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At least 523 records · Page 29

Multi-Modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation

As data collection and simulation capabilities advance, multi-modal learning, the task of learning from multiple modalities and sources of data, is becoming an increasingly important area of research. Surrogate models that learn from data of multiple auxiliary modalities to support the modeling of a highly expensive quantity of interest have the potential to aid outer loop applications such as optimization, inverse problems, or sensitivity analyses when multi-modal data are available. We develop two multi-modal Bayesian neural network surrogate models and leverage conditionally conjugate distributions in the last layer to estimate model parameters using stochastic variational inference (SVI). We provide a method to perform this conjugate SVI estimation in the presence of partially missing observations. Here, we demonstrate improved prediction accuracy and uncertainty quantification compared to unimodal surrogate models for both scalar and time series data.

97 MATHEMATICS AND COMPUTING↗

Density estimation via measure transport: Outlook for applications in the biological sciences

Abstract One among several advantages of measure transport methods is that they allow or a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results from computational studies aimed at assessing the potential of measure transport techniques, specifically, the use of triangular transport maps, as part of a workflow intended to support research in the biological sciences. Scenarios characterized by the availability of limited amount of sample data, which are common in domains such as radiation biology, are of particular interest. We find that when estimating a distribution density function given limited amount of sample data, adaptive transport maps are advantageous. In particular, statistics gathered from computing series of adaptive transport maps, trained on a series of randomly chosen subsets of the set of available data samples, leads to uncovering information hidden in the data. As a result, in the radiation biology application considered here, this approach provides a tool for generating hypotheses about gene relationships and their dynamics under radiation exposure.

gene expression data↗

A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

60 APPLIED LIFE SCIENCES↗

Comparative Study of Wind Energy Potential Estimation Methods for Wind Sites in Togo and Benin (West Sub-Saharan Africa)

The characterization of wind speed distribution and the optimal assessment of wind energy potential are critical factors in selecting a suitable site for wind power plants (WPP). The Weibull distribution law has been used extensively to analyze the wind characteristics of candidate WPP sites, and to estimate the available and deliverable energy. This paper presents a comparative study of five wind energy resource assessment methods as they applied to the context of wind sites in West Sub-Saharan Africa. We investigated three numerical approaches, namely, the adaptive neuro-fuzzy inference system (ANFIS), the multilayer perceptron method (MLP), and support vector regression (SVR), to derive the distribution law of wind speeds and to optimally quantify the corresponding wind energy potential. Next, we compared these three approaches to two well-known Weibull distribution law-based methods: the empirical method of Justus (EMJ) and the maximum likelihood method (MLM). Case study results indicated that the neural network-based methods, ANFIS and MLP, yielded the most accurate distribution fits and wind energy potential estimates, and consequently, are the most recommended methods for the wind sites in Togo and Benin. The orders of magnitude of the root mean squared error (RMSE) in estimating the recoverable energy using ANFIS were, respectively, 10-4 and 10-5 for Lomé and Cotonou, while MLP achieved an RMSE order of magnitude of 10-3 for both sites.

17 WIND ENERGY↗

Modified Eigen-Decomposition-based Interval Analysis (MEDIA) for Power System Dynamic State Estimation

The Bayesian approach has been used for the dynamic state estimation (DSE) of a power system. However, due to the complexity of noise resources, it is difficult to quantify measurement and process noise using probability density functions (PDFs). To overcome the difficulty, the authors of this paper propose a modified eigen-decomposition-based interval analysis (MEDIA) method, which employs bounds instead of PDFs to quantify the noise, and uses the eigen decomposition method to reduce the negative impact of the overestimation problem. Using the simulation data generated from IEEE 16-machine and IEEE 10-machine systems, it is shown that the proposed MEDIA method can estimate the hard boundaries of dynamic states in real time. Furthermore, comparison with the forward-backward propagation method and the extended set-membership filter also shows that the proposed MEDIA method performs better by providing narrower boundaries in the DSE.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Measurement-informed Dynamic Aggregation of Distribution Systems

This paper proposes a measurement-informed dynamic aggregation methodology in order to create equivalent representations of distribution systems that are compatible with large-scale transmission analysis. By optimizing an equivalent feeder parameters using time-series measurements of active power, reactive power, and voltage at the Point of Interconnection (POI), the approach yields simplified yet dynamically accurate equivalents. Implemented in PSCAD with models of photovoltaic–battery systems, three-phase motors, and static loads, the method employs hybrid differential evolution and bounded least-squares optimization laying the foundation for for real-time state estimation and optimized sensor placement in distribution networks.

Ahmed, Kazi Ishrak [University of Tennessee, Knoxv↗

Estimating the impact of tariff-driven behind-the-meter storage operation on distribution grid investments

Increasing growth of distributed solar photovoltaics (PV) and electric vehicles (EV) can strain local distribution networks and require costly upgrades. Distributed battery storage, often deployed alongside PV, can be used to mitigate those costs, depending on how batteries are operated. This study evaluates the potential deferral value of distributed battery storage across a range of tariff structures, focusing on the rate structures most commonly available to residential customers today and related variants. Deferrals are evaluated with a least-cost distribution grid expansion optimization model to identify requirements on line reconductoring, transformer upgrades, and voltage regulator installations under each tariff. Results show that TOU rates and net billing tariffs can yield meaningful deferral value, depending on specific tariff structure features. Under the best performing tariff structure tested, storage produced a median annualized deferral value of $7.18 per kW of storage capacity ( kW S ) across all feeders in the sample, though deferral values were considerably larger for feeders with peak loads that coincide with utility system peak, i.e., timing of TOU peak period. In contrast, under an unrestricted TOU design with no restrictions on grid charging or discharging, the median deferral value was $0/ kW S illustrating the critical importance of tariff structure details.

Rodriguez-Garcia, Luis↗

Optimal Portfolio Design of Distributed Energy Resources on Puerto Rico Distribution Feeders with Long Outages after Hurricane Maria

This work details a project to design reliable, resilient, and cost-effective networked microgrids considering grid constraints and resilience metrics focused on Puerto Rico distribution feeder locations with long outages after Hurricane Maria. The project consisted primarily of modeling and simulation tasks that accomplished the following objectives: 1. Selected 10 distribution feeder models in vulnerable areas. The sample feeders are geographically distributed across Puerto Rico and vary in length to capture the wide variety of feeders on the island. 2. Determined the optimal location and sizing of distributed energy resources (DERs) on the identified distribution feeders. The systems considered as part of the microgrid solutions were solar photovoltaic (PV), battery energy storage systems (BESS) and distributed fossil fuel generation (DFFG). 3. Estimated the cost-benefit of the proposed DER portfolios. 4. Provided a set of final recommendations that inform decision making on how to do targeted planning analysis for microgrids that can supply energy to critical infrastructures.

24 POWER TRANSMISSION AND DISTRIBUTION↗

IC Project: The Role of Compressibility in Regulating Magnetic Energy Conversion in Reconnection Processes with Turbulence and Implications for Particle Transport and Energization

Diagnostics for the contribution of different regions in low-energy injection: a) Distribution function for the time duration of E > B particles within E > B regions. The estimated time limits for achieving injection are labeled; b) Distribution of energy gain during injection (for E > B particles) for E > B regions (blue), before E > B crossing (red), and outside E > B regions after the first crossing (black); c) Spectra for self-consistent particles (blue), test-particles that do not see electric fields in E > B regions (red) and test-particles with a resetting energy approach (green).

79 ASTRONOMY AND ASTROPHYSICS↗

Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series

Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time series, however, is a challenging subject, owing to the intricate interdependencies among the constituent series. We hypothesize that anomalies occur in low density regions of a distribution and explore the use of normalizing flows for unsupervised anomaly detection, because of their superior quality in density estimation. Moreover, we propose a novel flow model by imposing a Bayesian network among constituent series. A Bayesian network is a directed acyclic graph (DAG) that models causal relationships; it factorizes the joint probability of the series into the product of easy-to-evaluate conditional probabilities. We call such a graph-augmented normalizing flow approach GANF and propose joint estimation of the DAG with flow parameters. We conduct extensive experiments on real-world datasets and demonstrate the effectiveness of GANF for density estimation, anomaly detection, and identification of time series distribution drift.

Dai, Enyan↗

Calculating Methane Emissions from Offshore Facilities Using Bottom-Up Methods

With changing demands in regulation, understanding methane emissions from offshore oil and gas production infrastructure has become increasingly important. Reported emissions from facilities in the Gulf of Mexico range from zero to thousands of tons of methane per hour, but these is currently no clear understanding of how this range compares to expected emissions from normally operating facilities. To generate realistic emission estimates, we create two bottom-up models that simulate emissions from facilities operating in the Gulf of Mexico. We estimate type 1 prototypical facilities (typically unmanned, older, lower-producing platforms in shallow water with little processing equipment, compressors, or storage tanks) to emit an average of 13 kg CH 4 h −1 , which corresponds to a loss of 2.7% of the average facility production. Type 2 prototypical facilities (continuously manned, higher production and operate in deeper water with processing equipment, oil storage tanks, compressors and power generation) emit an average of 88 kg CH 4 h −1 , which corresponds to a loss of 2.5% of production. The average measured emission from type 1 facilities was 18 kg CH 4 h −1 with a median production loss estimated at 8%. The average measured emission from type 2 facilities was 36 kg CH 4 h −1 with a median production loss estimated at 2.4%. Using emission factors that consider the long-tail emission distribution partly reconciles the difference between modelled and measured emission estimates, but we suggest the current the fugitive emission estimate may be an underestimate and more data on the number and size of fugitive emissions could explain differences between the modelled and measured emission estimate. We suggest the bottom-up approach described here that uses production data coupled with facility equipment could be used to identify facilities that have abnormally large measured emissions, caused by methodological failure or larger than expected fugitive emissions, which should be targeted for further evaluation resulting in remeasurement or identification of source type so that a more accurate estimates can be made on the absolute emission.

bottom-up↗

A General Decentralized Dynamic State Estimation With Synchronous Generator Magnetic Saturation

We report the saturation of the nonlinear magnetic circuit of synchronous generators is often neglected when performing Kalman filter-based dynamic state estimation (DSE), yielding significant estimation bias. This letter addresses this problem and proposes a generalized DSE framework to handle magnetic saturation. Moreover, this letter derives a state initialization procedure that improves the Kalman filter tracking speed. The framework is flexible in dealing with different saturation functions and generator models. Numerical results on the Texas 2000-bus system verify the effectiveness of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Solving high-dimensional inverse problems using amortized likelihood-free inference with noisy and incomplete data

Here, we present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously. We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.

conditional invertible neural network↗

Performance Comparison of Circular and Spherical Error Probable Estimators

This report compares the performance of three Circular Error Probable (CEP) estimators: the Grubbs-Patnaik estimator, a new, non-iterative, radial-integration estimator, and a median estimator. It also compares the performance of two Spherical Error Probable (SEP) estimators. The performance of each estimator is assessed in terms of bias, uncertainty, robustness, and computational complexity. Robustness is evaluated with respect to outliers, variations in the underlying statistical distribution characterizing munition impact positions, and impact-position measurement errors. The performance assessments indicate the radial-integration and Grubbs-Patnaik estimators perform nearly identically providing the statistical distribution of impact-position coordinates is jointly normal with zero means. In that case, both estimators outperform the median estimator by about 2% relative to the true CEP in terms of estimator uncertainty. The bias performance of the radial-integration and median estimators is close to zero for jointly normal impacts, however, the Grubbs-Patnaik estimator can be significantly biased for jointly normal impacts with non-zero means. When the statistical distribution characterizing impact positions is known, but not jointly normal, the radial-integration estimator is superior. In this case, the median estimator also outperforms the Grubbs-Patnaik estimator but is not quite as good as the radial-integration estimator. If the statistical distribution characterizing impacts is unknown and not jointly normal, or if distribution parameters are difficult or impractical to estimate, or if test data is corrupted with outliers, then the median estimator dramatically outperforms the other estimators, especially in terms of estimation bias. Unexpectedly, measurement noise did not significantly degrade the performance of any of the estimators, except for cases with signal to noise ratios less than five. Although the Grubbs-Patnaik estimator has remained the gold standard for CEP estimation for over half a century, the performance assessments indicate the new, non-iterative, radial-integration estimator and the median estimator offer significant advantages and, in most practical real-world conditions, are superior estimators. These estimators are also useful for SEP estimation whereas the Grubbs-Patnaik estimator does not extend to three dimensions.

97 MATHEMATICS AND COMPUTING↗

CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. Here, we propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.

97 MATHEMATICS AND COMPUTING↗

Utilizing the maximum likelihood estimator for flow analysis

We explore the possibility of evaluating flow harmonics by employing the maximum likelihood estimator (MLE). For a given finite multiplicity, the MLE simultaneously furnishes estimations for all the parameters of the underlying distribution function while efficiently suppressing the variance of measures. Also, the method provides a means to assess a specific class of mixed harmonics, which is not straightforwardly feasible by the approaches primarily based on particle correlations. The results are analyzed using the Wald, likelihood ratio, and score tests of hypotheses. Besides, the resultant flow harmonics obtained using MLE are compared with those derived using particle correlations and event plane methods. Here, the dependencies of extracted flow harmonics on the multiplicity of individual events and the total number of events are analyzed. It is shown that the proposed approach works efficiently to deal with the deficiency in detector acceptability. Moreover, we elaborate on a fictitious scenario where the event plane is not a well-defined quantity in the distribution function. For the latter case, the MLE is shown to largely perform better than the two-particle correlation estimator. In this regard, one concludes that the MLE furnishes a meaningful alternative to the existing approaches for flow analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Active operator learning with predictive uncertainty quantification for partial differential equations

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. Here, we propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework’s uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive with conventional solvers. We demonstrate how predictive uncertainties can be used in the context of Bayesian optimization and active learning problems to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures. In the active learning setup, we extend the framework to Fourier Neural Operators (FNO) and describe a generalized method for other operator networks. To enable real-time deployment, we introduce an inference strategy based on precomputed trunk outputs and a sparse placement matrix, reducing evaluation time by more than a factor of five. Our method provides a practical route to uncertainty-aware operator learning in time-sensitive settings.

97 MATHEMATICS AND COMPUTING↗

Detecting Anomalies in Time Series Using Kernel Density Approaches

This paper introduces a novel anomaly detection approach tailored for time series data with exclusive reliance on normal events during training. Our key innovation lies in the application of kernel-density estimation (KDE) to scrutinize reconstruction errors, providing an empirically derived probability distribution for normal events post-reconstruction. This non-parametric density estimation technique offers a nuanced understanding of anomaly detection, differentiating it from prevalent threshold-based mechanisms in existing methodologies. In post-training, events are encoded, decoded, and evaluated against the estimated density, providing a comprehensive notion of normality. In addition, we propose a data augmentation strategy involving variational autoencoder-generated events and a smoothing step for enhanced model robustness. The significance of our autoencoder-based approach is evident in its capacity to learn normal representation without prior anomaly knowledge. Through the KDE step on reconstruction errors, our method addresses the versatility of anomalies, departing from assumptions tied to larger reconstruction errors for anomalous events. Our proposed likelihood measure then distinguishes normal from anomalous events, providing a concise yet comprehensive anomaly detection solution. The extensive experimental results support the feasibility of our proposed method, yielding significantly improved classification performance by nearly 10% on the UCR benchmark data.

Frehner, Robin↗