STUDIES IN THE ASYMPTOTIC THEORY OF CONTROL SYSTEMS, I. STOCHASTIC AND DETERMINISTIC N-STAGE PROCESSES
Asymptotic theory of control - stochastic and deterministic n-stage processes
N-STAGE PROCESS↗
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Results for “deterministic method”
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.
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Assessing Effects of Climate and Technology Uncertainties in Large Natural Resource Allocation Problems
The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible, investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. In this paper, we apply the SCEQ algorithm (Cai and Judd, 2023) to solve a large-scale dynamic stochastic global land resource use problem with stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters and bounded shocks, the range of land conversion is considerably smaller for the dynamic stochastic model than for deterministic scenario analysis.
numerical methods↗
Algorithm 1049: The Delaunay Density Diagnostic
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.
97 MATHEMATICS AND COMPUTING↗
A Distributionally Robust Optimization Framework for Stochastic Assessment of Power System Flexibility in Economic Dispatch
Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the economic dispatch problem on four distinct IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.
distributionally robust optimization↗
Endogenizing Probabilistic Resource Adequacy Risks in Deterministic Capacity Expansion Models
In this work, we demonstrate how power system capacity expansion models can understate the stochastic effects of thermal outages when considering resource availabilities on an hourly expected value basis, yielding system designs with multiple orders of magnitude more shortfall risk than stated adequacy targets. We develop a novel approximation approach to efficiently endogenize awareness of this risk in a deterministic, linear capacity expansion framework. We compare this approach to exogenous tuning of an energy reserve margin, the leading alternative method to compensate for unmodeled probabilistic shortfall risk. Empirical results from a test system show that the new endogenous method cost-effectively meets all regional reliability targets with a single optimization solve, and produces a near-identical system design as the incumbent method without the need for repeated re-optimizations to find an appropriate reserve level. The endogenous method may also use iterative re-optimizations to further improve solution quality, although these incremental benefits were modest in the system studied.
capacity expansion modeling↗
Leveraging Inequality-Constrained Data for Enhanced Liquidus Temperature Prediction in Nuclear Waste Glass Melts
Inequality-constrained data are frequently discarded in engineering, leading to significant information loss in data-scarce domains like glass characterization in nuclear waste vitrification. This paper presents a nonparametric censored-data regression framework based on an l1-norm optimization criterion that leverages slack variables to integrate left-, right-, and interval-constrained observations into training without distributional assumptions. Validated on synthetic data and a Physics-Informed Neural Network (PINN) for predicting liquidus temperature (TL), the method improved R2 from 0.60 to 0.89 and reduced Mean Absolute Error (MAE) by 48% (51.46 to 26.89?rC) on deterministic values. The traditional models failed to satisfy any inequality constraints while the proposed l1-norm PINN satisfies 81.25% of the constraints. The proposed framework effectively extracts actionable information from previously unusable data to enhance predictive accuracy, reduce epistemic uncertainty, and ensure physical consistency in complex industrial applications.
Garcia-Morado, Erick↗
A procedure for combining acoustically induced and mechanically induced loads (first passage failure design criterion)
The combined load statistics are developed by taking the acoustically induced load to be a random population, assumed to be stationary. Each element of this ensemble of acoustically induced loads is assumed to have the same power spectral density (PSD), obtained previously from a random response analysis employing the given acoustic field in the STS cargo bay as a stationary random excitation. The mechanically induced load is treated as either (1) a known deterministic transient, or (2) a nonstationary random variable of known first and second statistical moments which vary with time. A method is then shown for determining the probability that the combined load would, at any time, have a value equal to or less than a certain level. Having obtained a statistical representation of how the acoustic and mechanical loads are expected to combine, an analytical approximation for defining design levels for these loads is presented using the First Passage failure criterion.
Crowe, D. R.↗
Structure of nonevaporating sprays. I - Initial conditions and mean properties
Structure measurements were completed within the dilute portion of axisymmetric nonevaporating sprays. Measurements included: mean velocities, velocity fluctuations, and Reynolds stress of the gas phase; and mean velocities, fluctuating velocities, mass flux, and diameter distributions of the drop phase. The measurements were used to evaluate three typical methods of analyzing sprays: (1) a locally homogeneous flow (LHF) analysis, where slip between the phases is neglected; (2) a deterministic separated flow (DSF) analysis, where slip is considered but effects of drop interactions with turbulence are ignored; and (3) a stochastic separated flow (SSF) analysis, where effects of both slip and turbulence are considered using random-walk computations for drop motion. Measurements of initial conditions of both phases near the injector, mean gas-phase properties, and liquid flux distributions are described herein. Best agreement between predictions and measurements was obtained with the SSF model, which provided a reasonable representation of turbulent dispersion of drops. A companion paper presents additional measurements of drop continuous phase properties.
Solomon, A. S. P.↗
Parameter estimation in linear models of the human operator in a closed loop with application of deterministic test signals
Parameter estimation techniques are discussed with emphasis on unbiased estimates in the presence of noise. A distinction between open and closed loop systems is made. A method is given based on the application of external forcing functions consisting of a sun of sinusoids; this method is thus based on the estimation of Fourier coefficients and is applicable for models with poles and zeros in open and closed loop systems.
Vanlunteren, A.↗
Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach
This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.
Aguilo, Miguel A.↗
A computational risk assessment approach to the integration of seismic and flooding hazards with internal hazards
Probabilistic risk assessment (PRA) of nuclear power plants historically focuses on internal events at the plant, rather than external hazards. Although the importance of external hazards risk analysis is now well recognized, the methods for assessing the risk associated with low probability external hazards rely heavily on subjective judgment of specialists, often using conservative elements in the analysis, as is the case with the Conservative Deterministic Failure Margin approach commonly used for seismic PRA. The U.S. Department of Energy Light Water Reactor Sustainability program has been investigating the use of first principles analyses to provide a more realistic assessment of the risk of external hazards, in a process called computational risk assessment (CRA). Efforts undertaken are described in the development of CRA methods to integrate the risk associated with seismic and flooding events into traditional PRA. Further, the results of four case studies are presented.
99 GENERAL AND MISCELLANEOUS↗
Effect of Cu dopant on the structural, magnetic and electrical properties of Ni-Zn ferrites
Highlights: • Ni{sub 0.8-x}Cu{sub x}Zn{sub 0.2}Fe{sub 2}O{sub 4} (x = 0.0, 0.2, 0.4, 0.6) Spinel ferrites synthesized through auto-combustion method and their structural and magnetic properties investigated by XRD, SEM, FTIR and VSM measurements. • Increase in crystal and particle size and decrease in saturation magnetization resulted from substitution on Ni by Cu. • Observed values of (ε) and (tanδ) of the samples show the deterministic role of density in electrical properties of spinel ferrites. - Abstract: Ni{sub 0.8-x}Cu{sub x}Zn{sub 0.2}Fe{sub 2}O{sub 4} (x = 0.0, 0.2, 0.4, 0.6) ferrite was synthesized through auto-combustion method. (XRD) patterns confirmed the crystallization of the samples in spinel structure. FESEM showed that the size of ferrite particles are about few hundred nanometers and with increase in Cu concentration (x) in the structure there is increase in particle size. Fourier transform infrared (FTIR) spectrometry indicates that octahedral and tetrahedral sites are formed. Vibrating sample magnetometer (VSM) results proved reduction of saturation magnetization (M{sub s}) by increasing Cu content, which is explained according to the ferrimagnetic nature of these samples in which Ni is replaced by Cu at octahedral site. Real part of dielectric constant (ε) and loss tangent (tanδ) of samples were also studied in frequency range of 100–20000 Hz. Results showed an increase in ε and tanδ of the sample with x = 0.6 which is considered to be the result of higher density of this sample.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Efficient Decision Trees for Tensor Regressions
Here, we proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variables are tensors (i.e., multi-way arrays). We devised and implemented fast randomized and deterministic algorithms for efficient fitting of scalar-on-tensor trees, making TT competitive against tensor-input GP models (Yu, Li, and Liu; Sun et al.). Based on scalar-on-tensor tree models, we extend our method to tensor-on-tensor problems using additive tree ensemble approaches. Theoretical justification and extensive experiments, including testing robustness to entrywise input tensor noise, are provided on real and synthetic datasets to illustrate the performance of TT. Our implementation is provided at https://github.com/hrluo/TensorDecisionTreeRegressor. Supplementary materials for this article are available online.
Decision tree regressions↗
Automated label flows for excited states of correlation functions in lattice gauge theory
Extracting excited states from lattice gauge theory correlation functions can be achieved through $χ^2$ minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. Further, as an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A Survey of Formal Methods for Intelligent Swarms
Swarms of intelligent autonomous spacecraft, involving complex behaviors and interactions, are being proposed for future space exploration missions. Such missions provide greater flexibility and offer the possibility of gathering more science data than traditional single spacecraft missions. The emergent properties of swarms make these missions powerful, but simultaneously far more difficult to design, and to assure that the proper behaviors will emerge. These missions are also considerably more complex than previous types of missions, and NASA, like other organizations, has little experience in developing or in verifying and validating these types of missions. A significant challenge when verifying and validating swarms of intelligent interacting agents is how to determine that the possible exponential interactions and emergent behaviors are producing the desired results. Assuring correct behavior and interactions of swarms will be critical to mission success. The Autonomous Nano Technology Swarm (ANTS) mission is an example of one of the swarm types of missions NASA is considering. The ANTS mission will use a swarm of picospacecraft that will fly from Earth orbit to the Asteroid Belt. Using an insect colony analogy, ANTS will be composed of specialized workers for asteroid exploration. Exploration would consist of cataloguing the mass, density, morphology, and chemical composition of the asteroids, including any anomalous concentrations of specific minerals. To perform this task, ANTS would carry miniaturized instruments, such as imagers, spectrometers, and detectors. Since ANTS and other similar missions are going to consist of autonomous spacecraft that may be out of contact with the earth for extended periods of time, and have low bandwidths due to weight constraints, it will be difficult to observe improper behavior and to correct any errors after launch. Providing V&V (verification and validation) for this type of mission is new to NASA, and represents the cutting edge in system correctness, and requires higher levels of assurance than other (traditional) missions that use a single or small number of spacecraft that are deterministic in nature and have near continuous communication access. One of the highest possible levels of assurance comes from the application of formal methods. Formal methods are mathematics-based tools and techniques for specifying and verifying (software and hardware) systems. They are particularly useful for specifying complex parallel systems, such as exemplified by the ANTS mission, where the entire system is difficult for a single person to fully understand, a problem that is multiplied with multiple developers. Once written, a formal specification can be used to prove properties of a system (e.g., the underlying system will go from one state to another or not into a specific state) and check for particular types of errors (e.g., race or livelock conditions). A formal specification can also be used as input to a model checker for further validation. This report gives the results of a survey of formal methods techniques for verification and validation of space missions that use swarm technology. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft using the ANTS mission as an example system. This report is the first result of the project to determine formal approaches that are promising for formally specifying swarm-based systems. From this survey, the most promising approaches were selected and are discussed relative to their possible application to the ANTS mission. Future work will include the application of an integrated approach, based on the selected approaches identified in this report, to the formal specification of the ANTS mission.
Truszkowski, Walt↗
Nested polynomial trends for the improvement of Gaussian process-based predictors
The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits
Large-scale arrays of quantum-dot spin qubits in Si/SiGe quantum wells require large or tunable energy splittings of the valley states associated with degenerate conduction band minima. Existing proposals to deterministically enhance the valley splitting rely on sharp interfaces or modifications in the quantum well barriers that can be difficult to grow. Here, we propose and demonstrate a new heterostructure, the “Wiggle Well”, whose key feature is Ge concentration oscillations inside the quantum well. Experimentally, we show that placing Ge in the quantum well does not significantly impact our ability to form and manipulate single-electron quantum dots. We further observe large and widely tunable valley splittings, from 54 to 239 μ eV. Tight-binding calculations, and the tunability of the valley splitting, indicate that these results can mainly be attributed to random concentration fluctuations that are amplified by the presence of Ge alloy in the heterostructure, as opposed to a deterministic enhancement due to the concentration oscillations. Quantitative predictions for several other heterostructures point to the Wiggle Well as a robust method for reliably enhancing the valley splitting in future qubit devices.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Structure Retrieval at Atomic Resolution in the Presence of Multiple Scattering of the Electron Probe
Here, the projected electrostatic potential of a thick crystal is reconstructed at atomic resolution from experimental scanning transmission electron microscopy data recorded using a new generation fast-readout electron camera. This practical and deterministic inversion of the equations encapsulating multiple scattering that were written down by Bethe in 1928 removes the restriction of established methods to ultrathin (≲50 Å) samples. Instruments already coming on line can overcome the remaining resolution-limiting effects in this approaching due to finite probe-forming aperture size, spatial incoherence, and residual lens aberrations.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗