Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties
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Mallen, Alex T. (ORCID:0000000251201350)↗
SEARCH · Engineering Papers
Results for “Probabilistic Uncertainty”
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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Final Technical Report: Probabilistic Learning, Dimension Reduction, and Spectral Representations for High-Dimensional Uncertainty Quantification
Final Technical Report
Ghanem, Roger [University of Southern California] ↗
Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling
Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.
42 ENGINEERING↗
Combined Data and Deep Learning Model Uncertainties: An Application to the Measurement of Solid Fuel Regression Rate
In complex physical process characterization, such as the measurement of the regression rate for solid hybrid rocket fuels, where both the observation data and the model used have uncertainties originating from multiple sources, combining these in a systematic way for quantities of interest (QoI) remains a challenge. In this paper, we present a forward propagation uncertainty quantification (UQ) process to produce a probabilistic distribution for the observed regression rate r. We characterized two input data uncertainty sources from the experiment (the distortion from the camera U c and the non-zero-angle fuel placement U Y ), the prediction and model form uncertainty from the deep neural network (U m ), as well as the variability from the manually segmented images used for training it (U s ). Here, we conducted seven case studies on combinations of these uncertainty sources with the model form uncertainty. The main contribution of this paper is the investigation and inclusion of the experimental image data uncertainties involved, and how to include them in a workflow when the QoI is the result of multiple sequential processes.
42 ENGINEERING↗
Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials
This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.
36 MATERIALS SCIENCE↗
Occlusion-Perturbed Deep Learning for Probabilistic Solar Forecasting via Sky Images
Solar forecasting is shifting to the probabilistic paradigm due to the inherent uncertainty within the solar resource. Input uncertainty quantification is one of the widely used and best-performing ways to model solar uncertainty. However, compared to other sources of inputs, such as numerical weather prediction models, pure sky image-based probabilistic solar forecasting lags behind. In this research, an occlusion-perturbed convolutional neural network, named the PSolarNet, is developed. The PSolarNet provides very short-term deterministic forecasts, forecast scenarios, and probabilistic forecasts of the global horizontal irradiance from sky image sequences. Case studies based on 6 years of open-source data show that the developed PSolarNet is able to generate accurate 10-minute ahead deterministic forecasts with a 5.62% normalized root mean square error, realistic and diverse forecast scenarios with a 0.966 average correlation with the actual time series, and reliable and sharp probabilistic forecasts with a 2.77% normalized continuous ranked probability score.
Bayesian model averaging↗
Occlusion-Perturbed Deep Learning for Probabilistic Solar Forecasting via Sky Images: Preprint
Solar forecasting is shifting to the probabilistic paradigm due to the inherent uncertainty within the solar resource. Input uncertainty quantification is one of the widely used and best-performing ways to model solar uncertainty. However, compared to other sources of inputs, such as numerical weather prediction models, pure sky image-based probabilistic solar forecasting lags behind. In this research, an occlusion-perturbed convolutional neural network, named the PSolarNet, is developed. The PSolarNet provides very short-term deterministic forecasts, forecast scenarios, and probabilistic forecasts of the global horizontal irradiance from sky image sequences. Case studies based on 6 years of open-source data show that the developed PSolarNet is able to generate accurate 10-minute ahead deterministic forecasts with a 5.62% normalized root mean square error, realistic and diverse forecast scenarios with a 0.966 average correlation with the actual time series, and reliable and sharp probabilistic forecasts with a 2.77% normalized continuous ranked probability score.
Bayesian model averaging↗
Quantifying uncertainties on fission fragment mass yields with mixture density networks
Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we explore the use of one such probabilistic network, the mixture density network (MDN), to reproduce fission yields and their uncertainties. In this paper, we study mass yields for the spontaneous fission of 252 Cf, exploring the number of training samples needed for converged predictions, how different levels of uncertainty propagate from the training set to the MDN predictions, and how well physical constraints of the yields—such as normalization and symmetry—are upheld by the algorithm. Finally, we test the ability of the MDN to interpolate between and extrapolate beyond samples in the training set using energy-dependent mass yields for the neutron-induced fission on 235 U. The MDN provides a reliable way to include and predict uncertainties and is a promising path forward for supplementing sparse sets of nuclear data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Probabilistic evolution of stochastic dynamical systems: A meso-scale perspective
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features are used to quantify and propagate uncertainties associated with the initial conditions, external excitations, etc. From a probabilistic modeling standing point, two broad classes of methods exist, i.e. macro-scale methods and micro-scale methods. Classically, macro-scale methods such as statistical moments-based strategies are usually too coarse to capture the multi-mode shape or tails of a non-Gaussian distribution. Micro-scale methods such as random samples-based approaches, on the other hand, become computationally very challenging in dealing with high-dimensional stochastic systems. In view of these potential limitations, a meso-scale scheme is proposed here that utilizes a meso-scale statistical structure to describe the dynamical evolution from a probabilistic perspective. The significance of this statistical structure is twofold. First, it can be tailored to any arbitrary random space. Second, it not only maintains the probability evolution around sample trajectories but also requires fewer meso-scale components than the micro-scale samples. To demonstrate the efficacy of the proposed meso-scale scheme, a set of examples of increasing complexity are provided. Connections to the benchmark stochastic models as conservative and Markov models along with practical implementation guidelines are presented.
97 MATHEMATICS AND COMPUTING↗
Microgrid energy scheduling under uncertain extreme weather: Adaptation from parallelized reinforcement learning agents
Microgrids are useful solutions for integrating renewable energy resources and providing seamless green electricity to minimize carbon footprint. In recent years, extreme weather events happened often worldwide and caused significant economic and societal losses. Such events bring uncertainties to the microgrid energy scheduling problems and increase the challenges of microgrid operation. Traditional optimization approaches suffer from the inaccuracy of the uncertain microgrid model and the unseen events. Existing reinforcement learning (RL) - based approaches are also hampered by the limited generalization and the increasing computational burden when stochastic formulations are required to accommodate the uncertainties. This paper proposes a new parallelized reinforcement learning (PRL) method based on the probabilistic events to handle the microgrid energy uncertainties. Specifically, several local learning agents are employed to interact with pertinent microgrid environments in a distributed manner and report outcomes to the global agent, which will optimize microgrid energy resources online during extreme events. The stochastic microgrid energy optimization problem is reformulated to include all possible scenarios with probabilities. The advantage estimate functions of learning agents are designed with a backward sweep to transfer the outcomes to the value function updating process. Two simulation studies, stochastic optimization and online testing, are performed to compare with several existing RL approaches. Results substantiate that the proposed PRL method can achieve up to 20% optimization performance improvement with 4 and 28 times less computation cost than Q-learning with experience replay and multi-agent Q-learning approaches, respectively.
24 POWER TRANSMISSION AND DISTRIBUTION↗
On the quantification and efficient propagation of imprecise probabilities with copula dependence
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be mutually independent or correlated by a multivariate Gaussian distribution. However, this subjective assumption may introduce bias in the response estimate if the real dependence structure deviates from this assumption. In this work, we overcome this limitation by introducing a flexible copula dependence model to capture complex dependencies. Here, a hierarchical Bayesian multimodel approach is proposed to quantify uncertainty in dependence model-form and model parameters that result from small data sets. This approach begins by identifying, through Bayesian multimodel inference, a set of candidate marginal models and their corresponding model probabilities, and then estimating the uncertainty in the copula-based dependence structure, which is conditional on the marginals and their parameters. The overall uncertainties integrating marginals and copulas are probabilistically represented by an ensemble of multivariate candidate densities. A novel importance sampling reweighting approach is proposed to efficiently propagate the overall uncertainties through a computational model. Through an example studying the influence of constituent properties on the out-of-plane properties of transversely isotropic E-glass fiber composites, we show that the composite property with copula-based dependence model converges to the true estimate as data set size increases, while an independence or arbitrary Gaussian correlation assumption leads to a biased estimate.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Probabilistic neural networks for improved analyses with phenomenological R -matrix
Here we present a method for measurement analyses based on probabilistic deep neural networks that provide several advantages over conventional analyses with phenomenological models. These include predicting physical quantities directly from data, the rapid generation of statistically robust uncertainties, and the ability to bypass some parameters that may induce ambiguities and complications in data analysis. As deep learning methods make predictions through “black boxes,” the uncertainty quantification is typically challenging. We use a probabilistic framework that provides thorough uncertainty quantification and is straightforward to follow in practice. With the network architecture based on the Transformer, we demonstrate the current method for predicting nuclear resonance parameters from scattering data using the phenomenological R-matrix model.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
EMPIRICAL VALIDATION OF MULTI-ZONE BUILDING AND HVAC SYSTEM MODELS UNDER UNCERTAINTY
This study implemented a framework of empirical validation of building energy models under uncertainty to a set of controlled experiments that aim to validate multi-zone building and HVAC system models. Energy models were created through iterative acquisitions of information and data and uses measurement data from various types of sensors as both inputs and as observations to validate predictions. Experimental and modeling uncertainties were quantified and propagated accordingly, and probabilistic accuracy metrics were used to evaluate the agreement between model predictions and observations under uncertainty. Sensitivity analysis was performed to identify the most influential uncertainties that will be prioritized to be addressed in the next steps. Current results of two cooling tests show an overall good agreement between predictions and observations on a set of HVAC system outputs despite considerable and influential uncertainty in DX cooling coil COP. Agreements on zone-level responses vary notably among individual rooms, likely because of significant uncertainties in room radiation heat gain and system supply air.
Li, Qi↗
A Preliminary Radiological Risk Assessment Model for Disposition of Remote-Handled Transuranic Wastes at Los Alamos National Laboratory Area G - 20116
The U.S. Department of Energy (DOE) operates a low-level radioactive waste (LLW) disposal site at Material Disposal Area G, in Los Alamos, New Mexico, USA. Area G has been the primary LLW disposal site for Los Alamos National Laboratory (LANL) since the 1960's. In addition to LLW, Area G is host to a variety of other wastes, the disposition of which must be determined before closure of the site. A probabilistic Radiological Risk Assessment (RRA) for Area G is used in order to support decision making regarding some wastes that are not addressed in the extant Area G Performance Assessment (PA) and Composite Analysis (CA). Between 1979 and 1987, 33 special shafts were augered into the Bandelier Tuff at Area G. This volcanic tuff is present across Pajarito Plateau on the eastern slopes of the Jemez Mountains, and varies widely in its consistency, from weakly indurated non-welded layers to welded layers that uphold the mesa cliffs of the Plateau. These mesas are home to LANL, Area G, and the townsites of Los Alamos and White Rock, with residences about 1400 m from Area G. The 33 Shafts were lined with steel casing, and contain remote-handled (RH) transuranic wastes (TRU) resulting from experiments and analysis performed in special glove boxes at the Chemistry and Metallurgy Research (CMR) facility at LANL. Some of these wastes originated as used nuclear fuel. The purpose of the Area G RRA is to evaluate the potential future risk to humans and the environment from the RH TRU in the 33 Shafts in the context of the risk associated with the surrounding wastes at Area G. The analysis is responsive to expectations outlined in DOE Order 458.1, Radiation Protection of the Public and the Environment, and is informed by the Manual and Guidance accompanying DOE O 435.1, Radioactive Waste Management. Because the waste meets the definition of TRU, the regulatory context necessarily takes into consideration the regulation governing the disposal of TRU from the U.S. Environmental Protection Agency (EPA): 40 CFR 191, Environmental Radiation Protection Standards for Management and Disposal of Spent Nuclear Fuel, High-Level and Transuranic Radioactive Wastes. Given the broader regulatory context for the RRA, the analysis is subject to different assumptions from those made in the existing DOE O 435.1 PA and CA, such as allowing for future occupation of the site. The analysis begins with a comprehensive evaluation of features, events, processes, and exposure scenarios (FEPS) for Area G and the wastes it contains. These FEPSs are screened to eliminate from further consideration those of extremely low probability and/or consequence, and a conceptual site model (CSM) is subsequently developed. The scope and structure of the Area G RRA Model is informed by this CSM, and the Area G RRA Model is developed using the GoldSim systems analysis modeling platform. This paper presents the initial version of a defensible, transparent, and reasonably realistic model, which is based on the state of knowledge of the wastes, the site, and the FEPSs that govern contaminant transport from wastes into the environment and subsequent exposures to humans and other biota. Probabilistic model input distributions represent uncertainties inherent in the real and modeled systems. The results of the Area G RRA Model inform decisions regarding the disposition of the RH TRU in the 33 Shafts. (authors)
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Probabilistic data fusion and physics-informed machine learning: A new paradigm for modeling under uncertainty, and its application to accelerating the discovery of new materials
In this report we summarize the work conducted by PI Perdikaris and his group under this Early Career project DE–SC0019116 during the period of 09/01/2018 – 08/31/2023. The central aim of the work was to introduce a new paradigm for scientific data analysis that can seamlessly synthesize rigorous mathematical modeling with data of variable fidelity (e.g., measurements at multiple scales/resolutions or predictions of variable fidelity models) and multiple modalities (e.g., images, time–series, or scattered measurements). The setting we are interested in involves complex systems that are partially observed and whose dynamical behavior could be hard to model or totally unknown. The inherent uncertainty associated with this setting necessitates a departure from the classical deterministic realm of modeling and scientific computation, and, consequently, our main building blocks can no longer be crisp deterministic numbers and governing laws, but instead we must operate with probabilistic models.
97 MATHEMATICS AND COMPUTING↗
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.
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Summary of the 5th IAEA technical meeting on fusion data processing, validation and analysis (FDPVA)
The purpose of the 5th International Atomic Energy Agency technical meeting on fusion data processing, validation and analysis (FDPVA) (Ghent University, Ghent, Belgium, 12–15 June 2023) was to provide a platform during which a set of topics relevant to FDPVA were discussed with the view of meeting the needs of next step fusion devices such as ITER. The validation and analysis of experimental data obtained from diagnostics used to characterize fusion plasmas are crucial for a knowledge-based understanding of the physical processes governing the dynamics of these plasmas. This paper presents the recent progress and achievements in the domain of plasma diagnostics data analysis and synthetic diagnostics reported at the meeting, including concept description of new devices; fusion databases; integrated data analysis; inverse problems; uncertainty propagation, verification and validation; probabilistic methods and machine learning. The relevant results underline trends observed in the current major fusion confinement devices.
fusion databases↗
Scenario development for safety assessment in deep geologic disposal of high-level radioactive waste and spent nuclear fuel: A review
Radiation and radioactive substances result in the production of radioactive wastes which require safe management and disposal to avoid risks to human health and the environment. To ensure permanent safe disposal, the performance of a deep geological repository for radioactive waste is assessed against internationally agreed risk-based standards. Assessing postclosure safety of the future system's evolution includes screening of features, events, and processes (FEPs) relevant to the situation, their subsequent development into scenarios, and finally the development and execution of safety assessment (SA) models. Global FEP catalogs describe important natural and man-made repository system features and identify events and processes that may affect these features into the future. By combining FEPs, many of which are uncertain, different possible future system evolution scenarios are derived. Repository licensing should consider both the reference or “base” evolution as well as alternative futures that may lead to radiation release, pollution, or exposures. Scenarios are used to derive and consider both base and alternative evolutions, often through production of scenario-specific SA models and the recombination of their results into an assessment of the risk of harm. Furthermore, while the FEP-based scenario development process outlined here has evolved somewhat since its development in the 1980s, the fundamental ideas remain unchanged. A spectrum of common approaches is given here (e.g., bottom–up vs. top–down scenario development, probabilistic vs. bounding handling of uncertainty), related to how individual numerical models for possible futures are converted into a determination as to whether the system is safe (i.e., how aleatoric uncertainty and scenarios are integrated through bounding or Monte Carlo approaches).
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