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A Survey of Uncertainty in Deep Neural Networks

Jakob Gawlikowski, Cedrique Rovile Njieutcheu Tassi, Mohsin Ali, Jongseok Lee, Matthias Humt, Jianxiang Feng, Anna Kruspe, Rudolph Triebel, Peter Jung, Ribana Roscher, Muhammad Shahzad, Wen Yang, Richard Bamler, Xiao Xiang Zhu

arXiv:2107.03342v3cs.LGstat.ML

TL;DR

Neural networks often lack reliable uncertainty estimates, while real-world deployment requires understanding uncertainty sources, calibration, and out-of-distribution behavior. This survey organizes uncertainty concepts and estimation approaches, compares practical evaluation and calibration methods, and discusses challenges limiting mission- and safety-critical use.

  • Problem

    Basic neural networks may provide no certainty estimates or become overconfident or underconfident, while real-world applications require reliable uncertainty information and out-of-distribution detection.

  • Method

    The survey introduces uncertainty sources and measures, reviews deterministic, Bayesian, ensemble, and test-time augmentation approaches, and covers calibration, evaluation, implementations, and applications.

  • Results

    The survey provides a broad overview and comparison of uncertainty estimation methods, their evaluation and calibration, practical applications, current limitations, and future challenges.

  • Takeaways & Limitations

    Real-world deployment should consider uncertainty sources, calibration, and out-of-distribution detection, while balancing theoretical strength, predictive performance, and computational efficiency.

  • Takeaways & Limitations

    Current methods remain limited by unclear uncertainty causes, the lack of a unified quantitative evaluation metric, and practical computational or data requirements.

Abstract

from arXiv · show

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.

I. INTRODUCTION

The survey frames uncertainty estimation as essential for deploying DNNs in high-risk and data-scarce settings. It organizes sources, estimation methods, measures, calibration, benchmarks, applications, and future challenges into a unified overview.

  • DNN deployment in safety-critical applications remains limited by unreliable uncertainty estimates, overconfident predictions, domain-shift sensitivity, opacity, and adversarial vulnerability.
  • Uncertainty estimates can support safer decisions by allowing uncertain predictions to be ignored or passed to human experts.
  • Predictive uncertainty is commonly separated into reducible model uncertainty and irreducible data uncertainty.
  • The survey connects uncertainty sources to estimation approaches, quality measures, calibration methods, evaluation resources, real-world applications, and future research directions.
  • It describes four stages from raw information to quantified prediction uncertainty: data acquisition, DNN building, inference modeling, and uncertainty modeling.

A. Data Acquisition

Data acquisition introduces uncertainty because measurements and targets imperfectly represent real-world situations. The survey highlights environmental variability, measurement limitations, noise, labeling errors, and insufficient training coverage.

  • Measurements and targets represent real-world situations but can be affected by noise, information loss, and labeling errors.
  • Finite training data may insufficiently cover the real-world sample space, making predictions for new situations uncertain.
  • Real-world variability changes factors such as temperature, illumination, clutter, and object appearance relative to the training data.
  • Measurement systems create uncertainty through limited resolution, missing modalities, sensor noise, motion, mechanical stress, and false labeling.

B. Deep Neural Network Design and Training

DNN design, stochastic training, and inference on unfamiliar inputs introduce additional sources of predictive uncertainty. These sources include structural assumptions, optimization randomness, and unknown or distributionally mismatched data.

  • Network structure affects uncertainty through inductive bias, parameter capacity, architecture choices, activation functions, optimization, regularization, and augmentation.
  • Deeper networks tend to produce overconfident softmax outputs, assigning excessive probability to the highest-scoring class.
  • Random initialization, data ordering, regularization, batch size, learning rate, and training duration can lead to different local optima and models.
  • Unknown inputs create uncertainty because networks may process samples from a different world or task than the training data.
  • Predictive uncertainty reflects both model-dependent and input-data-dependent errors, with some approaches additionally modeling distributional uncertainty.

1) Model- and Data Uncertainty:

The survey distinguishes model uncertainty from data uncertainty and explains how Bayesian formulations represent them. It also separates predictive uncertainty by whether inputs are in-domain, domain-shifted, or out-of-domain.

  • Model uncertainty arises from training errors, insufficient structure, unknown samples, or poor training-data coverage, whereas data uncertainty stems directly from the data.
  • Model uncertainty is theoretically reducible through better architecture, learning, or training data, while data uncertainty cannot be explained away.
  • Bayesian modeling represents model uncertainty with a parameter distribution and data uncertainty with an output distribution, yielding a predictive distribution.
  • Ensembles approximate the posterior by learning multiple parameter settings and averaging their resulting models.
  • Uncertainty measures and estimation approaches differ across tasks and may explicitly represent distributional uncertainty for out-of-distribution detection.
  • Predictive uncertainty can be classified as in-domain, domain-shift, or out-of-domain uncertainty according to the input data domain.

III. UNCERTAINTY ESTIMATION

The survey organizes predictive uncertainty around multiple sources and presents four broad estimation-method families. It distinguishes reducible model uncertainty from irreducible data uncertainty and illustrates how methods represent both.

  • Sources of uncertainty: Real-world variability, insufficient or noisy measurements, model structure, stochastic training, and unknown inputs contribute to predictive uncertainty.The earth-observation example links these factors to changing environments, measurement limitations, network structure, training randomness, and unfamiliar images.
  • Method families: Uncertainty-estimation methods are grouped into single deterministic, Bayesian, ensemble, and test-time augmentation approaches.The groups differ by the number and nature of the neural networks used and by whether test inputs are augmented.
  • Single deterministic methods: Single deterministic methods use one forward pass and either predict uncertainty directly or derive it with additional methods.Internal approaches affect training and predictions, whereas external approaches operate on already trained networks without modifying their predictions.
  • Method families: Bayesian, ensemble, and test-time augmentation methods obtain uncertainty from stochastic networks, multiple deterministic networks, or multiple predictions from augmented inputs.The general framework represents a prediction together with model- and data-uncertainty values.
  • Limitations of basic outputs: Softmax probabilities can reflect data uncertainty but are often overconfident, poorly calibrated, and unable to represent model uncertainty.Out-of-distribution inputs may therefore receive falsely confident class predictions.
  • Dirichlet representations: Dirichlet-based representations use sharp distributions for certain predictions, central sharp distributions for high data uncertainty, and flat distributions for high distributional uncertainty.These behaviors are illustrated over categorical distributions on a probability simplex.

2) External Uncertainty Quantification Approaches:

External uncertainty quantification separates uncertainty evaluation from the underlying prediction task. The section then introduces Bayesian neural networks, whose predictive uncertainty comes from averaging over uncertainty in network parameters.

  • External uncertainty quantification: External uncertainty-quantification approaches leave the model’s predictions unchanged and can be applied to already trained networks.Multiple external approaches can also be applied simultaneously without affecting one another.
  • Bayesian neural networks: Bayesian neural networks infer a probability distribution over network parameters using a prior and the posterior p(θ|x, y).This replaces a single parameter estimate with a distribution over parameters.
  • Bayesian prediction: Bayesian prediction marginalizes the likelihood over the posterior distribution of network parameters to produce predictive uncertainty.The resulting integral is generally intractable, so approximation techniques are typically used.
  • Bayesian prediction: Monte Carlo approximation estimates the Bayesian expectation using the mean of N deterministic networks parameterized by posterior samples.Each network corresponds to a sampled parameter setting from the posterior distribution.
  • Bayesian approaches: The survey classifies Bayesian neural networks by posterior-inference strategy into variational inference, sampling approaches, and Laplace approximation.These categories approximate Bayesian inference in different ways.

1) Variational Inference:

Variational inference approximates an intractable Bayesian posterior with a tractable distribution family optimized to remain close to that posterior. Sampling methods instead represent uncertainty through draws from the target distribution.

  • Variational inference: Variational inference approximates p(θ|x, y) with a tractable parametric family q(θ).The family’s parameters are optimized so q(θ) approaches the posterior of interest.
  • Variational inference: Because the posterior prevents direct KL-divergence minimization, variational methods optimize the evidence lower bound instead.The ELBO equals the KL divergence up to a constant.
  • Variational inference: Monte Carlo Dropout interprets dropout layers as Bernoulli random variables and approximates variational inference during neural-network training.This makes dropout a widely used variational approach for predictive uncertainty.
  • Sampling methods: Sampling methods draw hypotheses from a distribution without restricting its representation to a parametric form.This supports nonparametric uncertainty representations that may be multimodal or non-Gaussian.
  • Sampling methods: Markov Chain Monte Carlo generates samples iteratively, accepting or rejecting proposed samples according to specified rules.As more samples are produced, their values can approximate the desired distribution.
  • Sampling methods: Hamiltonian Monte Carlo uses momentum and Hamiltonian dynamics, but processing the entire dataset per iteration becomes computationally expensive at very large dataset sizes.This motivates modern methods that address scalability and computational cost.

3) Laplace Approximation:

The Laplace Approximation estimates a Gaussian posterior over neural-network parameters around a local mode, representing model uncertainty through curvature of the loss surface. It can retrofit uncertainty estimation onto trained networks, but scaling Hessian computation to modern networks remains difficult.

  • Laplace Approximation: The Laplace Approximation fits a multivariate normal posterior over network parameters around a local mode of the loss surface.It uses a second-order Taylor expansion of the log posterior around the MAP estimate.
  • Laplace Approximation: The resulting Gaussian has mean ˆθ and covariance (H + τI)−1, with H representing the Hessian of the log posterior.The Hessian encodes local curvature and therefore the model uncertainty around the estimated parameters.
  • Applicability: Unlike the other described methods, Laplace Approximation can be applied to already trained networks using standard losses and piece-wise linear activations.Examples include mean squared error, cross entropy, and ReLU activations.
  • Limitations: Exact Hessian computation is infeasible for modern neural networks because of their enormous parameter counts, motivating approximations such as layer-wise Kronecker factors.Researchers have explored diagonal and off-diagonal approximations to improve scalability.
  • Related Bayesian Approaches: Bayesian deep-learning advances increasingly rely on stochastic mini-batch inference and scalable approximations such as MC-dropout and Laplace Approximation.These methods provide practical alternatives to more expensive posterior-inference procedures.

2) Single- and Multi-Mode Evaluation:

Single-mode methods evaluate one optimum, while ensembles evaluate multiple optima to capture diverse predictive behaviors. Ensembles can improve uncertainty estimation and performance, but their computational and memory costs increase with ensemble size.

  • Single- and Multi-Mode Evaluation: Deterministic networks converge to one local optimum, whereas Bayesian methods account for uncertainty around one optimum and ensembles target several optima.This distinction defines single-mode versus multi-mode evaluation.
  • Single- and Multi-Mode Evaluation: Multi-mode ensembles seek members with different strengths and weaknesses so their combination can produce synergy and reduce isolated false predictions.Figure 7 contrasts pointwise deterministic evaluation, neighborhood-aware Bayesian evaluation, and multi-mode ensemble evaluation.
  • Creating Diversity: Ensemble diversity can be increased through random initialization, data shuffling, bagging, boosting, data augmentation, or different network architectures.Random initialization and data shuffling may already provide sufficient variety for some architectures and datasets.
  • Ensemble Applications: Ensembles represent model uncertainty through variation among member predictions and have been applied across bioinformatics, remote sensing, reinforcement learning, and climate prediction.Their use targets both improved accuracy and uncertainty characterization.
  • Limitations: Ensemble members must be trained independently for standard ensembles, so memory and computational requirements increase with the number of members.Batch-ensemble approaches reduce parameter growth but require members to be trained in parallel rather than independently.
  • Efficient Ensembles: Ensemble distillation, shared trunks, and batch-ensembles reduce deployment costs by compressing or sharing computation across members.Batch-ensembles use one shared weight matrix with member-specific rank-one factors, while distillation transfers ensemble behavior to one network.

6) Sum Up Ensemble Methods:

Ensemble and test-time augmentation methods offer practical routes to predictive uncertainty, but real-world deployment depends on computational constraints, uncertainty type, augmentation choices, and evaluation quality. Major open issues include out-of-distribution detection and the absence of unified uncertainty metrics.

  • Ensemble Methods: Ensembles are easy to apply and can use random initialization, data shuffling, and augmentations to support accuracy, uncertainty quantification, and out-of-distribution detection.Their independent members make training parallelizable, but resource use grows linearly with ensemble size.
  • Test-Time Augmentation: Test-time augmentation creates multiple transformed versions of each test sample and uses their predictions to form a predictive distribution for uncertainty estimation.The transformations provide different views of the input at inference time.
  • Test-Time Augmentation: The uncertainty captured by test-time augmentation depends on augmentation type and on how many augmented samples are used.Simple reflection may capture less uncertainty than domain-specific stretching or shearing, while large-scale inference makes augmentation counts costly.
  • Real-World Applications: Real-world method selection must balance memory, computational power, reaction time, implementation effort, and the desired uncertainty representation.Deterministic methods are most efficient, while Bayesian methods provide a stronger theoretical description and ensembles are relatively easy to apply.
  • Real-World Applications: Out-of-distribution detection remains a central real-world challenge because deployment tasks are more difficult than dataset-based comparisons such as MNIST or CIFAR.Evaluation across multiple real-world datasets is identified as a major need.
  • Real-World Applications: Ensemble evaluation is described as powerful for real-world applications, while Bayesian approaches retain strong results and a theoretical foundation.Efficient ensemble strategies, Bayesian approaches, and lower-cost deterministic methods represent different practical trade-offs.
  • Uncertainty Measures and Quality: Uncertainty-quality assessment is complicated by method-dependent estimates, missing ground-truth uncertainty, and the lack of a unified quantitative metric across tasks.Classification and segmentation commonly use entropy, whereas regression uses prediction intervals or standard deviations.
  • Uncertainty Measures and Quality: Raw softmax confidence is unreliable and cannot represent all sources of uncertainty, so additional measures and approaches are needed.Maximum probability directly represents certainty, while entropy summarizes average information in the categorical output.

2) Measuring Model Uncertainty in Classification Tasks:

Classification model uncertainty is estimated by treating predictions across Bayesian, ensemble, or test-time augmentation samples as variable outputs, then measuring their disagreement. These measures support uncertainty assessment but can remain falsely confident under distribution shifts or out-of-distribution inputs.

  • Bayesian posterior approximations make the softmax output a random variable, enabling uncertainty measures based on prediction distributions.Monte Carlo approximations replace intractable expectations with averages over sampled predictions.
  • Mutual information measures model uncertainty by comparing entropy of the expected softmax output with expected entropy across parameter-conditioned predictions.The measure is minimal when model-parameter knowledge adds no information to the final prediction.
  • Expected KL divergence and predictive variance quantify disagreement or variability among possible softmax outputs.Both use variation in model outputs as an indicator of uncertainty on the model’s prediction.
  • Variability-based uncertainty measures can fail on distribution shifts when all predictors assign high probability to the same false class.Logit magnitude and evidence-based methods are introduced to address this limitation, including Dirichlet or evidence interpretations.
  • Prediction-set measures such as ROC, PR, and AUC evaluate how well uncertainty separates correct from false or in-domain from out-of-distribution samples.ROC and PR vary thresholds, while AUC summarizes the probability that a positive sample receives a higher measure than a negative sample.

2) Measuring Model Uncertainty in Regression Predictions:

Regression networks can represent data uncertainty by predicting distribution parameters or prediction intervals, while model uncertainty is handled as in classification. Calibration and reliability visualization are used to assess whether predictive confidence matches observed outcomes.

  • Model uncertainty has the same main causes and effects in regression and classification, so regression can use analogous approximate-prediction measures.Relevant causes include architecture, training process, and underrepresented regions of the training data.
  • Calibration compares predictive confidence or intervals with empirical correctness, and reliability diagrams visualize this relationship.A model is under-confident when empirical terms exceed the stated confidence; reliability diagrams display the comparison.
  • Deeper networks tend to be more overconfident than shallower networks, linking calibration errors mainly to model uncertainty.The paper relates this to the distinction between reducible model uncertainty and underlying data uncertainty.

A. Calibration Methods

Calibration methods act during training, after training, or through uncertainty-estimation approaches. They modify objectives, data, or confidence estimates to reduce miscalibration and improve the correspondence between predicted and actual uncertainty.

  • A. Calibration Methods: Calibration methods fall into regularization, post-processing, and neural-network uncertainty-estimation groups based on when or how they are applied.The groups respectively modify training, recalibrate held-out outputs, or reduce model uncertainty in confidence predictions.
  • 1) Regularization Methods: Regularization methods modify the objective, optimization, regularization procedure, or training data to build inherently calibrated networks.They differ from uncertainty-estimation methods by targeting calibration rather than directly quantifying model and data uncertainty.
  • 1) Regularization Methods: Label smoothing reduces calibration error by redistributing some true-class probability mass to false classes, often increasing accuracy despite higher training loss.It prevents the logits of the correct class from becoming excessively larger than incorrect-class logits.
  • 1) Regularization Methods: Mixup combines training pairs into virtual samples, while calibration-aware loss terms can regularize miscalibration induced by mixing.The batchwise expected calibration error is added to the standard loss with a weighting hyperparameter.
  • 1) Regularization Methods: On-manifold adversarial training experimentally outperforms mixup training for improving calibration, and out-of-distribution training examples can also help.These approaches use data augmentation or exposure to atypical examples during training.

2) Post-Processing Methods:

Post-processing learns a recalibration map on held-out data, while calibration-quality evaluation compares confidence with empirical accuracy. The paper reviews requirements, visualization, calibration errors, adaptive binning, and class-imbalance limitations.

  • 2) Post-Processing Methods: Post-hoc calibration applies a learned recalibration function to network outputs using a held-out calibration subset.Desired properties are accuracy preservation, data efficiency, and accurate map estimation when sufficient calibration data is available.
  • 2) Post-Processing Methods: No existing post-hoc approach fulfills all three requirements of preserving accuracy, using little data, and approximating the correct recalibration map.The requirements are presented as a practical limitation of current methods.
  • 2) Post-Processing Methods: Temperature scaling changes prediction entropy without replacing likelihood-based training losses: T > 1 decreases confidence, whereas T ∈ (0, 1) increases it.For T = 1, the transformation remains the standard softmax function.
  • 2) Post-Processing Methods: Standard-deviation scaling analogously rescales predicted regression standard deviations and can be trained with Gaussian log-likelihood.The method calibrates uncertainty estimates rather than changing the regression predictions themselves.
  • B. Evaluating Calibration Quality: Reliability diagrams plot bin confidence against bin accuracy, with well-calibrated models lying near the diagonal.Multidimensional reliability diagrams additionally distinguish calibration across classes.
  • B. Evaluating Calibration Quality: ECE uses top-label confidence, whereas SCE evaluates calibration for all classes; all-label measures were empirically more effective than top-label measures.Adaptive variants use equal numbers of predictions per bin and are more robust to the number of bins than equal-width variants.
  • B. Evaluating Calibration Quality: Multi-class calibration errors can be dominated by larger classes, masking poor calibration in smaller classes even with classwise computation.This creates a test-data imbalance limitation for calibration measures.

VI. DATA SETS AND BASELINES

This section surveys benchmark tasks, datasets, baselines, and implementations commonly used to evaluate uncertainty estimation methods. It emphasizes methodological organization and practitioner access to comparison resources.

  • Purpose: The section aims to help researchers and practitioners understand recent benchmark tasks, datasets, baselines, and comparison practices.It presents commonly used experiments and baselines rather than proposing a new benchmark.
  • Organization: The review organizes benchmark approaches, tasks, and datasets into taxonomy-based table blocks for concise comparison and literature lookup.The table focuses on methodological comparison rather than architecture choice.
  • Evaluation tasks: Regression, classification calibration, out-of-distribution detection, and adversarial robustness are frequent evaluation tasks.Medical semantic-segmentation calibration is another noteworthy application.
  • Datasets: Toy and UCI datasets dominate regression studies, while MNIST, CIFAR10/100, SVHN, and ImageNet variants are common for calibration and OOD detection.Toy datasets support uncertainty-interval visualization, whereas UCI datasets support negative log-likelihood comparisons.
  • Baselines: MC Dropout and deep ensembles are the most common baselines, with deterministic softmax outputs serving as a surrogate baseline.Bayesian methods are often compared with variational-inference methods such as Bayes’ by Backprop and Probabilistic Backpropagation.
  • Implementations: Official implementations are linked where available, with highly ranked GitHub implementations supplied otherwise.The implementation list includes common methods across deterministic, Bayesian, ensemble, and augmentation approaches.

VII. APPLICATIONS OF UNCERTAINTY ESTIMATES

Uncertainty estimates support practical decision-making across active learning, reinforcement learning, medicine, robotics, and other domains. Applications use uncertainty to select data, balance actions, and manage risks under incomplete or challenging information.

  • Active learning: Active learning uses uncertainty-based acquisition to select unlabeled samples for annotation and sequentially expand the training set.The selected samples are added to labeled data, after which the predictor is retrained.
  • Reinforcement learning: Reinforcement learning uses uncertainty estimates to balance exploration of unknown environments against exploitation of learned knowledge.Uncertainty associated with a predicted action can help determine whether the agent should execute it.
  • Cross-domain motivation: Uncertainty quantification is motivated by risk minimization and difficult data sources that make trustworthy ground truth challenging to produce.The review presents applications across multiple domains, including medical imaging, robotics, and Earth observation.
  • Medical imaging: Predictive uncertainty is important in medical image analysis because disease size, shape, and location vary substantially across patients.Applications include lesion detection and segmentation of lung nodes, brain tumors, and parasites.
  • Robotics: Robotics requires uncertainty-aware deep learning because agents act with incomplete world knowledge and mistakes can jeopardize missions or human lives.Robotics research also faces real-time computation, sequential sensing, and uncertainty-selection challenges.
  • Robotics methods: Robotics uncertainty research includes novelty detection, uncertainty-aware localization, failure learning, and predictor-inconsistency detection.The field has developed both task-specific methods and practical applications.

3) Earth Observation(EO):

Earth observation applies uncertainty estimation to variable, multisensor data used for critical decisions, while current methods remain constrained by validation, evaluation, explainability, and physical-model gaps. The section outlines research directions intended to improve real-world adoption.

  • Earth observation context: Earth observation supports critical decisions in urban planning, resource management, and disaster response, while its deep-learning inputs vary substantially.The field includes hundreds of satellites operated by public and private organizations.
  • Distribution shift: Out-of-distribution detection is important because deployment images may differ from training data, such as when clouds obstruct previously clear scenes.Uncertainty measurements play an important role in identifying such cases.
  • Data fusion: Earth-observation data fusion must quantify uncertainty contributions from heterogeneous channels and identify the trustworthy source for each sample.Sources can include optical data with hundreds of channels and sensors differing in spatial, temporal, and semantic properties.
  • Physical uncertainty: Sensor sensitivity, atmospheric absorption, and surface reflectance contribute uncertainty, motivating integration of physical Earth-observation system knowledge.Assimilating EO-derived geovariables into process models requires probability distributions for estimated variables.
  • Validation limitations: Current uncertainty methods lack broad validation on complex real-world data, because many baselines rely on standard datasets unlike noisy or low-resolution satellite inputs.A structured evaluation across real-world applications is not yet available.
  • Evaluation limitations: Standard metrics often evaluate whole test sets, so uncertainty for individual samples or small groups can be biased by the rest of the dataset.This limits assessment of reliability for practical single decisions.
  • Ground-truth limitations: Uncertainty ground truths are generally unavailable, and calibration on one dataset cannot simply transfer across distribution shifts.The gap between estimated and real uncertainty limits adoption.
  • Explainability and outlook: Uncertainty predictions often do not reveal what caused the uncertainty, making transfer across datasets or domains harder and hindering safety-critical use.Explainability and physically based models are proposed as research opportunities for improving trust and engineering.
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