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DOE OSTI2025

Towards a Robust Adaptive Digital Twin for Fusion Applications

The development of a digital twin system for fusion applications is essential for enhancing the prediction, analysis, and optimization of complex plasma processes. Machine learning (ML), particularly deep learning has demonstrated strong capabilities in modeling such highly nonlinear and intricate systems. However, two critical challenges limit the deployment of deep learning-based digital twins: Uncertainty Quantification (UQ) and data drift. UQ is vital for ensuring trustworthy predictions, especially in decision-support scenarios. Additionally, data-driven models are often sensitive to changes in the underlying data distribution, such as shot-to-shot variations in fusion experiments, which can lead to performance degradation over time. To address these challenges, we are developing an uncertainty-aware, adaptive digital twin framework. Our approach incorporates deep learning models enhanced with Gaussian Process approximations for predictive uncertainty estimation, coupled with an online learning mechanism that enables continuous model adaptation to new experimental data. This adaptive capability allows the data driven models to respond effectively to evolving plasma behaviors and equipment conditions. Specifically, to mitigate the effects of shot-to-shot drift, our system updates itself incrementally as new data becomes available, improving both robustness and fidelity. Our vision is to evolve this data driven model into a self-sustaining digital twin system that leverages UQ based feedback to continuously refine itself and potentially support real-time decision making. This presentation will cover a brief background on uncertainty quantification for ML, our ongoing effort on development of UQ capabilities for ML, our data science pipeline from data collection to model development and analysis and online learning framework for modeling coil deflection at DIII-D. I will also briefly touch upon opportunities and challenges in development of digital twin framework.

Sammuli, Brian [General Atomics]↗

DOE OSTI2017

Closing the scale gap between land surface parameterizations and GCMs with a new scheme, SiB3-Bins: SOIL MOISTURE SCALE GAP

The interaction of land with the atmosphere is sensitive to soil moisture (W). Evapotranspiration (ET) reacts to soil moisture in a nonlinear way, f(W), as soils dry from saturation to wilt point. This nonlinear behavior and the fact that soil moisture varies on scales as small as 1–10 m in nature, while numerical general circulation models (GCMs) have grid cell sizes on the order of 1 to 100s of kilometers, makes the calculation of grid cell-average ET problematic. It is impractical to simulate the land in GCMs on the small scales seen in nature, so techniques have been developed to represent subgrid scale heterogeneity, including: (1) statistical-dynamical representations of grid subelements of varying wetness, (2) relaxation of f(W), (3) moderating f(W) with approximations of catchment hydrology, (4) “tiling” the landscape into vegetation types, and (5) hyperresolution. Here we present an alternative method for representing subgrid variability in W, one proven in a conceptual framework where landscape-scale W is represented as a series of “Bins” of increasing wetness from dry to saturated. The grid cell-level f(W) is defined by the integral of the fractional area of the wetness bins and the value of f(W) associated with each. This approach accounts for the spatiotemporal dynamics of W. We implemented this approach in the SiB3 land surface parameterization and then evaluated its performance against a control, which assumes a horizontally uniform field of W. We demonstrate that the Bins method, with a physical basis, attenuates unrealistic jumps in model state and ET seen in the control runs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Network-Cognizant Model Reduction of Grid-Tied Three-Phase Inverters

Power-electronics inverters are expected to satisfy a significant fraction of system load in next-generation power networks with the growing integration of renewable resources and flexible loads. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. In our previous work, we have shown that a system of parallel-connected grid-tied three-phase inverters can be modeled as one aggregated inverter unit with the same structure and state-space dimension as any individual inverter in the system. Here, we extend this result to networks with arbitrary topologies by leveraging a classical aggregation method for coherent synchronous generators in transmission networks, and a linear approximation of the AC power-flow equations to ease computational burden. Numerical simulation results for a prototypical distribution feeder demonstrate the accuracy and computational benefits of the approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2017

Optimal Power Flow of Radial Networks and Its Variations: A Sequential Convex Optimization Approach

This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the e-constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method.

bi-objective optimization↗

DOE OSTI2015

Exactly solvable model of resonance tunneling of an electromagnetic wave in plasma containing short-scale inhomogeneities

Different variants of resonance tunneling of a transverse electromagnetic wave through a plasma layer containing short-scale (subwavelength) inhomogeneities, including evanescence regions to which approximate methods are inapplicable, are analyzed in the framework of an exactly solvable one-dimensional model. Complex plasma density profiles described by a number of free parameters determining the permittivity modulation depth, the characteristic scale lengths of plasma structures, their number, and the thickness of the inhomogeneous plasma layer are considered. It is demonstrated that reflection-free propagation of the wave incident on the layer from vacuum (the effect of wave-barrier transillumination) can be achieved for various sets of such structures, including plasma density profiles containing a stochastic component. Taking into account cubic nonlinearity, it is also possible to obtain an exact solution to the one-dimensional problem on the nonlinear transillumination of nonuniform plasma. In this case, the thicknesses of the evanescence regions decrease appreciably. The problem of resonance tunneling of electromagnetic waves through such barriers is of interest for a number of practical applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Global Simulations of Gravitational Instability in Protostellar Disks with Full Radiation Transport. II. Locality of Gravitoturbulence, Clumpy Spirals, and Implications for Observable Substructure

Spiral perturbations in a gravitationally unstable accretion disk regulate disk evolution through angular momentum transport and heating and provide an observational signature of gravitational instability (GI). We use global 3D simulations to systematically characterize and understand these spiral perturbations. The spiral perturbations and the resulting transport are overall insensitive to the cooling type, with the exception that radiative cooling, especially in the optically thick regime, reduces the amplitude of temperature perturbations. Spiral perturbations are localized around corotation, allowing transport to be approximated by a local α viscosity to zeroth order in aspect ratio (H/R), but only after averaging over multiple orbits in time and/or multiple scale heights in space. Meanwhile, large-amplitude perturbations from strong gravitoturbulence can cause $\mathcal{O}$(α 1/2 ) deviation in the cooling rate of the disk. We develop empirical prescriptions for the angular momentum transport, heating, and cooling in a gravitoturbulent disk that capture the deviation from a viscous, unperturbed disk to first order in H/R and α 1/2 . The spiral perturbations in saturated gravitoturbulence are clumpy, with dense clumps forming through the nonlinear coupling between multiple modes at different m. Observationally, the clumpy gravitoturbulence produced by saturated GI can be mistaken with observational noise or embedded companions, especially under finite resolution. Meanwhile, grand-design spirals with m-fold symmetry may be uncommon among disks in saturated gravitoturbulence, and we speculate that they may instead be a signature of recently triggered or decaying GI.

Gravitational instability↗

DOE OSTI2015

Structural and optical properties of cobalt slanted nanopillars conformally coated with few-layer graphene

Optical characterization of anisotropic multicomponent nanostructures is generally not a trivial task, since the relation between a material's structural properties and its permittivity tensor is nonlinear. In this regard, an array of slanted cobalt nanopillars that are conformally coated with few-layer graphene is a particularly challenging object for optical characterization, as it has a complex anisotropic geometry and comprises several materials with different topologies and filling fractions. Normally, a detailed characterization of such complex nanostructures would require a combination of several microscopic and spectroscopic techniques. In this letter, we demonstrate that the important structural parameters of these graphene-coated sculptured thin films can be determined using a fast and simple generalized spectroscopic ellipsometry test combined with an anisotropic Bruggeman effective medium approximation. The graphene coverage as well as structural parameters of nanostructured thin films agree excellently with electron microscopy and Raman spectroscopy observations. The demonstrated optical approach may also be applied to the characterization of other nanostructured materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange

In this report, electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact exchange or hybrid functionals are associated with large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Though orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use gradient expansion of the kinetic energy, nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C 4 H 2 , C 4 N 2 and C 3 O 2 . We show that by using data from model one-dimensional KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems as well as electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

A path to practical Solar Pumped Lasers via Radiative Energy Transfer

The optical conversion of incoherent solar radiation into a bright, coherent laser beam enables the application of nonlinear optics to solar energy conversion and storage. Here, we present an architecture for solar pumped lasers that uses a luminescent solar concentrator to decouple the conventional trade-off between solar absorption efficiency and the mode volume of the optical gain material. We report a 750-μm-thick Nd 3+ -doped YAG planar waveguide sensitized by a luminescent CdSe/CdZnS (core/shell) colloidal nanocrystal, yielding a peak cascade energy transfer of 14%, a broad spectral response in the visible portion of the solar spectrum, and an equivalent quasi-CW solar lasing threshold of 23 W-cm -2 , or approximately 230 suns. The efficient coupling of incoherent, spectrally broad sunlight in small gain volumes should allow the generation of coherent laser light from intensities of less than 100 suns.

14 SOLAR ENERGY↗

DOE OSTI2016

Global kinetic ballooning mode simulations in BOUT++

We report on simulation results of a 3+1 gyro-Landau-fluid (GLF) model in BOUT++ framework, which contributes to increasing the physics understanding of the edge turbulence. We find that there is no second stability region of kinetic ballooning modes (KBM) in the concentric circular geometry. The first unstable β of KBM decreases below the ideal ballooning mode threshold with increasing ${{\eta}_{i}}$. In order to study the KBM in the real tokamak equilibrium, we find that the approximation of shifted circular geometry ($\beta \ll {{\varepsilon}^{2}}$ ) is not valid for a high β global equilibrium near the second stability region of KBM. Thus we generate a series of real equilibria from a global equilibrium solver CORSICA, including both Shafranov shift and elongation effects, but not including bootstrap current. In these real equilibria, the second stability region of KBM are observed in our global linear simulations. The most unstable mode for different β are the same while the mode number spectrum near the second stability region is wider than the case near the first stability region. Here, the nonlinear simulations show that the energy loss of an ELM keeps increasing with β, because the linear drive of the turbulence remains strong for the case near the second stability region during profile evolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Hysteretic Superconducting Heat-Flux Quantum Modulator

In this work, we discuss heat transport in a thermally biased superconducting quantum-interference device (SQUID) in the presence of an external magnetic flux, when a non-negligible inductance of the SQUID ring is taken into account. A properly sweeping driving flux causes the thermal current to modulate and behave hysteretically. The response of this device is analyzed as a function of both the hysteresis parameter and the degree of asymmetry of the SQUID, highlighting the parameter range over which hysteretic behavior is observable. Markedly, the temperature of the SQUID also shows hysteretic evolution, with sharp transitions characterized by temperature jumps up to, e.g., approximately 0.02 K for a realistic Al-based setup. In view of these results, the proposed device can effectively find an application as a temperature-based superconducting memory element, working even at gigahertz frequencies by suitably choosing the superconductor on which the device is based.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Spontaneous magnon decays from nonrelativistic time-reversal symmetry breaking in altermagnets

Quasiparticles are central to condensed matter physics, but their stability can be undermined by quantum many-body interactions. Magnons, i.e., quasiparticles in quantum magnets, are particularly intriguing because their properties are governed by both real and spin space. While crystal symmetries may be low, spin interactions often remain approximately isotropic, limiting spontaneous magnon decay. Textbook wisdom holds that collinear Heisenberg magnets follow a dichotomy: ferromagnets host stable magnons, while antiferromagnetic magnons may decay depending on dispersion curvature. Up to now, relativistic spin-orbit coupling and noncollinear order that connect spin space to real space were shown to introduce more complex magnon instability mechanisms. Here, we show that even in nonrelativistic isotropic collinear systems, this conventional dichotomy is disrupted in altermagnets. Altermagnets, a newly identified class of collinear magnets, exhibit compensated spin order with nonrelativistic time-reversal symmetry breaking and even-parity band splitting. Using kinematic analysis, nonlinear spin-wave theory, and quantum simulations, we reveal that even weak band splitting opens a decay phase space, driving quasiparticle breakdown. Additionally, 𝑑-wave altermagnets form a rare “island of stability” at the Brillouin-zone center. Furthermore, our findings establish a quasiparticle stability trichotomy in collinear Heisenberg magnets and position altermagnets as a promising platform for unconventional spin dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

A fully coupled two-level Schwarz preconditioner based on smoothed aggregation for the transient multigroup neutron diffusion equations

The neutron multigroup diffusion equations is an important approximation of the neutron transport equation, and has been widely used for studying the motion of neutrons and their interactions with the stationary background materials. Solving the multigroup diffusion equations faces challenging because many variables are coupled together and a lot of computing resources are required. In this paper, we focus on the development of a scalable parallel algorithm framework for the system of equations arising from the discretization of the multigroup diffusion equations using a finite element method in space and using an implicit scheme in time. The parallel agorithm framweork consists of an inexact Jacobian-free Newton for the nonlinear equations, a Krylov subspace method for the Jacobian system and a parallel Schwarz preconditioner for the acceleration of the algorithm convergence. A coarse space based on smoothed aggregation is introduced to construct a two-level method to improve the parallel performance of the Schwarz preconditioner. We numerically shown that compared with the one-level method, the proposed two-level method works significantly better in terms of the number of linear iterations and the compute time for a system of equations with millions of unknowns and a supercomputer with thousands of processors.

97 MATHEMATICS AND COMPUTING↗

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 OSTI2016

A mathematical and numerical framework for the analysis of compressible thermal convection in gases at very high temperatures

The relevance of non-equilibrium phenomena, nonlinear behavior, gravitational effects and fluid compressibility in a wide range of problems related to high-temperature gas-dynamics, especially in thermal, mechanical and nuclear engineering, calls for a concerted approach using the tools of the kinetic theory of gases, statistical physics, quantum mechanics, thermodynamics and mathematical modeling in synergy with advanced numerical strategies for the solution of the Navier–Stokes equations. The reason behind such a need is that in many instances of relevance in this field one witnesses a departure from canonical models and the resulting inadequacy of standard CFD approaches, especially those traditionally used to deal with thermal (buoyancy) convection problems. Starting from microscopic considerations and typical concepts of molecular dynamics, passing through the Boltzmann equation and its known solutions, we show how it is possible to remove past assumptions and elaborate an algorithm capable of targeting the broadest range of applications. Moving beyond the Boussinesq approximation, the Sutherland law and the principle of energy equipartition, the resulting method allows most of the fluid properties (density, viscosity, thermal conductivity, heat capacity and diffusivity, etc.) to be derived in a rational and natural way while keeping empirical contamination to the minimum. Special attention is deserved as well to the well-known pressure issue. With the application of the socalled multiple pressure variables concept and a projection-like numerical approach, difficulties with such a term in the momentum equation are circumvented by allowing the hydrodynamic pressure to decouple from its thermodynamic counterpart. The final result is a flexible and modular framework that on the one hand is able to account for all the molecule (translational, rotational and vibrational) degrees of freedom and their effective excitation, and on the other hand can guarantee adequate interplay between molecular and macroscopic-level entities and processes. Performances are demonstrated by computing some incompressible and compressible benchmark test cases for thermal (gravitational) convection, which are then extended to the high-temperature regime taking advantage of the newly developed features.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Central Compact Finite‐Difference Scheme With High Spectral Resolution for KdV Equation

This work presents a combination of cell‐node and cell‐centered compact finite difference scheme for the approximation of third derivatives involved in Korteweg–de Vries (KdV) equations. This approach employs a half‐shifted derivative construction at cell centers, avoiding the need for compact interpolation, thereby removing transfer errors; hence, it improves spectral resolution and maintains high‐order accuracy. Fourier analysis is performed to show the spectral properties of the proposed formulation, which provides higher spectral resolutions as compared to node‐based compact schemes. A filtering strategy is incorporated to suppress high‐frequency oscillations without compromising the accuracy of the numerical scheme, and the total variation diminishing Runge Kutta (TVDRK3) method is applied for time integration. Numerical experiments on linear, nonlinear, and coupled KdV systems are conducted, and a comparative analysis with cell‐node compact schemes confirms that the proposed scheme consistently reduces errors by up to an order of magnitude and achieves high spectral resolution properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Projection-based multifidelity linear regression for data-scarce applications

Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear regression approaches with linear and nonlinear features that leverage principal component basis vectors for dimensionality reduction and combine multifidelity data through: (i) a direct data augmentation using low-fidelity data, and (ii) a data augmentation incorporating explicit linear corrections between low-fidelity and high-fidelity data. The data augmentation approaches combine high-fidelity and low-fidelity data into a unified training set and train the linear regression model through weighted least squares with fidelity-specific weights. We introduce a proximity-based weighting scheme with automatic weight selection strategy through cross-validation. Here, the proposed multifidelity linear regression methods are demonstrated on approximating the surface pressure field of a hypersonic vehicle in flight and the temperature field on an aircraft disc braking system. In an ultra low-data regime of no more than twelve high-fidelity samples, multifidelity linear regression achieves approximately 2% – 12% improvement in median accuracy and a higher R 2 score relative to single-fidelity methods at comparable computational cost.

data augmentation↗

DOE OSTI2018

Wilson Prize article: Reflections on our experiences with developing the theory of intrabeam scattering

We discuss our experiences with developing detailed theoretical descriptions of intrabeam scattering in particle accelerators. We focus on the historical importance of understanding intrabeam scattering for the successful operation of a variety of accelerators around the world. In doing so, we highlight the fact that the theoretical understanding of intrabeam scattering played a crucial role in the discovery of the top quark at Fermilab, intermediate vector bosons W ± , Z and the Higgs particle at CERN, and the perfect liquid quark-gluon plasma at Brookhaven’s Relativistic Heavy Ion Collider. We describe several useful high energy approximations to intrabeam scattering, including those that utilize a Modified Piwinski high energy approximation by Karl Bane that has gained wide usage in applications to electron damping rings and advanced light sources. Finally, we comment on the fact that a detailed understanding of intrabeam scattering at synchrotron-based advanced light sources is empowering many transformational discoveries in a myriad of disciplines.

43 PARTICLE ACCELERATORS↗