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DOE OSTI2026

Physics-aware adaptive checkpointing with shadow systems for nonlinear PDE simulations

Large-scale simulations of nonlinear partial differential equations (PDEs) that exhibit strongly transient behavior and pattern-forming dynamics produce enormous amounts of data, which, even with modern storage systems, cannot be stored for later curation. Current I/O strategies either write dense time series of snapshots, which is often prohibitive in I/O and storage, or store a few checkpoints that enable restart but incur expensive recomputation cost and provide no control over post-restart error growth, especially when lossy compression is used. Moreover, most, if not all, existing strategies take no account of the actual physical state of the system. Here, we present a simple physics-aware I/O framework in which a low-cost shadow system adaptively triggers lossy checkpoints when the shadow system deviates from the fine-scale simulation. The shadow system can be a coarsened replica of the fine-scale simulation that evolves concurrently. This means that checkpoints are taken based on the physical state of the system: fewer checkpoints are triggered when the system is quiescent while more are taken when the system undergoes a rapid change. This type of behavior is observed in many systems such as Brusselator and FitzHugh–Nagumo. We illustrate that our framework maintains stable restarts, keeps fine-scale restart errors bounded by shadow errors, and reconstructs the time history with significantly lower error and storage than interpolating fixed-interval snapshots, with low-cost shadow replay and modest online synchronization overhead.

Gong, Qian [ORNL] (ORCID:0000000235704142)↗

DOE OSTI2024

Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by [Huggins et al ., Nature (London) 603 , 416 (2022)] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling postprocessing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [Commun. Math. Phys. 404 , 629 (2023)], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical postprocessing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm.

Monte Carlo methods↗

NASA NTRS1972

Brightness of forbidden O I lines and properties of shadow bands during the eclipse of 7 March 1970.

Results of two types of measurements made at a site in the center of the eclipse track during the total eclipse of Mar. 7, 1970. The O I forbidden 5577-A and 6300-A lines were measured looking vertically through the eclipse shadow. The intensities were approximately 1 kR, essentially the values obtained in recent rocket measurements of normal day airglow at altitudes above 100 km. This is consistent with the hypothesis that these lines originate primarily at altitudes well above the shadow from mechanisms which are not appreciably perturbed by the approaching shadow. Measurements were also made of the time variation of intensity of incident light during the shadow-band period before second contact. There are saw-tooth fluctuations with steep leading edges, as well as many high-frequency components of smaller amplitude. This time variation does not appear to be obviously related in a simple way to current theories of their production mechanisms, or to the visual appearance of shadow bands.

Kerr, D. E.↗

NASA NTRS1984

Generating soft shadows with a depth buffer algorithm

Computer-synthesized shadows used to appear with a sharp edge when cast onto a surface. At present the production of more realistic, soft shadows is considered. However, significant costs arise in connection with such a representation. The current investigation is concerned with a pragmatic approach, which combines an existing shadowing method with a popular visible surface rendering technique, called a 'depth buffer', to generate soft shadows resulting from light sources of finite extent. The considered method represents an extension of Crow's (1977) shadow volume algorithm.

Brotman, L. S.↗

DOE OSTI2024

Quantum Circuit Cutting for Classical Shadows

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits and discuss the mechanisms for this advantage.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Shadow masks predictions in SPARC tokamak plasma-facing components using HEAT code and machine learning methods

Here, this work uses machine learning (ML) to complement HEAT (Heat flux Engineering Analysis Toolkit) by developing 3-D footprint surrogate models for fast and accurate heat load calculations in the divertor of the SPARC tokamak. The focus is on shadowed regions, or magnetic shadows, caused by the 3-D geometry of plasma-facing components (PFCs). ML classifiers are employed to create a surrogate model for HEAT generated shadow masks, predicting these shadow masks and divertor heat flux profiles based on a diverse range of equilibria and only the plasma current, safety factor(q95) at the edge, and magnetic flux angles as input parameters. The ultimate goal is to integrate the model for real-time control and future operational decisions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Group-theoretic error mitigation enabled by classical shadows and symmetries

Abstract Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy called symmetry-adjusted classical shadows , by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global U(1) symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry.

Zhao, Andrew (ORCID:0000000202990277)↗

NASA NTRS1972

Crater shadowing effects at low sun angles, part Q

A comparison of Apollo 15 lunar surface photographs taken at low sun-elevation angles with photographs of an experimentally cratered surface at low lighting angles is discussed. The comparison revealed marked similarities, the most significant being that the smallest craters in both sets of photographs are filled with shadows that form beadlike chains and clusters. It was also found that the fraction of area covered by shadows within the smaller craters is so large that 30 to 40 percent of the total field of view is covered by shadow. It is concluded that: the fraction of area covered by resolvable craters, which should be somewhat less than the fraction of area covered by shadow for photographs with very low sun elevation angles, may be calculated using the steady state crater frequency distribution for craters from 20 to 100 m in diameter and then adding the area covered by larger craters for which the crater frequency distribution has the form of the crater-production frequency distribution.

Moore, H. J.↗

NASA NTRS1972

The shadow band phenomenon.

Observation of shadow bands during the solar eclipse of Mar. 7, 1970. Data were gathered by recording onto magnetic tape of the output from six collimated photocells whose spectral responses ranged from the ultraviolet to the infrared, and by visual and mechanical measurement of the orientation and motion of the bands. The recorded data were later processed using the output from a frequency spectrum analyzer. Most of the energy of the shadow bands ranges between 1 and 25 Hz, and appears not unlike plots of scintillation spectra. The onset, amplitude, and duration of the shadow bands seem to be spectrally related to the limb darkening of the sun's photosphere. Other results of the experiment conclusively indicate that the shadow band phenomenon is a manifestation of atmospheric turbulence in the form of air packets of different density from that of their environment (density schlieren), made visible by the light from the crescent sun.

Quann, J. J.↗

NASA NTRS1972

An analytical and experimental evaluation of shadow shields and their support members.

Review of the major results of an analytical and experimental program aimed at determining the potential effectiveness of shadow shields in minimizing radiant heat transfer into cryogenic propellant tanks on long-duration interplanetary missions, taking into account the thermal interaction between shields and their support structures. Analytical procedures are developed and applied that include the strut-shield interaction in predicting shadow shield performance. The results of experimental studies of the effects of configuration variables on the performance of a scale model of a shadow shield system are presented. The experimental results are used to verify the validity of analytical predictions. The results obtained show that: (1) shadow shields can be effective in reducing the heat transfer into cryogenic propellant tanks, and (2) the conductive heat transfer through supports can be reduced by selective surface coatings.

Stochl, R. J.↗

NASA NTRS1976

Magnetic shadowing of charged particles by an extended surface

The problem of particle shadowing by the lunar surface is examined. Shadow zones are obtained analytically for small-aperture detectors on an infinite flat surface and are shown to be in good agreement with those obtained by numerical trajectory tracing. The shadow zones cover about half of all possible external field orientations for a vertical detector, which may result in serious underestimations of the frequency of observation of a particular plasma region. Shadowing may cause wide variations between observed and actual pitch angle distributions even in the case of multiple- or large-aperture detectors. Since the particle flux can be considered approximately isotropic only for magnetic fields within 35 deg of the surface normal, the electron flux to the surface may be overestimated in current balance calculations ignoring the magnetic field direction. In addition, photoelectrons may be returned to the surface by the magnetic field.

Reiff, P. H.↗

NASA NTRS1984

Self-shadowing effects on the thermal-structural response of orbiting trusses

An investigation of self-shadowing effects on the thermal-structural response of orbiting trusses is described. The shadowing, heating, thermal and structural analyses are summarized. The significance of shadowing on the thermal-structural behavior of a single member and a beam constructed from truss members is described. For the trusses considered, the study shows that member self-shadowing effects significantly alter the behavior and must be included to predict the thermal-structural response correctly.

Thornton, E. A.↗

NASA NTRS1985

The shadow world of superstring theories

Some possible astrophysical and cosmological implications of 'shadow matter', a form of matter which only interacts gravitationally with ordinary matter and which may or may not be identical in its properties to ordinary matter, are considered. The possible existence, amount, and location of shadow matter in the solar system are discussed, and the significance of shadow matter for primordial nucleosynthesis, macroscopic asymmetry, baryogenesis, double-bubble inflation, and asymmetric microphysics is addressed. Massive shadow states are discussed.

Kolb, E. W.↗

NASA NTRS1988

Curvature of blended rolled edge reflectors at the shadow boundary contour

A technique is advanced for computing the radius of curvature of blended rolled edge reflector surfaces at the shadow boundary, in the plane perpendicular to the shadow boundary contour. This curvature must be known in order to compute the spurious endpoint contributions in the physical optics (PO) solution for the scattering from reflectors with rolled edges. The technique is applicable to reflectors with radially-defined rim-shapes and rolled edge terminations. The radius of curvature for several basic reflector systems is computed, and it is shown that this curvature can vary greatly along the shadow boundary contour. Finally, the total PO field in the target zone of a sample compact range system is computed and corrected using the shadow boundary radius of curvature, obtained using the technique. It is shown that the fields obtained are a better approximation to the true scattered fields.

Ellingson, S. W.↗

NASA NTRS1990

Scattering of sound by atmospheric turbulence predictions in a refractive shadow zone

According to ray theory, regions exist in an upward refracting atmosphere where no sound should be present. Experiments show, however, that appreciable sound levels penetrate these so-called shadow zones. Two mechanisms contribute to sound in the shadow zone: diffraction and turbulent scattering of sound. Diffractive effects can be pronounced at lower frequencies but are small at high frequencies. In the short wavelength limit, then, scattering due to turbulence should be the predominant mechanism involved in producing the sound levels measured in shadow zones. No existing analytical method includes turbulence effects in the prediction of sound pressure levels in upward refractive shadow zones. In order to obtain quantitative average sound pressure level predictions, a numerical simulation of the effect of atmospheric turbulence on sound propagation is performed. The simulation is based on scattering from randomly distributed scattering centers ('turbules'). Sound pressure levels are computed for many realizations of a turbulent atmosphere. Predictions from the numerical simulation are compared with existing theories and experimental data.

Mcbride, Walton E.↗

NASA NTRS1990

Functional relation among subpixel canopy cover, ground shadow, and illuminated ground at large sampling scales

The functional relation among subpixel canopy cover, illuminated soil, and shadowed soil, which progressively develops with increasing pixel size, is investigated for Poisson distributed plants using a geometric canopy simulation model. An analytical relation among cover components is shown to be applicable when the scale of the pixel is much larger than the scale of the plant and ground shadow. The analysis is facilitated through the use of a nondimensional solar-geometric similarity parameter, eta, equal to the ratio of the area of one plant canopy to its associated ground shadow area, as viewed from nadir. A sampling scale ratio, defined as the ratio of the area of the pixel to the mean area of a single plant shadow, is tested as a quantitative criterion to evaluate when the functional relation among subpixel components occurs. The results of a remote sensing experiment over a natural conifer landscape provide preliminary confirmation of the theoretical analysis.

Jasinski, Michael F.↗

NASA NTRS1992

Interpreting asteroid photometry and polarimetry using a model of shadowing and coherent backscattering

The shadow-hiding models for the opposition effect and negative polarization of atmosphereless solar system bodies do not explain some experimental findings, such as the enhancing opposition effect and negative polarization with decreasing particle size down to wavelength scales. The enhancement for laboratory photometric and polarimetric data on artificial glass samples with different particle size is shown. These results are in agreement with the so-called coherent backscattering or interference mechanism proposed for the interpretation of the opposition effect and negative polarization. Two different approaches for describing the opposition effect and negative polarization produced by the shadow-interference mechanism were developed. One is based on exact electromagnetic solutions for simple scattering systems that include dipole-dipole and dipole-surface coupling; The other is based on a point-scatterer approximation characterized by model photometric and polarimetric phase functions, and the mutual shadowing effect is derived using virtual volumes associated with the point-scatterers. Both approaches yield qualitatively similar results, although neither is entirely satisfactory. We regard them as prototypes for a future unified model of shadowing and coherent backscattering. The sharp opposition effect of 44 Nysa and the asteroid albedo-polarization rule are here explained using the point-scatterer approach.

Shkuratov, Y. G.↗

NASA NTRS1993

The X-ray shadow of the high-latitude molecular cloud MBM 12

ROSAT XRT/PSPC observations show a deep shadow cast by the high-latitude molecular cloud MBM 12 in the 3/4 keV diffuse background. Modeling of the shadow implies that less than 20 percent of the typical high-latitude 3/4 keV diffuse background intensity is emitted in front of the cloud (D = 60-70 pc). A weaker shadow consistent with the lower optical depth at higher energies was observed in the 1.5 keV band. Since little shadowing was seen in the 1/4 keV band, this observation places strong constraints on the amount of 0.5-2 keV emission that is intermixed with the source of the observed 1/4 keV flux.

Snowden, S. L.↗