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DOE OSTI2022

Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of en-semble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.

Han, Mengjiao↗

DOE OSTI2023

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

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

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Root Cause Correlation Analysis of Software Failures via Orthogonal Defect Classification and Natural Language Processing

Systems theoretic process analysis (STPA) is becoming an increasingly popular technique to assess how complex digital software systems can fail. Rather than defining failures by their observable failure events, which may be sparse especially for safety rated nuclear digital instrumentation and control systems (DI&C), failures are defined as postulated unsafe actions under specific contextual conditions. This permits a top-down analysis of system hazards and identifies whether imposed constraints and requirements can sufficiently address undesirable hazards. However, STPA is a qualitative approach at identifying inadequacies in the development process and cannot currently be used to quantify unsafe action likelihoods for probabilistic risk assessment. Therefore, in this work, we examine the root causes of software failure and explore whether a consistent correlation can be linked to specific unsafe action classes. We implement Lbl2Vec, an unsupervised document classification and retrieval algorithm, on a database of 4,096 software defect reports acquired from various open-source software systems. By analyzing sentence structure, embedded labels, and word vectors, we show that certain defect types positively correlate to specific unsafe action classes over others. The correlations developed can be used to estimate the failure probability of safety intended DI&C systems which provides a licensing basis for nuclear plant modernization efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Sizing ramping reserve using probabilistic solar forecasts: A data-driven method

Ramping products have been introduced or proposed in several U.S. power markets to mitigate the impact of load and renewable uncertainties on market efficiency and reliability. Current methods often rely on historical data to estimate the requirements of ramping products and fail to take into account the effects of the latest weather conditions and their uncertainties, which could lead to overly conservative or insufficient requirements. This study proposes a k-nearest-neighbor-based method to give weather-informed estimates of ramping needs based on short-term probabilistic solar irradiance forecasts. Forecasts from multiple sites are employed in conjunction with principal component analysis to derive numerical classifiers to characterize system-level weather conditions. In addition, we develop a data-driven method to optimize the model parameters in a rolling-forward manner. By using real-world data from the California Independent System Operator, we design two metrics to evaluate method performance: 1) frequency of shortage and 2) oversupply of ramping product. Our proposed method presents advantages in comparison with the baseline and a set of benchmark methods: without compromising system reliability, it reduces system ramping requirements by up to 25%, therefore improving both system reliability and economics.

14 SOLAR ENERGY↗

DOE OSTI2020

Dynamic PRA Methods to Evaluate the Impact on Accident Progression of Accident Tolerant Fuels

Accident tolerant fuels (ATFs) are new nuclear fuels developed in response to the accident at the Fukushima power station in March 2011. The goal of ATFs is to withstand accident scenarios through better performance compared to currently employed fuels (e.g., small-scale hydrogen generation). This paper targets a method for evaluating and comparing ATF performance from a probabilistic risk assessment (PRA) perspective by employing a newly developed combination of event trees and dynamic PRA methods. Compared to classical PRA methods based on event trees and fault trees, dynamic PRA can evaluate with higher resolution the safety impacts of physics dynamics and the timing/sequencing of events on the accident progression without the need to introduce overly conservative modeling assumptions and success criteria. In this paper, we analyze the impact on the accident progression of three different cladding configurations for two initiating events [a large break loss-of-coolant accident (LB-LOCA) and a station blackout (SBO)] by employing dynamic PRA methods. The goal is to compare the safety performance of ATFs (FeCrAl and Cr-coated cladding) and the currently employed Zr-based clad fuel. We employ two different strategies. The first focuses on the identification of success criteria discrepancies between the accident sequences generated by the classical PRA model and the set of simulation runs generated by dynamic PRA using ATF. The second one, on the other hand, directly uses dynamic PRA to evaluate the impact of timing of events (e.g., recovery actions) on accident progression. In conclusion, by applying these methods to the LB-LOCA and SBO initiating events, we show how dynamic PRA methods can provide analysts with detailed and quantitative information on the safety impact of ATFs.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗

DOE OSTI2025

Advancing Multi-Hazard Risk and Safety Considerations for Aging Nuclear Facilities (Revision 1)

This project will demonstrate a multi-hazard time-dependent probabilistic risk assessment (PRA) approach for nuclear facilities considering aging-related deterioration of structures. A generic pressurized water reactor (PWR) reactor subjected to seismic mainshock-aftershock sequences considering the aging of the containment structure will be used as a case study to demonstrate the multi-hazard PRA approach. Using advanced modeling and simulation, seismic mainshock-aftershock fragility functions will be simulated for the containment structure considering aging effects. A multi-hazard PRA model for a generic PWR reactor will be built to quantify the multi-hazard core damage frequency (CDF) and large early release frequency (LERF) with explicit time-dependent modeling of event sequences. To date, the cascading impacts of multi-hazards are not adequately accounted for in the PRA models for nuclear facilities. In addition, for both initial and periodic evaluation of facilities to withstand natural phenomena hazards (NPH), deterioration of the SSCs due to aging and other effects is not adequately considered. By advancing multi-hazard considerations accounting for aging effects, this project will contribute to improved understanding of the safety of aging nuclear facilities. Project outcomes such as the multi-hazard CDF and LERF will also allow facility owners to optimize upgrade and retrofit protocols. This project is divided into two components: (1) advanced modeling and simulations; and (2) multi-hazard PRA. For the first component, Idaho National Laboratory’s (INL) Multi-hazard Analysis for STOchastic time-DOmaiN phenomena (MASTODON) and BlackBear codes will be used to simulate the seismic response and damage of a containment structure under cascading mainshock-aftershock sequences with aging effects. Uncertainties related to the seismic inputs, material parameters, and environmental factors such as temperature and humidity will be identified and propagated to the fragility functions. These fragility functions, which consider aging effects, will be time dependent. The second component will take the fragility information from the first component to build a multi-hazard time-dependent PRA model starting from a generic PWR model to evaluate the multi-hazard CDF and LERF and characterize the associated consequences. For this component, OpenPRA Web Application and SAPHIRE code will be used. Events such as the Fukushima Daiichi accident have highlighted the importance of considering the cascading impacts of multi-hazards for PRA. Moreover, many of the reactors in the current nuclear fleet in the United States (US) are already operating well beyond their initially planned design life, and applications for further extensions to operating licenses are being considered. Therefore, considering multi-hazard effects and aging deterioration in the NPH risk assessment process will contribute to the safety of both existing and future nuclear facilities. Outcomes of this project will thus directly benefit the standards DOE-STD-1020-16 and DOE-HDBK-1224-18.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Copacabana: a probabilistic membership assignment method for galaxy clusters

Cosmological analyses using galaxy clusters in optical/near-infrared photometric surveys require robust characterization of their galaxy content. Precisely determining which galaxies belong to a cluster is crucial. In this paper, we present the COlor Probabilistic Assignment of Clusters And BAyesiaN Analysis (Copacabana) algorithm. Copacabana computes membership probabilities for all galaxies within an aperture centred on the cluster using photometric redshifts, colours, and projected radial probability density functions. We use simulations to validate Copacabana and we show that it achieves up to 89 per cent membership accuracy with a mild dependence on photometric redshift uncertainties and choice of aperture size. We find that the precision of the photometric redshifts has the largest impact on the determination of the membership probabilities followed by the choice of the cluster aperture size. We also quantify how much these uncertainties in the membership probabilities affect the stellar mass–cluster mass scaling relation, a relation that directly impacts cosmology. Using the sum of the stellar masses weighted by membership probabilities (⁠μ * ⁠) as the observable, we find that Copacabana can reach an accuracy of 0.06 dex in the measurement of the scaling relation at low redshift for a Legacy Survey of Space and Time type survey. These results indicate the potential of Copacabana and μ * to be used in cosmological analyses of optically selected clusters in the future.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Framework for Quantitative Evaluation of Resilience Solutions: An Approach to Determine the Value of Resilience for a Particular Site

The paper provides the approach to providing a benefit cost analysis of energy and water alternatives to provide resilience to extreme events. The approach estimates the costs and returns of providing greater resilience of water and energy infrastructure. Extreme events are defined as high impact, low-frequency events such as, but not limited to, hurricanes, floods, storm surges and earthquakes. The provides justification for hardening water and energy infrastructure. Resilience is defined as “the ability to prepare for and to withstand an extreme event with little or no damage, or to recover more quickly from an extreme event.” The approach can be summarized as follows. The approach requires the development of a baseline with which to compare alternatives. The baseline is used to evaluate the baseline’s resilience to hazards through the probability of the hazard(s), the likelihood of damage from that the hazard through a vulnerability analysis, and the consequence to calculate a cost of the damage. The approach then evaluates proposed mitigation alternatives that would improve the resilience of the system. Each alternative is evaluated based on probability of the hazard, probability of vulnerability and consequence to determine the reduced damage that each alternative presents. The approach includes any monetary and non-monetary benefits that can quantified for each of the alternatives. Non-quantifiable benefits are evaluated based on the relative importance of each alternative to the criteria used to determine how well the alternative meets the goals and objectives of the site/facility. Then, a life cycle cost analysis should be conducted for the baseline and alternatives. Finally, the results of the life cycle analysis should be presented in a decision matrix with cost, net present value, benefit/cost ratios, and any non-monetary criteria ranked to show how well the alternatives met the criteria, weighted with the decision maker’s weights and the results presented.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Assessing Uncertainty in Modeling Stress Corrosion Cracking

This report summarizes the collaboration between Sandia National Laboratories (SNL) and the Nuclear Regulatory Commission (NRC) to improve the state of knowledge on chloride induced stress corrosion cracking (CISCC). The foundation of this work relied on using SNL’s CISCC computer code to assess the current state of knowledge for probabilistically modeling CISCC on stainless steel canisters. This work is presented as three tasks. The first task is exploring and independently comparing crack growth rate (CGR) models typically used in CISCC modeling by the research community. The second task is implementing two of the more conservative CGR models from the first task into SNL’s full CISCC code to understand the impact of the different CGR models on a full probabilistic analysis while studying uncertainty from three key input parameters. The combined work of the first two tasks showed that properly measuring salt deposition rates is impactful to reducing uncertainty when modeling CISCC. The work in Task 2 also showed how probabilistic CGR models can be more appropriate at capturing aleatory uncertainty when modeling SCC. Lastly, appropriate and realistic input parameters relevant for CISCC modeling were documented in the last task as a product of the simulations considered in the first two tasks.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Stealthy Cyber Anomaly Detection On Large Noisy Multi-material 3D Printer Datasets Using Probabilistic Models

As Additive Layer Manufacturing (ALM) becomes pervasive in industry, its applications in safety critical component manufacturing are being explored and adopted. However, ALM's reliance on embedded computing renders it vulnerable to tampering through cyber-attacks. Sensor instrumentation of ALM devices allows for rigorous process and security monitoring, but also results in a massive volume of noisy data for each run. As such, in-situ, near-real-time anomaly detection is very challenging. The ideal algorithm for this context is simple, computationally efficient, minimizes false positives, and is accurate enough to resolve small deviations. In this paper, we present a probabilistic-model-based approach to address this challenge. To test our approach, we analyze current measurements from a polymer composite 3D printer during emulated tampering attacks. Our results show that our approach can consistently and efficiently locate small changes in the presence of substantial operational noise.

Yoginath, Srikanth↗

DOE OSTI2024

Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications

Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve the understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainties with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of the classification of winter precipitation type and regression of surface-layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. To encourage broader adoption of evidential deep learning, we have developed a new Python package, Machine Integration and Learning for Earth Systems (MILES) group Generalized Uncertainty for Earth System Science (GUESS) (MILES-GUESS) ( https://github.com/ai2es/miles-guess ), that enables users to train and evaluate both evidential and ensemble deep learning. Significance Statement This study demonstrates a new technique, evidential deep learning, for robust and computationally efficient uncertainty quantification in modeling the Earth system. The method integrates probabilistic principles into deep neural networks, enabling the estimation of both aleatoric uncertainty from noisy data and epistemic uncertainty from model limitations using a single model. Our analyses reveal how decomposing these uncertainties provides valuable insights into reliability, accuracy, and model shortcomings. We show that the approach can rival standard methods in classification and regression tasks within atmospheric science while offering practical advantages such as computational efficiency. With further advances, evidential networks have the potential to enhance risk assessment and decision-making across meteorology by improving uncertainty quantification, a longstanding challenge. This work establishes a strong foundation and motivation for the broader adoption of evidential learning, where properly quantifying uncertainties is critical yet lacking.

Schreck, John S.↗

DOE OSTI2020

Classical versus quantum models in machine learning: insights from a finance application

Although several models have been proposed towards assisting machine learning (ML) tasks with quantum computers, a direct comparison of the expressive power and efficiency of classical versus quantum models for datasets originating from real-world applications is one of the key milestones towards a quantum ready era. Here, we take a first step towards addressing this challenge by performing a comparison of the widely used classical ML models known as restricted Boltzmann machines (RBMs), against a recently proposed quantum model, now known as quantum circuit Born machines (QCBMs). Both models address the same hard tasks in unsupervised generative modeling, with QCBMs exploiting the probabilistic nature of quantum mechanics and a candidate for near-term quantum computers, as experimentally demonstrated in three different quantum hardware architectures to date. To address the question of the performance of the quantum model on real-world classical data sets, we construct scenarios from a probabilistic version out of the well-known portfolio optimization problem in finance, by using time-series pricing data from asset subsets of the S&P500 stock market index. It is remarkable to find that, under the same number of resources in terms of parameters for both classical and quantum models, the quantum models seem to have superior performance on typical instances when compared with the canonical training of the RBMs. Our simulations are grounded on a hardware efficient realization of the QCBMs on ion-trap quantum computers, by using their native gate sets, and therefore readily implementable in near-term quantum devices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Stochastic Thermo-Hydro Modeling and Neural Network Surrogate Development for Thermal Resource Assessment of the Galleries-to-Calories Geobattery

The Galleries-to-Calories Geobattery concept explores the use of abandoned coal mine workings for large-scale thermal energy transport and storage. The system involves injecting waste heat from a supercomputing facility into flooded mine galleries, where groundwater flow can store and transport thermal energy for potential recovery in downgradient district heating and cooling applications. To evaluate the feasibility and performance of the Geobattery under geological and operational uncertainty, we developed a suite of stochastic thermo-hydrological (TH) simulations using Monte Carlo sampling of key uncertain parameters (e.g., permeability, porosity, thermal conductivity, specific heat capacity) and operating conditions (e.g., injection rate, injection temperature). Results identified injection rate and temperature as the most influential parameters governing thermal front propagation, while the geometry of the room-and-pillar structure played a critical role in directing the extent and orientation of thermal advancement. Optimal combinations of material properties for maximizing heat recovery were also determined. To address the high computational cost of coupled-process stochastic modeling, we trained a neural network surrogate model on 24,000 physics-based realizations, achieving an R² > 0.99 and MAE < 0.1 for temperature predictions at monitoring locations. This surrogate enabled an additional 100,000 realizations for global sensitivity analysis and probabilistic thermal resource assessment. The integrated stochastic physics–surrogate modeling framework offers a computationally efficient tool for quantifying uncertainty, identifying key drivers, and informing early-stage design decisions for Geobattery systems.

15 - GEOTHERMAL ENERGY↗

DOE OSTI2023

Comparing quantile regression forest and mixture density long short-term memory models for probabilistic post-processing of satellite precipitation-driven streamflow simulations

Abstract. Deep learning (DL) and machine learning (ML) are widely used in hydrological modelling, which plays a critical role in improving the accuracy of hydrological predictions. However, the trade-off between model performance and computational cost has always been a challenge for hydrologists when selecting a suitable model, particularly for probabilistic post-processing with large ensemble members. This study aims to systematically compare the quantile regression forest (QRF) model and countable mixtures of asymmetric Laplacians long short-term memory (CMAL-LSTM) model as hydrological probabilistic post-processors. Specifically, we evaluate their ability in dealing with biased streamflow simulations driven by three satellite precipitation products across 522 nested sub-basins of the Yalong River basin in China. Model performance is comprehensively assessed using a series of scoring metrics from both probabilistic and deterministic perspectives. Our results show that the QRF model and the CMAL-LSTM model are comparable in terms of probabilistic prediction, and their performances are closely related to the flow accumulation area (FAA) of the sub-basin. The QRF model outperforms the CMAL-LSTM model in most sub-basins with smaller FAA, while the CMAL-LSTM model has an undebatable advantage in sub-basins with FAA larger than 60 000 km2 in the Yalong River basin. In terms of deterministic predictions, the CMAL-LSTM model is preferred, especially when the raw streamflow is poorly simulated and used as input. However, setting aside the differences in model performance, the QRF model with 100-member quantiles demonstrates a noteworthy advantage by exhibiting a 50 % reduction in computation time compared to the CMAL-LSTM model with the same ensemble members in all experiments. As a result, this study provides insights into model selection in hydrological post-processing and the trade-offs between model performance and computational efficiency. The findings highlight the importance of considering the specific application scenario, such as the catchment size and the required accuracy level, when selecting a suitable model for hydrological post-processing.

Geology↗

DOE OSTI2021

Integrating static PRA information with risk informed safety margin characterization (RISMC) simulation methods

The overall objective of the project was to develop a computationally feasible and user-friendly mechanized process to integrate traditional probabilistic risk assessment (PRA) and dynamic PRA (DPRA) results. Starting with the systematic identification of items in an existing PRA that need dynamic augmentation, the project used a generic 4-loop pressurized reactor (PWR) and 3-loop PWR as example plants. Station blackout (SBO) and large break loss of coolant accident SBLOCA) were selected as the example initiating events. Using the traditional event-tree (ET)/fault-tree (FT) methodology augmented by dynamic evet tree approach, the potential consequences of the initiating events were simulated with RELAP-3D and MELCOR/RASCAL codes to cover Level 1 through Level 3 of PRA. RAVEN and ADAPT software were used to generate Level 1 simulations with RELAP-3D and Level 2/3 simulations with MELCOR (Level 2)/RASCAL (Level 3), respectively. Example branching conditions (BCs) for SBO included AC power recovery time, valve repair failure time, reactor coolant pump leak time/break size and emergency power supply duration to a total of 9. Example BCs for LOCA included off-site power recovery time, diesel generator power recovery time, auxiliary feed water system operation time, safety relief valve failure to open upon demand, reactor coolant pump seal break time and size to a total of 21. Each RELAP-3D simulation (9,587 scenarios) was labelled OK or Core Damage based on the maximum allowed peak clad temperature (2,100oF). Each MELCOR simulation (4610 scenarios) was labeled as Bin over 10rem or Bin 0-10rem based on the dose at the site boundary. The scenarios were clustered based on the criteria above using the mean shift methodology. Classical PRA (CPRA) and DPRA results were compared to identify the ET sequences that need DPRA augmentation. Several approaches were proposed for the incorporation of these sequences into CPRA using clustering with the mean shift methodology, restructuring the CPRA ETs by adding new BCs/sequences, and using the concept of a limit surface. Procedures for decision making regarding the possible consequences of an initiating event (e.g. core damage or not, site evacuation or not) were developed using a convolutional neural network (CNN), a recurrent neural network (RNN) and a transformer neural network (TNN). The project has led to two PhD degrees, three archival journal papers and five refereed conference proceedings.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Neural Posterior Estimation for Scalable and Accurate Inverse Parameter Inference in Li-Ion Batteries

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter estimation via Bayesian calibration, diagnostics can account for the uncertainty due to model fitness, data noise, and the observability of any given parameter. However, Bayesian calibration in Li-ion batteries using electrochemical data is computationally intensive even when using a fast surrogate in place of physics-based models, requiring many thousands of model evaluations. A fully amortized alternative is neural posterior estimation (NPE). NPE shifts the computational burden from the parameter estimation step to data generation and model training, reducing the parameter estimation time from minutes to milliseconds, enabling real-time applications. The present work shows that NPE can infer parameters equally or more accurately than Bayesian calibration, even if it leads to higher voltage reconstruction errors. We also demonstrate that the higher computational costs for data generation are tractable even in high-dimensional cases (ranging from 6 to 27 estimated parameters). The NPE method also offers several interpretability advantages over Bayesian calibration, such as local parameter sensitivity to specific regions of the voltage curve. The NPE method is demonstrated using an experimental fast charge dataset, with parameter estimates validated against measurements of loss of lithium inventory and loss of active material. The implementation is made available in a companion repository (https://github.com/NatLabRockies/BatFIT).

25 ENERGY STORAGE↗

DOE OSTI2025

Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. Here, in this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

97 MATHEMATICS AND COMPUTING↗