Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic approximation”

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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

DeepONet-grid-UQ: A trustworthy deep operator framework for predicting the power grid’s post-fault trajectories

This paper proposes a novel data-driven method for the reliable prediction of the power grid’s post-fault trajectories, i.e., the power grid’s dynamic response after a disturbance or fault. Here, the proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods’ predictive power and uncertainty quantification capability using the New York-New England power grid model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1992

Stochastic gyroresonant electron acceleration in a low-beta plasma. I - Interaction with parallel transverse cold plasma waves

The gyroresonance of electrons with parallel transverse cold plasma waves is considered, and the Fokker-Planck equation describing the evolution of the electron distribution function in the presence of a spectrum of turbulence is derived. A new resonance which produces a divergence in the Fokker-Planck coefficients is identified; it results when the electron is in gyroresonance with a wave that has a group velocity equal to the velocity of the electron along the magnetic field. Under the assumption of a power-law spectral density, the Fokker-Planck coefficients are calculated numerically, and their complicated momentum and pitch-angle dependence, as well as the influence of various approximations to the dispersion relation, gyroresonance condition, and spectral density are discussed. It is found that there is no resonance gap at any pitch angle as long as the full gyroresonance condition is used and waves propagating on both directions are present.

Steinacker, Juergen↗
DOE OSTI2026

Score-based deterministic density sampling

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

The Postshock Chemical Lifetimes of Outflow Tracers and a Possible New Mechanism to Produce Water Ice Mantles

We have used a coupled time-dependent chemical and dynamical model to investigate the lifetime of the chemical legacy in the wake of C-type shocks. We concentrate this study on the chemistry of H2O and O2, two molecules which are predicted to have abundances that are significantly affected in shock-heated gas. Two models are presented: (1) a three-stage model of preshock, shocked, and postshock gas; and (2) a Monte Carlo cloud simulation where we explore the effects of stochastic shock activity on molecular gas over a cloud lifetime. For both models we separately examine the pure gas-phase chemistry as well as the chemistry including the interactions of molecules with grain surfaces. In agreement with previous studies, we find that shock velocities in excess of 10 km/s are required to convert all of the oxygen not locked in CO into H2O before the gas has an opportunity to cool. For pure gas phase models the lifetime of the high water abundances, or "H2O legacy," in the postshock gas is approximately (4-7) x 10(exp 5) yr, independent of the gas density. A density dependence for the lifetime of H2O is found in gas-grain models as the water molecules deplete onto grains at the depletion timescale. Through the Monte Carlo cloud simulation we demonstrate that the time-average abundance of H2O, the weighted average of the amount of time gas spends in preshock, shock, and postshock stages, is a sensitive function of the frequency of shocks. Thus we predict that the abundance of H2O, and to a lesser extent O2, can be used to trace the history of shock activity in molecular gas. We use previous large-scale surveys of molecular outflows to constrain the frequency of 10 km/s shocks in regions with varying star formation properties and discuss the observations required to test these results. We discuss the postshock lifetimes for other possible outflow tracers (e.g., SiO and CH3OH) and show that the differences between the lifetimes for various tracers can produce potentially observable chemical variations between younger and older outflows. For gas-grain models we find that the abundance of water-ice on grain surfaces can be quite large and is comparable to that observed in molecular clouds. This offers a possible alternative method to create water mantles without resorting to grain surface chemistry: gas heating and chemical modification due to a C-type shock and subsequent depletion of the gas-phase species onto grain mantles.

Bergin, Edwin A.↗
DOE OSTI2020

Improved Fast Randomized Iteration Approach to Full Configuration Interaction

In this work, we present three modifications to our recently introduced fast randomized iteration method for full configuration interaction (FCI-FRI) and investigate their effects on the method’s performance for Ne, H 2 O, and N 2 . The initiator approximation, originally developed for full configuration interaction quantum Monte Carlo, significantly reduces statistical error in FCI-FRI when few samples are used in compression operations, enabling its application to larger chemical systems. The semistochastic extension, which involves exactly preserving a fixed subset of elements in each compression, improves statistical efficiency in some cases but reduces it in others. We also developed a new approach to sampling excitations that yields consistent improvements in statistical efficiency and reductions in computational cost. We discuss possible strategies based on our findings for improving the performance of stochastic quantum chemistry methods more generally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Initial study on cross-section generation requirements for a PBR equilibrium core

A Serpent model of the equilibrium core HTR-PM small modular nuclear reactor in China, was developed for use in cross-section preparation studies in order to guide methods development for the Griffin reactor multiphysics application. The model includes detailed isotopics for 10 distinct pebble burnup groups in 126 core zones with unique fuel and moderator temperatures obtained from a coupled neutronics-thermal-fluids equilibrium core calculation using Griffin-Pronghorn. A sensitivity study of the fuel and moderator temperatures for various core regions was performed with the MOOSE stochastic tools. The results show that the uncertainties are, not unexpectedly, dominated by the value of the fluid temperature and that the power level, heat transfer coefficient and effective conduction to neighboring pebbles and fluid constitute, at best, second order effects. The temperature uncertainty range varies from 28 K to 57 K between the core entry and exit planes, respectively, but these values are probably higher. We still have to quantify the significance of these uncertainties in the preparation of cross-sections in future work. In addition, we verified that the effective pebble approximation used in the PEBBED and V.S.O.P. computer codes works well for the preparation of region averaged cross-sections. Nevertheless, there are some discrepancies in the cross-sections when compared to the multi-pebble model, which could affect the prediction of peak values and the depletion calculation. We conclude that is highly desirable for future studies with Griffin to be able to handle both the 'effective' pebble approximation and the multi-pebble approach for various pebble burnup groups. This enables Griffin users with the flexibility to perform higher-fidelity studies. Finally, we initiated the preparation of cross-sections for various core regions from the full core Serpent reference model. We quantified the differences in 26 group cross-sections from infinite domain models versus the full core approach. These reference cross-sections will serve to verify the double heterogeneity, self-shielding, and spectrum-correction methods in Griffin. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

A Vibrational Energy Harvesting Sensor Based on Linear and Rotational Electromechanical Effects

In this investigation, a magnetically coupled double-spring design is presented for harvesting low-level non-stationary random vibrational energy. The sensor relies on multimodal coupling between the translation and rotation of a two-spring magnet and coil system to widen the harvesting bandwidth. Energy methods are used to develop a model to characterize the electromechanical response of the system, the solution of which is obtained using stochastic techniques based on a particle swarm algorithm. This approach provides an efficient method to estimate system parameters that otherwise are difficult or impossible to determine with independent measurements. The experimental results demonstrate agreement with the theoretical predictions over a limited bandwidth. The sensor can effectively harvest non-stationary vibration energy down to 10 -4 g within a limited bandwidth of 130–150 Hz. The sensor prototype has an operational volume of 2.6 cm 3 with a calculated power density of 0.2 W/cm 3 . The sensor’s small size results in a coupling efficiency of approximately 6% across the tested bandwidth.

42 ENGINEERING↗
NASA NTRS2015

Simulation of DNA Damage in Human Cells from Space Radiation Using a Physical Model of Stochastic Particle Tracks and Chromosomes

The formation of double-strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a recently developed model, in which chromosomes simulated by NASARTI (NASA Radiation Tracks Image) is combined with nanoscopic dose calculations performed with the Monte-Carlo simulation by RITRACKS (Relativistic Ion Tracks) in a voxelized space. The model produces the number of DSBs, as a function of dose for high-energy iron, oxygen, and carbon ions, and He ions. The combined model calculates yields of radiation-induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The merged computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The merged model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex-type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation.

Ponomarev, Artem↗
DOE OSTI2020

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2017

Evaluation of Galvanic Vestibular Stimulation System

Microgravity exposure results in an adaptive central reinterpretation of information from multiple sensory sources to produce a sensorimotor state appropriate for motor actions in this unique environment, but this new adaptive state is no longer appropriate for the 1-g gravitational environment on Earth. During these gravitational transitions, astronauts experience deficits in both perceptual and motor functions including impaired postural control, disruption in spatial orientation, impaired control of locomotion that include alterations in muscle activation variability, modified lower limb kinematics, alterations in head-trunk coordination as well as reduced dynamic visual acuity. Post-flight changes in postural and locomotor control might have adverse consequences if a rapid egress was required following a long-duration mission, where support personnel may not be available to aid crewmembers. The act of emergency egress includes, but is not limited to standing, walking, climbing a ladder, jumping down, monitoring displays, actuating discrete controls, operating auxiliary equipment, and communicating with Mission Control and recovery teams while maintaining spatial orientation, mobility and postural stability in order to escape safely. The average time to recover impaired postural control and functional mobility to preflight levels of performance has been shown to be approximately two weeks after long-duration spaceflight. The postflight alterations are due in part to central reinterpretation of vestibular information caused by exposure to microgravity. In this study we will use a commonly used technique of transcutaneous electrical stimulation applied across the vestibular end organs (galvanic vestibular stimulation, GVS) to disrupt vestibular function as a simulation of post-flight disturbances. The goal of this project is an engineering human-in-the-loop evaluation of a device that can degrade performance of functional tasks (e.g. to maintain upright balance) similar to what astronauts experience during transitions to new gravitational environments. Stochastic electrical stimulation can be applied to the vestibular system through electrodes placed over the mastoid process behind the ears in the binaural configuration resulting in stimulation in the mediolateral (side-to-side) plane. An additional electrode can be placed over the bony landmark of the tip of the c7 spinous process for the double monaural configuration, which will cause stimulation in the anteroposterior (forward-backward) plane. A portable constant current bipolar stimulator with subject isolation was designed and built to deliver the stimulus. The unit is powered using a 3.7 V battery pack and designed to produce currents up to 5 mA. The stimulator, controlled by a Raspberry Pi 3 computer, offers several stimulus signal generation options including a standalone mode, which uses onboard signal files stored on the flash memory card. Stochastic stimulation signals will be generated in 0-30 Hz frequency bandwidth. Stimulation amplitude can be increased incrementally to a maximum amplitude of 5.0 mA (e.g., 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 mA). In control trials, subjects will be experiencing vestibular stimulation with 0-mA current applied through the electrodes. The system will be evaluated at various levels of stimulation and in both the binaural and double monaural electrode configurations. One of the objectives is to identify stimulation levels producing effects most comparable to the post-flight disturbances. This is a pilot study that will set the stage for a larger, more comprehensive study that will investigate wider aspects of post-flight sensorimotor dysfunction and set sensorimotor standards for crew health.

Kofman, I. S.↗
DOE OSTI2020

Modeling Time-Dependent Surrogates of Additive-Manufactured Nuclear Fuels Processes

Additive manufacturing (AM) technology is being increasingly adopted in a wide variety of application areas for its ability to rapidly produce, prototype, and customize designs. Recently, a hybrid AM technique was successfully developed at Idaho National Laboratory (INL) to manufacture nuclear fuels [1]. Despite the advantages, this AM technique needs optimization due to defects from a highly complex melting and sintering process. The complex metallurgical phenomena during AM processes are strongly related to parameters such as applied laser power, traveling speed, and scan style, which could lead to differences in density, residual stress, crystallographic texture, and mechanical properties. In addition, stochastic variations in laser energy interaction and associated multiscale/multiphysics phenomena cause variations in microstructure evolution and mechanical properties. Currently, researchers at INL are focusing on developing a comprehensive modeling framework, leveraging INL’s simulation tools MOOSE/MARMOT/BISON/RAVEN [2-4] to describe all steps of this AM process across multiple length scales. Although this advanced framework plays a critical role in enabling enhancements to traditional trial and error approaches for design and optimization of nuclear fuel materials, it remains computationally intense, limiting its use in sensitivity and optimization analysis. In this case, an accurate and inexpensive surrogate becomes an effective tool for providing a tractable approximation of the underlying underline physics. Surrogate models generally not based on the physics of a system are purely mathematical models used to capture the relationships between specific system inputs and outputs. Popular approaches, including neural networks [5], response surfaces [6], and subspace-based reduced order models [7], have been applied to a wide range of disciplines, such as nuclear reactor design, aerospace design and automotive design. In this summary, we employ advanced time-dependent surrogate models such as high-dimensional model representation (HDMR) [8] and physics-informed deep neural network (PINNs) [9] to accelerate the design and optimization of AM process.

42 ENGINEERING↗
DOE OSTI2025

Effective description of ajar systems with a 𝑈⁡(1) symmetry

We introduce the concept of “ajar systems” as an intermediate case between closed and open systems, where the time scale for charge exchange with the environment is parametrically larger than all other characteristic time scales. The Schwinger-Keldysh effective action for such finite-temperature systems exhibits a symmetry group G 1 × G 2 weakly broken to its diagonal subgroup G diag , which we systematically describe using spurion techniques. For G = U(1), we calculate leading-order corrections to correlation functions in both diffusive and spontaneously broken phases. Unlike systems with approximate symmetries where both real and imaginary parts of dispersion relations receive corrections, ajar systems modify only the imaginary part—preserving gapless modes while adding finite damping.

Effective field theory↗
DOE OSTI2021

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, in this work, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Growth phase estimation for abundant bacterial populations sampled longitudinally from human stool metagenomes

Longitudinal sampling of the stool has yielded important insights into the ecological dynamics of the human gut microbiome. However, human stool samples are available approximately once per day, while commensal population doubling times are likely on the order of minutes-to-hours. Despite this mismatch in timescales, much of the prior work on human gut microbiome time series modeling has assumed that day-to-day fluctuations in taxon abundances are related to population growth or death rates, which is likely not the case. Here, we propose an alternative model of the human gut as a stationary system, where population dynamics occur internally and the bacterial population sizes measured in a bolus of stool represent a steady-state endpoint of these dynamics. We formalize this idea as stochastic logistic growth. We show how this model provides a path toward estimating the growth phases of gut bacterial populations in situ. We validate our model predictions using an in vitro Escherichia coli growth experiment. Finally, we show how this method can be applied to densely-sampled human stool metagenomic time series data. We discuss how these growth phase estimates may be used to better inform metabolic modeling in flow-through ecosystems, like animal guts or industrial bioreactors.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1994

Design and evaluation of a Stochastic Optimal Feed-forward and Feedback Technology (SOFFT) flight control architecture

This paper describes the design and evaluation of a stochastic optimal feed-forward and feedback technology (SOFFT) control architecture with emphasis on the feed-forward controller design. The SOFFT approach allows the designer to independently design the feed-forward and feedback controllers to meet separate objectives and then integrate the two controllers. The feed-forward controller has been integrated with an existing high-angle-of-attack (high-alpha) feedback controller. The feed-forward controller includes a variable command model with parameters selected to satisfy level 1 flying qualities with a high-alpha adjustment to achieve desired agility guidelines, a nonlinear interpolation approach that scales entire matrices for approximation of the plant model, and equations for calculating feed-forward gains developed for perfect plant-model tracking. The SOFFT design was applied to a nonlinear batch simulation model of an F/A-18 aircraft modified for thrust vectoring. Simulation results show that agility guidelines are met and that the SOFFT controller filters undesired pilot-induced frequencies more effectively during a tracking task than a flight controller that has the same feedback control law but does not have the SOFFT feed-forward control.

Ostroff, Aaron J.↗
DOE OSTI2023

Dynamic scaling of order parameter fluctuations in model B

Brookhaven National Laboratory has performed a dedicated set of experiments, called the Beam Energy Scan (BES), with the goal of location a possible critical point in the phase diagram of nuclear matter, This point is analogous to the endpoint of the liquid-gas phase transition in water, where the liquid phase corresponds to a phase of hadrons, and the gas phase to a plasma of quarks and gluons. In order to describe the data generated by these experiments we have studied numerical simulations of the stochastic diffusion equation with a conserved charge. Here, we focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent z ≃ 3.972(2), which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Mechanistic within-host mathematical model of inhalational anthrax

We present a mathematical model of the dynamics of Bacillus anthracis bacteria within the lymph nodes and blood of a host, following inhalation of an initial dose of spores. We also incorporate the dynamics of protective antigen, which is the binding component of the anthrax toxin produced by the bacteria. The model offers a mechanistic description of the early infection dynamics of inhalational anthrax, while its stochastic nature allows us to study the probabilities of different outcomes (for example, how likely it is that the infection will be cleared for a given inhaled dose of spores) in order to explain dose-response data for inhalational anthrax. The model is calibrated via a Bayesian approach, using in vivo data from New Zealand white rabbit and guinea pig infection studies, enabling within-host parameters to be estimated. We also leverage incubation-period data from the Sverdlovsk 1979 anthrax outbreak to show that the model can accurately describe human time-to-symptoms data under reasonable parameter regimes. Finally, we derive a simple approximate formula for the probability of symptom onset before time t, assuming that the number of inhaled spores has a Poisson distribution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green’s function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(N e 3 ), where N e is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗