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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 109 records · Page 6
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NASA NTRSDate not supplied

Safety Expertise and the Perils of Novelty

Emerging aviation markets such as urban air mobility are giving rise to new technologies and means of operation. However, novelty may hide ‘unknown unknowns,’ raising new hazards. This paper examines how expertise and safety techniques enable transformative technologies such as reduced crew operations, hybrid wing-borne and rotor-born flight, federated air traffic services, and urban operations. We explore how analysts use expertise to address common-cause failures, collect and interpret safety data, and perform exacting tradeoffs between dissimilarity, redundancy, independence, and diversity (human, process lifecycle, or otherwise) to ensure safety. When novelty is present, analysts might not possess the expertise needed to fully understand the implications of design decisions and tradeoffs being made, especially in early lifecycle phases, on emergent properties such as safety. Safety expertise must be carefully cultivated. The conflicting views of safety experts must be unpacked to identify the divergence in fundamental assumptions, models, means, and methods that may be causing them. Once systems venture beyond the basis of what safety expertise can reliably guarantee, projects take on risk that must be managed. The paper contains key takeaways and actionable recommendations for novel OEMs and regulators touching on topics such as robust monitoring; clear and transparent reporting; incremental approaches to fielding novel systems in hazard-rich, risk-tolerant environments; the cultivation of safety culture and expertise in an organization; and the use of scientific study to reduce epistemic uncertainty in novel operations with new technologies. Since excessive novelty in aviation can undermine the current foundation of safety, humility and incrementalism are necessary to enable emerging aviation markets safely.

safety expertise↗
NASA NTRSDate not supplied

Safety Expertise and the Perils of Novelty

Emerging aviation markets such as urban air mobility are giving rise to new technologies and means of operation. However, novelty may hide ‘unknown unknowns,’ raising new hazards. This paper examines how expertise and safety techniques enable transformative technologies such as reduced crew operations, hybrid wing-borne and rotor-born flight, federated air traffic services, and urban operations. We explore how analysts use expertise to address common-cause failures, collect and interpret safety data, and perform exacting tradeoffs between dissimilarity, redundancy, independence, and diversity (human, process lifecycle, or otherwise) to ensure safety. When novelty is present, analysts might not possess the expertise needed to fully understand the implications of design decisions and tradeoffs being made, especially in early lifecycle phases, on emergent properties such as safety. Safety expertise must be carefully cultivated. The conflicting views of safety experts must be unpacked to identify the divergence in fundamental assumptions, models, means, and methods that may be causing them. Once systems venture beyond the basis of what safety expertise can reliably guarantee, projects take on risk that must be managed. The paper contains key takeaways and actionable recommendations for novel OEMs and regulators touching on topics such as robust monitoring; clear and transparent reporting; incremental approaches to fielding novel systems in hazard-rich, risk-tolerant environments; the cultivation of safety culture and expertise in an organization; and the use of scientific study to reduce epistemic uncertainty in novel operations with new technologies. Since excessive novelty in aviation can undermine the current foundation of safety, humility and incrementalism are necessary to enable emerging aviation markets safely.

safety expertise↗
DOE OSTI2022

A Data Quality-Aware Framework to Reliably Forecast Photovoltaic Generation and Consumer Load for an Improved Resilience of Microgrids

Photovoltaic (PV) power and consumer load forecasting plays a critical role to ensure operational resilience of the electric grid. Most data-driven forecasting algorithms rely heavily on the continuous availability of good quality data for periodic training and validation. When deployed at the grid’s edge, prolonged disruptions to communications during extreme events degrade data quality. Factors such as missing observations, epistemic uncertainties, data drift, and concept drift are manifestations of data quality that impact the generalization of such field-deployed forecasting models. Currently, there exists no mechanism in the literature to dynamically switch between models under varying degrees of data quality as quantified by certain metrics for each factor highlighted above. This paper addresses this shortcoming by conceptually introducing a data qualityaware framework for reliable PV generation and consumer load forecasting. The framework’s design incorporates components of missing values, divergence tests, and continuous monitoring of generalization performance to detect changes in data quality caused by communications disruptions and trigger specific classes of forecasting models grouped under three use cases (UC1- UC3). As a first step towards validating this framework, real data collected from an actual field microgrid system is used to demonstrate the viability of the three use cases. Results show that the performance is the best in UC1 with an unadjusted R-square value of 0.954, followed by 0.939 for UC2 and 0.757 for UC3.

Sundararajan, Aditya↗
DOE OSTI2023

Deep Learning with Physics Priors as Generalized Regularizers

In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method to incorporate these approximate models as physics priors in modeling, to prevent overfitting and enhancing the generalization capabilities of the trained models. Utilizing the structural risk minimization (SRM) inductive principle pioneered by Vapnik, this approach structures the physics priors into generalized regularizers. The experimental results demonstrate that our method achieves up to two orders of magnitude of improvement in testing accuracy.

Liu, Frank↗
DOE OSTI2023

Fuel performance uncertainty quantification and sensitivity analysis in the presence of epistemic and aleatoric sources of uncertainties

Fuel performance modeling and simulation includes many uncertain parameters from models to boundary conditions, manufacturing parameters and material properties. These parameters exhibit large uncertainties and can have an epistemic or aleatoric nature, something that renders fuel performance code-to-code and code-to-measurements comparisons for complex phenomena such as the pellet cladding mechanical interaction (PCMI) very challenging. Additionally, PCMI and other complex phenomena found in fuel performance modeling and simulation induce strong discontinuities and non-linearities that can render difficult to extract meaningful conclusions form uncertainty quantification (UQ) and sensitivity analysis (SA) studies. In this work, we develop and apply a consistent treatment of epistemic and aleatoric uncertainties for both UQ and SA in fuel performance calculations and use historical benchmark-quality measurement data to demonstrate it. More specifically, the developed methodology is applied to the OECD/NEA Multi-physics Pellet Cladding Mechanical Interaction Validation benchmark. A cold ramp test leading to PCMI is modeled. Two measured quantities of interest are considered: the cladding axial elongation during the irradiations and the cladding outer diameter after the cold ramp. The fuel performance code used to perform the simulation is FAST. The developed methodology involves various steps including a Morris screening to decrease the number of uncertain inputs, a nested loop approach for propagating the epistemic and aleatoric sources of uncertainties, and a global SA using Sobol indices. The obtained results indicate that the fuel and cladding thermal conductivities as well as the cladding outer diameter uncertainties are the three inputs having the largest impact on the measured quantities. More importantly, it was found that the epistemic uncertainties can have a significant impact on the measured quantities and can affect the outcome of the global sensitivity analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRSDate not supplied

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗
DOE OSTI2026

Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials

Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Probabilistic flux limiters

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters have been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Conventional flux limiters are deterministic and lack the capacity to address uncertainties, both aleatoric (inherent randomness) and epistemic (modeling uncertainty due to limited knowledge), which arise in coarse-grained numerical simulations. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. Unlike traditional single-function flux limiters, these new probabilistic flux limiters incorporate multiple flux limiting functions, each applied with a learned probability drawn from high-resolution data to mitigate the effects of uncertainty in numerical simulations. This approach departs from traditional single-function limiters by explicitly modeling and incorporating uncertainty into the shock capturing process. Using the example of Burgers' equation as a testbed, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Probabilistic Modeling of a Three-Stage Human Landing System Architecture

Space Policy Directive-1 has led to NASA partnerships with commercial entities on procurement which includes the development of the Human Landing System (HLS) [1]. With the goal of delivering human crew to the lunar surface by 2024, system uncertainties become an important obstacle to the maturation of multiple new, driving technologies and mission concepts of the HLS program. As unmitigated uncertainties have previously led to failed development programs, these risks and their impacts must be understood and handled to ensure program success [2]. Sources of uncertainty include novel engine designs and configurations, increased reliance on cryogenic fluid management(CFM), and refueling technologies—which propagate as high-level performance metrics such as overall propellant mass and engine performance. Also, the occurrence of operational uncertainties—e.g. launch conditions or need to abort during the mission—can cause cascading effects on the rest of the mission that are difficult to definitively quantify, and are outside the scope of control. These concrete examples and other occurrences can be categorized as either epistemic or aleatory uncertainties.Epistemic uncertainty arises due to a lack of knowledge and can be alleviated with design and program maturation. Aleatory uncertainty is due to the inherent randomness of the system and cannot be directly reduced, unlike epistemic uncertainty. Robust design and probabilistic methods can compensate for aleatory effects. A taxonomy of uncertainty is referred to for this work [3]. In this paper, a probabilistic methodology to handle uncertainties has been demonstrated on a three-element HLS concept [1, 4], which allows tracking of current best estimates of the concept and assessment of concept design robustness against uncertainties. A sample case has been completed for this abstract, and an expansion on the methodology will be included in the final paper. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. This abstract will cover the basics of the approach used, and further details and justifications will be in the final paper.The mission profile associated with this three-element concept (Fig 1) was modeled as a set of mission events that facilitated mass changes, idles, or spacecraft maneuvers. The mission profile scope starts with each element’s NRHO orbit insertion and aggregation and ends at post-sortie rendezvous with Orion. More detail on the mission profile will be in the final paper. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as the physics framework to model the HLS architecture for applying the probabilistic methodology [5, 6]. Specifically, a parametric representation of the lander, ascent, and transfer elements and the mission profile of each element was established, with vehicle and mission parameters available as inputs to allow for a dynamic model. Each vehicle stage was modeled with high-level performance metrics, using Isp and propellant mass fraction (PMF) to remain parametric. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. These parameters were frozen at their nominal values for the purposes of baselining architecture performance and sizing the vehicle appropriately based on reference documentation [1]. Range estimating—a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities—is traditionally used with Mass Equipment Lists (MELs), but has been adapted with operational parameters as well as vehicle parameters in theDYREQT model to capture mission uncertainty alongside vehicle uncertainty [7, 3]. This method was selected due to its application and insight on a system from a bottom-up perspective, independence from historical rules of thumb, and ability to generate sensitivities based on design decisions and uncertainties. As a sample case for the abstract, the boiloff rates of the vehicle elements and the loiter times during the mission (simulating launch time variations and changing window of opportunities) were used with range estimating to provide preliminary results. To perform the range estimation portion of this methodology (depicted in Fig. 3, further details in final paper), the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the sample set of uncertainty parameters; 5,000 cases via Latin Hypercube Sampling were computed on the DYREQT architecture model. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Range estimating was applied to the surrogates instead of the actual models, which saves computational expense due to the bulk of cases needed for the Monte Carlo simulation as part of range estimating. Uncertainty parameters were sampled independently from triangular distributions using the DoE ranges as ‘min’ and ‘max’, and the nominal value as ‘most likely’. Based engineering intuition, some uncertainty parameters are correlated—e.g. if the main propellant has a high boil-off rate, the oxidizer should follow suit as both are related to CFM technology.While a Monte Carlo simulation samples all inputs as independent, the results would show model correlations; thus, it is efficient to sample the inputs as correlated. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo. A table for the DoE ranges and probability distribution parameters is shown in Table 1, and more details on Correlated Monte Carlo Simulations will be discussed in the final paper. The model’s resulting DoE showed that multivariate polynomial equations fit via least squares method captured its behavior accurately for the sample case. For the Correlated Monte Carlo Simulation, a positive correlation between fuel and oxidizer boiloff rates was used as a demonstration. 10,000 cases were computed with the surrogates and the launched masses for each vehicle element was collated. The results can be displayed in a probability density function (PDF), showing the impact of the uncertainty parameters chosen. Integrating the PDFs will yield a cumulative distribution function (CDF) that shows the cumulative probability of a given value on the x-axis. For the sample case, the elements’ launch mass margin was calculated and represented in as CDFs, as a demonstrated representation of figures of merit for the HLS concept. For the lander and ascent elements, the NRHO mass insertion limit is 16t; the transfer element has a limit of 30t [1]. It can be seen with Figure 2 that this probabilistic methodology can provide insight into mass margin with respect to the uncertainties being modeled. Currently, the results show that the lander (descent) vehicle element has the most restrictive design space; it is the only element to show a 10% probability of negative margin. Further analysis on the Monte Carlo results will show sensitivities for driving constraints and parameters for architecture feasibility, which can lead to establishing potential mission rules.The combination of range estimating with a parametric architecture model for HLS demonstrated the capability of this probabilistic methodology in a sample case. As the HLS development progresses, this methodology has the potential for keeping current best estimates of architecture performance for awarded concepts due to the flexibility in DYREQT’s modeling framework and its parametric nature. Concept maturation and increased epistemic knowledge can be injected into the model probabilistic modeling, and thus continue to track probability of mission success.

Stephanie Y Zhu↗
DOE OSTI2021

A quantitative assessment of the model form error of friction models across different interface representations for jointed structures

Hysteretic models are widely used to model frictional interactions in joints to recreate experimental behavior. However, it is unclear which models are best suited for fitting or predicting the responses of structures. Here, the present study evaluates 26 friction model/interface representation combinations to quantify the model form error. A Quasi-Static Modal Analysis approach (termed Rayleigh Quotient Nonlinear Modal Analysis) is adopted to calculate the nonlinear system response, and a Multi-Objective Optimization is solved to fit experimental data of the first mode of the Brake-Reuß Beam. Optimized parameters from the first mode are applied to the second and third bending modes to quantify the predictive ability of the models. Formulations for both tracing full hysteresis loops and recreating hysteresis loops from a single loading curve (Masing assumptions) are considered. Smoothly varying models applied to a five patch representation showed the highest flexibility (for fitting mode 1) and good predictive potential (for modes 2 and 3). For a second formulation, which uses 152 frictional elements to represent the interface, the physically motivated spring in series with a Coulomb slip model (elastic dry friction) has high error for fitting mode 1 and performs near the middle for predicting higher modes. For both interface representation, the best fit models are not the most physical, but rather the ones with the most parameters (as expected); however, the more physical models perform somewhat better for predicting the higher modes.

42 ENGINEERING↗
DOE OSTI2021

Evidence Theory Representations for Properties Associated With Weak Link/Strong Link Systems, Part 1: Loss of Assured Safety

The use of evidence theory in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Furthermore, article content includes (i) an introduction to evidence theory, (ii) definition of two WLs and two SLs used for illustration, (iii) belief and plausibility for the occurrence of LOAS for a one WL/two SL system, and (iv) a sampling-based procedure for the verification of belief and plausibility calculations. The presented results can be generalized to systems with more than one WL and two SLs.

42 ENGINEERING↗
DOE OSTI2021

Evidence Theory Representations for Properties Associated With Weak Link/Strong Link Systems, Part 2: Failure Time and Failure Temperature

The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of loss of assured safety (LOAS) for weak link (WL)/strong link (SL) systems is introduced and illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) time at which LOAS occurs for a one WL/two SL system, (ii) time at which a two-link system fails, (iii) temperature at which a two-link system fails, and (iv) temperature at which LOAS occurs for a one WL/two SL system. The presented results can be generalized to systems with more than one WL and two SLs.

42 ENGINEERING↗
DOE OSTI2021

Evidence Theory Representations for Properties Associated With Weak Link/Strong Link Systems, Part 3: Margins for Failure Time and Failure Temperature

The use of evidence theory and associated cumulative plausibility functions (CPFs), cumulative belief functions (CBFs), cumulative distribution functions (CDFs), complementary cumulative plausibility functions (CCPFs), complementary cumulative belief functions (CCBFs), and complementary cumulative distribution functions (CCDFs) in the analysis of time and temperature margins associated with loss of assured safety (LOAS) for one weak link (WL)/two strong link (SL) systems is illustrated. Article content includes cumulative and complementary cumulative belief, plausibility, and probability for (i) SL/WL failure time margins defined by (time at which SL failure potentially causes LOAS) – (time at which WL failure potentially prevents LOAS), (ii) SL/WL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature at which WL failure potentially prevents LOAS), and (iii) SL/SL failure temperature margins defined by (the temperature at which SL failure potentially causes LOAS) – (the temperature of SL whose failure potentially causes LOAS at the time at which WL failure potentially prevents LOAS).

42 ENGINEERING↗
DOE OSTI2021

Overview of the Tolerance Limit Calculations with Application to TSURFER

To establish confidence in the results of computerized physics models, a key regulatory requirement is to develop a scientifically defendable process. The methods employed for confidence, characterization, and consolidation, or C3, are statistically involved and are often accessible only to avid statisticians. This manuscript serves as a pedagogical presentation of the C3 process to all stakeholders—including researchers, industrial practitioners, and regulators—to impart an intuitive understanding of the key concepts and mathematical methods entailed by C3. The primary focus is on calculation of tolerance limits, which is the overall goal of the C3 process. Tolerance limits encode the confidence in the calculation results as communicated to the regulator. Understanding the C3 process is especially critical today, as the nuclear industry is considering more innovative ways to assess new technologies, including new reactor and fuel concepts, via an integrated approach that optimally combines modeling and simulation and minimal targeted validation experiments. This manuscript employs intuitive, analytical, numerical, and visual representations to explain how tolerance limits may be calculated for a wide range of configurations, and it also describes how their values may be interpreted. Various verification tests have been developed to test the calculated tolerance limits and to help delineate their values. The manuscript demonstrates the calculation of tolerance limits for TSURFER, a computer code developed by the Oak Ridge National Laboratory for criticality safety applications. The goal is to evaluate the tolerance limit for TSURFER-determined criticality biases to support the determination of upper, subcritical limits for regulatory purposes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Pragmatic Uncertainty Quantification and Propagation in Inverse Estimation of Structural Dynamics Parameters given Material Property Uncertainties and Limited Sensor Data

In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.

36 MATERIALS SCIENCE↗
DOE OSTI2026

E-PINNs: Epistemic Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify uncertainty in these networks. While techniques such as Bayesian PINNs (B-PINNs) provide a principled approach to capturing epistemic uncertainty through Bayesian inference, they can be computationally expensive for large-scale applications. In this work, we propose Epistemic Physics-Informed Neural Networks (E-PINNs), a framework that uses a small network, the epinet, to efficiently quantify epistemic uncertainty in PINNs. The proposed approach works as an add-on to existing, pre-trained PINNs with a small computational overhead. We demonstrate the applicability of the proposed framework in various test cases and compare the results with B-PINNs using Hamiltonian Monte Carlo (HMC) posterior estimation and dropout-equipped PINNs (Dropout-PINNs). In our experiments, E-PINNs achieve calibrated coverage with competitive sharpness at substantially lower cost. We demonstrate that when B-PINNs produce narrower bands, they under-cover in our tests. E-PINNs also show better calibration than Dropout-PINNs in these examples, indicating a favorable accuracy-efficiency trade-off.

AI for Science↗