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DOE OSTI2020

hi_class background evolution, initial conditions and approximation schemes

Cosmological datasets have great potential to elucidate the nature of dark energy and test gravity on the largest scales available to observation. Theoretical predictions can be computed with hi_class (www.hiclass-code.net), an accurate, fast and flexible code for linear cosmology, incorporating a wide range of dark energy theories and modifications to general relativity. We introduce three new functionalities into hi_class: (1) Support for models based on covariant Lagrangians, including a constraint-preserving integration scheme for the background evolution and a series of worked-out examples: Galileon, nKGB, quintessence (monomial, tracker) and Brans-Dicke. (2) Consistent initial conditions for the scalar-field perturbations in the deep radiation era, identifying the conditions under which modified-gravity isocurvature perturbations may grow faster than adiabatic modes leading to a loss of predictivity. (3) An automated quasistatic approximation scheme allowing order-of-magnitude improvement in computing performance without sacrificing accuracy for wide classes of models. These enhancements bring the treatment of dark energy and modified gravity models to the level of detail comparable to software tools restricted to standard $\Lambda$CDM cosmologies. Finally, the hi_class code is publicly available (https://github.com/miguelzuma/hi_class_public), ready to explore current data and prepare for next-generation experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows

Abstract. Wind turbine wake models typically require approximations, such as wake superposition and deflection models, to accurately describe wake physics. However, capturing the phenomena of interest, such as the curled wake and interaction of multiple wakes, in wind power plant flows comes with an increased computational cost. To address this, we propose a new hybrid method that uses analytical solutions with an approximate form of the Reynolds-averaged Navier–Stokes equations to solve the time-averaged flow over a wind plant. We compare results from the solver to supervisory control and data acquisition data from the Lillgrund wind plant obtaining wake model predictions which are generally within 1 standard deviation of the mean power data. We perform simulations of flow over the Columbia River Gorge to demonstrate the capabilities of the model in complex terrain. We also apply the solver to a case with wake steering, which agreed well with large-eddy simulations. This new solver reduces the time – and therefore the related cost – it takes to simulate a steady-state wind plant flow (on the order of seconds using one core). Because the model is computationally efficient, it can also be used for different applications including wake steering for wind power plants and layout optimization.

17 WIND ENERGY↗

DOE OSTI2021

Heuristic methods and performance bounds for photonic design

In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical optimization problem that is computationally difficult to solve globally. Because of this, several heuristic methods have been developed to approximately solve such problems. These methods often produce very good designs, and, in many practical applications, easily outperform ‘traditional’ designs that rely on human intuition. Yet, because these heuristic methods do not guarantee that the approximate solution found is globally optimal, the question remains of just how much better a designer might hope to do. This question is addressed by performance bounds or impossibility results, which determine a performance level that no design can achieve. We focus on algorithmic performance bounds, which involve substantial computation to determine. We illustrate a variety of both heuristic methods and performance bounds on two examples. In these examples (and many others not reported here) the performance bounds show that the heuristic designs are nearly optimal, and can be considered globally optimal in practice. This review serves to clearly set up the photonic design problem and unify existing approaches for calculating performance bounds, while also providing some natural generalizations and properties.

Angeris, Guillermo (ORCID:0000000249503990)↗

DOE OSTI2024

A data-driven sensor placement approach for detecting voltage violations in distribution systems

Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. Here, in this paper, we consider a sensor placement problem which seeks to identify locations for installing sensors that can capture all possible violations of voltage magnitude limits. We formulate a bilevel optimization problem that minimizes the number of sensors and avoids false sensor alarms in the upper level while ensuring detection of any voltage violations in the lower level. This problem is challenging due to the nonlinearity of the power flow equations and the presence of binary variables. Accordingly, we employ recently developed conservative linear approximations of the power flow equations that overestimate or underestimate the voltage magnitudes. By replacing the nonlinear power flow equations with conservative linear approximations, we can ensure that the resulting sensor locations and thresholds are sufficient to identify any constraint violations. Additionally, we apply various problem reformulations to significantly improve computational tractability while simultaneously ensuring an appropriate placement of sensors. Lastly, we improve the quality of the results via an approximate gradient descent method that adjusts the sensor thresholds. We demonstrate the effectiveness of our proposed method for several test cases, including a system with multiple switching configurations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Computational Methods for Multi-Physics Simulation of Melting in Steelmaking

Iron and steel production accounts for approximately 8% of global carbon dioxide (CO) emissions. Pathways to decarbonize include replacing fossil fuels in iron ore reduction and electrifying other steelmaking processes. Iron pellets produced by hydrogen, called Hydrogen Direct Reduced Iron (HDRI), have property differences from those produced using conventional DRI processes. These differences may impact melting in electric arc furnaces (EAF) and other downstream processes. The physical properties of iron pellets vary significantly with temperature during heating, complicating predictions of their behavior. In this project, we seek to develop an integrated simulation, including the fluid flow and convective thermal transport around the pellet particle. We also examine conduction and phase changes within the particle as they impact the melting process. We use adaptive mesh refinement (AMR) to resolve both the changing size of the particle and the complex physics of the interaction between the pellet and the surrounding fluid. We base our simulations on the AMReX-incflo module, which allows large-scale Navier-Stokes simulation while resolving the changing particle size during melting. As we advance our numerical tools, we anticipate an improved understanding of the dynamics of HDRI melting, which will, in turn, accelerate the adoption of low-carbon technologies in the steelmaking industry.

AMReX↗

DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗

DOE OSTI2020

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Watertight Tensor-Product Spline Reconstruction (KCNSC PDRD Technical Report)

The standard for representing geometric models in Computer Aided Design (CAD) systems is boundary representation with trimmed surfaces. However, the approximate nature of surface-surface intersections in CAD systems leaves many small gaps between mating surfaces. These gaps lead to problems for downstream analysis and manufacturing applications, requiring time consuming repair operations and further approximation of the geometry as polygonal meshes, which do not support design iteration. In this study, nVariate, Inc. evaluated its watertight reconstruction technology on a test part. The resulting watertight model has the same absolute model accuracy of the original model zero gaps, providing a representation that requires no repair and supports further design iterations in the CAD system.

42 ENGINEERING↗

DOE OSTI2024

Electroweak scattering at the muon shot

It has long been recognized that the scattering of electroweak particles at very high energies is dominated by vector boson fusion, which probes the origin of electroweak symmetry breaking and offers a unique window into the ultraviolet regime of the Standard Model (SM). Previous studies assume SM-like couplings and rely on the effective W approximation (or electroweak parton distribution), whose validity is well established within the SM but not yet studied in the presence of anomalous Higgs couplings. In this work, we critically examine the electroweak production of two Higgs bosons in the presence of anomalous V V h and V V h h couplings. We compute the corresponding helicity amplitudes and compare the cross section results in the effective W approximation with the full fixed-order calculation. In particular, we identify two distinct classes of anomalous Higgs couplings, whose effects are not captured by vector boson fusion and effective W approximation. Such very-high-energy electroweak scatterings can be probed at the muon shot, a multi-TeV muon collider upon which we base our study, although similar considerations apply to other high-energy colliders. Published by the American Physical Society 2024

Han, Tao↗

DOE OSTI2020

A status review on the thermal stratification modeling methods for Sodium-cooled Fast Reactors

The thermal stratification phenomenon plays a crucial role in the safety of various nuclear systems, including the Gen-III + Light Water Reactors (LWR) and the Gen-IV reactors. The phenomenon is of particular importance for the pool-type Sodium-cooled Fast Reactors (SFRs) because it may cause neutronic and thermal-hydraulic in- stabilities in the reactor core, or lead to damages of both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracking. More significantly, thermal stratification could impede the establishment of the natural circulation during accidental scenarios and introduce uncertainties to the core safety of SFRs. Efforts for modeling of the thermal stratification in SFRs have been made for decades to prevent or mitigate the damage caused by the phenomenon. This paper gives a review of the advances that have been made in recent 10 years on the computational modeling methods for thermal stratification phenomenon in SFRs. These methods can be generally drawn into two categories. The first one is the system-level methods which provide fast-running but approximate calculations, and the second one is the CFD methods which provide high-resolution calculations at high computational expense. Finally, after introducing the efforts that have been made to improve the one- dimensional (1-D) models, the paper envisioned the possible research directions that could be pursued to enhance the modeling of thermal stratification in the near future.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Tensor network simulations of quasi-GPDs in the massive Schwinger model

Generalized parton distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED 2 ), within the Hamiltonian formulation of lattice field theory. Quasidistributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasiparton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Identification and Online Updating of Dynamic Models for Demand Response of an Industrial Air Separation Unit

Demand-response operation of air separation units requires frequent changes in production rate(s), and scheduling calculations must explicitly consider process dynamics to ensure feasibility of the solutions. To this end, scale-bridging models (SBMs) approximate the scheduling-relevant dynamics of a process and its controller in a low-order representation. In contrast to previous works that have employed nonlinear SBMs, this paper proposes linear SBMs, developed using time-series analysis, to facilitate online scheduling computations. Using a year-long industrial dataset, we nd that compact linear SBMs are suitable approximations over typical scheduling horizons, but that their accuracies are unpredictable over time. We introduce a strategy for online updating of the SBMs, based on Kalman ltering schemes for online parameter estimation. The approach greatly improves the accuracy of SBM predictions and will enable the use of linear SBM-based demand-response scheduling in the future.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

PhILMs: Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems

The landscape of computational science and engineering is continually evolving, with the challenge of high-dimensional regression problems standing as a significant hurdle in numerous scientific endeavors. Addressing this challenge, our research, funded by this award, has led to the development of an innovative computational framework known as Probabilistic Partition of Unity Networks (PPOU-Nets). This initiative represents a collaborative effort to harness the potential of mathematics and physics-informed machine learning in tackling multiscale and multiphysics problems prevalent in high-dimensional spaces. Through this work, we have proposed a novel methodology that seamlessly integrates adaptive dimensionality reduction and a mixture of experts model, thereby facilitating a more efficient and accurate approximation of complex functions. This research effort has not only advanced the state of computational science but also opened new avenues for exploration in quantum computing and beyond. This report outlines the motivation, methodology, key findings, and implications of our work, underscoring our contributions to the broader scientific community and the potential pathways for future research.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow

We develop, in this paper, a machine learning approach to optimize the real-time operation of electric power grids. In particular, we learn feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps. The AC OPF problem aims at identifying optimal operational conditions of the power grids that minimize power losses and/or generation costs. Due to the computational challenges with solving this nonconvex problem, many efforts have focused on linearizing or approximating the problem in order to solve the AC OPF on faster timescales. However, many of these approximations can be fairly poor representations of the actual system state and still require solving an optimization problem, which can be time consuming for large networks. In this work, we learn a mapping between the system loading and optimal generation values, enabling us to find near-optimal and feasible AC OPF solutions. This allows us to bypass solving the traditionally nonconvex AC OPF problem, resulting in a significant decrease in computational burden for grid operators.

machine learning↗

DOE OSTI2020

Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow: Preprint

machine learning↗

DOE OSTI2021

Photoluminescence spectra of point defects in semiconductors: Validation of first-principles calculations

Optically and magnetically active point defects in semiconductors are interesting platforms for the development of solid state quantum technologies. Their optical properties are usually probed by measuring photoluminescence spectra, which provide information on excitation energies and on the interaction of electrons with lattice vibrations. We present a combined computational and experimental study of photoluminescence spectra of defects in diamond and SiC, aimed at assessing the validity of theoretical and numerical approximations used in first-principles calculations, including the use of the Franck-Condon principle and the displaced harmonic oscillator approximation. We focus on prototypical examples of solid state qubits, the divacancy centers in SiC and the nitrogen-vacancy in diamond, and we report computed photoluminescence spectra as a function of temperature that are in very good agreement with the measured ones. As expected we find that the use of hybrid functionals leads to more accurate results than semilocal functionals. Interestingly our calculations show that constrained density functional theory (CDFT) and time-dependent hybrid DFT perform equally well in describing the excited state potential energy surface of triplet states; our findings indicate that CDFT, a relatively cheap computational approach, is sufficiently accurate for the calculations of photoluminescence spectra of the defects studied here. Finally, we find that only by correcting for finite-size effects and extrapolating to the dilute limit can one obtain a good agreement between theory and experiment. Our results provide a detailed validation protocol of first-principles calculations of photoluminescence spectra, necessary both for the interpretation of experiments and for robust predictions of the electronic properties of point defects in semiconductors.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation

We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulting hierarchy of discretizations gives rise to a hierarchy of upscaled models, in the sense that they provide approximation in the natural norms (in the mixed setting). This property enables us to utilize them in three applications: (i) as an accurate reduced model, (ii) as a tool in multilevel Monte Carlo simulations (in application to finite volume discretizations), and (iii) for providing a sequence of nonlinear operators in a full approximation scheme for solving nonlinear pressure equations discretized by the conservative two-point flux approximation. Finally, we illustrate the potential of the proposed multilevel technique in all three applications on a number of popular benchmark problems used in reservoir simulation.

multilevel Monte Carlo↗