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DOE OSTI2021

A review of ptychographic techniques for ultrashort pulse measurement

The measurement of optical ultrafast laser pulses is done indirectly because the required bandwidth to measure these pulses exceeds the bandwidth of current electronics. As a result, this measurement problem is often posed as a 1-D phase retrieval problem, which is fraught with ambiguities. The phase retrieval method known as ptychography solves this problem by making it possible to measure ultrafast pulses in either the time domain or the frequency domain. One well known algorithm is the principal components generalized projections algorithm (PCGPA) for extracting pulses from Frequency-Resolved Optical Gating (FROG) measurements. In this work, we discuss the development of the PCPGA and introduce new developments including an operator formalism that allows for the convenient addition of external constraints and the development of more robust algorithms. A close cousin, the ptychographic iterative engine will also be covered and compared to the PCGPA. Additional developments using other algorithmic strategies will also be discussed along with new developments combining optics and high-speed electronics to achieve megahertz measurement rates.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Ethane and methane at high pressures: Structure and stability

We have performed a combined experimental and theoretical study of ethane and methane at high pressures of up to 120 GPa at 300 K using x-ray diffraction and Raman spectroscopies and the USPEX ab initio evolutionary structural search algorithm, respectively. For ethane, we have determined the crystallization point, for room temperature, at 2.7 GPa and also the low pressure crystal structure (phase A). This crystal structure is orientationally disordered (plastic phase) and deviates from the known crystal structures for ethane at low temperatures. Moreover, a pressure induced phase transition has been identified, for the first time, at 13.6 GPa to a monoclinic phase B, the structure of which is solved based on good agreement with the experimental results and theoretical predictions. For methane, our x-ray diffraction measurements are in agreement with the previously reported high-pressure structures and equation of state (EOS). Finally, we have determined the EOSs of ethane and methane, which provides a solid basis for the discussion of their relative stability at high pressures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely determine the semi-discrete source. This means the observed area can be extremely small, and that is the reason we call it sparse boundary data. For the numerical reconstruction, we formulate the problem from the Bayesian sequential prediction perspective and conduct the numerical examples which estimate the space-time-dependent source state by state. To better demonstrate the method’s performance, we solve two common multiscale problems from two models with a long source sequence. The numerical results illustrate that the inversion is accurate and efficient.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Noise dynamics of quantum annealers: estimating the effective noise using idle qubits

Quantum annealing is a type of analog computation that aims to use quantum mechanical fluctuations in search of optimal solutions of QUBO (quadratic unconstrained binary optimization) or, equivalently, Ising problems. Since NP-hard problems can in general be mapped to Ising and QUBO formulations, the quantum annealing paradigm has the potential to help solve various NP-hard problems. Current quantum annealers, such as those manufactured by D-Wave Systems, Inc. have various practical limitations including the size (number of qubits) of the problem that can be solved, the qubit connectivity, and error due to the environment or system calibration, which can reduce the quality of the solutions. Typically, for an arbitrary problem instance, the corresponding QUBO (or Ising) structure will not natively embed onto the available qubit architecture on the quantum chip. Thus, in these cases, a minor embedding of the problem structure onto the device is necessary. However, minor embeddings on these devices do not always make use of the full sparse chip hardware graph, and a large portion of the available qubits stay unused during quantum annealing. In this work, we embed a disjoint random QUBO on the unused parts of the chip alongside the QUBO to be solved, which acts as an indicator of the solution quality of the device over time. Using experiments on three different D-Wave quantum annealers, we demonstrate that (i) long term trends in solution quality exist on the D-Wave device, and (ii) the unused qubits can be used to measure the current level of noise of the quantum system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

nnopf

SAND2026-19433O The nnopf tool addresses the optimal power flow (OPF) problem by optimizing electricity delivery from generating plants to consumers. At the same time, it minimizes costs and adheres to power grid constraints. While traditional methods for solving OPF can be computationally intensive, the tool mitigates this challenge by training neural networks on power grids to predict optimal solutions for the OPF problem. 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.

Hart, William [Sandia National Lab. (SNL-CA), Live↗

DOE OSTI2021

Orbital Conflict: Cutting Planes for Symmetric Integer Programs

Cutting planes have been an important factor in the impressive progress made by integer programming (IP) solvers in the past two decades. However, cutting planes have had little impact on improving performance for symmetric IPs. Rather, the main breakthroughs for solving symmetric IPs have been achieved by cleverly exploiting symmetry in the enumeration phase of branch and bound. In this work, we introduce a hierarchy of cutting planes that arise from a reinterpretation of symmetry-exploiting branching methods. There are too many inequalities in the hierarchy to be used efficiently in a direct manner. However, the lowest levels of this cutting-plane hierarchy can be implicitly exploited by enhancing the conflict graph of the integer programming instance and by generating inequalities such as clique cuts valid for the stable set relaxation of the instance. We provide computational evidence that the resulting symmetry-powered clique cuts can improve state-of-the-art symmetry-exploiting methods. Furthermore, the inequalities are then employed in a two-phase approach with high-throughput computations to solve heretofore unsolved symmetric integer programs arising from covering designs, establishing for the first time the covering radii of two binary-ternary codes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Hydrodynamic instabilities and heat transfer characteristics in the duct flow of a fluid in the supercritical thermodynamic regime

The behavior of fluids at supercritical thermodynamic conditions is inherently complex due to large variations in thermodynamic and transport properties. Recent numerical and experimental investigations illustrate ongoing interest for these fluids, especially supercritical CO 2 and supercritical water, for a variety of applications. For example, supercritical water reactors (SCWR) operate in this extreme condition of high-pressure and temperature, resulting in highly dynamic flow fields and unexpected heat transfer regimes. The potential heat transfer benefits in this regime are directly associated with the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. This work characterizes the hydrodynamic instabilities that arise for fluids at supercritical thermodynamic conditions when buoyancy forces are significant. Two specific configurations are considered, a natural convection cavity flow, and a mixed convection, heated, horizontal channel flow. Natural convection flow in a cavity is a classical configuration with expected behavior below the critical point. This configuration aids in characterizing the effect of the variable properties in the supercritical thermodynamic regime. Further, limited studies in the existing literature have been conducted for low-Reynolds and intermediate-Rayleigh numbers, mixed-convection channel flows for supercritical water, which is the focus of the channel flow configuration. To investigate the thermally driven hydrodynamic instabilities in this regime, a high-order fully-implicit numerical method is used. Such strong variations in thermophysical properties (in particular, density) are difficult to simulate and an altogether compressible framework is needed. Therefore, the compressible Navier-Stokes equations are solved without any additional assumptions. The fully implicit, high-order in space and time, reconstructed discontinuous Galerkin method as implemented within the multi-physics code called ALE3D (Arbitrary Lagrangian and Eulerian in 2D and 3D), developed at Lawrence Livermore National Laboratory (LLNL), is used. This fully implicit, L-stable method accurately captures the compressible nature of the ow in the limit of very low Mach number. It has been widely accepted that above the critical point, only one phase is observed. However, recent research has indicated the existence of the distinct gas-like and liquid-like regions separated by the Widom line, the locus of the maxima of the specific heat. Along the Widom line, density decreases 6-fold, viscosity drops by a factor of 2, while specific heat spikes by an order of magnitude. These variations, specifically in density and viscosity, produce a thick pseudo-interface and flow dynamics behavior akin to film boiling. A pseudo-film at the heated wall of the cavity and the horizontal channel is observed where buoyancy forces induce mixing through the specific configurations. Further the local Rayleigh and Richardson numbers provide maps of the flow field and the buoyancy forces driving the microscopic mixing. In the first chapter, I describe a background of supercritical fluid and the various applications. The second chapter focuses on the mathematical model and numerical method used for simulations, where a description of the equation of state for supercritical water is described. The third chapter focuses on the natural convection cavity with a heated bottom wall. In this cavity a gas-like and a liquid-like flow within the supercritical thermodynamic regime are observed. The fourth chapter focuses on a forced convection, horizontal channel, distinguishing between the gas-like, liquid-like, and mixed flow regimes. Mixed convection flow, with the addition of gravitational forces in the horizontal channel show the influence of variable properties on the hydrodynamic development, heat transfer, and rising instabilities. The last chapter of this research focuses on characterizing the unstable hydrodynamics through time-averaging processes and analysis of the movement of energy through the developing plumes.

42 ENGINEERING↗

DOE OSTI2022

Deep Learning At Depth: Estimating subsurface parameters from geophysical monitoring data

Geophysical imaging techniques are a non-invasive way to image the subsurface and understand both subsurface solid (rock/soil) and fluid property distributions and their evolution in time. Inversions of the geophysical data, such as Electrical Resistance Tomography (ERT) data, are solved to estimate the subsurface property distributions, such as conductivity, and many inversion techniques smooth out sharp gradients in rock or fluid property distributions. Sharp gradients in subsurface properties tend to be present in situations with complex subsurface structures, which are common in many subsurface applications. We have successfully demonstrated that it is possible to inform, or constrain, inversions with neural networks trained on synthetic data with complex subsurface structures. Initial results suggest this process may be optimizable to yield property distributions that better represent the true property distributions than the same inversion process without the neural network constraint. Future work would optimize the neural network performance for this application and then apply the synthetic-data trained neural network to real data to understand the utility and performance of this technique for real data sets.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

What Does the Milky Way Look Like?

In spite of much work, the overall spiral structure morphology of the Milky Way remains somewhat uncertain. In the last two decades, accurate distance measurements have provided us with an opportunity to solve this issue. Using the precise locations of very young objects, for the first time, we propose that our galaxy has a multiple-arm morphology that consists of two-arm symmetry (the Perseus and Norma Arms) in the inner parts and that extends to the outer parts, where there are several long, irregular arms (the Centaurus, Sagittarius, Carina, Outer, and Local Arms).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Enabling Real-Time Communication in Multi-Agent Systems: A Graph Neural Network Based Approach

Global connectivity enables effective coordination in Multi-Agent Systems (MAS). Solving these connection problems under hardware constraints is an NP-hard non-Euclidean Degree Constrained Minimum Spanning Tree (DCMST) problem. Prior MAS controllers coordinate team movement for task completion and collision avoidance; some considering Line-of-Sight (LOS) maintenance but prioritizing flexibility over guarantees. Evolutionary Algorithms (EA) have been shown to find good solutions for DCMST, but their performance degrades with larger populations required to support a large MAS. We present a method based on edge graph attention networks, trained offline to reduce online computation times. Empirical comparisons with greedy polynomial-time solvers and EA show that our method leverages latent graph information to consistently find constraint-satisfying solutions in less time.

connectivity maintenance↗

DOE OSTI2026

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Time correlations from steady-state expectation values

Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.

Górecki, Wojciech [INFN, Pavia]↗

DOE OSTI2025

Time correlations from steady-state expectation values

Górecki, Wojciech [INFN, Pavia]↗

DOE OSTI2024

ARPA-E Grid Optimization (GO) Competition Challenge 3

Synthetic Input Data and Team Results for the GO Competition Challenge 3 for Events 1 - 4 and the Sandbox, along with problem and format descriptions and code to validate data and solutions, are available here. Data for industry scenarios will not be made public. The Grid Optimization (GO) Competition Challenge 3 focused on the security-constrained optimal power flow (SCOPF) problem. It is part of a continuing effort begun with Challenges 1 and 2, to successfully discover, develop, and test innovative and disruptive software solutions for critical energy challenges and to overcome existing barriers. The broader goal of the of the GO Competition is to accelerate the development of transformational and disruptive methods for solving problems related to the electric power grid and to provide a transparent, fair, and comprehensive evaluation of new solution methods. Challenge 3 used multiperiod dynamic markets, including advisory models for extreme weather events, day-ahead markets, and the real-time markets with an extended look-ahead. In Event 4, whose submission window was August 31-September 4, 2023, 14 teams solved for the objective values of 669 scenarios (39 scenarios required solutions both with and without line switching being allowed). The 591 synthetic scenarios from 9 network models (3.6 GB) are available here. Ten teams were funded to participate and 7 won prizes totaling $2,400,000. The largest prize ($550,000) went to Mississippi State University. An additional $600,000 was awarded in Event 3 (6/15-16/2023). No prizes were awarded in Events 1 (1/25-27/2023) or 2 (4/13-14/2023). For more information on the competition and challenge see the "GO Competition Challenge 3 Information" resource below.

ACOPF↗

DOE OSTI2020

Particle-number distribution in large fluctuations at the tip of branching random walks

Here, we investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times t , focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected position, but still within a distance smaller than the diffusion radius ~$\sqrt{t}$. Our approach consists in a study of the generating function $G_{Δx}(λ) = Σ_n$ ${λ^n}p_n(Δx)$ for the probabilities $p_n(Δx)$ of observing $\textit{n}$ particles in an interval of given size $Δ\textit{x}$ from the lead particle to its left, fixing the position of the latter. This generating function can be expressed with the help of functions solving the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation with suitable initial conditions. In the infinite-time and large-$Δ\textit{x}$ limits, we find that the mean number of particles in the interval grows exponentially with $Δ\textit{x}$, and that the generating function obeys a nontrivial scaling law, depending on $Δ\textit{x}$ and λ through the combined variable $[Δx — f(λ)]^3 / Δx^2$, where $\textit{f}$(λ) ≡ – ln(1 – λ) – ln [– ln(1 – λ)]. From this property, one may conjecture that the growth of the typical particle number with the size of the interval is slower than exponential, but, surprisingly enough, only by a subleading factor at large Δ$\textit{x}$. The scaling we argue is consistent with results from a numerical integration of the FKPP equation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Production of neutron-rich heavy nuclei in deep-inelastic 208 Pb + 208 Pb collisions within the stochastic mean-field theory

In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗