Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “STOCHASTIC PROCESSES”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

Here, we develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics d X t = a (X t ) dt + b(X t ) d W t . We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u (x) = E x [$∫^{τ}_{0}$ g (X t ) dt ] + E x [ f (X τ )] for a domain Ω and the exit stopping time τ = inf t { t >0 | X i Ω}, where f , g are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward- Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case f = 0, g = 1 where u (x) = E x [τ]. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Statistical patterns of theory uncertainties

A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a description. We study uncertainty estimates for cross-section predictions based on scale variations across a large set of processes. We find patterns similar to a stochastic origin, with accurate uncertainties for processes mediated by the strong force, but a systematic underestimate for electroweak processes. We propose an improved scheme, based on the scale variation of reference processes, which reduces outliers in the mapping from leading order to next-to-leading-order in perturbation theory.

Ghosh, Aishik↗
DOE OSTI2021

Application of Sequential Design of Experiments (SDoE) to Large Pilot-Scale Solvent-Based CO2 Capture Process at Technology Centre Mongstad (TCM)

The United States Department of Energy’s Carbon Capture Simulation for Industry Impact (CCSI2) program has developed a framework for sequential design of experiments (SDoE) that aims to maximize knowledge gained from budget- and schedule-limited pilot scale testing. SDoE was applied to the planning and execution of campaigns for testing CO2 capture systems at pilot-scale in order to optimally allocate resources available for the testing. In this methodology, a stochastic process model is developed by quantifying the parametric uncertainty in submodels of interest; for a solvent-based CO2 capture system, these may include physical properties and equipment performance submodels (e.g., mass transfer, interfacial area). This uncertainty is propagated through the full process model, over variable operating conditions, for estimating the resulting uncertainty in key model outputs (e.g., percentage of CO2 capture, solvent regeneration energy requirement). In developing a data collection plan, the predicted output uncertainty is incorporated into an algorithm that seeks simultaneously to select process operating conditions for which the predicted uncertainty is relatively high and to ensure that the entire space of operation is well represented. This test plan is then used to guide operation of the pilot plant at varying steady-state conditions, with resulting process data incorporated into the existing model using Bayesian inference to refine parameter distributions. The updated stochastic model, with reduced parametric uncertainty from data collected, is then used to guide additional data collection, thus the sequential nature of the experimental design. The SDoE process was implemented at the pilot test unit (12 MWe in scale) at Norway’s Technology Centre Mongstad (TCM) in a summer 2018 test campaign with aqueous monoethanolamine (MEA). During the test campaign, the varied operating conditions included the flowrates of circulated solvent, flue gas, and reboiler steam and the CO2 concentration in the flue gas. The process data were used to update probability distributions of mass transfer and interfacial area parameters of a stochastic process model developed by the CCSI2 team. Two iterations of the SDoE process were executed, resulting in the uncertainty in model predicted CO2 capture percentage decreasing by an average of 58.0 ± 4.7% over the full input space of interest. This work demonstrates the potential of the SDoE process for model refinement through reduction in process model parametric uncertainty, and ultimately risk in scale-up, in CO2 capture technology performance.

carbon capture↗
DOE OSTI2021

Stochastic Kinetics of Nanocatalytic Systems

Catalytic reaction events occurring on the surface of a nanoparticle constitute a complex stochastic process. Although advances in modern single-molecule experiments enable direct measurements of individual catalytic turnover events occurring on a segment of a single nanoparticle, we do not yet know how to measure the number of catalytic sites in each segment or how the catalytic turnover counting statistics and the catalytic turnover time distribution are related to the microscopic dynamics of catalytic reactions. Here, we address these issues by presenting a stochastic kinetics for nanoparticle catalytic systems. We propose a new experimental measure of the number of catalytic sites in terms of the mean and variance of the catalytic event count. By considering three types of nanocatalytic systems, we investigate how the mean, the variance, and the distribution of the catalytic turnover time depend on the catalytic reaction dynamics, the heterogeneity of catalytic activity, and communication among catalytic sites. This work enables accurate quantitative analyses of single-molecule experiments for nanocatalytic systems and enzymes with multiple catalytic sites.

Statistical Physics↗
DOE OSTI2021

Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greater efficiency than fully-resolved classical models. In this review article, we first provide a broad overview of fractional-order derivatives with a clear emphasis on the stochastic processes that underlie their use. We then survey three exemplary application areas – subsurface transport, turbulence, and anomalous materials – in which fractional-order differential equations provide accurate and predictive models. For each area, we report on the evidence of anomalous behavior that justifies the use of fractional-order models, and survey both foundational models as well as more expressive state-of-the-art models. We also propose avenues for future research, including more advanced and physically sound models, as well as tools for calibration and discovery of fractional-order models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Multistage Stochastic optimization for mid-term integrated generation and maintenance scheduling of cascaded hydroelectric system with renewable energy uncertainty

The uncertainties resulting from the escalating penetration of renewable energy resources pose severe challenges to the efficient operation of modern power systems. Hydroelectricity is characterized by its flexibility, controllability, and reliability, and thus becomes one of the most ideal energy resources to hedge against such uncertainties. This paper studies the mid-term integrated generation and maintenance scheduling of a cascaded hydroelectric system (CHS) consisting of multiple cascaded reservoirs and hydroelectric units. To precisely describe the mid-term water regulation policies, the hydraulic coupling relationship and water-energy nexus of CHS are incorporated into the proposed optimization model. The uncertainties of natural water inflow and the power outputs of wind/solar energy generation are taken into consideration and captured via a stochastic process modeled by a scenario tree. A multistage stochastic optimization (MSO) approach is developed to coordinate the complementary operations of multiple energy resources, by optimizing the mid-term water resource management, generation scheduling, and maintenance scheduling of CHS. The proposed MSO model is formulated as a large-scale mixed-integer linear program that presents significant computational intractability. To address this issue, a tailored Benders decomposition algorithm is developed. Two real-world case studies are conducted to demonstrate the capability and characteristics of the proposed model and algorithm. The computational results show that the proposed MSO model can exploit the flexibility of hydroelectricity to efficiently respond to variable wind and solar power, and reserve water resources for the generation in peak months to reduce the consumption of fossil fuel. Furthermore, the proposed solution approach also exhibits promising computational efficiency when handling large-scale models.

13 HYDRO ENERGY↗
DOE OSTI2020

Probabilistic analysis of masked loads with aggregated photovoltaic production

In this paper we present a probabilistic analysis framework to estimate behind-the-meter photovoltaic generation in real time. We develop a forward model consisting of a spatiotemporal stochastic process that represents the photovoltaic generation and a stochastic differential equation with jumps that represents the demand. Here, we employ this model to disaggregate the behind-the-meter photovoltaic generation using net load and irradiance measurements.

14 SOLAR ENERGY↗
DOE OSTI2022

Microbiome assembly in thawing permafrost and its feedbacks to climate

Abstract The physical and chemical changes that accompany permafrost thaw directly influence the microbial communities that mediate the decomposition of formerly frozen organic matter, leading to uncertainty in permafrost–climate feedbacks. Although changes to microbial metabolism and community structure are documented following thaw, the generality of post‐thaw assembly patterns across permafrost soils of the world remains uncertain, limiting our ability to predict biogeochemistry and microbial community responses to climate change. Based on our review of the Arctic microbiome, permafrost microbiology, and community ecology, we propose that Assembly Theory provides a framework to better understand thaw‐mediated microbiome changes and the implications for community function and climate feedbacks. This framework posits that the prevalence of deterministic or stochastic processes indicates whether the community is well‐suited to thrive in changing environmental conditions. We predict that on a short timescale and following high‐disturbance thaw (e.g., thermokarst), stochasticity dominates post‐thaw microbiome assembly, suggesting that functional predictions will be aided by detailed information about the microbiome. At a longer timescale and lower‐intensity disturbance (e.g., active layer deepening), deterministic processes likely dominate, making environmental parameters sufficient for predicting function. We propose that the contribution of stochastic and deterministic processes to post‐thaw microbiome assembly depends on the characteristics of the thaw disturbance, as well as characteristics of the microbial community, such as the ecological and phylogenetic breadth of functional guilds, their functional redundancy, and biotic interactions. These propagate across space and time, potentially providing a means for predicting the microbial forcing of greenhouse gas feedbacks to global climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Latent Stochastic Differential Equations for Modeling Quasar Variability and Inferring Black Hole Properties

Quasars are bright and unobscured active galactic nuclei (AGN) thought to be powered by the accretion of matter around supermassive black holes at the centers of galaxies. The temporal variability of a quasar’s brightness contains valuable information about its physical properties. The UV/optical variability is thought to be a stochastic process, often represented as a damped random walk described by a stochastic differential equation (SDE). Upcoming wide-field telescopes such as the Rubin Observatory Legacy Survey of Space and Time (LSST) are expected to observe tens of millions of AGN in multiple filters over a ten year period, so there is a need for efficient and automated modeling techniques that can handle the large volume of data. Latent SDEs are machine learning models well suited for modeling quasar variability, as they can explicitly capture the underlying stochastic dynamics. In this work, we adapt latent SDEs to jointly reconstruct multivariate quasar light curves and infer their physical properties such as the black hole mass, inclination angle, and temperature slope. Our model is trained on realistic simulations of LSST ten year quasar light curves, and we demonstrate its ability to reconstruct quasar light curves even in the presence of long seasonal gaps and irregular sampling across different bands, outperforming a multioutput Gaussian process regression baseline. Our method has the potential to provide a deeper understanding of the physical properties of quasars and is applicable to a wide range of other multivariate time series with missing data and irregular sampling.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Stochastic and deterministic processes shape bioenergy crop microbiomes along a vertical soil niche

Abstract Sustainable biofuel cropping systems aim to address climate change while meeting energy needs. Understanding how soil and plant‐associated microbes respond to these different cropping systems is key to promoting agriculture sustainability and evaluating changes in ecosystem functions. Here, we leverage a long‐term biofuel cropping system field experiment to dissect soil and root microbiome changes across a soil‐depth gradient in poplar, restored prairie and switchgrass to understand their effects on the microbial communities. High throughput amplicon sequencing of the fungal internal transcribed spacer (ITS) and prokaryotic 16S DNA regions showed a common trend of root and soil microbial community richness decreasing and evenness increasing with depth. Ecological niche (root vs. soil) had the strongest effect on community structure, followed by depth, then crop. Stochastic processes dominated the structuring of fungal communities in deeper soil layers while operational taxonomic units (OTUs) in surface soil layers were more likely to co‐occur and to be enriched by plant hosts. Prokaryotic communities were dispersal limited at deeper depths. Microbial networks showed a higher density, connectedness, average degree and module size in deeper soils. We observed a decrease in fungal‐fungal links and an increase of bacteria–bacteria links with increasing depth in all crops, particularly in the root microbiome.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties

It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗
DOE OSTI2022

Random field optimization

Herein we present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Microbial community dynamics in the soil-root continuum are linked with plant species turnover during secondary succession

Grazing exclusion and land abandonment are commonly adopted to restore degraded ecosystems in semiarid and arid regions worldwide. However, the temporal variation in the soil- versus root-associated microbiome over plant species turnover during secondary succession has rarely been quantified. Using the chronosequence restored from fenced grassland and abandoned farmlands on the Loess Plateau of China, we characterized the dynamics of the soil- and root-associated microbiome of host plant with different dominance statuses during secondary succession from 0 to 40 years. Our results revealed that the root microhabitat, the host plant and their interactions were the main contributors to the bacterial community shift (R 2 = 15.5%, 8.1%, and 22.3%, respectively), and plant interspecies replacement had a greater effect on the shift in the root-associated microbial community than intraspecies replacement did during succession. The root-associated bacterial community of pioneer plants was particularly responsive to succession, especially the endosphere community. Endosphere microbial diversity was positively correlated with host plant coverage change, and the diversity and abundance of taxon recruitment into the endosphere of pioneer plants from the surrounding environment decreased as succession progressed. The community assembly processes also indicated that the endosphere microbiota are strongly selected in younger host plants, whereas stochastic processes dominate in aged host plants. Our study provides evidence of the unique response of the root-associated microbiome to the replacement of plant species during secondary succession, and the function of endosphere microbes should be considered when studying plant–microbe feedback.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Iyer, Gopal R.↗
DOE OSTI2022

Learning stochastic dynamics with statistics-informed neural network

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. Here, we devise mechanisms for training the neural network model to reproduce the correct statistical behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Code for the manuscript titled "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces"

We would like to disclose two scripts, written in Jupyter notebook, in which we implement the "Blackout Diffusion Process" described in the manuscript "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces" (LA-UR-23-20509), to be submitted to the International Conference of Machine Learning (ICML). The abstract of the manuscript is append below. == Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, which occur in many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process. We relate the theory to the existing continuous-state Gaussian diffusion and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce "Blackout Diffusion", which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10 dataset confirm the feasibility of generative diffusion modeling in a discrete space. Generalizing from specific (Gaussian) forward processes to a more general framework also sheds light on how to interpret generative diffusion models and their mathematical structure, which we comment on.

Lin, Yen Ting↗
DOE OSTI2024

Epigenetic drift underlies epigenetic clock signals, but displays distinct responses to lifespan interventions, development, and cellular dedifferentiation

Changes in DNA methylation with age are observed across the tree of life. The stereotypical nature of these changes can be modeled to produce epigenetic clocks capable of predicting chronological age with unprecedented accuracy. Despite the predictive ability of epigenetic clocks and their utility as biomarkers in clinical applications, the underlying processes that produce clock signals are not fully resolved, which limits their interpretability. Here, we develop a computational approach to spatially resolve the within read variability or “disorder” in DNA methylation patterns and test if age-associated changes in DNA methylation disorder underlie signals comprising epigenetic clocks. We find that epigenetic clock loci are enriched in regions that both accumulate and lose disorder with age, suggesting a link between DNA methylation disorder and epigenetic clocks. We then develop epigenetic clocks that are based on regional disorder of DNA methylation patterns and compare their performance to other epigenetic clocks by investigating the influences of development, lifespan interventions, and cellular dedifferentiation. We identify common responses as well as critical differences between canonical epigenetic clocks and those based on regional disorder, demonstrating a fundamental decoupling of epigenetic aging processes. Collectively, we identify key linkages between epigenetic disorder and epigenetic clocks and demonstrate the multifaceted nature of epigenetic aging in which stochastic processes occurring at non-random loci produce predictable outcomes.

59 BASIC BIOLOGICAL SCIENCES↗