Comprehensive Uncertainty Quantification Research Articles

Uncertainty quantification for damage detection in 3D printed auxetic structures based on ultrasonic guided-wave using Flipout probabilistic convolutional neural network

Abstract The auxetic structure is widely used in aviation, bio-engineering, automation, and other industries due to its outstanding properties, such as being lightweight, high strength-to-weight ratio, and absorbing energy. Neural network methods have been popularly used for auxetic structures’ structural health monitoring. However, the performance of neural network methods in unknown areas is limited. To increase the reliability of the network model, more comprehensive uncertainty quantification is needed for damage detection in unknown areas. This paper introduces a comprehensive framework for health diagnosis and uncertainty quantification in 3D-printed auxetic structures made of polylactic acid. The framework involves quasi-static uniaxial compression and ultrasonic tests conducted simultaneously to capture ultrasonic signals at different deformation states. Critical damage deformation is identified based on observed deformation patterns and variations in signal energy. Using the Hilbert transform, two damage-sensitive features—envelope and phase—are extracted. These features serve as input data for the Flipout probabilistic convolutional neural network (FPCNN) model, which integrates pseudo-independent weight perturbations and a Gaussian probabilistic layer within the visual geometry group 13 architecture to predict structural deformations and associated uncertainties. The uncertainty quantification framework, based on variational inference and the conditional covariance law, effectively separates and quantifies the predictive variance of the network model into aleatoric and epistemic uncertainty. This framework’s feasibility is demonstrated through compression and ultrasonic tests, utilizing the FPCNN. This showcases the uncertainty quantification capabilities of the FPCNN model.

A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage

Integrating monitoring data to efficiently update reservoir pressure and CO2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. We applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

Uncertainty quantification for damage detection in 3D-printed auxetic structures using ultrasonic guided waves and a probabilistic neural network

Auxetic structures hold significant potential for applications due to their outstanding properties. Ultrasonic waves and neural networks are the popular technologies used for structural health monitoring (SHM). To increase the reliability of the neural network output for SHM, comprehensive uncertainty quantification is needed for damage detection in unknown areas of auxetic structures. This paper presents the first comprehensive framework for health diagnosis and uncertainty quantification based on ultrasonic guided waves in two 3D-printed star hourglass honeycomb auxetic structures. The proposed framework integrates in-plane compression with simultaneous ultrasonic testing to receive ultrasonic signals across various deformation states. Additionally, fully elastic and elasto-plastic finite element simulations are conducted to analyze wave energy variations and mechanical responses in auxetic structure. Critical damage deformation is identified based on observed deformation patterns and variations in signal energy. The Hilbert transform is used to extract two damage-sensitive features, namely envelope and phase. These features serve as input data for the Flipout probabilistic convolutional neural network (FPCNN) model, which integrates pseudo-independent weight perturbations and a Gaussian probabilistic layer within the visual geometry group 13 architecture to predict structural deformations and associated uncertainties. The UQ framework effectively separates and quantifies the predictive variance of the FPCNN model into aleatoric and epistemic uncertainty. The framework’s effectiveness is demonstrated through the comprehensive approach, combining compression and ultrasonic tests, finite element simulation, and the FPCNN technique.

An AI-Enhanced Systematic Review of Climate Adaptation Costs: Approaches and Advancements, 2010–2021

This study addresses the critical global challenge of climate adaptation by assessing the inadequacies in current methodologies for estimating adaptation costs. Broad assessments reveal a significant investment shortfall in adaptation strategies, highlighting the necessity for precise cost analysis to guide effective policy-making. By employing the PRISMA 2020 protocol and enhancing it with the prismAId tool, this review systematically analyzes the recent evolution of cost assessment methodologies using state-of-the-art generative AI. The AI-enhanced approach facilitates rapid and replicable research extensions. The analysis reveals a significant geographical and sectoral disparity in research on climate adaptation costs, with notable underrepresentation of crucial areas and sectors that are most vulnerable to climate impacts. The study also highlights a predominant reliance on secondary data and a lack of comprehensive uncertainty quantification in economic assessments, suggesting an urgent need for methodological enhancements. It concludes that extending analyses beyond merely verifying that benefits exceed costs is crucial for supporting effective climate adaptation. By assessing the profitability of adaptation investments, it becomes possible to prioritize these investments not only against similar interventions but also across the broader spectrum of public spending.

Partitioning Uncertainty in Model Predictions from Compartmental Modeling of Global Carbon Cycle

Our comprehension of the real world remains perpetually incomplete, compelling us to rely on models to decipher intricate real-world phenomena. However, these models, at their pinnacle, serve merely as close approximations of the systems they seek to emulate, inherently laden with uncertainty. Therefore, investigating the disparities between observed system behaviors and model-derived predictions is of paramount importance. Although achieving absolute quantification of uncertainty in the model-building process remains challenging, there are avenues for both mitigating and highlighting areas of uncertainty. Central to this study are three key sources of uncertainty, each exerting significant influence: (i) structural uncertainty arising from inadequacies in mathematical formulations within the conceptual models; (ii) scenario uncertainty stemming from our limited foresight or inability to forecast future conditions; and (iii) input factor uncertainty resulting from vaguely defined or estimated input factors. Through uncertainty analysis, this research endeavors to understand these uncertainty domains within compartmental models, which are instrumental in depicting the complexities of the global carbon cycle. The results indicate that parameter uncertainty has the most significant impact on model outputs, followed by structural and scenario uncertainties. Evident deviations between the observed atmospheric CO2 content and simulated data underscore the substantial contribution of certain uncertainties to the overall estimated uncertainty. The conclusions emphasize the need for comprehensive uncertainty quantification to enhance model reliability and the importance of addressing these uncertainties to improve predictions related to global carbon dynamics and inform policy decisions. This paper employs partitioning techniques to discern the contributions of the aforementioned primary sources of uncertainty to the overarching prediction uncertainty.

UNCERTAINTY QUANTIFICATION AND GLOBAL SENSITIVITY ANALYSIS OF SEISMIC FRAGILITY CURVES USING KRIGING

Seismic fragility curves have been introduced as key components of seismic probabilistic risk assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into account various sources of uncertainties, the so-called epistemic uncertainties (i.e., coming from the uncertainty on the mechanical parameters of the structure) and the aleatory uncertainties (i.e., coming from the randomness of the seismic ground motions). For simulation-based approaches we propose a methodology to build and calibrate a Gaussian process surrogate model to estimate a family of nonparametric seismic fragility curves for a mechanical structure by propagating both the surrogate model uncertainty and the epistemic ones. Gaussian processes have indeed the main advantage to propose both a predictor and an assessment of the uncertainty of its predictions. In addition, we extend this methodology to sensitivity analysis. Global sensitivity indices such as aggregated Sobol' indices and kernel-based indices are proposed to know how the uncertainty on the seismic fragility curves is apportioned according to each uncertain mechanical parameter. This comprehensive uncertainty quantification framework is finally applied to an industrial test case consisting of a part of a piping system of a pressurized water reactor.

A personal touch to demand response: An occupant-centric control strategy for HVAC systems using personalized comfort models

HAVC systems account for the majority of energy use in buildings. Therefore, research efforts have been made to develop control strategies to improve energy efficiency during the day and peak time. Studies have traditionally emphasized energy optimization while treating occupant experience using temperature constraints or standard generic metrics of comfort. A well-known strategy, in this category, is the use of a penalizing term when the temperature in an environment is deviated from a pre-defined setpoint. However, in reality, individual differences lead to diverse preferences and sensitivities to indoor thermal environments. Prior studies have not systematically evaluated the impact of such differences on user experience when using advanced control strategies for demand response. Accordingly, in this study, we have proposed a novel occupant-centric control framework (PICO: Personalization-Integrated Co-Optimization) that seeks to minimize energy cost (using dynamic pricing) with a penalizing term that is informed by probabilistic personalized comfort models of the occupants. We hypothesized that such integration results in increased efficiency (during the day and peak time) and improved user experience. Through a comprehensive uncertainty quantification analysis (to account for diversity in occupants' preferences, sensitivities, and number of occupants), we evaluated this framework by comparing it against three commonly used control strategies with varying levels of emphasis on user experience. Our analysis using numerous realizations of the framework operation for different combinations of simulated occupants showed that the proposed framework can adapt to different scenarios and improve the efficiency of operations. Summarizing the energy saving and user comfort experience metrics in an energy productivity measure (that quantifies the comfort gain per unit of energy use) we demonstrated that PICO increases peak time productivity up to 18.37% across various realizations. Moreover, the framework was demonstrated to be more consistent in providing an improved user experience reflected in a considerable reduction of standard deviations for thermal comfort experience, specifically for one occupant scenarios.

Modeling and material uncertainty quantification of RC structural components

It is well established that various sources of uncertainties play a critical role in the safety assessment of engineering structures. Some widely used frameworks, such as performance-based earthquake engineering (PBEE), explicitly consider the ground motion record-to-record randomness, while the material and modeling uncertainty remain to be primarily based on judgments or limited analysis. This paper presents the results of a comprehensive uncertainty quantification and sensitivity analysis of a reinforced concrete structural component. First, different modeling strategies are adopted to develop several parent models. Next, various sources of uncertainty are propagated through the parent models to generate thousands of children models. The children models are further combined with material uncertainty to produce grandchildren models, and nonlinear transient simulations are conducted using an innovative artificial acceleration at different seismic intensity levels. The results are post-processed using a range of probabilistic, statistical, and machine learning methods. The study finds that the modeling strategy and its associated variability can cause significant bias and dispersion in the drift response, while material uncertainty has a relatively minor effect. The study quantifies the importance of modeling uncertainty, which is often overlooked in engineering practice.

Towards Accurate Radiometric Calibration of INSAT-3D and INSAT-3DR IMAGER: Addressing Uncertainty and Error Sources

ABSTRACT The proper radiometric calibration of the INSAT-3D and −3DR IMAGER is of utmost importance for effective weather forecasting and monitoring. Accurate and reliable images are crucial for predicting weather patterns, tracking storms, and assessing the impact of natural disasters. This research paper presents an evaluation of the radiometric calibration of the INSAT-3D and −3DR IMAGER using a reflectance-based method referenced to in-situ ground site measurements. Calibration campaigns were conducted at the Great Rann of Kutch (GROK) in Gujarat, India during February 2022 to ensure synchronous measurements of surface reflectance and atmospheric variables. In this study, the radiative transfer model called 6 SV (Second Simulation of a Satellite Signal in the Solar Spectrum Vector) was employed to simulate the Top-Of-Atmospheric (TOA) radiance. The calibration coefficients for the Visible (VIS) and Short Wave Infrared (SWIR) bands of the IMAGER were determined by comparing the TOA radiance obtained from the radiative transfer model with the Level 1B product of satellite data. The results convincingly demonstrate that the reflectance-based calibration method yields highly accurate and reliable radiometric calibration for both the VIS and SWIR bands of the INSAT-3D and −3DR IMAGER, with an uncertainty significantly smaller than the expected sensor degradation. Specifically, it was found that the VIS band of INSAT-3D underestimates the radiance value by 9.05%, while the VIS band of INSAT-3DR underestimates it by 4.88%. The study also discusses various sources of uncertainty and emphasizes the need for comprehensive uncertainty quantification to ensure the radiometric accuracy of the IMAGER data. Overall, the calibration results indicate that the absolute radiometric accuracy for the VIS and SWIR bands of the IMAGER on-board INSAT-3D and INSAT-3DR satellites is better than 4%. This research contributes to enhancing the reliability and usability of the INSAT-3D and −3DR IMAGER data for weather forecasting and monitoring applications.

Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Given Boundary Data

This work aims to estimate temperature-dependent thermal conductivity and heat capacity given measurements of temperature and heat flux at the boundaries. This estimation problem has many engineering and industrial applications, such as those for the building sector and chemical reactors. Two approaches are proposed to address this problem. The first method uses an integral approach and a polynomial approximation of the temperature profile. The second method uses a numerical solver for the nonlinear heat equation and an optimization algorithm. The performance of the two methods is compared using synthetic data generated with different boundary conditions and configurations. The results demonstrate that the integral approach works in limited scenarios, whereas the numerical approach is effective in estimating temperature-dependent thermal properties. The second method is also extended to account for noisy measurements and a comprehensive uncertainty quantification framework is developed.

Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction

AbstractThe ambient solar wind plays a significant role in propagating interplanetary coronal mass ejections and is an important driver of space weather geomagnetic storms. A computationally efficient and widely used method to predict the ambient solar wind radial velocity near Earth involves coupling three models: Potential Field Source Surface, Wang‐Sheeley‐Arge (WSA), and Heliospheric Upwind eXtrapolation. However, the model chain has 11 uncertain parameters that are mainly non‐physical due to empirical relations and simplified physics assumptions. We, therefore, propose a comprehensive uncertainty quantification (UQ) framework that is able to successfully quantify and reduce parametric uncertainties in the model chain. The UQ framework utilizes variance‐based global sensitivity analysis followed by Bayesian inference via Markov chain Monte Carlo to learn the posterior densities of the most influential parameters. The sensitivity analysis results indicate that the five most influential parameters are all WSA parameters. Additionally, we show that the posterior densities of such influential parameters vary greatly from one Carrington rotation to the next. The influential parameters are trying to overcompensate for the missing physics in the model chain, highlighting the need to enhance the robustness of the model chain to the choice of WSA parameters. The ensemble predictions generated from the learned posterior densities significantly reduce the uncertainty in solar wind velocity predictions near Earth.

On quantifying uncertainty in lightning strike damage of composite laminates: A hybrid stochastic framework of coupled transient thermal-electrical simulations

Lightning strike damage can severely affect the thermo-mechanical performance of composite laminates. It is essential to quantify the effect of lightning strikes considering the inevitable influence of material and geometric uncertainties for ensuring the operational safety of aircraft. This paper presents an efficient support vector machine (SVM)-based surrogate approach coupled with computationally intensive transient thermal-electrical finite element simulations to quantify the uncertainty in lightning strike damage. The uncertainty in epoxy matrix thermal damage and electrical responses of unprotected carbon/epoxy composite laminates is probabilistically quantified considering the stochasticity in temperature-dependent multi-physical material properties and ply orientations. Further, the SVM models are exploited for variance-based global sensitivity analysis to investigate the input parameters' relative influence on the lightning strike-induced damage behavior. Due to the adoption of a coupled SVM-based simulation approach here, it has become possible to carry out a comprehensive uncertainty quantification leading to complete probabilistic descriptions of the electrical and lightning damage parameters despite the requirement of performing a large number of computationally intensive function evaluations. The results reveal that source-uncertainty of the unprotected laminates significantly influences the epoxy matrix decomposition, electrical current density and electric potential, wherein longitudinal electrical conductivity is most sensitive to stochastic variations followed by other electrical, thermal and geometric parameters.

Comprehensive capacitance sensor calibration for high-speed fluid-machinery tip clearance characterization

This paper aims to lay a foundation for high-fidelity tip clearance measurements with capacitance sensors that can be adapted to any highspeed fluid machine, such as high-pressure turbines and compressors. A novel calibration procedure that does not involve rotating components is investigated and compared against established methods. First, a calibration bench is developed to demonstrate the static and dynamic performance of the sensors and perform quasi-static and dynamic calibrations in a controlled environment. Second, an in-situ methodology is developed to calibrate the sensors once installed in a turbine rig without complex positioning systems. A comprehensive uncertainty quantification analysis based on Markov Chain Monte Carlo sampling techniques shows that combined standard uncertainties as low as uc = 2.40 μm and uc = 4.69 μm could be achieved with the proposed bench and in-situ methodologies, respectively.

Probabilistic Wildfire Segmentation Using Supervised Deep Generative Model from Satellite Imagery

Wildfires are one of the major disasters among many and are responsible for more than 6 million acres burned in the United States alone every year. Accurate, insightful, and timely wildfire detection is needed to help authorities mitigate and prevent further destruction. Uncertainty quantification is always a crucial part of the detection of natural disasters, such as wildfires, and modeling products can be misinterpreted without proper uncertainty quantification. In this study, we propose a supervised deep generative machine-learning model that generates stochastic wildfire detection, allowing fast and comprehensive uncertainty quantification for individual and collective events. In the proposed approach, we also aim to address the patchy and discontinuous Moderate Resolution Imaging Spectroradiometer (MODIS) wildfire product by training the proposed model with MODIS raw and combined bands to detect fire. This approach allows us to generate diverse but plausible segmentations to represent the disagreements regarding the delineation of wildfire boundaries by subject matter experts. The proposed approach generates stochastic segmentation via two model streams in which one learns meaningful stochastic latent distributions, and the other learns the visual features. Two model branches join eventually to become a supervised stochastic image-to-image wildfire detection model. The model is compared to two baseline stochastic machine-learning models: (1) with permanent dropout in training and test phases and (2) with Stochastic ReLU activations. The visual and statistical metrics demonstrate better agreements between the ground truth and the proposed model segmentations. Furthermore, we used multiple scenarios to evaluate the model comprehension, and the proposed Probabilistic U-Net model demonstrates a better understanding of the underlying physical dynamics of wildfires compared to the baselines.

Experimental spectrum averaged cross sections (SACS) in 252Cf(sf) neutron field and its impact on the evaluation of neutron standards

A new evaluation of spectrum averaged cross sections (SACS) of 235U, 238U, and 239Pu measured in the 252Cf(sf) reference neutron field is presented and found to be consistent with the original Mannhart SACS evaluation in IRDF-2002. The comprehensive vetted experimental database that includes SACS ratio and absolute SACS measurements of major actinides is being used to update the SACS database employed as input of the new GMApy code to derive the Neutron Standards. An update of the current neutron standards based on Time Projection Chamber (TPC) shape data, a new comprehensive uncertainty quantification, and revised SACS experimental database is proposed which result in a 0.7% increase of the evaluated 239Pu(n,f)/235U(n,f) crosssection ratio in the 1–5 MeV energy region. The increase is due to a 0.3% reduction of the standard 235U(n,f) cross section and a 0.4% increase of the 239Pu(n,f) reference cross section in the 1–5 MeV energy region. Those changes are well within estimated USU fission cross-section uncertainties of 1.2%, but are relevant for the evaluated mean values.

Templates of expected measurement uncertainties

The covariance committee of CSEWG (Cross Section Evaluation Working Group) established templates of expected measurement uncertainties for neutron-induced total, (n,γ), neutron-induced charged-particle, and (n,xn) reaction cross sections as well as prompt fission neutron spectra, average prompt and total fission neutron multiplicities, and fission yields. Templates provide a list of what uncertainty sources are expected for each measurement type and observable, and suggest typical ranges of these uncertainties and correlations based on a survey of experimental data, associated literature, and feedback from experimenters. Information needed to faithfully include the experimental data in the nuclear-data evaluation process is also provided. These templates could assist (a) experimenters and EXFOR compilers in delivering more complete uncertainties and measurement information relevant for evaluations of new experimental data, and (b) evaluators in achieving a more comprehensive uncertainty quantification for evaluation purposes. This effort might ultimately lead to more realistic evaluated covariances for nuclear-data applications. In this topical issue, we cover the templates coming out of this CSEWG effort–typically, one observable per paper. This paper here prefaces this topical issue by introducing the concept and mathematical framework of templates, discussing potential use cases, and giving an example of how they can be applied (estimating missing experimental uncertainties of 235U(n,f) average prompt fission neutron multiplicities), and their impact on nuclear-data evaluations.

Physics-Informed Uncertainty Quantification in Modeling of Machining-Induced Residual Stress

Machining processes involve various sources of uncertainty which lead to inaccurate interpretation of results in the surface integrity of machined products. This work presents a physics-informed, data-driven modeling framework for achieving comprehensive uncertainty quantification (UQ) of the impact of process and material variability on machining-induced residual stress (RS). Uncertainty due to the variation in bulk material properties and model input parameters in machining are considered. Preliminary results showed that variations in calibration parameters have a substantial effect on modeling RS, while the variation in material properties has a smaller effect. Further research directions for UQ in machining are also outlined.

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification.

Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A variety of regression techniques have been developed for producing the linear model approximation whose solutions are exponentials in time. For spatio-temporal data, DMD provides low-rank and interpretable models in the form of dominant modal structures along with their exponential/oscillatory behaviour in time. The majority of DMD algorithms, however, are prone to bias errors from noisy measurements of the dynamics, leading to poor model fits and unstable forecasting capabilities. The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities. Here, the optimized DMD algorithm is improved by using statistical bagging methods whereby a single set of snapshots is used to produce an ensemble of optimized DMD models. The outputs of these models are averaged to produce a bagging, optimized dynamic mode decomposition (BOP-DMD). BOP-DMD improves performance by stabilizing and cross-validating the DMD model by ensembling; it also robustifies the model and provides both spatial and temporal uncertainty quantification (UQ). Thus, unlike currently available DMD algorithms, BOP-DMD provides a stable and robust model for probabilistic, or Bayesian, forecasting with comprehensive UQ metrics. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

Efficient emulation of relativistic heavy ion collisions with transfer learning

Measurements from the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) can be used to study the properties of quark-gluon plasma. Systematic constraints on these properties must combine measurements from different collision systems and methodically account for experimental and theoretical uncertainties. Such studies require a vast number of costly numerical simulations. While computationally inexpensive surrogate models ("emulators") can be used to efficiently approximate the predictions of heavy ion simulations across a broad range of model parameters, training a reliable emulator remains a computationally expensive task. We use transfer learning to map the parameter dependencies of one model emulator onto another, leveraging similarities between different simulations of heavy ion collisions. By limiting the need for large numbers of simulations to only one of the emulators, this technique reduces the numerical cost of comprehensive uncertainty quantification when studying multiple collision systems and exploring different models.

Flow field tomography with uncertainty quantification using a Bayesian physics-informed neural network

We report a new approach to flow field tomography that uses the Navier–Stokes and advection–diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a series of line-of-sight (LoS) integrated measurements using a wide array of imaging modalities. The high-dimensional flow field is reconstructed from low-dimensional measurements by inverting a projection model that comprises path integrals along each LoS through the region of interest. Regularization techniques are needed to obtain realistic estimates, but current methods rely on truncating an iterative solution or adding a penalty term that is incompatible with the flow physics to varying degrees. Physics-informed neural networks (PINNs) are new tools for inverse analysis that enable regularization of the flow field estimates using the governing physics. We demonstrate how a PINN can be leveraged to reconstruct a 2D flow field from sparse LoS-integrated measurements with no knowledge of the boundary conditions by incorporating the measurement model into the loss function used to train the network. The resulting reconstructions are remarkably superior to reconstructions produced by state-of-the-art algorithms, even when a PINN is used for post-processing. However, as with conventional iterative algorithms, our approach is susceptible to semi-convergence when there is a high level of noise. We address this issue through the use of a Bayesian PINN, which facilitates comprehensive uncertainty quantification of the reconstructions, enables the use of a more intuitive loss function, and reveals the source of semi-convergence.