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DOE OSTI2025

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multidimensional) puzzle tiles. The independent variables for the evolution equations (their “space” and “time”) as well as their effective parameters are all emergent , i.e. determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based questionnaire approach to build a smooth parametrization of our emergent space/time/parameter space for the data. This approach iteratively processes the data by successively observing them on the “space,” the “time” and the “parameter” axes of a tensor. Once the data become organized, we use machine learning (here, neural networks) to approximate the operators governing the evolution equations in this emergent space. Our illustrative examples are based (i) on a simple advection–diffusion model; (ii) on a previously developed vertex-plus-signaling model of Drosophila embryonic development; and (iii) on two complex dynamic network models (one neuronal and one coupled oscillator model) for which no obvious smooth embedding geometry is known a priori. This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability.

generative models↗

DOE OSTI2024

Transient fading X-ray emission detected during the optical rise of a tidal disruption event

ABSTRACT We report on the SRG/eROSITA detection of ultra-soft ($kT=47^{+5}_{-5}$ eV) X-ray emission (LX =$2.5^{+0.6}_{-0.5} \times 10^{43}$ erg s−1) from the tidal disruption event (TDE) candidate AT 2022dsb ∼14 d before peak optical brightness. As the optical luminosity increases after the eROSITA detection, then the 0.2–2 keV observed flux decays, decreasing by a factor of ∼39 over the 19 d after the initial X-ray detection. Multi-epoch optical spectroscopic follow-up observations reveal transient broad Balmer emission lines and a broad He ii 4686 Å emission complex with respect to the pre-outburst spectrum. Despite the early drop in the observed X-ray flux, the He ii 4686 Å complex is still detected for ∼40 d after the optical peak, suggesting the persistence of an obscured hard ionizing source in the system. Three outflow signatures are also detected at early times: (i) blueshifted H α emission lines in a pre-peak optical spectrum, (ii) transient radio emission, and (iii) blueshifted Ly α absorption lines. The joint evolution of this early-time X-ray emission, the He ii 4686 Å complex, and these outflow signatures suggests that the X-ray emitting disc (formed promptly in this TDE) is still present after optical peak, but may have been enshrouded by optically thick debris, leading to the X-ray faintness in the months after the disruption. If the observed early-time properties in this TDE are not unique to this system, then other TDEs may also be X-ray bright at early times and become X-ray faint upon being veiled by debris launched shortly after the onset of circularization.

Malyali, A. (ORCID:0000000288514019)↗

DOE OSTI2024

Comments on the double cone wormhole

In this paper we revisit the double cone wormhole introduced by Saad, Shenker and Stanford (SSS), which was shown to reproduce the ramp in the spectral form factor. As a first approximation we can say that this solution computes Tr[e –iKT ], a trace of the “evolution” operator that generates Schwarzschild time translations on the two sided wormhole geometry. This point of view leads to a simple way to compute the normalization factor of the wormhole. When we have bulk matter fields, SSS suggested using a modified evolution K ~ which involves a slightly complex geometry, so that we are really computing Tr[e –iK ~ T ]. We argue that, for general black holes, the spectrum of K ~ is given by quasinormal mode frequencies. We explain that this reproduces various features that were previously predicted from the spectral form factor on hydrodynamics grounds. We also give a general algebraic construction of the modified boost in terms of operators constructed from half sided modular inclusions. For the special case of JT gravity, we work out the backreaction of matter on the geometry of the double cone and find that it deforms the geometry in an undesirable direction. We finally give some comments on the possible physical interpretation of K ~ .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Insights Into Thermal Runaway Mechanisms: Fast Tomography Analysis of Metal Agglomerates in Lithium-Ion Batteries

Thermal Runaway (TR) in lithium-ion batteries (LIB) is a critical technological and social concern. Whilst such events are rare, TR is characterized by uncontrollable heating leading to catastrophic failures. To deepen the understanding of the failure process and subsequently develop more accurate TR prediction models and as a result safer battery systems, we present in this work high-speed X-ray tomography for in-depth investigations of the copper current collector melting and agglomeration during TR. The melting process presents valuable real-time internal information about heat evolution during TR, previously challenging to access but crucially important for validating TR models. In this work, controlled failure studies combined with high-speed X-ray tomography were performed on two different commercial LIB models, subjecting them to both external heating and nail penetration to induce TR. Through real-time observation via high-speed tomography, followed by segmentation, rendering, and analysis, the formation of copper agglomerates was qualitatively and quantitatively characterized and visualized for the first time. Agglomerates tended to form either from the battery's outermost layers or centrally, depending on the method of TR initiation, and gives an indirect insight into the internal temperature evolution and distribution. Moreover, an initial comparative analysis between the battery models also revealed differences in agglomerate size, which has been linked to the thicker copper current collectors of one of the cell models. We further discuss the impact of larger copper agglomerates on heat distribution and safety. This study not only sheds light on the intricate dynamics of TR in LIBs but also underscores the pivotal role of 'gold-standard' imaging techniques in advancing battery safety, crucial for the robust modeling of TR and the future design of electric vehicle safety systems.

25 ENERGY STORAGE↗

DOE OSTI2025

How are Heterogeneous Nucleation Rate Observations Influenced by Instrument Resolution?

Experimental measurements of the heterogeneous nucleation rate rely on counting the number of nuclei with time. However, the size of a thermodynamically stable nucleus is often a few nanometers in diameter and is below the resolution of most (in situ) measurement techniques that provide a statistically valid sample. Due to the finite resolution of the instruments and analysis methods, it is challenging to capture the incipient nuclei and the subsequent evolution of nuclei density over time. In this work, we demonstrate the impact of instrument resolution on observed nuclei densities by comparing numerical modeling with experimental results. Further, to achieve this, we implemented heterogeneous nucleation within the pore-scale reactive transport modeling framework using classical nucleation theory (CNT). We compared the modeling results with nucleation rates measured using X-ray nanotomography (XnT) and evaluated how these impact the apparent values of the prefactor and interfacial energy based on CNT and the crystal growth rate. Specifically, we applied a resolution threshold (artificial resolution limit) in the model during nuclei counting to resemble an experimental resolution, ranging from 15 to 500 nm. The findings reveal that the instrument resolution significantly impacts the apparent prefactor and interfacial energy. Both apparent prefactor and interfacial energy decrease with a decrease in the instrument resolution. While deviation in the prefactor due to resolution is anticipated, those in the interfacial energy are unexpected. The approach described here allows one to correct apparent nucleation rates that depend on the instrument’s resolution to derive “intrinsic” CNT parameters for the prefactor and interfacial energy.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Eocene-Oligocene Metamorphism, Fluid Flow and Deformation in the Ruby Mountains-East Humboldt Range Metamorphic Core Complex

Metamorphic core complexes are ubiquitous in collapsed orogens globally and play a primary role in crustal exhumation. Here, we investigate the metamorphic history of the Ruby Mountains-East Humboldt Range metamorphic core complex, Nevada, using petrochronology to understand how magmatism, metamorphism and deformation interact to modulate crustal rheology, and the timing of exhumation within the Sevier orogenic belt. Field study, microstructural analysis, thermobarometry and laser ablation split-stream monazite, titanite and allanite petrochronology of the mylonitic footwall were integrated to elucidate the pressure-temperature-time (P-T-t) evolution. Major-, trace-element and quartz-in-garnet thermobarometry show peak metamorphism occurred at 5.5–6 kbar and 600–650°C across the study area. Monazite and titanite U-(Th)-Pb petrochronology constrain this episode of metamorphism to 88–81 Ma with the structurally deepest samples yielding dates down to ca. 71 Ma. The preservation of peak metamorphic mineral assemblages indicates these rocks remained at near-peak temperature conditions into the Cenozoic. Cenozoic metamorphism occurred during a punctuated episode contemporaneous with the Great Basin ignimbrite flare up. All samples show a distinct 39–37 Ma population of monazite, titanite and allanite dates that correlate with the emplacement of quartz diorite and gabbro intrusions throughout the footwall. Accessory phases contain zoning textures in backscattered electron images that are consistent with fluid-mediated dissolution-reprecipitation reactions. The U-(Th)-Pb analyses from these zones yield 39–27 Ma dates interpreted as the timing of fluid flow. The results of this study elucidate the integrated importance of magmatism, melting and fluid flow in driving the coupled evolution of Late Cretaceous metamorphism within the Sevier hinterland and the subsequent Cenozoic metamorphic core complex development that exhumed the middle crust.

58 GEOSCIENCES↗

DOE OSTI2026

Advancing specialized biofoundries via automated adaptive laboratory evolution

Adaptive laboratory evolution (ALE) is a powerful strategy for improving microbial phenotypes by harnessing natural selection under defined environmental conditions. Through applying selection regimes, beneficial mutations accumulate, enabling the generation of strains with enhanced properties. However, conventional ALE is labor-intensive and difficult to scale, limiting reproducibility and broader discovery of evolutionary principles. Recent advances in robotics, automation, and computational infrastructure are transforming ALE into a scalable, data-rich experimental paradigm. Automated platforms enable standardized and complex protocols, real-time monitoring, and highly parallel evolution campaigns, improving consistency while generating longitudinal datasets that reveal convergent adaptive mechanisms. Here, we discuss the role of specialized biofoundries in advancing automated ALE and enabling large-scale evolutionary engineering. We review major automated ALE formats and outline key design principles for effective ALE biofoundries, highlighting how automated ALE can support autonomous experimentation and AI-guided strain engineering.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Broadband Rotational Spectroscopy in Uniform Supersonic Flows: Chirped Pulse/Uniform Flow for Reaction Dynamics and Low Temperature Kinetics

ConspectusThe study of gas-phase chemical reactions at very low temperatures first became possible with the development and implementation of the CRESU (French acronym for Reaction Kinetics in Uniform Supersonic Flows) technique. CRESU relies on a uniform supersonic flow produced by expansion of a gas through a Laval (convergent-divergent) nozzle to produce a wall-less reactor at temperatures from 10 to 200 K and densities of 1016-1018 cm-3 for the study of low temperature kinetics, with particular application to astrochemistry. In recent years, we have combined uniform flows with revolutionary advances in broadband rotational spectroscopy to yield an instrument that affords near-universal detection for novel applications in photodissociation, reaction dynamics, and kinetics. This combination of uniform supersonic flows with chirped-pulse Fourier-transform microwave spectroscopy (Chirped-Pulse/Uniform Flow, CPUF) permits detection of any species with a modest dipole moment, thermalized to the uniform temperature of the gas flow, with isomer, conformer, and vibrational state specificity. In addition, the use of broadband, high-resolution, and time-dependent (microsecond time scale) micro- and mm-wave spectroscopy makes it an ideal tool for characterizing both transient and stable molecules, as well as studying their spectroscopy and dynamics.In this Account, we review recent advances made using the CPUF technique, including studies of photodissociation, radical-radical reaction dynamics, and low temperature kinetics. These studies highlight both the strength of universal and multiplexed detection and the challenges of coupling it to a high-density collisional environment. Product branching and product evolution as a function of time have been measured for astrochemically relevant systems, relying on the detailed characterization of these flow conditions via experiments and fluid dynamics simulations. In the photodissociation of isoxazole, an unusual heterocyclic molecule with a very low-energy conical intersection, we have identified 7 products in 5 reaction channels and determined the product branching, pointing to both direct and indirect pathways. We have also approached the same system from separated NO and C3H3 reactants to explore a broader range of the potential energy surface, demonstrating the power of multichannel branching measurements for complex radical-radical reactions. We determined the product branching in the C3H2 isomers in the photodissociation of the propargyl radical and identified the importance of a hydrogen atom catalyzed isomerization to the lowest energy cyclic form. This then motivated a study of direct D-H exchange reaction in radicals, in which we demonstrate that it is an important and overlooked pathway for deuterium fractionation in astrochemical environments. Recently, we have shown the measurement of low temperature kinetics inside an extended Laval nozzle, after which a shock-free secondary expansion to low temperature and density affords an ideal environment for detection by rotational spectroscopy. These results highlight the power and potential of the CPUF approach, and future prospects will also be discussed in light of these developments.

Dias, Nureshan↗

DOE OSTI2026

Multiscale geographically and temporally weighted regression (MGTWR): exploring the spatiotemporal heterogeneity of EV market adoption

As an innovative vehicle technology, electric vehicles are experiencing growing sales and have made significant inroads into the traditional automotive market in the United States and around the world. However, EV adoption rates vary significantly across space and over time, influenced by a complex interplay of socio-economic and infrastructural factors alongside federal and state policies. Here, this paper presents a comprehensive spatial–temporal investigation of EV market adoption within one city in the US, that of Chicago, utilizing Multiscale Geographically and Temporally Weighted Regression (MGTWR) alongside Multiscale Geographically Weighted Regression (MGWR). The aim is to unravel the spatial and temporal dynamics affecting EV adoption and to explore how the influence of various determinants of EV adoption, such as demographic factors and economic conditions, vary spatially. Moreover, by utilizing MGTWR, we provide insights into the evolution of these relationships over time, offering a predictive outlook on future EV market growth. Our findings, with an 86.6% prediction accuracy for EV market adoption, tailored policy measures to support accelerated EV adoption. Methodologically, this work advances MGWR frameworks by integrating temporal dynamics to examine nonstationary processes in spatially disaggregated contexts. These findings offer evidence–based guidance for policymakers, urban planners, and stakeholders in the automotive industry, supporting the transition toward a more sustainable and efficient transportation system.

EV Market Adoption↗

DOE OSTI2026

PyJMAK: An Open-Source Python Toolkit for Modeling Solid-State Metallurgical Phase Transformations

Accurate prediction of metallurgical phase transformations is an essential basis for autonomous optimization and rapid part qualification. Several methods can be used to estimate the evolution of phase fractions such as JMAK kinetics-based models, phase-field models, thermodynamic models, and data-driven machine learning models. Thermodynamic and phase-field-based methodologies solve multiphysics equations requiring numerous calibration parameters and significant computational resources. As a result, the computation domain is limited to a point or on order of micron-meters. The data-driven models rely on large datasets from experiments and simulations. While the JMAK model only provides information about phase fraction evolution, it can predict this evolution in near real-time using thermal history and thermodynamic data without restriction on the domain. JMAK models have been popularly used by researchers to model phase transformations occuring during additive manufacturing or over arbitrary temperature profiles. Commercial proprietary software such as Abaqus and Ansys or closed-source in-house implementations offer the ability to model JMAK based kinetics to predict phase transformation. However, these software packages are not open-source or freely available for use and development in conjunction with manufacturing machines, sensors, and machine learning algorithms. In addition, the use of the model is restricted by a license token. In contrast, given temperature profiles at multiple points in the domain, this Python-based PyJMAK model can compute phase evolution in parallel due to its stand-alone modular, voxel-based structure, and it can be executed on high-performance computing resources without any license restrictions.

Prabhune, Bhagya [Oak Ridge National Laboratory (O↗

DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture

Data-driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as multi-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. While standard fracture benchmarks represent realistic scenarios frequently observed in practice, they typically do not provide sufficiently challenging tests for data-driven methods. Here, to address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1000 random initial crack configurations for a total of 6000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO), and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.

Benchmark dataset↗

DOE OSTI2026

Evaluation of the beam-induced depolarization of the HJET target at the EIC

The Polarized Atomic Hydrogen Gas Jet Target (HJET) has played a central role in the absolute calibration of proton beam polarization at RHIC and is foreseen as a key component of the hadron polarimetry program at the future Electron–Ion Collider (EIC). The substantially higher beam current, reduced bunch spacing, and shorter bunch length planned for EIC operation motivate a careful reassessment of possible beam-induced depolarization of the jet target. In this paper, the depolarization of ground-state hydrogen atoms caused by the time-dependent magnetic field of the circulating polarized proton beam is quantitatively evaluated. The hydrogen atom is treated as a four-level hyperfine system in a holding magnetic field, and transitions driven by harmonic components of the bunch-induced magnetic field are analyzed using time-dependent quantum-mechanical evolution along atomic trajectories. Numerical tracking of hydrogen atoms through the beam region is performed using nominal EIC beam parameters. It is shown that, for a holding field of 120 mT (as used at RHIC), the resulting depolarization of the jet target at the EIC is negligibly small, ≲ 0.01 %, and well below the level relevant for EIC polarization accuracy requirements. The stability of this result with respect to plausible variations of the EIC proton beam parameters is also evaluated. In addition, possible effects under alternative experimental conditions are also examined.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

The Association Between Cloud Droplet Number over the Summer Southern Ocean and Air Mass History

The cloud properties and governing processes in Southern Ocean marine boundary layer clouds have emerged as a central issue in understanding the Earth's climate sensitivity. While our understanding of Southern Ocean cloud feedbacks have evolved in the most recent climate model intercomparison, the background properties of simulated summertime clouds in the Southern Ocean are not consistent with measurements due to known biases in simulating cloud condensation nuclei concentrations. This paper presents several case studies collected during the Capricorn 2 and Marcus campaigns held aboard Australian research vessels in the Austral Summer of 2018. Combining the surface–observed cases with MODIS data along forward and backward air mass trajectories, we demonstrate the evolution of cloud properties with time. These cases are consistent with multi–year statistics showing that long trajectories of air masses over the Antarctic ice sheet are critical to creating high droplet number clouds in the high latitude summer Southern Ocean. We speculate that secondary aerosol production via the oxidation of biogenically derived aerosol precursor gasses over the high actinic flux region of the high latitude ice sheets is fundamental to maintaining relatively high droplet numbers in Southern Ocean clouds during Summer.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Multichannel Doppler fiber-imager spectrometer for spatiotemporal characterization of high-intensity laser-driven plasmas

Here, we demonstrate a flexible multichannel fiber-based imaging Doppler spectrometer to characterize plasmas in high intensity (≥1 × 10 18 W/cm 2 ) laser-plasma experiments at high repetition rates. This instrument collects data from ×21 different plasma locations combining optical fibers and a single imaging spectrometer. This diagnostic maps the plasma velocity evolution as a function of time with sub-pico-second resolution. Experimental results showing 2D velocity measurements of plasma with 20 μm spatial resolution are presented. Intensities of the order of 10 18 W/cm 2 were used to generate a plasma, while a much less intense, frequency doubled (400 nm), probe beam (10 11 W/cm 2 ) was used to measure the Doppler shift from the plasma critical surface. The instrument can be scaled to a larger number of channels (e.g., 100) still using a single spectrometer.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

Recent research has shown that wavefunction evolution in real and imaginary time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Fast ion stabilization of tilt in large radius FRCs

The field reversed configuration (FRC) has been a curious case in plasma physics research in that early MHD analysis suggested FRCs should be grossly unstable, while experimental results contradicted that prediction. Later, this theory was able to resolve this contradiction by understanding that finite Larmor radius effects largely negated the MHD predictions. Similarly, previous theoretical studies of beam driven FRCs predicted that such system would be unstable to beam driven modes while, again, experimental results indicated the contradiction. In this paper, we reconcile the theoretical understanding of beam driven modes with experimental observations of stability in these systems. By self-consistently capturing fast ion generation from neutral beam injection and its impact on the plasma equilibrium, we show that low amplitude perturbations in the magnetic field, driven by betatron particles, modify the precession frequencies of the betatron particles such that the drive for compressional Alfvén waves in the thermal plasma is reduced. Finally, we are able to demonstrate, for the first time, stable beam driven FRC evolution at high S*/E in 3D kinetic simulations.

Betatrons↗

DOE OSTI2024

Robust Restoration From Cyber-Physical Attacks in Active Distribution Grids With Grid-Edge IBRs

The inverter-based resources (IBRs) have enabled the integration of renewable energy at the grid edge with enhanced control capabilities to support the reliable operation of power grids. Different control frameworks, such as hierarchical or distributed architecture, have been proposed with the expansion of cyber networks for real-time monitoring and control. This evolution of critical infrastructure into cyber-physical systems also brings more vulnerabilities for the broadened attack surfaces, and significantly increases the possibility of physical system failures or outages caused by cyberattacks. Among tremendous efforts in the defense-in-depth approach, it remains challenging to provide prompt detection and accurate location of attack entry points or paths. Therefore, the prevailing restoration framework may struggle to fully consider the cyber-physical interdependence, successfully isolate the compromised cyber and physical components, and safely recover the systems without the potential risks leading to secondary outages. This paper is motivated to develop a cyber-physical restoration framework for distribution grids to recover from cyber attacks by harnessing grid-edge IBRs. The framework is first built on the operational guidelines of IBRs considering the compromised cyber layer. Then, an ambiguity set is established to represent the uncertainty of attack scenarios and their possibility levels. Next, a distributionally robust optimization model is developed to provide the optimal load restoration strategy across all scenarios. The effectiveness of the proposed model is demonstrated through various use cases on the modified IEEE 13-node and 123-node test systems. Finally, simulation results demonstrate the effectiveness and advancement of developed post-attack restoration strategies.

Cybersecurity↗