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DOE OSTI2023

Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen a priori in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at $E$ $beam$ / $A$ =1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. In conclusion, we find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Assessing variation in faecal glucocorticoid concentrations in gray whales exposed to anthropogenic stressors

Understanding how individual animals respond to stressors behaviourally and physiologically is a critical step towards quantifying long-term population consequences and informing management efforts. Glucocorticoid (GC) metabolite accumulation in various matrices provides an integrated measure of adrenal activation in baleen whales and could thus be used to investigate physiological changes following exposure to stressors. In this study, we measured GC concentrations in faecal samples of Pacific Coast Feeding Group (PCFG) gray whales (Eschrichtius robustus) collected over seven consecutive years to assess the association between GC content and metrics of exposure to sound levels and vessel traffic at different temporal scales, while controlling for contextual variables such as sex, reproductive status, age, body condition, year, time of year and location. We develop a Bayesian Generalized Additive Modelling approach that accommodates the many complexities of these data, including non-linear variation in hormone concentrations, missing covariate values, repeated samples, sampling variability and some hormone concentrations below the limit of detection. Estimated relationships showed large variability, but emerging patterns indicate a strong context-dependency of physiological variation, depending on sex, body condition and proximity to a port. Our results highlight the need to control for baseline hormone variation related to context, which otherwise can obscure the functional relationship between faecal GCs and stressor exposure. Therefore, extensive data collection to determine sources of baseline variation in well-studied populations, such as PCFG gray whales, could shed light on cetacean stress physiology and be used to extend applicability to less-well-studied taxa. GC analyses may offer greatest utility when employed as part of a suite of markers that, in aggregate, provide a multivariate measure of physiological status, better informing estimates of individuals’ health and ultimately the consequences of anthropogenic stressors on populations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Baltimore Turfgrass Field Experiment Campaign Report

The Baltimore Turfgrass Field Experiment (BTFE) consisted of an observation eddy covariance flux station, measuring CO 2 , H 2 O, and turbulent energy fluxes between the turfgrass field and the atmosphere. The tower was sited before the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility’s arrival, but for the purposes of this report, we can say that the campaign lasted as long as the Coast-Urban-Rural Atmospheric Gradient Experiment (CoURAGE) campaign, 12 months, 12/2024 through 11/2025. As stated, the flux tower was part of the COURAGE campaign on the M1 site. We set out to measure turfgrass because it is a ubiquitous part of the urban environment—in fact, it is the dominant vegetation land cover type in Baltimore and most cities. It contributes small but significantly to greenhouse gas balances as well as the energy balance in the urban environment. We also installed a soil temperature and matric potential profiling system as part of this experiment. Additionally, AmeriFlux asked us to participate in their soil matric potential soil moisture mapping experiment. We collected 12 soil samples to be analyzed by a team in Bloomington, Indiana: results are pending.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARY Full-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

58 GEOSCIENCES↗

DOE OSTI2023

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗