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DOE OSTI2020

A discrete integral transform for rapid spectral synthesis

Accurate synthetic spectra that rely on large Line-By-Line (LBL)-databases are used in a wide range of applications such as high temperature combustion, atmospheric re-entry, planetary surveillance and laboratory plasmas. Conventionally synthetic spectra are calculated by computing a lineshape for every spectral line in the database and adding those together, which may take multiple hours for large databases. In this paper we propose a new approach for spectral synthesis based on an integral transform: the synthetic spectrum is calculated as the integral over the product of a Voigt profile and a newly proposed three-dimensional “lineshape distribution function”, which is a function of spectral position and Gaussian- & Lorentzian width coordinates. A fast discrete version of this transform based on the Fast Fourier Transform (FFT) is proposed, which improves performance compared to the conventional approach by several orders of magnitude while maintaining accuracy. Strategies that minimize the discretization error are discussed. A Python implementation of the method is compared against state-of-the-art spectral code RADIS, and is since adopted as RADIS's default synthesis method. The synthesis of a benchmark CO2 spectrum consisting of 1.8 M spectral lines and 200k spectral points took only 3.1 s using the proposed method (1011 lines × spectral points/s), a factor ~300 improvement over the state-of-the-art, with the relative improvement generally increasing for higher number of lines and/or number of spectral points. Finally, an experimental GPU-implementation of the method was also benchmarked, which demonstrated another 2~3 orders performance increase, achieving up to 5 ∙ 10 14 lines × spectral points/s.

42 ENGINEERING↗

DOE OSTI2025

Scalable freeform optimization of wide-aperture 3D metalenses by zoned discrete axisymmetry

We introduce a novel framework for design and optimization of 3D freeform metalenses that attains nearly linear scaling of computational cost with diameter, by breaking the lens into a sequence of radial “zones” with 𝑛-fold discrete axisymmetry, where 𝑛 increases with radius. This allows vastly more design freedom than imposing continuous axisymmetry, while avoiding the compromises of the locally periodic approximation (LPA) or scalar diffraction theory. Using a GPU-accelerated finite-difference time-domain (FDTD) solver in cylindrical coordinates, we perform full-wave simulation and topology optimization within each supra-wavelength zone. We validate our approach by designing millimeter and centimeter-scale, poly-achromatic, 3D freeform metalenses which outperform the state of the art. By demonstrating the scalability and resulting optical performance enabled by our “zoned discrete axisymmetry” (ZDA) and supra-wavelength domain decomposition, we highlight the potential of our framework to advance large-scale meta-optics and next-generation photonic technologies.

Sun, Mengdi [Wesleyan University]↗

DOE OSTI2026

From Points to Planes: A Workflow for Converting Three‐Dimensional Point Cloud Data Into Discrete Fracture Network Flow and Transport Models

We present the Point cLoud Algorithm for NEtwork Extraction of Discrete Fracture Networks (PLANE-DFN), a point cloud–based algorithm for automatic fracture network extraction designed to support discrete fracture network (DFN) modeling workflows. PLANE-DFN segments three-dimensional fracture planes from raw point cloud data using RANdom SAmple Consensus coupled with statistical outlier removal and density-based clustering to isolate individual fracture features. Each candidate plane is constrained against site-specific structural constraints based on strike and dip. After segmentation, each fracture is converted into a 2-D convex polygon suitable for meshing and simulation. The PLANE-DFN algorithm is validated by comparing geometric and flow and transport data against data from dfnWorks simulations with ensembles of plane-fit networks. We find that the flow and transport in plane-fit networks are comparable to dfnWorks-generated networks when realistic network geometry is maintained. The PLANE-DFN algorithm provides an automated and streamlined workflow to transform point clouds of data into DFN network geometry.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Realization of two-dimensional discrete time crystals with anisotropic Heisenberg coupling

A discrete time crystal (DTC) is an out-of-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry. Previous studies have been limited to a set of models with Ising-like couplings - and mostly only in one dimension - thus precluding our understanding of the existence (or not) of DTCs in models with more realistic interactions. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. We uncover a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, and identify the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.

Phase transitions and critical phenomena↗

DOE OSTI2021

Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes

Abstract We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.

Physics↗

DOE OSTI2023

Kinetic pathways of fast lithium transport in solid electrolyte interphases with discrete inorganic components

The transport of lithium ions in the solid electrolyte interphase (SEI) has been previously accepted to proceed in two steps: a fast pore diffusion through the outer, porous organic layer followed by a slow knock-off or vacancy diffusion in the inner, dense inorganic layer. The second step is believed to be the rate-limiting step during fast-charging. In this study, we have intentionally constructed a thicker SEI (SEI-rich) structure on the surface of monoclinic Nb 2 O 5 (H-Nb 2 O 5 ) by adding LiNO 3 into a conventional ethylene carbonate based electrolyte. The electrochemical performance of two electrodes, one SEI-rich and one with few SEI (SEI-lean), was found to be almost the same, including their fast-charging capability and cycling stability, despite the significant difference in their SEI structure. Importantly, analysis using cryogenic scanning/transmission electron microscopy showed the discrete decoration of individual inorganic particles (e.g., Li 2 O) and amorphous species (LiN x O y /organic components) over the surface of H-Nb 2 O 5 . These discrete inorganic particles are in contradiction to the formation of dense inner inorganic layer, which has been commonly postulated. Based on these findings, we propose a new mechanism for Li ion transport through the SEI: one-step pore diffusion, without the second step slow diffusion. This one-step pore diffusion process provides an extremely fast Li ion transport, and effectively removes the kinetic limitation of Li ion transport in the SEI for fast charging. Finally, these results strongly suggest that the influence of SEI structure on the transport kinetics of lithium ions is much less significant than previously accepted. These results offer a new understanding of possible lithium ion transport pathway within SEI and may have implications for the future designs of fast-charging battery materials.

25 ENERGY STORAGE↗

DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗

DOE OSTI2021

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

In light of the recently published complete set of statistically correct Grønbech–Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely, the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has at least weak second order accuracy in the applied time step. It further helps identify a novel half-step velocity, which simultaneously produces both correct kinetic statistics and correct transport measures for any of the statistically sound GJ methods. Explicit algorithmic expressions are given for the integration of the new half-step velocity into the GJ set of methods. Finally, numerical simulations, including quantum-based molecular dynamics (QMD) using the QMD suite Los Alamos Transferable Tight-Binding for Energetics, highlight the discussed properties of the algorithms as well as exhibit the direct application of robust, time-step-independent stochastic integrators to QMD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A self-consistent Hamiltonian model of the ponderomotive force and its structure preserving discretization

In the presence of an inhomogeneous oscillatory electric field, charged particles experience a net force, averaged over the oscillatory timescale, known as the ponderomotive force. We derive a one-dimensional Hamiltonian model which self-consistently couples the electromagnetic field to a plasma which experiences the ponderomotive force. We derive a family of structure preserving discretizations of the model of varying order in space and time using conforming and broken finite element exterior calculus spectral element methods. In all variants of our discretization framework, the method is found to conserve the Casimir invariants of the continuous model to machine precision and the energy to the order of the splitting method used.

Physics↗

DOE OSTI2020

Self-compression of laser pulses in a discrete medium

Using the discrete nonlinear Schrödinger equation, we study the laser radiation self-action dynamics in a nanostructured waveguide system. It is shown that for a laser pulse energy exceeding the critical value, the nonlinear evolution of the wave field markedly differs from the corresponding process in a continuous medium. While the pulse propagates in a discrete medium, its length decreases to values comparable to the scale of the structure and the velocity decreases to zero. The system parameters are determined at which the wave field after the laser pulse termination begins to propagate in the opposite direction in a compressed form. The process of slowing down and stopping the pulse is accompanied by strong radiation losses, so that about a third of the energy of the initial field distribution remains in the final compressed state. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Discretized hexagonal boron nitride quantum emitters and their chemical interconversion

Quantum emitters in two-dimensional hexagonal boron nitride (hBN) are of significant interest because of their unique photophysical properties, such as single-photon emission at room temperature, and promising applications in quantum computing and communications. The photoemission from hBN defects covers a wide range of emission energies but identifying and modulating the properties of specific emitters remain challenging due to uncontrolled formation of hBN defects. In this study, more than 2000 spectra are collected consisting of single, isolated zero-phonon lines (ZPLs) between 1.59 and 2.25 eV from diverse sample types. Most of ZPLs are organized into seven discretized emission energies. All emitters exhibit a range of lifetimes from 1 to 6 ns, and phonon sidebands offset by the dominant lattice phonon in hBN near 1370 cm -1 . Two chemical processing schemes are developed based on water and boric acid etching that generate or preferentially interconvert specific emitters, respectively. The identification and chemical interconversion of these discretized emitters should significantly advance the understanding of solid-state chemistry and photophysics of hBN quantum emission.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Gravitational wave signatures from discrete flavor symmetries

Non-Abelian discrete symmetries have been widely used to explain the patterns of lepton masses and flavor mixing. In these models, a given symmetry is assumed at a high scale and then is spontaneously broken by scalars (the flavons), which acquire vacuum expectation values. Typically, the resulting leading order predictions for the oscillation parameters require corrections in order to comply with neutrino oscillation data. Here, we introduce such corrections through an explicit small breaking of the symmetry. This has the advantage of solving the cosmological problems of these models without resorting to inflation. The explicit breaking induces an energy difference or "bias" between different vacua and drives the evolution of the domain walls, unavoidably produced after the symmetry breaking, towards their annihilation. Importantly, the wall annihilation leads to gravitational waves which may be observed in current and/or future experiments. We show that a distinctive pattern of gravitational waves with multiple overlapped peaks is generated when walls annihilate, which is within the reach of future detectors. We also show that cosmic walls from discrete flavor symmetries can be cosmologically safe for any spontaneous breaking scale between 1 and 10 18 GeV, if the bias is chosen adequately, without the need to inflate the walls away. We use as an example a particular A 4 model in which an explicit breaking is included in right-handed neutrino mass terms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Reinforcement learning in discrete action space applied to inverse defect design

Abstract Reinforcement learning (RL) algorithms that include Monte Carlo Tree Search (MCTS) have found tremendous success in computer games such as Go, Shiga and Chess. Such learning algorithms have demonstrated super-human capabilities in navigating through an exhaustive discrete action search space. Motivated by their success in computer games, we demonstrate that RL can be applied to inverse materials design problems. We deploy RL for a representative case of the optimal atomic scale inverse design of extended defects via rearrangement of chalcogen (e.g. S) vacancies in 2D transition metal dichalcogenides (e.g. MoS 2 ). These defect rearrangements and their dynamics are important from the perspective of tunable phase transition in 2D materials i.e. 2H (semi-conducting) to 1T (metallic) in MoS 2 . We demonstrate the ability of MCTS interfaced with a reactive molecular dynamics simulator to efficiently sample the defect phase space and perform inverse design—starting from randomly distributed S vacancies, the optimal defect rearrangement of defects corresponds a line defect of S vacancies. We compare MCTS performance with evolutionary optimization i.e. genetic algorithms and show that MCTS converges to a better optimal solution (lower objective) and in fewer evaluations compared to GA. We also comprehensively evaluate and discuss the effect of MCTS hyperparameters on the convergence to solution. Overall, our study demonstrates the effectives of using RL approaches that operate in discrete action space for inverse defect design problems.

42 ENGINEERING↗

DOE OSTI2021

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Dark Energy Survey Year 3 results: marginalization over redshift distribution uncertainties using ranking of discrete realizations

ABSTRACT Cosmological information from weak lensing surveys is maximized by sorting source galaxies into tomographic redshift subsamples. Any uncertainties on these redshift distributions must be correctly propagated into the cosmological results. We present hyperrank, a new method for marginalizing over redshift distribution uncertainties, using discrete samples from the space of all possible redshift distributions, improving over simple parametrized models. In hyperrank, the set of proposed redshift distributions is ranked according to a small (between one and four) number of summary values, which are then sampled, along with other nuisance parameters and cosmological parameters in the Monte Carlo chain used for inference. This approach can be regarded as a general method for marginalizing over discrete realizations of data vector variation with nuisance parameters, which can consequently be sampled separately from the main parameters of interest, allowing for increased computational efficiency. We focus on the case of weak lensing cosmic shear analyses and demonstrate our method using simulations made for the Dark Energy Survey (DES). We show that the method can correctly and efficiently marginalize over a wide range of models for the redshift distribution uncertainty. Finally, we compare hyperrank to the common mean-shifting method of marginalizing over redshift uncertainty, validating that this simpler model is sufficient for use in the DES Year 3 cosmology results presented in companion papers.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Gauge constrained algorithm of variational discrete action theory at N = 3 for the multiorbital Hubbard model

The recently developed variational discrete action theory (VDAT) provides a systematic variational approach to the ground state of the quantum many-body problem, where the quality of the solution is controlled by an integer N, and increasing N monotonically approaches the exact solution. VDAT can be exactly evaluated in the d = ∞ multiorbital Hubbard model using the self-consistent canonical discrete action theory (SCDA), which requires a self-consistency condition for the integer time Green's functions. Previous work demonstrates that N = 3 accurately captures multiorbital Mott/Hund physics at a cost similar to the Gutzwiller approximation. Here we employ a gauge constraint to automatically satisfy the self-consistency condition of the SCDA at N = 3, yielding an even more efficient algorithm with enhanced numerical stability. We derive closed form expressions of the gauge constrained algorithm for the multiorbital Hubbard model with general density-density interactions, allowing VDAT at N = 3 to be straightforwardly applied to the seven-orbital Hubbard model. We present results and a performance analysis using N = 2 and N = 3 for the SU⁡(2⁢N orb ) Hubbard model in d = ∞ with N orb = 2–8, and compare to numerically exact dynamical mean-field theory solutions where available. Finally, the developments in this work will greatly facilitate the application of VDAT at N = 3 to strongly correlated electron materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Discrete gravity with local Lorentz invariance

A novel structure-preserving algorithm for general relativity in vacuum is derived from a lattice gauge theoretic discretization of the tetradic Palatini action. Here, the resulting model of discrete gravity is demonstrated to preserve local Lorentz invariance and symplectic structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗