Equipping deep learning models with a principled uncertainty quantification (UQ) has become essential for ensuring their reliable performance in the open world. To handle uncertainty arising from two prevalent sources – distribution shift and out-of-distribution (OOD) – in the open-world settings, this paper presents a unified uncertainty-informed approach for quantifying and managing the risks these factors pose to the dependable function of deep learning models. Toward this goal, we propose leveraging a principled UQ approach — Spectral-normalized Neural Gaussian Process (SNGP) — to quantify the epistemic uncertainty associated with model predictions. Unlike other UQ methods in the literature, SNGP is characterized by two unique properties: (1) applying spectral normalization to the weights of the neural network’s hidden layers to preserve the relative distances among data points during data transformations; (2) replacing the traditional output layer of neural networks with a Gaussian process to enable distance-aware uncertainty estimation. Based on SNGP’s uncertainty estimate, we apply Youden’s index to determine an optimal threshold for categorizing the uncertainty into distinct levels, thereby enabling decision-makers to make uncertainty-informed decisions. Two datasets of varying scale are used to demonstrate how the proposed method facilitates risk assessment and management of deep learning models in the open environment. Computational results reveal that the proposed method achieves prediction performance comparable to Monte Carlo dropout and deep ensemble methods. Importantly, the proposed approach outperforms the other two methods by providing a computationally efficient, consistent, and principled uncertainty estimation under no distribution shift, distribution shift, and OOD conditions.

Multi-state systems (MSS) are widely used for modeling the behavior of engineering applications, where the system and its components can have more than two distinct states. Physics-Informed Neural Networks (PINNs) offer a viable solution for characterizing the dynamic state evolution of MSS. However, existing methods predominantly rely on uniformly sampled collocation points across the problem domain when training PINNs. Although some residual-based active learning methods exist, they are inherently static and local, and often fail to capture a crucial aspect of PINN training: identification and accurate modeling of the “critical transition regions” within the problem domain. To address this fundamental challenge, we treat PINN as a dynamic system and introduce a novel active learning method grounded in chaos theory to identify regions within the problem domain that are highly sensitive to initial conditions. Specifically, our method quantifies the degree of chaos at candidate collocation points by introducing small perturbations and using PINN’s forward propagation to simulate the dynamic evolution of both the original and perturbed collocation points. Collocation points that exhibit pronounced chaotic behavior—- where evolutionary trajectories diverge rapidly following perturbation—are identified as the system’s most unstable and valuable regions for PINN training. By prioritizing these dynamically unstable points, our method directs PINN to focus its learning on accurately delineating the boundaries of state transitions, thereby significantly enhancing the accuracy of reliability analysis. Experimental results on multiple benchmark partial differential equations (PDEs) and several MSSs demonstrate that, compared to other PINN learning schemes, our method shows superior accuracy and computational efficiency in MSS reliability assessment.

Accurate and reliable prediction has profound implications to a wide range of applications, such as hospital admissions, inventory control, route planning. In this study, we focus on an instance of spatio-temporal learning problem–traffic prediction–to demonstrate an advanced deep learning model developed for making accurate and reliable prediction. Despite the significant progress in traffic prediction, limited studies have incorporated both explicit (e.g., road network topology) and implicit (e.g., causality-related traffic phenomena and impact of exogenous factors) traffic patterns simultaneously to improve prediction performance. Meanwhile, the variability nature of traffic states necessitates quantifying the uncertainty of model predictions in a statistically principled way; however, extant studies offer no provable guarantee on the statistical validity of confidence intervals in reflecting its actual likelihood of containing the ground truth. In this paper, we propose an end-to-end traffic prediction framework that leverages three primary components to generate accurate and reliable traffic predictions: dynamic causal structure learning for discovering implicit traffic patterns from massive traffic data, causally-aware spatio-temporal multi-graph convolution network (CASTMGCN) for learning spatio-temporal dependencies, and conformal prediction for uncertainty quantification. In particular, CASTMGCN fuses several graphs that characterize different important aspects of traffic networks (including physical road structure, time-lagged causal effect, contemporaneous causal relationships) and an auxiliary graph that captures the effect of exogenous factors on the road network. On this basis, a conformal prediction approach tailored to spatio-temporal data is further developed for quantifying the uncertainty in node-wise traffic predictions over varying prediction horizons. Experimental results on two real-world traffic datasets of varying scale demonstrate that the proposed method outperforms several state-of-the-art models in prediction accuracy; moreover, it generates more efficient prediction regions than several other methods while strictly satisfying the statistical validity in coverage.

Understanding causal relationships between traffic states throughout the system is of great significance for enhancing traffic management and optimization in urban traffic networks. Unfortunately, few studies in the literature have systematically analyzed causal structure characterizing the evolution of traffic states over time and gauged the importance of traffic nodes from a causal perspective, particularly in the context of large-scale traffic networks. Moreover, the dynamic nature of traffic patterns necessitates a robust method to reliably discover causal relationships, which are often overlooked in existing studies. To address these issues, we propose a Spatio-Temporal Causal Structure Learning and Analysis (STCSLA) framework for analyzing large-scale urban traffic networks at a mesoscopic level from a causal lens. The proposed framework comprises three main components: decomposition of spatio-temporal traffic data into localized traffic subprocesses; a Bayesian Information Criterion-guided spatio-temporal causal structure learning combined with temporal-dependencies preserving sampling for deriving reliable causal graph to uncover time-lagged and contemporaneous causal effects; establishing several causality-oriented indicators to identify causally critical nodes, mediator nodes, and bottleneck nodes in traffic networks. Experimental results on both a synthetic dataset and the real-world Hong Kong traffic dataset demonstrate that the proposed STCSLA framework accurately uncovers time-varying causal relationships and identifies key nodes that play various causal roles in influencing traffic dynamics. These findings underscore the potential of the proposed framework to improve traffic management and provide a comprehensive causality-driven approach for analyzing urban traffic networks.