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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.

Engineering↗
DOE OSTI2013

A probabilistic graphical model approach to stochastic multiscale partial differential equations

We develop a probabilistic graphical model based methodology to efficiently perform uncertainty quantification in the presence of both stochastic input and multiple scales. Both the stochastic input and model responses are treated as random variables in this framework. Their relationships are modeled by graphical models which give explicit factorization of a high-dimensional joint probability distribution. The hyperparameters in the probabilistic model are learned using sequential Monte Carlo (SMC) method, which is superior to standard Markov chain Monte Carlo (MCMC) methods for multi-modal distributions. Finally, we make predictions from the probabilistic graphical model using the belief propagation algorithm. Numerical examples are presented to show the accuracy and efficiency of the predictive capability of the developed graphical model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion

Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This paper presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery. The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2020

Benchmark probabilistic solar forecasts: Characteristics and recommendations

We illustrate and compare commonly used benchmark, or reference, methods for probabilistic solar forecasting that researchers use to measure the performance of their proposed techniques. A thorough review of the literature indicates wide variation in the benchmarks implemented in probabilistic solar forecast studies. To promote consistent and sensible methodological comparisons, we implement and compare ten variants from six common benchmark classes at two temporal scales: intra-hourly forecasts and hourly resolution forecasts. Using open-source Surface Radiation Budget Network (SURFRAD) data from 2018, these benchmark methods are compared using proper probabilistic metrics and common diagnostic tools. Practical implementation issues, such as the impact of missing data and applicability for operational forecasting, are also discussed. Furthermore, we make recommendations for practitioners on the appropriate selection of benchmark methods to properly showcase state-of-the-art improvements in forecast reliability and sharpness. All code and open-source data are available on Github for reproducibility and for other researchers to apply the same benchmark methods to their own data.

14 SOLAR ENERGY↗
DOE OSTI2012

CONSTRUCTION OF A CALIBRATED PROBABILISTIC CLASSIFICATION CATALOG: APPLICATION TO 50k VARIABLE SOURCES IN THE ALL-SKY AUTOMATED SURVEY

With growing data volumes from synoptic surveys, astronomers necessarily must become more abstracted from the discovery and introspection processes. Given the scarcity of follow-up resources, there is a particularly sharp onus on the frameworks that replace these human roles to provide accurate and well-calibrated probabilistic classification catalogs. Such catalogs inform the subsequent follow-up, allowing consumers to optimize the selection of specific sources for further study and permitting rigorous treatment of classification purities and efficiencies for population studies. Here, we describe a process to produce a probabilistic classification catalog of variability with machine learning from a multi-epoch photometric survey. In addition to producing accurate classifications, we show how to estimate calibrated class probabilities and motivate the importance of probability calibration. We also introduce a methodology for feature-based anomaly detection, which allows discovery of objects in the survey that do not fit within the predefined class taxonomy. Finally, we apply these methods to sources observed by the All-Sky Automated Survey (ASAS), and release the Machine-learned ASAS Classification Catalog (MACC), a 28 class probabilistic classification catalog of 50,124 ASAS sources in the ASAS Catalog of Variable Stars. We estimate that MACC achieves a sub-20% classification error rate and demonstrate that the class posterior probabilities are reasonably calibrated. MACC classifications compare favorably to the classifications of several previous domain-specific ASAS papers and to the ASAS Catalog of Variable Stars, which had classified only 24% of those sources into one of 12 science classes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Economic Dispatch for Microgrid Containing Electric Vehicles via Probabilistic Modelling

In this paper, an economic dispatch model with probabilistic modeling is developed for microgrid. Electric power supply in microgrid consists of conventional power plants and renewable energy power plants, such as wind and solar power plants. Due to the fluctuation of solar and wind plants' output, an empirical probabilistic model is developed to predict their hourly output. According to different characteristics of wind and solar plants, the parameters for probabilistic distribution are further adjusted individually for both power plants. On the other hand, with the growing trend of Plug-in Electric Vehicle (PHEV), an integrated microgrid system must also consider the impact of PHEVs. Not only the charging loads from PHEVs, but also the discharging output via Vehicle to Grid (V2G) method can greatly affect the economic dispatch for all the micro energy sources in microgrid. This paper presents an optimization method for economic dispatch in microgrid considering conventional, renewable power plants, and PHEVs. The simulation results reveal that PHEVs with V2G capability can be an indispensable supplement in modern microgrid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Probabilistic Wind Power Ramp Forecasting Based on a Scenario Generation Method

Wind power ramps (WPRs) are particularly important in the management and dispatch of wind power and currently drawing the attention of balancing authorities. With the aim to reduce the impact of WPRs for power system operations, this paper develops a probabilistic ramp forecasting method based on a large number of simulated scenarios. An ensemble machine learning technique is first adopted to forecast the basic wind power forecasting scenario and calculate the historical forecasting errors. A continuous Gaussian mixture model (GMM) is used to fit the probability distribution function (PDF) of forecasting errors. The cumulative distribution function (CDF) is analytically deduced. The inverse transform method based on Monte Carlo sampling and the CDF is used to generate a massive number of forecasting error scenarios. An optimized swinging door algorithm is adopted to extract all the WPRs from the complete set of wind power forecasting scenarios. The probabilistic forecasting results of ramp duration and start-time are generated based on all scenarios. Numerical simulations on publicly available wind power data show that within a predefined tolerance level, the developed probabilistic wind power ramp forecasting method is able to predict WPRs with a high level of sharpness and accuracy.

17 WIND ENERGY↗
DOE OSTI2018

Probabilistic Short-Term Wind Forecasting Based on Pinball Loss Optimization

Probabilistic wind power forecasts that quantify the uncertainty in wind output have the potential to aid in the economic grid integration of wind power at large penetration levels. In this paper, a novel probabilistic wind forecasting approach based on pinball loss optimization is proposed, in conjunction with a multi-model machine learning based ensemble deterministic forecasting framework. By assuming the point-forecasted value as the mean at each point, one unknown parameter (i.e., standard deviation) of a predictive distribution at each forecasting point is determined by minimizing the pinball loss. A surrogate model is developed to represent the unknown distribution parameter as a function of deterministic forecasts. This surrogate model can be used together with deterministic forecasts to predict the unknown distribution parameter and thereby generate probabilistic forecasts. Numerical results of case studies show that the proposed method has improved the pinball loss by up to 35% compared to a baseline quantile regression forecasting model.

17 WIND ENERGY↗
DOE OSTI2018

Coherent Probabilistic Solar Power Forecasting

Solar power has been growing rapidly in recent years. Many countries have invested in solar energy technology, especially in Photovoltaic (PV) power generation. With the increased penetration level, solar power forecasting becomes more challenging. To cope with solar power uncertainties, probabilistic forecasting provides more information than traditional point forecasting. Moreover, multiple PV sites with spatial-temporal correlations need to be taken into account. To produce probabilistic forecasts, this paper applies quantile regression on top of time series models. Considering the coherency among multiple PV sites, a reconciliation is applied using a copula-based bottom-up method or proportion-based top-down method. Numerical results show that the proposed methods efficiently produce accurate and coherent probabilistic solar power forecasts.

quantile regression↗
DOE OSTI2022

Data-Driven Probabilistic Voltage Risk Assessment of MiniWECC System with Uncertain PVs and Wind Generations using Realistic Data

Here, it is found from actual data that due to generation dispatch and uncertain renewable generations and loads with complicated correlations, inferring the probabilistic distributions for uncertain inputs is challenging. Many probabilistic power flow approaches have been developed in the literature but their validations using realistic systems and data are lacking. This paper proposes a data-driven probabilistic analysis approach for system risk assessment of the miniWECC system using actual data. The sparse Gaussian process (SGP) is advocated to quantify the impacts of uncertain inputs on voltage security. SGP does not need the probability distribution function of uncertain inputs, can handle correlations and is highly computationally efficient. Results on the miniWECC system using realistic data show that SGP outperforms existing approaches and is able to quantify the voltage violation risks.

17 WIND ENERGY↗
DOE OSTI2016

Probabilistic distributions of pinhole defects in atomic layer deposited films on polymeric substrates

Pinhole defects in atomic layer deposition (ALD) coatings were measured in an area of 30 cm{sup 2} in an ALD reactor, and these defects were represented by a probabilistic cluster model instead of a single defect density value with number of defects over area. With the probabilistic cluster model, the pinhole defects were simulated over a manufacturing scale surface area of ∼1 m{sup 2}. Large-area pinhole defect simulations were used to develop an improved and enhanced design method for ALD-based devices. A flexible thermal ground plane (FTGP) device requiring ALD hermetic coatings was used as an example. Using a single defect density value, it was determined that for an application with operation temperatures higher than 60 °C, the FTGP device would not be possible. The new probabilistic cluster model shows that up to 40.3% of the FTGP would be acceptable. With this new approach the manufacturing yield of ALD-enabled or other thin film based devices with different design configurations can be determined. It is important to guide process optimization and control and design for manufacturability.

42 ENGINEERING↗
DOE OSTI2015

Multiattribute probabilistic prostate elastic registration (MAPPER): Application to fusion of ultrasound and magnetic resonance imaging

Purpose: Transrectal ultrasound (TRUS)-guided needle biopsy is the current gold standard for prostate cancer diagnosis. However, up to 40% of prostate cancer lesions appears isoechoic on TRUS. Hence, TRUS-guided biopsy has a high false negative rate for prostate cancer diagnosis. Magnetic resonance imaging (MRI) is better able to distinguish prostate cancer from benign tissue. However, MRI-guided biopsy requires special equipment and training and a longer procedure time. MRI-TRUS fusion, where MRI is acquired preoperatively and then aligned to TRUS, allows for advantages of both modalities to be leveraged during biopsy. MRI-TRUS-guided biopsy increases the yield of cancer positive biopsies. In this work, the authors present multiattribute probabilistic postate elastic registration (MAPPER) to align prostate MRI and TRUS imagery. Methods: MAPPER involves (1) segmenting the prostate on MRI, (2) calculating a multiattribute probabilistic map of prostate location on TRUS, and (3) maximizing overlap between the prostate segmentation on MRI and the multiattribute probabilistic map on TRUS, thereby driving registration of MRI onto TRUS. MAPPER represents a significant advancement over the current state-of-the-art as it requires no user interaction during the biopsy procedure by leveraging texture and spatial information to determine the prostate location on TRUS. Although MAPPER requires manual interaction to segment the prostate on MRI, this step is performed prior to biopsy and will not substantially increase biopsy procedure time. Results: MAPPER was evaluated on 13 patient studies from two independent datasets—Dataset 1 has 6 studies acquired with a side-firing TRUS probe and a 1.5 T pelvic phased-array coil MRI; Dataset 2 has 7 studies acquired with a volumetric end-firing TRUS probe and a 3.0 T endorectal coil MRI. MAPPER has a root-mean-square error (RMSE) for expert selected fiducials of 3.36 ± 1.10 mm for Dataset 1 and 3.14 ± 0.75 mm for Dataset 2. State-of-the-art MRI-TRUS fusion methods report RMSE of 3.06–2.07 mm. Conclusions: MAPPER aligns MRI and TRUS imagery without manual intervention ensuring efficient, reproducible registration. MAPPER has a similar RMSE to state-of-the-art methods that require manual intervention.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-C-BRB-05: Determining the Adequacy of Auto-Contouring Via Probabilistic Assessment of Ensuing Treatment Plan Metrics in Comparison with Manual Contours

Purpose: To determine if auto-contour and manual-contour—based plans differ when evaluated with respect to probabilistic coverage metrics and biological model endpoints for prostate IMRT. Methods: Manual and auto-contours were created for 149 CT image sets acquired from 16 unique prostate patients. A single physician manually contoured all images. Auto-contouring was completed utilizing Pinnacle’s Smart Probabilistic Image Contouring Engine (SPICE). For each CT, three different 78 Gy/39 fraction 7-beam IMRT plans are created; PD with drawn ROIs, PAS with auto-contoured ROIs, and PM with auto-contoured OARs with the manually drawn target. For each plan, 1000 virtual treatment simulations with different sampled systematic errors for each simulation and a different sampled random error for each fraction were performed using our in-house GPU-accelerated robustness analyzer tool which reports the statistical probability of achieving dose-volume metrics, NTCP, TCP, and the probability of achieving the optimization criteria for both auto-contoured (AS) and manually drawn (D) ROIs. Metrics are reported for all possible cross-evaluation pairs of ROI types (AS,D) and planning scenarios (PD,PAS,PM). Bhattacharyya coefficient (BC) is calculated to measure the PDF similarities for the dose-volume metric, NTCP, TCP, and objectives with respect to the manually drawn contour evaluated on base plan (D-PD). Results: We observe high BC values (BC≥0.94) for all OAR objectives. BC values of max dose objective on CTV also signify high resemblance (BC≥0.93) between the distributions. On the other hand, BC values for CTV’s D95 and Dmin objectives are small for AS-PM, AS-PD. NTCP distributions are similar across all evaluation pairs, while TCP distributions of AS-PM, AS-PD sustain variations up to %6 compared to other evaluated pairs. Conclusion: No significant probabilistic differences are observed in the metrics when auto-contoured OARs are used. The prostate auto-contour needs improvement to achieve clinically equivalent plans.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Multi-Hazard Advanced Seismic Probabilistic Risk Assessment Tools and Applications

Design of nuclear power plant (NPP) facilities to resist natural hazards has been a part of the regulatory process from the beginning of the NPP industry in the United States (US), but has evolved substantially over time. The original set of approaches and methods was entirely deterministic in nature and focused on a traditional engineering margins-based approach. However, over time probabilistic and risk-informed approaches were also developed and implemented in US Nuclear Regulatory Commission (NRC) guidance and regulation. A defense-in-depth framework has also been incorporated into US regulatory guidance over time. As a result, today, the US regulatory framework incorporates deterministic and probabilistic approaches for a range of different applications and for a range of natural hazard considerations. This framework will continue to evolve as a result of improved knowledge and newly identified regulatory needs and objectives, most notably in response to the NRC activities developed in response to the 2011 Fukushima accident in Japan. Although the US regulatory framework has continued to evolve over time, the tools, methods and data available to the US nuclear industry to meet the changing requirements have not kept pace. Notably, there is significant room for improvement in the tools and methods available for external event probabilistic risk assessment (PRA), which is the principal assessment approach used in risk-informed regulations and risk-informed decision-making applied to natural hazard assessment and design. This is particularly true if PRA is applied to natural hazards other than seismic loading. Development of a new set of tools and methods that incorporate current knowledge, modern best practice, and state-of-the-art computational resources would lead to more reliable assessment of facility risk and risk insights (e.g., the SSCs and accident sequences that are most risk-significant), with less uncertainty and reduced conservatisms.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Coordinated Ramping Product and Regulation Reserve Procurements in CAISO and MISO using Multi-Scale Probabilistic Solar Power Forecasts (Pro2R)

How can probabilistic solar forecasts lower costs and improve reliability for independent system operator (ISO) markets? We tackle this question in three steps. First, we enhance an existing solar forecasting system to provide well-calibrated hours-ahead probabilistic forecasts. We then relate the degree of uncertainty in those forecasts to error distributions for net load ramps for the California ISO (CAISO) using statistical and machine learning methods. Projected net load errors conditioned on solar uncertainty are translated into flexible ramp requirements that therefore reflect real-time meteorological and solar conditions, improving on typical ISO procedures. Finally, a multi-period look-ahead production cost model quantifies how conditional ramp requirements can a) decrease operating costs by lowering requirements compared to often conservative unconditional methods, and b) reduce generation scarcity events and consequently improve reliability by increasing flexibility requirements at times when unconditional forecast-based requirements understate actual ramp uncertainty. In addition to the products just described (quantification of solar uncertainty, its translation into requirements for ramp capability product, and quantification of the benefits of more accurate ramp requirements), this project also developed a visualization system that alerts system operators of ramp and uncertainty conditions within the network based on solar forecasts. The system is called Resource Forecast and Ramp Visualization for Situational Awareness (RaVIS). These four products represent significant advances in the state-of-the-art of probabilistic solar forecasting, development of weather-informed reserve requirements, production costing methods for estimating the benefits of more accurate reserve requirements, and visualization of system status, respectively. Yet the products are also practical and can be immediately implemented, potentially enabling system operators to save millions of dollars in ramp product procurement costs per year.

14 SOLAR ENERGY↗
NASA NTRS1994

Probabilistic progressive buckling of trusses

A three-bay, space, cantilever truss is probabilistically evaluated to describe progressive buckling and truss collapse in view of the numerous uncertainties associated with the structural, material, and load variables that describe the truss. Initially, the truss is deterministically analyzed for member forces, and members in which the axial force exceeds the Euler buckling load are identified. These members are then discretized with several intermediate nodes, and a probabilistic buckling analysis is performed on the truss to obtain its probabilistic buckling loads and the respective mode shapes. Furthermore, sensitivities associated with the uncertainties in the primitive variables are investigated, margin of safety values for the truss are determined, and truss end node displacements are noted. These steps are repeated by sequentially removing buckled members until onset of truss collapse is reached. Results show that this procedure yields an optimum truss configuration for a given loading and for a specified reliability.

PROBABILISTIC BUCKLING ANALYSI↗
NASA NTRS2001

Distribution functions of probabilistic automata

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Denotational semantics↗