Search NASA⌕ Search

SEARCH · Search NASA

Results for “univariate function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

26 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Multivariate Space‐Time Dynamic Model for Characterizing the Atmospheric Impacts Following the Mt. Pinatubo Eruption

The June 1991 Mt. Pinatubo eruption resulted in a massive increase of sulfate aerosols in the atmosphere, absorbing radiation and leading to global changes in surface and stratospheric temperatures. A volcanic eruption of this magnitude serves as a natural analog for stratospheric aerosol injection, a proposed solar radiation modification method to combat a warming climate. The impacts of such an event are multifaceted and region-specific. Our goal is to characterize the multivariate and dynamic nature of the atmospheric impacts following the Mt. Pinatubo eruption. We developed a multivariate space-time dynamic linear model to understand the full extent of the spatially- and temporally-varying impacts. Specifically, spatial variation is modeled using a flexible set of basis functions for which the basis coefficients are allowed to vary in time through a vector autoregressive (VAR) structure. This novel model is cast in a Dynamic Linear Model (DLM) framework and estimated via a customized MCMC approach. We demonstrate how the model quantifies the relationships between key atmospheric parameters prior to and following the Mt. Pinatubo eruption with reanalysis data from MERRA-2 and highlight when such a model is advantageous over univariate models.

Dynamic Linear Model↗
DOE OSTI2022

Small angle scattering of diblock copolymers profiled by machine learning

We outline a machine learning strategy for quantitively determining the conformation of AB-type diblock copolymers with excluded volume effects using small angle scattering. Complemented by computer simulations, a correlation matrix connecting conformations of different copolymers according to their scattering features is established on the mathematical framework of a Gaussian process, a multivariate extension of the familiar univariate Gaussian distribution. We show that the relevant conformational characteristics of copolymers can be probabilistically inferred from their coherent scattering cross sections without any restriction imposed by model assumptions. This work not only facilitates the quantitative structural analysis of copolymer solutions but also provides the reliable benchmarking for the related theoretical development of scattering functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Does the leaf economic spectrum hold within plant functional types? A Bayesian multivariate trait meta-analysis

The leaf economic spectrum is a widely-studied axis of plant trait variability that defines a trade-off between leaf longevity and productivity. While this has been investigated at the global scale, where it is robust, and at local scales, where deviations from it are common, it has received less attention at the intermediate scale of PFTs. We investigated whether global leaf economic relationships are also present within the scale of plant functional types (PFTs) commonly used by Earth System models, and the extent to which this global-PFT hierarchy can be used to constrain trait estimates. We developed a hierarchical multivariate Bayesian model that assumes separate means and covariance structures within and across PFTs and fit this model to seven leaf traits from the TRY database related to leaf longevity, morphology, biochemistry, and photosynthetic metabolism. Although patterns of trait covariation were generally consistent with the leaf economic spectrum, we found three approximate tiers to this consistency. Relationships among morphological and biochemical traits (SLA, N, P) were the most robust within and across PFTs, suggesting that covariation in these traits is driven by universal leaf construction trade-offs and stoichiometry. Relationships among metabolic traits (R_d, V_{c,max}, J_max) were slightly less consistent, reflecting in part their much sparser sampling (especially for high-latitude PFTs), but also pointing to more flexible plasticity in plant metabolistm. Finally, relationships involving leaf lifespan were the least consistent, indicating that leaf economic relationships related to leaf lifespan are dominated by across-PFT differences and that within-PFT variation in leaf lifespan is more complex and idiosyncratic. Across all traits, these covariance were an important source of information, as evidenced by the improved imputation accuracy and reduced predictive uncertainty in multivariate models compared to univariate models. Ultimately, our study reaffirms the value of studying not just individual traits but the multivariate trait space and the utility of hierarchical modeling for studying the scale dependence of trait relationships.

biodiversity, ecological modeling, ecology, leaf b↗
DOE OSTI2021

Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance

The ability of neural networks to provide ‘best in class’ approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train (choose) the parameters defining the network. In general, neural networks are trained by gradient descent type optimization methods,a stochastic variant thereof. In practice, such methods result in the loss function decreases rapidly at the beginning of training but then, after a relatively small number of steps, significantly slow down. The loss may even appear to stagnate over the period of a large number of epochs, only to then suddenly start to decrease fast again for no apparent reason. This so-called plateau phenomenon manifests itself in many learning tasks. The present work aims to identify and quantify the root causes of plateau phenomenon.analysis is carried out in the setting of univariate ReLU networks. No assumptions are made on the number of neurons relative to the number of training data, and our results hold for both the lazy and adaptive regimes. Here, the main findings are: plateaux correspond to periods during which activation patterns remain constant, where activation pattern refers to the number of data points that activate a given neuron; quantification of convergence of the gradient flow dynamics; and, characterization stationary points in terms solutions of local least squares regression lines over subsets of the training data. Based on these conclusions, we propose a new iterative training method, the Active Neuron Least Squares (ANLS), characterised by the explicit adjustment of the activation pattern at each step, which is designed to enable a quick exit from a plateau. Illustrative numerical examples are included throughout.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

PV Generation and Load Forecasting for Adjuntas PR Community Microgrids

Existing frameworks to forecast time-series photovoltaic (PV) output power and consumer load for microgrid operations and controls assume a near-continuous availability of real-time input features from the field assets such as PV inverters, energy meters, and weather station. These incoming data points are used to periodically retrain models and update forecast snapshots over a moving horizon window, be it one hour-ahead, one-day ahead, or one-week ahead. However, such frameworks are not resilient to disruptions in data availability caused by losses in communications between the field sensors and data loggers. Hence, there is a need for programs that assume no availability of real-time microgrid asset data and still make reliable forecasts that can be used for decision-making. Such programs would be apt to function in extreme weather events such as hurricanes and would use lightweight recursive time-series models to independently forecast solar irradiance and ambient temperature, then compute PV power from those forecasts, as well as independently forecast consumer load. The codebase performs forecasting for the scenario of when the microgrid does not have a reliable access to forecasts or real-time observations of solar irradiance (I) and ambient temperature (AT) and load (Load) to be able to adequately forecast, in real-time, the PV power production or a business' load. In this case, using historical values of PV power and load, a univariate forecasting of generation and consumption are respectively made. The use-case in particular has two sub-scenarios: one, a normal 7-day ahead forecast where the unavailability of real-time data is assumed due to infrastructure issues such as loss of communication or sensor maintenance or service downtimes. Whereas a hurricane-caused unavailability of real-time data requires a second model trained specifically on historical hurricane days to be able to capture the extreme day behavior of generation in particular, and load if applicable. A gradient boosted regression tree comprises an ensemble of additive models that map between the input of historical values (be it irradiance, temperature, or load) and their corresponding output forecasts of a given horizon such that the individual learner predictions are summed up over the total number of such learners in the ensemble to produce an aggregate forecast. A weighting mechanism is applied to the training data in each iteration, where actual and forecast values are compared to penalize incorrect forecasts by increasing the weight and reducing it to reward correct forecasts. The code's benefits are that it: (a) accounts for a contingency where communication loss renders newly measured real-time data unavailable for model tuning and snapshot updates; (b) presents blind forecasting that recursively determines the next time-step value in a horizon using the forecast of the same attribute from a prior step; and (c) employs lightweight models that, once trained, can reliably generalize for different horizons, which make them suitable for enhancing the resilience of field microgrids prone to extreme events that encounter disruptions to data availability.

Sundararajan, Aditya [Oak Ridge National Laborator↗
DOE OSTI2024

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Furthermore, our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A surrogate-model-based approach for estimating the first and second-order moments of offshore wind power

Power curve, the functional relationship that governs the process of converting a set of weather variables experienced by a wind turbine into electric power, is widely used in the wind industry to estimate power output for planning and operational purposes. Existing methods for power curve estimation have three main limitations: (i) they mostly rely on wind speed as the sole input, thus ignoring the secondary, yet possibly significant effects of other environmental factors, (ii) they largely overlook the complex marine environment in which offshore turbines operate, potentially compromising their value in offshore wind energy applications, and (ii) they solely focus on the first-order properties of wind power, with little (or null) information about the variation around the mean behavior, which is important for ensuring reliable grid integration, asset health monitoring, and energy storage, among others. In light of that, this study investigates the impact of several wind-and wave-related factors on offshore wind power variability, with the ultimate goal of accurately predicting its first two moments. Further, our approach couples OpenFAST—a multi-physics wind turbine simulator—with Gaussian Process (GP) regression to reveal the underlying relationships governing offshore weather-to-power conversion. We first find that a multi-input power curve which captures the combined impact of wind speed, direction, and air density, can provide double-digit improvements, in terms of prediction accuracy, relative to univariate methods which rely on wind speed as the sole explanatory variable (e.g. the standard method of bins). Wave-related variables are found not important for predicting the average power output, but interestingly, appear to be extremely relevant in describing the fluctuation of the offshore power around its mean. Tested on real-world data collected at the New York/New Jersey bight, our proposed multi-input models demonstrate a high explanatory power in predicting the first two moments of offshore wind generation, testifying their potential value to the offshore wind industry.

17 WIND ENERGY↗
DOE OSTI2024

Linking leaf dark respiration to leaf traits and reflectance spectroscopy across diverse forest types

Leaf dark respiration (R dark ), an important yet rarely quantified component of carbon cycling in forest ecosystems, is often simulated from leaf traits such as the maximum carboxylation capacity (V cmax ), leaf mass per area (LMA), nitrogen (N) and phosphorus (P) concentrations, in terrestrial biosphere models. However, the validity of these relationships across forest types remains to be thoroughly assessed. Here, in this study, we analyzed R dark variability and its associations with V cmax and other leaf traits across three temperate, subtropical and tropical forests in China, evaluating the effectiveness of leaf spectroscopy as a superior monitoring alternative. We found that leaf magnesium and calcium concentrations were more significant in explaining cross-site R dark than commonly used traits like LMA, N and P concentrations, but univariate trait–R dark relationships were always weak (r 2 ≤ 0.15) and forest-specific. Although multivariate relationships of leaf traits improved the model performance, leaf spectroscopy outperformed trait–R dark relationships, accurately predicted cross-site R dark (r 2 = 0.65) and pinpointed the factors contributing to R dark variability. Our findings reveal a few novel traits with greater cross-site scalability regarding R dark , challenging the use of empirical trait–R dark relationships in process models and emphasize the potential of leaf spectroscopy as a promising alternative for estimating R dark , which could ultimately improve process modeling of terrestrial plant respiration.

59 BASIC BIOLOGICAL SCIENCES↗