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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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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Co-Simulation Meets AI: MCP-Driven Power System Analysis

GridGPT, a fine-tuned Generative AI model is designed for on-premise use in grid control rooms. This presentation will demonstrate how eGridGPT can seamlessly integrate with control room solutions to offer operators, engineers, and corporate users enhanced guidance and decision support. It is to show how this innovative AI solution can improve state estimation, boost variable energy forecasting, and optimize grid operations. By leveraging eGridGPT's unique features, audience will learn to unlock new levels of automation, predictive analytics, and reliability within their power systems, ultimately leading to reduced downtime and improved operational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Exploring Advanced Computational Tools and Techniques with Artificial Intelligence and Machine Learning in Operating Nuclear Plants

This report presents the project Idaho National Laboratory conducted for Nuclear Regulatory Commission to explore the advanced computational tools and techniques, such as artificial intelligence (AI) and machine learning (ML), for operating nuclear plants. The report reviews the nuclear data sources, with the focus on the operating experience data, that could be applied by advanced computational tools and techniques. Plant-specific and generic (national and international) data from different sources are described. The report describes the relationships between statistics and AI/ML and then introduces the most widely used AI/ML algorithms in both supervised and unsupervised learning. The report reviews the recent applications of advanced computational tools and techniques in various fields of nuclear industry, such as reactor system design and analysis, plant operation and maintenance, and nuclear safety and risk analysis. Finally, the report presents the insights from the project on the potential applicability of AI/ML techniques in improving advanced computational capabilities, how the advanced tools and techniques could contribute to the understanding of safety and risk, and what information would be needed to provide meaningful insights to decision makers. The report also documents an NRC survey on the current state of commercial nuclear power operations relative to the use of AI and ML tools as well as the role of AI/ML tools in nuclear power operations was published by the NRC as in FRN NRC-2021-0048 in April 2021. A summary of the survey including the survey questions, survey participants, survey responses, and the conclusions and insights derived from the survey is provided in the report. Finally, the report investigates potential applications of using AI/ML in operating NPPs and advanced reactors (both advanced LWRs and advanced NLWRs) to improve nuclear plant safety and efficiency. Three main application fields are defined and discussed: (1) plant safety and security assessments; (2) plant degradation modeling, fault and accident diagnosis and prognosis; and (3) plant operation and maintenance efficiency improvement.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

A novel machine learning-based optimization algorithm (ActivO) for accelerating simulation-driven engine design

A novel design optimization approach (ActivO) that employs an ensemble of machine learning algorithms is presented. The proposed approach is a surrogate-based scheme, where the predictions of a weak leaner and a strong learner are utilized within an active learning loop. The weak learner is used to identify promising regions within the design space to explore, while the strong learner is used to determine the exact location of the optimum within promising regions. For each design iteration, exploration is done by randomly selecting evaluation points within regions where the weak learner-predicted fitness is high. The global optimum obtained by using the strong learner as a surrogate is also evaluated to enable rapid convergence once the most promising region has been identified. First, the performance of ActivO was compared against five other optimizers on a cosine mixture function with 25 local optima and one global optimum. In the second problem, the objective was to minimize indicated specific fuel consumption of a compression-ignition internal combustion (IC) engine while adhering to desired constraints associated with in-cylinder pressure and emissions. In this work, the efficacy of the proposed approach is compared to that of a genetic algorithm, which is widely used within the internal combustion engine community for engine optimization, showing that ActivO reduces the number of function evaluations needed to reach the global optimum, and thereby time-to-design by 80%. Furthermore, the optimization of engine design parameters leads to savings of around 1.9% in energy consumption, while maintaining operability and acceptable pollutant emissions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Not so HOT Triangulations

Here, we propose primal–dual mesh optimization algorithms that overcome shortcomings of the standard algorithm while retaining some of its desirable features. “Hodge-Optimized Triangulations” defines the “HOT energy” as a bound on the discretization error of the diagonalized Delaunay Hodge star operator. HOT energy is a natural choice for an objective function, but unstable for both mathematical and algorithmic reasons: it has minima for collapsed edges, and its extrapolation to non-regular triangulations is inaccurate and has unbounded minima. We propose a different extrapolation with a stronger theoretical foundation, and avoid extrapolation by recalculating the objective just beyond the flip threshold. We propose new objectives, based on normalizations of the HOT energy, with barriers to edge collapses and other undesirable configurations. We propose mesh improvement algorithms coupling these. When HOT optimization nearly collapses an edge, we actually collapse the edge. Otherwise, we use the barrier objective to update positions and weights and remove vertices. By combining discrete connectivity changes with continuous optimization, we more fully explore the space of possible meshes and obtain higher quality solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

HPC Forecast: Cloudy and Uncertain

An examination of how the technology landscape has changed and possible future directions for HPC operations and innovation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Pyomo v6.2

SAND2022-4010 O Pyomo supports the formulation and analysis of mathematical models for complex optimization applications. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Woodruff, David↗
DOE OSTI2020

Performance Assessment of AFQMC Implementation (ECP Milestone 5.2 Report)

The auxiliary field quantum Monte Carlo algorithm in QMCPACK was ported to run on AMD GPUs using HIP. Initial performance measurements on early access hardware indicate a 4x slowdown compared to NVIDIA V100s. The slowdown was determined to be a result of suboptimal ROCM libraries for small matrix sizes coupled with some poorly performing hipified CUDA kernels. Through a preliminary analysis of HIP kernel performance we determined a strategy for pro ling and tuning kernels. We request that ROCM libraries are optimized for smaller problem sizes particularly for batched operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An unstructured C-grid type variational formulation for the sea ice dynamics

Historically, B-grid formulations of sea ice dynamics have been dominant because they have matched the grid type used by ocean models. The reason for the grid match is simple – it facilitates penetration of the curl of ice-ocean stress into the deep ocean with minimal numerical diffusivity because sea ice and ocean velocity are co-located. In recent years, as ocean models have increasingly progressed to C-grids, sea ice models have followed suit on quadrilateral meshes, but the implementation of an unstructured C-grid sea ice models is new. We present an unstructured C-grid discretization of the Elastic Viscous Plastic (EVP) rheology, where the velocity unknowns are discretized at the edges of the mesh cells with n-sides, where typically n is greater than or equal to four, rather than at the vertices, as in the B-grid. Our framework of choice is the Model for Prediction Across Scales (MPAS) within E3SM, the climate model of the U.S. Department of Energy, although our approach is general and could be applied to other models as well. While MPAS-Seaice is currently defined on a B-grid, MPAS-Ocean runs on a C-grid, hence interpolation operators are heavily used when coupled simulations are performed. In this work, we describe a mathematical formulation to transition the dynamics of MPAS-Seaice to a C-grid, in order to ultimately facilitate the coupling with MPAS-Ocean and reduce numerical errors associated with this communication. Numerical results are reported to highlight the features of the method.

58 GEOSCIENCES↗
DOE OSTI2022

Technology Integration to Gain Commercial Efficiency for the Urban Goods Delivery System, Meet Future Demand for City Passenger and Delivery Load/Unload Spaces, and Reduce Energy Consumption

This three-year project supported by the U.S. Department of Energy Vehicle Technologies Office has the potential to radically improve the urban freight system in ways that help both the public and private sectors. Working from 2018-2021, project researchers at the University of Washington’s Urban Freight Lab and collaborators at the Pacific Northwest National Laboratory have produced key data, tested technologies in complex urban settings, developed a prototype parking availability app, and helped close major knowledge gaps. All the fruits of this project can be harnessed to help cities better understand, support and actively manage truck load/unload operations and their urban freight transport infrastructure. Project learnings and tools can be used to help make goods delivery firms more efficient by reducing miles traveled and the time it takes to complete deliveries, benefitting businesses and residents who rely on the urban freight system for supplies of goods. And, ultimately, these project learnings and tools can be used to make cities more livable by minimizing wasted travel, which, in turn, contributes to reductions in fuel consumption and emissions. Cities today are challenged to effectively and efficiently manage their infrastructure to absorb the impacts of ever-increasing e-commerce-fueled delivery demand. All delivery trucks need to park somewhere to unload and load. Yet today’s delivery drivers have no visibility on available parking until they arrive at a site, which may be full. That means they can wind up cruising for parking, which wastes time and fuel and contributes to congestion. Once drivers do find parking, the faster they can unload at the spot, the faster they free up space for other drivers, helping others avoid circling for parking. This makes the parking space—and thus the greater load/unload network—more productive. To this end, the research team successfully met the project’s three goals, developing and piloting strategies and technologies to: 1. Reduce parking-seeking behavior in the study area by 20%; 2. Reduce parcel truck dwell time (the time a truck spends in a spot to load/unload) in the study area by 30%; 3. Increase curb space, alley space and private loading bay occupancy rates in the study area. The research team met these goals by creating and piloting on Seattle streets OpenPark, a first-of-its-kind real-time and forecasting curb parking app customized for commercial delivery drivers—giving drivers the “missing link” in their commonly used routing tools that tell them how best to get to delivery locations, but not what parking is available to use when they get there. Installing in-ground sensors on commercial vehicle load zones (CVLZs) and passenger load zones (PLZs) in the 10-block study area in Seattle’s downtown neighbourhood of Belltown let researchers glean real-time curb parking data. The research team also met project goals by piloting three parcel lockers in public and private spaces open to any delivery carrier, creating a consolidated delivery hub that lets drivers complete deliveries faster and spend less time parked. Researchers collected and analysed data to produce the first empirical, robust, statistically significant results as to the impact of the lockers, and app, on on-the-ground operations. In addition to collecting and analyzing sensor and other real-time and historical data, researchers rode along with delivery drivers to confirm real-world routing and parking behavior. Researchers also surveyed building managers on their private loading bay operations to understand how to boost usage.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Cybersecurity and Digital Components: Supply Chain Deep Dive Assessment

The report “America’s Strategy to Secure the Supply Chain for a Robust Clean Energy Transition” lays out the challenges and opportunities faced by the United States in the energy supply chain as well as the federal government plans to address these challenges and opportunities. It is accompanied by several issue-specific deep dive assessments, including this one, in response to Executive Order 14017 “America’s Supply Chains,” which directs the Secretary of Energy to submit a report on supply chains for the energy sector industrial base. The Executive Order is helping the federal government to build more secure and diverse U.S. supply chains, including energy supply chains. As the energy sector has become more globalized and increasingly complex, digitized, and even virtualized, its supply chain risk for digital components – the software, virtual platforms and services, and data – in energy systems has evolved and expanded. All digital components in U.S. energy sector systems are vulnerable and may be subject to cyber supply cha in risks stemming from a variety of threats, vulnerabilities, and impacts. This includes digital components in all systems within the ESIB, namely those systems operated by asset owners across different energy subsectors (e.g., electricity, oil and natural gas, and renewables) and the systems operated by a worldwide industrial complex with capabilities to perform research and development and design, produce, operate, and maintain energy sector systems, subsystems, components, or parts to meet U.S. energy requirements. Supply chain risks for digital components including software, virtual platforms and services, and data have grown in recent years as increasingly sophisticated cyber adversaries have targeted exploiting vulnerabilities in these digital assets. Supply chain risks for digital components in energy sector systems will continue to evolve and likely increase as these systems are increasingly interconnected, digitized, and remotely operated.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Evaluating the Accuracy of Machine Learning Forecasts

To improve the accuracy of forecasting in machine learning, we must investigate multiple machine learning models and see how accurately they can predict values after training. We used seven machine learning models to try and get more accurate predictions. The models that were used were ARIMA, SES, MLP, CART, LightGBM, and XGBoost. We used a processed dataset from a Terminal at LAX that had the number of people traveling through terminal X every hour in March from 2015-2019. We trained our models with the dates March 6 - March 19 to predict the value for March 20th and the hours 6:00 am to 6:00 pm since those are the most popular traveling hours. By using the different models, we had varying results of accuracy when estimating the amount of people traveling through terminal X on March 20th. We know that machine learning models are helpful for forecasting and by seeing how accurately these models can predict, we can see how forecasting can be helpful for other issues. Using these methods, airports can use forecasting to predict the amount of people coming in and out and can use these predictions to prepare their resource management, operational efficiency, and overall passenger experience.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Method and apparatus for maintaining data coherence in a non-uniform compute device

A data processing apparatus includes one or more host processors with first processing units, one or more caches with second processing unit, a non-cache memory having a third processing unit and a reorder buffer operable to maintain data order during execution of a program of instructions. An instruction scheduler routes instructions to the processing units. Data coherence is maintained by control logic that blocks access to data locations in use by a selected processing unit other than the selected processing unit until data associated with the data locations are released from the reorder buffer. Data stored in the cache is written to the memory if it is already in a modified state, otherwise the state is set to the modified state. A memory controller may be used to restrict access to memory locations to be operated on.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Emergency Asset Positioning for Resilient Transmission Grid Operation

In this paper we study a problem of hurricane emergency preparedness via placement of emergency generation assets prior to its strike. We present a two-stage stochastic model for choosing locations and quantities of emergency storage to help support the power grid through a hurricane event. The expectation of losses in our two-stage model is estimated using the sample average approximation. We construct damage scenarios for sample average approximation using WIND Toolkit meteorological data and fragility curves of various electric grid components. We demonstrate the efficacy of our two-stage planning model by simulating operations during Hurricane Dolly on the 2000-bus transmission test system. Our model, coupled with our scenario selection strategy, is effective at mitigating loss of load when compared to a model without emergency generation assets placed prior to an extreme event.

emergency preparedness↗
DOE OSTI2023

Precursor Analysis Report: JBS Foods Ransomware Attack 2021

The JBS Foods 2021 Ransomware Attack Precursor Analysis Report leverages publicly available information about the JBS ransomware cyber attack and catalogs anomalous observables for each technique employed in the attack. This analysis is based upon the methodology of the Cybersecurity for the Operational Technology Environment (CyOTE) program. In late May 2021, one of the world’s largest meat producers, JBS Foods, announced they had fallen victim to a worldwide ransomware attack, later found to be REvil ransomware. In the United States alone, JBS Foods accounts for nearly 25% of beef and roughly 20% of pork production. Adversaries initially launched a Distributed Denial of Service (DDoS) attack on the company’s Information Technology (IT) networks in Australia, but the attack impacted operations in Brazil, Canada, and the United States, as well. The attack caused plant operations in all four countries to shut down for at least one day. All nine of the U.S. meatpacking plants temporarily shut down because of the attack. The adversaries initially demanded a $\$$22 million ransom for the company’s data, but later negotiated the ransom down to $\$$11 million even after JBS Foods restored most of their systems. JBS Foods eventually paid the $\$$11 Million for reassurance from the adversaries that none of their customers’ data would be compromised in the future. Despite its short duration, the attack still caused large stocks of meat to spoil. The incident also underscored how adversaries can simultaneously compromise and move laterally through global subsidiaries of an organization. Researchers and analysts identified 22 unique techniques (in a sequence of 21 steps) utilized during the attack with a total of 361 observables using MITRE ATT&CK® for Industrial Control Systems. The CyOTE program assesses observables accompanying techniques used prior to the triggering event to identify opportunities to detect malicious activity. If observables accompanying the attack techniques are perceived and investigated prior to the triggering event, earlier comprehension of malicious activity can take place. Sixteen of the identified techniques used during the JBS Foods cyber attack were precursors to the triggering event. Analysis identified 308 observables associated with these precursor techniques, 163 of which were assessed to have an increased likelihood of being perceived in the 75 days preceding the triggering event. The response and comprehension time could have been reduced if the observables had been identified earlier. The information gathered in this report contributes to a library of observables tied to a repository of artifacts, data sources, and technique detection references for practitioners and developers to support the comprehension of indicators of attack. Asset owners and operators can use these products if they experience similar observables or to prepare for comparable scenarios.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2023

Precursor Analysis Report: SQL Slammer Worm Infection of Davis-Besse Nuclear Power Plant 2003

The SQL Slammer Worm Infection of Davis-Besse Nuclear Power Plant 2003 Precursor Analysis Report leverages publicly available information about Davis-Besse’s 2003 cyber attack and catalogs anomalous observables for each technique employed in the attack. This analysis is based upon the methodology of the Cybersecurity for the Operational Technology Environment (CyOTE) program. On 25 January 2003, the SQL Slammer worm infected more than 90% of vulnerable hosts and crashed the internet in 10 to 15 minutes, making it one of the fastest spreading worms in history. SQL Slammer is a fileless, memory-resident worm that remotely exploits a stack-based buffer overflow vulnerability on local hosts to intensively scan and rapidly self-propagate across the internet. The worm infected approximately 300,000 unpatched hosts running Microsoft Structured Query Language (SQL) Server 2000 or Microsoft Desktop Engine (MSDE) 2000 with SQL Server Resolution Service. The SQL Slammer worm indirectly infected FirstEnergy’s Davis-Besse nuclear power plant by first infecting a consultant’s company network server and then propagating through an external misconfigured connection into Davis-Besse’s site network. The infection caused major network congestion, slow performance, data overloads, and the inability of local hosts to communicate with each other, which eventually caused a loss of availability and a loss of view when the Safety Parameter Display System (SPDS) and Plant Process Computer (PPC) crashed. At the time of the infection, the plant was already offline, the digital monitoring systems had redundant analog backups, and the plant control and safety functions were not affected, so there were no concerns of a safety breach. However, this incident resulted in many lessons learned and spawned important discussions about cybersecurity’s role in nuclear safety and electric power reliability regulation, policy, and guidance. Researchers and analysts identified 10 unique techniques utilized during the attack with a total of 640 observables using MITRE ATT&CK® for Industrial Control Systems. The CyOTE program assesses observables accompanying techniques used prior to the triggering event to identify opportunities to detect malicious activity. If observables accompanying the attack techniques are perceived and investigated prior to the triggering event, earlier comprehension of malicious activity can take place. Eight of the identified techniques used during Davis-Besse cyber attack were precursors to the triggering event. Analysis identified 596 observables associated with these precursor techniques, 428 of which were assessed to have an increased likelihood of being perceived in the 331 days preceding the triggering event. The response and comprehension time could have been reduced if the observables had been identified earlier. The information gathered in this report contributes to a library of observables tied to a repository of artifacts, data sources, and technique detection references for practitioners and developers to support the comprehension of indicators of attack. Asset owners and operators can use these products if they experience similar observables or to prepare for comparable scenarios.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

Precursor Analysis Report: Industroyer Targeting Ukraine Electric Power Transport Utility (Ukrenergo) 2016

The Industroyer Targeting Ukraine Electric Power Transport Utility (Ukrenergo) 2016 Precursor Analysis Report leverages publicly available information about the December 2016 cyber attack against the Ukrainian Ukrenergo electric transmission utility and catalogs anomalous observables for each technique employed in the attack. This analysis is based upon the methodology of the Cybersecurity for the Operational Technology Environment (CyOTE) program. Industroyer is a modular malware framework designed to deploy several Industrial Control System (ICS) protocol-specific attack payloads to disrupt electricity distribution. Adversaries deployed Industroyer within the target network on a Microsoft Windows endpoint capable of directly manipulating or communicating with ICS. Industroyer abuses the functionality of a targeted ICS’s legitimate control system to achieve its intended impact. Adversaries likely first gained access to Ukrenergo enterprise networks in early 2016 after a successful spearphishing campaign against organizations in the electric power sector. Adversaries then began capturing credentials beginning on 1 December 2016. This allowed access to the ICS environment at the Pivnichna electric transmission substation outside Kyiv through a device dual-homed on the Information Technology (IT) and ICS networks. Adversaries conducted discovery, targeting, and access to this device using information and previously captured credentials from compromised enterprise IT machines. Finally, the adversaries deployed and launched the Industroyer malware just before midnight on 17 December. By midnight, Ukrenergo had lost control of a targeted substation, resulting in electric power outages for over an hour in the city of Kyiv and the Kyiv region. Researchers and analysts identified 31 unique techniques (used in a sequence of 33 steps) utilized during the attack with a total of 846 observables using MITRE ATT&CK® for Industrial Control Systems. The CyOTE program assesses observables accompanying techniques used prior to the triggering event to identify opportunities to detect malicious activity. If observables accompanying the attack techniques are perceived and investigated prior to the triggering event, earlier comprehension of malicious activity can take place. Twenty-nine of the identified techniques used during the Industroyer cyber attack were precursors to the triggering event. Analysis identified 548 observables associated with these precursor techniques, 353 of which were assessed to have an increased likelihood of being perceived in the 300 days preceding the triggering event. The response and comprehension time could have been reduced if the observables had been identified earlier. The information gathered in this report contributes to a library of observables tied to a repository of artifacts, data sources, and technique detection references for practitioners and developers to support the comprehension of indicators of attack. Asset owners and operators can use these products if they experience similar observables or to prepare for comparable scenarios.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD

Here, the Deep Operator Network (DeepONet) is a neural network architecture used to approximate operators, including the solution operator of parametric PDEs. DeepONets have shown remarkable approximation ability. However, the performance of DeepONets deteriorates when the training data is polluted with noise, a scenario that occurs in practice. To handle noisy data, we propose a Bayesian DeepONet based on replica exchange Langevin diffusion (reLD). Replica exchange uses two particles. The first particle trains a DeepONet to exploit the loss landscape and make predictions. The other particle trains a different DeepONet to explore the loss landscape and escape local minima via swapping. Compared to DeepONets trained with state-of-the-art gradient-based algorithms (e.g., Adam), the proposed Bayesian DeepONet greatly improves the training convergence for noisy scenarios and accurately estimates the uncertainty. To further reduce the high computational cost of the reLD training of DeepONets, we propose (1) an accelerated training framework that exploits the DeepONet's architecture to reduce its computational cost up to 25% without compromising performance and (2) a transfer learning strategy that accelerates training DeepONets for PDEs with different parameter values. Finally, we illustrate the effectiveness of the proposed Bayesian DeepONet using four parametric PDE problems.

97 MATHEMATICS AND COMPUTING↗