Search NASA⌕ Search

SEARCH · Search NASA

Results for “variable order”

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.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Spatial analysis of concentrations of multiple air pollutants using NASA DISCOVER-AQ aircraft measurements: Implications for exposure assessment

Highlights: • Aircraft measurements showed spatially varying relations of multiple air pollutants. • NO{sub x}, toluene, and xylenes/ethylbenzene were reasonable proxies of traffic and urban air pollution. • Between-pollutant concentration correlations and ratios varied by space. • Multiple pollutant relations provided insights for exposure assessment and multipollutant epidemiology. In recent years, multipollutant approaches have been employed to investigate the association with health outcomes to better represent real-world conditions than more traditional analysis that considers a single pollutant. With regard to the exposure assessment of a mixture of air pollutants, it is critical to understand the spatial variability in multipollutant relations in order to assess their potential health implications. In this study, we investigated the spatial relations of multiple pollutant concentrations (i.e., NO{sub x}, NO{sub y}, black carbon, carbon monoxide, acetaldehyde, formaldehyde, toluene, xylenes/ethylbenzene, ozone, water-soluble organic carbon, and aerosol extinction) observed from the P-3B aircraft in the 2011 NASA field campaign in Baltimore/Washington D.C. areas during July 2011. The between-pollutant Pearson correlations and Z-scores (calculated from log-transformed concentrations) between near-highways and non-highways and between near-urban centers and non-urban centers varied by pollutant pair and space. We found generally lower correlations between NO{sub x} and other pollutants for near-highways (average r = 0.36) than for non-highways (average r = 0.41) and also for non-urban centers (average r = 0.37) than for near-urban centers (average r = 0.41). This indicated that the temporal associations between NO{sub x} and health outcomes might be less affected by other pollutants, which were also related to same health outcomes, for near-highways and non-urban centers. The analysis of between-pollutant Z-scores showed varying spatial relations for popular traffic-related pollutants with the Z-score differences of 0.43 (NO{sub x}-carbon monoxide), 0.29 (NO{sub x}-black carbon), and 0.17 (black carbon-carbon monoxide) between near-highways and non-highways. This result exhibited heterogeneous traffic-related pollutant mixtures with the proximity to highways, potentially leading to the diverse extent of health associations. Furthermore, a mixed effects model presented pollutant-specific associations between the concentrations and the proximity to highways and urban centers, showing larger declines for NO{sub x}, xylenes/ethylbenzene, toluene, and NO{sub y} than those for the pollutants related to secondary pollutant formation. The model also demonstrated the different sensitivity of each pollutant to meteorological parameters, which may modify the spatial and temporal variability in the relations between the pollutants. Our findings provide insights for exposure assessment studies to better understand the cumulative health consequences associated with multiple air pollutants simultaneously.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
DOE OSTI2018

On the relative roles of the atmosphere and ocean in the Atlantic Multi-decadal Variability

The relative roles of the ocean and the atmosphere in driving the Atlantic Multi-decadal Oscillation (AMO) are investigated by isolating the AMO components forced by anomalous surface heat fluxes and ocean dynamics in a fully- and partially-coupled experiments. The impact of the ocean-dynamics-forced SST on air-sea interaction is disabled in the partially-coupled experiment in order to isolate the atmosphere-forced variability. In the partially-coupled experiment, the ocean-forced AMO component exhibits a strong multi-decadal variability (25- to 50-yr periods), while the atmosphere-forced component has weak multi-decadal variability. This ocean-forced variability is imprinted on the fully-coupled surface heat fluxes, which however, damp the ocean-forced SST variability inducing them, so that the fully-coupled AMO multi-decadal power is only slightly stronger than that forced by the atmosphere alone. Our results suggest that the multi-decadal variability of the AMO is largely driven by ocean dynamics, but its power is also determined by the strength air-sea coupling.

Garuba, Oluwayemi A.↗
DOE OSTI2018

Linear fractional differential equations and eigenfunctions of fractional differential operators

Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the analytical solution of some linear sequential fractional differential equations. As a first application, we discuss analytical solutions for the so-called fractional Helmholtz equation with one variable, obtained from the standard equation in one dimension by replacing the integer order derivative by the Riemann–Liouville fractional derivative. A second application consists of an initial value problem for a fractional wave equation in two dimensions in which the integer order partial derivative with respect to the time variable is replaced by the Caputo fractional derivative. The classical Mittag-Leffler functions are important in the theory of fractional calculus because they emerge as solutions of fractional differential equations. Starting with the solution of a specific fractional differential equation in terms of these functions, we find a way to express the exponential function in terms of classical Mittag-Leffler functions. A remarkable characteristic of this relation is that it is true for any value of the parameter n appearing in the definition of the functions, i.e., we have an infinite family of different expressions for e{sup x} in terms of classical Mittag-Leffler functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

IMPLEMENTATION OF DETAILED CHEMISTRY MECHANISMS IN ENGINE SIMULATIONS

The stiffness of large chemistry mechanisms has been proved to be a major hurdle toward predictive engine simulations. As a result, detailed chemistry mechanisms with a few thousand species need to be reduced based on target conditions so that they can be accommodated within the available computational resources. The computational cost of simulations typically increases super-linearly with the number of species and reactions. This work aims to bring detailed chemistry mechanisms within the realm of engine simulations by coupling the framework of unsteady flamelets and fast chemistry solvers. A previously developed tabulated flamelet model (TFM) framework for nonpremixed combustion was used in this study. The flamelet solver consists of the traditional operator-splitting scheme with variable coefficient ordinary differential equation (ODE) solver (VODE) and a numerical Jacobian for solving the chemistry. In order to use detailed mechanisms with thousands of species, a new framework with the Livermore solver for ODEs in sparse form (LSODES) chemistry solver and an analytical Jacobian was implemented in this work. Results from 1D simulations show that with the new framework, the computational cost is linearly proportional to the number of species in a given chemistry mechanism. As a result, the new framework is 2-3 orders of magnitude faster than the conventional variable coefficient ODE (VODE) solver for large chemistry mechanisms. This new framework was used to generate unsteady flamelet libraries for ndodecane using a detailed chemistry mechanism with 2755 species and 11,173 reactions. The engine combustion network (ECN) spray A experiments, which consist of an igniting n-dodecane spray in turbulent, high-pressure engine conditions are simulated using large eddy simulations (LES) coupled with detailed mechanisms. A grid with 0.06 mm minimum cell size and 22 x 10(6) peak cell count was implemented. The framework is validated across a range of ambient temperatures against ignition delay and liftoff lengths (LOLs). Qualitative results from the simulations were compared against experimental OH and CH2O planar laser-induced fluorescence (PLIF) data. The models are able to capture the spatial and temporal trends in species compared to those observed in the experiments. Quantitative and qualitative comparisons between the predictions of the reduced and detailed mechanisms are presented in detail. The main goal of this study is to demonstrate that detailed reaction mechanisms (similar to 1000 species) can now be used in engine simulations with a linear increase in computation cost with number of species during the tabulation process and a small increase in the 3D simulation cost.

Kundu, Prithwish↗
DOE OSTI2024

Near-global summer circulation response to the spring surface temperature anomaly in Tibetan Plateau –– the GEWEX/LS4P first phase experiment

Subseasonal to seasonal (S2S) prediction of droughts and floods is one of the major challenges of weather and climate prediction. Recent studies suggest that the springtime land surface temperature/subsurface temperature (LST/SUBT) over the Tibetan Plateau (TP) can be a new source of S2S predictability. The project “Impact of Initialized Land Surface Temperature and Snowpack on Subseasonal to Seasonal Prediction (LS4P)” was initiated to study the impact of springtime LST/SUBT anomalies over high mountain areas on summertime precipitation predictions. The present work explores the simulated global scale response of the atmospheric circulation to the springtime TP land surface cooling by 16 current state-of-the-art Earth System Models (ESMs) participating in the LS4P Phase I (LS4P-I) experiment. The LS4P-I results show, for the first time, that springtime TP surface anomalies can modulate a persistent quasi-barotropic Tibetan Plateau-Rocky Mountain Circumglobal (TRC) wave train from the TP via the northeast Asia and Bering Strait to the western part of the North America, along with the springtime westerly jet from TP across the whole North Pacific basin. The TRC wave train modulated by the TP thermal anomaly play a critical role on the early summer surface air temperature and precipitation anomalies in the regions along the wave train, especially over the northwest North America and the southern Great Plains. The participant models that fail in capturing the TRC wave train greatly under-predict climate anomalies in reference to observations and the successful models. These results suggest that the TP LST/SUBT anomaly via the TRC wave train is the first order source of the S2S variability in the regions mentioned. Furthermore, the TP surface temperature anomaly can influence the Southern Hemispheric circulation by generating cross-equator wave trains. However, the simulated propagation pathways from the TP into the Southern Hemisphere show large inter-model differences. More dynamical understanding of the TRC wave train as well as its cross-equator propagation into the Southern Hemisphere will be explored in the newly launched LS4P phase II experiment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

In this study, we apply a semi-Lagrangian spectral method for the Vlasov–Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space–velocity domain with a BDF time-stepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Construction and applications of the manifestly gauge invariant expressions of the solutions of the cosmological perturbation theory

After giving how to construct the gauge invariant perturbation variable in an arbitrarily high order and in the arbitrary background spacetime, we consider the manifestly gauge invariant theory of the cosmological perturbations in the long wavelength limit with the spatially flat homogeneous isotropic universe being the background spacetime. In the previous paper, the physical laws, such as the evolution equations, the constraint equations and the junction conditions become manifestly gauge invariant, by writing them in terms of only the single time background/scalar like objects defined by our previous paper. In the present paper, by extending our definition of the background/scalar like objects from the single time case to the many time case and by writing the solution of the physical law in the form where many time background/scalar like objects are vanishing, the solutions become the manifestly gauge invariant. We derive the formula changing the bases of the many time background/scalar like objects by which we can change the time slices for many times appearing in the solution including the initial time and the final time. We use this formula to our treatment of the evolution of the several slow rolling scalar fields using the τ function introduced by our previous paper. In the manifestly gauge invariant manner, we discuss the solution of the many step reheating, that is, the reheating with the arbitrarily many energy transfer steps. Using the energy density ρ as the evolution parameter, we discuss how well the junction model in which the energy transfers from the oscillatory scalar field fluid to the radiation fluid are described by the metric junctions approximates the reheating process described by the differential equations with the decay terms. By using the useful parametrization of the many step reheating, we manifestly prove that in the many step reheating system where any initial perturbation of each component does not become extremely large compared with the initial perturbations of the other components, compared with the effects of the prominent fluctuation generation processes the nearest to the present time the effects of all the fluctuations generated by the previous fluctuation generation processes become negligibly small. Therefore it can be concluded that in order to know the first/second order Bardeen parameters at the present time it is sufficient to calculate only the effects of the fluctuation of the scalar field fluid which becomes energetically dominant lastly (the curvaton mechanism) and the fluctuation of the decay parameter by which this scalar field fluid decays into the radiation (the modulated reheating mechanism).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Thermal and mechanical stabilization process of the organic fraction of the municipal solid waste

Graphical abstract: Display Omitted - Highlights: • A domestic scale prototype for the pre-treatment of OFMSW has been tested. • Two grinding techniques are compared and thermopress is used for the drying stage. • Increasing temperature up to 170 °C reduces energy consumption of the drying stage. • In the range 5–10 bar a reduction of 97% of the initial volume is obtained. • In most cases energy recovery from the dried waste matches energy consumption. - Abstract: In the present study a thermo-mechanical treatment for the disposal of the Organic Fraction of Municipal Solid Waste (OFMSW) at apartment or condominium scale is proposed. The process presents several advantages allowing to perform a significant volume and moisture reduction of the produced waste at domestic scale thus producing a material with an increased storability and improved characteristics (e.g. calorific value) that make it available for further alternative uses. The assessment of the applicability of the proposed waste pretreatment in a new scheme of waste management system requires several research steps involving different competences and application scales. In this context, a preliminary study is needed targeting to the evaluation and minimization of the energy consumption associated to the process. To this aim, in the present paper, two configurations of a domestic appliance prototype have been presented and the effect of some operating variables has been investigated in order to select the proper configuration and the best set of operating conditions capable to minimize the duration and the energy consumption of the process. The performances of the prototype have been also tested on three model mixtures representing a possible daily domestic waste and compared with an existing commercially available appliance. The results obtained show that a daily application of the process is feasible given the short treatment time required and the energy consumption comparable to the one of the common domestic appliances. Finally, the evaluation of the energy recovered in the final product per unit weight of raw material shows that in most cases it is comparable to the energy required from the treatment.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Comparison With Global Soil Radiocarbon Observations Indicates Needed Carbon Cycle Improvements in the E3SM Land Model

We evaluated global soil organic carbon (SOC) stocks and turnover time predictions from a global land model (ELMv1-ECA) integrated in an Earth System Model (E3SM) by comparing them with observed soil bulk and Δ 14 C values around the world. We analyzed observed and simulated SOC stocks and Δ 14 C values using machine learning methods at the Earth System Model grid cell scale (~200 km). In grid cells with sufficient observations, the model provided reasonable estimates of soil carbon stocks across soil depth and Δ 14 C values near the surface but underestimated Δ 14 C at depth. Among many explanatory variables, soil albedo index, soil order, plant function type, air temperature, and SOC content were major factors affecting predicted SOC Δ 14 C values. The influences of soil albedo index, soil order, and air temperature were primarily important in the shallow subsurface (≤30 cm). We also performed sensitivity studies using different vertical root distributions and decomposition turnover times and compared to observed SOC stock and Δ 14 C profiles. The analyses support the role of vegetation in affecting soil carbon turnover, particularly in deep soil, possibly through supplying fresh carbon and degrading physical-chemical protection of SOC via root activities. Allowing for grid cell-specific rooting and decomposition rates substantially reduced discrepancies between observed and predicted Δ 14 C values and SOC content. Furthermore, our results highlight the need for more explicit representation of roots, microbes, and soil physical protection in land models.

58 GEOSCIENCES↗
DOE OSTI2015

Humidity trends imply increased sensitivity to clouds in a warming Arctic

Infrared radiative processes are implicated in Arctic warming and sea-ice decline. The infrared cloud radiative effect (CRE) at the surface is modulated by cloud properties; however, CRE also depends on humidity because clouds emit at wavelengths that are semi-transparent to greenhouse gases, most notably water vapour. Here we show how temperature and humidity control CRE through competing influences between the mid- and far-infrared. At constant relative humidity, CRE does not decrease with increasing temperature/absolute humidity as expected, but rather is found to be approximately constant for temperatures characteristic of the Arctic. This stability is disrupted if relative humidity varies. Our findings explain observed seasonal and regional variability in Arctic CRE of order 10Wm 2 . With the physical properties of Arctic clouds held constant, we calculate recent increases in CRE of 1–5Wm 2 in autumn and winter, which are projected to reach 5–15Wm 2 by 2050, implying increased sensitivity of the surface to clouds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization

We prove an L{sup 2}-estimate for the homogenization of an elliptic operator A{sub ε} in a domain Ω with a Neumann boundary condition on the boundary ∂Ω. The coefficients of the operator A{sub ε} are rapidly oscillating over different groups of variables with periods of different orders of smallness as ε→0. We assume minimal regularity of the data, which makes it possible to impart to the result the meaning of an estimate in the operator (L{sup 2}(Ω)→L{sup 2}(Ω))-norm for the difference of the resolvents of the original and homogenized problems. We also find an approximation to the resolvent of the original problem in the operator (L{sup 2}(Ω)→H{sup 1}(Ω))-norm. Bibliography: 24 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

4-Clique network minor embedding for quantum annealers

Quantum annealing is a quantum algorithm for computing solutions to combinatorial optimization problems. This study proposes a method for minor embedding optimization problems onto sparse quantum annealing hardware graphs called 4-clique network minor embedding. This method is in contrast to the standard minor embedding technique of using a path of linearly connected qubits in order to represent a logical variable state. The 4-clique minor embedding is possible on Pegasus graph connectivity, which is the native hardware graph for some of the current D-Wave quantum annealers. The Pegasus hardware graph contains many cliques of size 4, making it possible to form a graph composed entirely of paths of connected 4-cliques on which a problem can be minor-embedded. The 4-clique chains come at the cost of additional qubit usage on the hardware graph, but they allow for stronger coupling within each chain, thereby increasing chain integrity, reducing chain breaks, and allow for greater usage of the available energy scale for programming logical problem coefficients on current quantum annealers. The 4-clique minor embedding technique is compared with the standard linear path minor embedding with experiments on two D-Wave quantum annealing processors with Pegasus hardware graphs. We show proof-of-concept experiments where the 4-clique minor embeddings can use weak chain strengths while successfully carrying out the computation of minimizing random all-to-all spin glass problem instances. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

WE-H-BRC-02: Failure Mode and Effect Analysis of Liver Stereotactic Body Radiotherapy

Purpose: To identify areas of improvement in our liver stereotactic body radiation therapy (SBRT) program, using failure mode and effect analysis (FMEA). Methods: A multidisciplinary group consisting of one physician, three physicists, one dosimetrist and two therapists was formed. A process map covering 10 major stages of the liver SBRT program from the initial diagnosis to post treatment follow-up was generated. A total of 102 failure modes, together with their causes and effects, were identified. The occurrence (O), severity (S) and lack of detectability (D) were independently scored. The ranking was done using the risk probability number (RPN) defined as the product of average O, S and D numbers for each mode. The scores were normalized to remove inter-observer variability, while preserving individual ranking order. Further, a correlation analysis on the overall agreement on rank order of all failure modes resulted in positive values for successive pairs of evaluators. The failure modes with the highest RPN value were considered for further investigation. Results: The average normalized RPN values for all modes were 39 with a range of 9 to 103. The FMEA analysis resulted in the identification of the top 10 critical failures modes as: Incorrect CT-MR registration, MR scan not performed in treatment position, patient movement between CBCT acquisition and treatment, daily IGRT QA not verified, incorrect or incomplete ITV delineation, OAR contours not verified, inaccurate normal liver effective dose (Veff) calculation, failure of bolus tracking for 4D CT scan, setup instructions not followed for treatment and plan evaluation metrics missed. Conclusion: The application of FMEA to our liver SBRT program led to the identification and possible improvement of areas affecting patient safety.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Strangeness-neutral equation of state for QCD with a critical point

We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth-order in µ B /T. It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trejectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Toward Improving the Generation Quality of Autoregressive Slot VAEs

Unconditional scene inference and generation are challenging to learn jointly with a single compositional model. Despite encouraging progress on models that extract object-centric representations (“slots”) from images, unconditional generation of scenes from slots has received less attention. This is primarily because learning the multiobject relations necessary to imagine coherent scenes is difficult. We hypothesize that most existing slot-based models have a limited ability to learn object correlations. We propose two improvements that strengthen object correlation learning. The first is to condition the slots on a global, scene-level variable that captures higher-order correlations between slots. Second, we address the fundamental lack of a canonical order for objects in images by proposing to learn a consistent order to use for the autoregressive generation of scene objects. Specifically, we train an autoregressive slot prior to sequentially generate scene objects following a learned order. Ordered slot inference entails first estimating a randomly ordered set of slots using existing approaches for extracting slots from images, then aligning those slots to ordered slots generated autoregressively with the slot prior. Our experiments across three multiobject environments demonstrate clear gains in unconditional scene generation quality. Detailed ablation studies are also provided that validate the two proposed improvements.

MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗