD, which provides intuition for how the desirable asymptotic qualities of the unconstrained generalized fiducial distribution are inherited by the CGFD, is provided. To illustrate the practical use of the CGFD, we provide a proof-of-concept example in the context of a linear logspline density estimation problem, and demonstrate that CGFD-based confidence sets exhibit desirable coverage properties via simulation. As an application, we fit a CGFD to COVID-19 case count data from North Carolina, USA.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Generalized representative structures for atomistic systems

A new method is presented to generate atomic structures that reproduce the essential characteristics of arbitrary material systems, phases, or ensembles. Previous methods allow one to reproduce the essential characteristics (e.g. the chemical disorder) of a large random alloy within a small crystal structure. The ability to generate small representations of random alloys, along with the restriction to crystal systems, results from using the fixed-lattice cluster correlations to describe structural characteristics. A more general description of the structural characteristics of atomic systems is obtained using complete sets of atomic environment descriptors. These are used within for generating representative atomic structures without restriction to fixed lattices. A general data-driven approach is provided here utilizing the atomic cluster expansion (ACE) basis. The N-body ACE descriptors are a complete set of atomic environment descriptors that span both chemical and spatial degrees of freedom and are used within for describing atomic structures. The generalized representative structure (GRS) method presented within generates small atomic structures that reproduce ACE descriptor distributions corresponding to arbitrary structural and chemical complexity. It is shown that systematically improvable representations of crystalline systems on fixed parent lattices, amorphous materials, liquids, and ensembles of atomic structures may be produced efficiently through optimization algorithms. With the GRS method, we highlight reduced representations of atomistic machine-learning training datasets that contain similar amounts of information and small 40–72 atom representations of liquid phases. The ability to use GRS methodology as a driver for informed novel structure generation is also demonstrated. The advantages over other data-driven methods and state-of-the-art methods restricted to high-symmetry systems are highlighted.

atomic cluster expansion↗

DOE OSTI2025

Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension ≥3, tighten existing bounds—in some cases by an arbitrarily large multiplicative constant. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. We also derive two upper bounds on the generalized quantum Fisher information in terms of the condition number of the density matrix. One of these bounds applies only to coherent dynamics and depends also on the variance of the Hamiltonian. The other bound depends also on the so-called Wigner-Yanase skew information. These bounds generalize well-known bounds on the symmetric logarithmic derivative quantum Fisher information and are tighter than the existing bounds for sufficiently mixed states (e.g., for sufficiently high temperature thermal states).

open quantum systems & decoherence↗

DOE OSTI2024

Generalized entanglement capacity of de Sitter space

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1 + 1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of de Sitter (dS). The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggest it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2025

Generalized symmetries of nonsupersymmetric orbifolds

We determine generalized symmetries for 4D theories engineered via type II strings on nonsupersymmetric orbifold backgrounds ℝ 3,1 × ℝ 6 /Γ. Probe branes detect generalized symmetries via the adjacency matrix for fermionic degrees of freedom in an associated quiver gauge theory. In situations where the tachyons are sequestered away from the boundary 𝑆 5 /Γ, this exactly matches the result extracted from singular homology. In situations with an unsequestered tachyon which stretches out to the boundary, the presence of tachyonic pulses partitions up the space into several distinct sectors, and the net contribution again matches with the answer expected via quiver methods. For IIA backgrounds, the presence of a localized closed string tachyon leads to transitions in the spectrum of states, generalized symmetries, higher-group symmetries, as well as the level matrix of the associated symmetry topological field theory (SymTFT). For IIB backgrounds with a stack of spacetime filling probe D3-branes, the onset of a radiatively generated potential leads to similar considerations involving scale dependent transitions in the symmetries of the theory, including structures such as duality defects/interfaces.

compactification↗

DOE OSTI2024

Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation

The multivariate adaptive regression spline (MARS) approach of Friedman and its Bayesian counterpart are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. Here, we propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, and interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions, and a general form of “Normal-Wald” regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models, and we show that it compares favorably to several popular alternatives.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding Numbers

Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry is not met, such methods are either unusable, or prone to misclassifications that can lead to cascading errors in downstream applications. More robust point classification schemes based on generalized winding numbers have been proposed, as they are indifferent to these imperfections. However, existing algorithms are limited to point clouds and collections of linear elements. We extend this methodology to encompass more general curved shapes with an algorithm that evaluates the winding number scalar field over unstructured collections of rational parametric curves. In particular, we evaluate the winding number for each curve independently, making the derived containment query robust to how the curves are arranged. We ensure geometric fidelity in our queries by treating each curve as equivalent to an adaptively constructed polyline that provably has the same generalized winding number at the point of interest. Our algorithm is numerically stable for points that are arbitrarily close to the model, and explicitly treats points that are coincident with curves. We demonstrate the improvements in computational performance granted by this method over conventional techniques as well as the robustness induced by its application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

CRADA Final Report: CRADA Number NFE-22-09330 with General Fusion

General Fusion is developing a magnetized target fusion (MTF) approach that involves compressing an initial magnetically confined plasma inside a cavity formed in liquid metal. This approach builds from concepts initially developed under the Linus program at the U.S. Naval Research Laboratory and combines it with advances from compact toroid experiment (CTX) and sustained spheromak plasma experiment (SSPX) in compact toroid plasmas and coaxial Marshall gun systems. Modeling the tokamak during compression is central to designing a successful MTF device. The plasma is formed by coaxial helicity injection in the General Fusion device. Immediately after formation, the plasma has a diverted tokamak configuration with a single null. As the wall moves inwards, the plasma is repelled from the conducting surface and driven inwards by currents induced by its magnetic field in the liquid metal wall. As the liquid metal closes (or bridges) the opening of the coaxial plasma injector, the magnetic field topology alters to remove the null. Due to this, the plasma moves from a diverted to a wall-limited configuration. The liquid metal liner continues to close in and change shape, reducing in radius by a factor of ten at the peak of plasma compression. A model of the MTF plasma must be able to handle this continually varying geometry, and to be predictive, it must faithfully include the real imperfections arising in the process. In this project, we pursued a Monte Carlo approach to closures for MHD by computing kinetic electron trajectories in an MHD plasma background from simulations of GF devices. This requires enhancing the capabilities of the KORC-T code for running large ensembles of kinetic trajectories by porting it to GPU architectures and enabling workflows for large ensembles on OLCF machines. With these capabilities, it is possible to produce a large library of kinetic calculations of electron orbits evolving in plasma configurations spanning the magnetic configurations and plasma density profiles, including non-axisymmetry, arising in the General Fusion’s existing PI3 spherical tokamak device. Using ensembles will capture particles passing a single point in space in a given magnetic configuration, and the entire dataset will cover a range of global magnetic field geometries. By sampling around many starting points, this dataset will capture the spatial dependence of the plasma parameters. From this large dataset, it is possible to produce a reduced model for the kinetic effects not captured in MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗

DOE OSTI2025

X-Ray Spectra from General Relativistic Radiation Magnetohydrodynamic Simulations of Thin Disks

We compare X-ray emission from several general relativistic, multifrequency, radiation magnetohydrodynamic simulations of thin black hole accretion disks with different accretion rates and spins. The simulations were performed using the M1 closure scheme, resolved with 12 frequency (energy) bins logarithmically spaced from 5 × 10 −3 to 5 × 10 3 keV. We apply a general relativistic Monte Carlo transport code to postprocess the simulation data with greater fidelity in frequency resolution and Compton scattering treatment. Despite the relatively few energy bins and Kompaneets approximation to Compton scattering utilized in the M1 method, we find generally good agreement between the methods. Both produce prominent thermal profiles with peaks around 2–2.5 keV, where agreement is particularly strong and representative of the soft state. Both also find weaker (lower-luminosity) thermally sourced emission extending out to 100 keV due to the hotter innermost regions of the disks. Inverse Compton scattering becomes increasingly effective at hardening spectral outputs with increasing black hole spin, and becomes the dominant mechanism for photons that escape with energies between 10 to several hundred keV. At very high rates of spin, the radiation flux in this upscattered component becomes comparable to the thermal flux, a phenomenon typically associated with intermediate states. Beyond 10 4 keV, we observe faint, free–free emission from hot, optically thin coronal regions developing near the horizon, common to both spinning and nonspinning black holes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Few measurement shots challenge generalization in learning to classify entanglement

The ability to extract general laws from a few known examples depends on the complexity of the problem and on the amount of training data. In the quantum setting, the learner's generalization performance is further challenged by the destructive nature of quantum measurements that, together with the no-cloning theorem, limits the amount of information that can be extracted from each training sample. In this paper we focus on hybrid quantum learning techniques where classical machine-learning methods are paired with quantum algorithms and show that, in some settings, the uncertainty coming from a few measurement shots can be the dominant source of errors. We identify an instance of this possibly general issue by focusing on the classification of maximally entangled vs. separable states, showing that this toy problem becomes challenging for learners unaware of entanglement theory. Finally, we introduce an estimator based on classical shadows that performs better in the big data, few copy regime. Our results show that the naive application of classical machine-learning methods to the quantum setting is problematic, and that a better theoretical foundation of quantum learning is required.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness

We compute the one-loop contributions to spin-averaged generalized parton distributions (GPDs) in the proton from pseudoscalar mesons with intermediate octet and decuplet baryon states at nonzero skewness. Our framework is based on nonlocal covariant chiral effective theory, with ultraviolet divergences regularized by introducing a relativistic regulator derived consistently from the nonlocal Lagrangian. Using the splitting functions calculated from the nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by convoluting with the phenomenological pion GPD and the generalized distribution amplitude, and verify that these satisfy the correct polynomiality properties. We also compute the lowest two moments of GPDs to quantify the meson loop effects on the Dirac, Pauli, and gravitational form factors of the proton.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

First Global Extraction of Generalized Parton Distributions from Experiment and Lattice Data with Next-to-Leading-Order Accuracy

We report the first global extraction of generalized parton distributions, GUMP 1.0, by combining deeply virtual Compton scattering and 𝜌-meson production data from Jefferson Lab and the Hadron-Electron Ring Accelerator with global fits of parton distribution functions, charge form factors, and lattice quantum chromodynamics simulations. Using a conformal moment space parametrization, we achieve a unified description across low- and high-𝑥 regions at next to leading order accuracy in perturbative corrections. The results provide state-of-the-art generalized parton distributions consistent with almost all known facts, enabling three-dimensional nucleon imaging in impact parameter space and, at the same time, establishing a benchmark for future theoretical and experimental studies of the nucleon structure.

Form factors↗

DOE OSTI2024

On the Training and Generalization of Deep Operator Networks

Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.

deep operator networks↗