Physics-informed deep learning (PIDL) neural networks have shown their capability as a useful instrument for transportation practitioners in utilizing the underlying relationship between the state variables for traffic state estimation (TSE). Another efficient traffic management approach is implementing varying speed limits (VSLs) on transportation corridors to control traffic and mitigate congestion. However, the existing training architecture of PIDL in the literature cannot accommodate the changing traffic characteristics on a freeway with VSL. To tackle this challenge, we propose a novel framework integrating teacher-student ensemble training with PIDL neural networks for TSE under VSL scenarios. The physics of flow conservation law is encoded locally in the teacher models by PIDL, and the student model uses a multi-layer perceptron classifier (MLP) to identify traffic characteristics and selects the ensemble member of PIDL neural networks for TSE. This integrated framework provides a natural solution for capturing the heterogeneity of VSL and accurately addressing the TSE problem. The case study results validate the proposed ensemble approach, demonstrating its superior performance in TSE compared to other popular baseline methods, as indicated by relative L2 error.
Traffic state estimation from sparse fixed sensors is challenging because physics-informed neural networks (PINNs) tend to over-smooth sharp transitions admitted by the Lighthill-Whitham--Richards (LWR) model. This study proposes Two-Stage Domain Decomposition Physics-Informed Neural Networks (TSDD-PINN), an observation-aligned framework for LWR-based offline speed-field reconstruction. The framework supports spatial, temporal, and space--time refinement. Matched direction analysis shows that spatial refinement has the lowest mean error and less than half the training time of space--time refinement in the tested setting, while temporal refinement is faster. A global parent PINN is first trained. In the controlled spatial implementation, its residual profile guides a deterministic partition for warm-started child networks. An optional operational safeguard retains Stage~1 when the prespecified screen does not activate. The primary I-24 MOTION evaluation spans five days, five sensor configurations, and ten seeds per configuration, yielding 1{,}500 runs. Controlled TSDD-PINN attains the lowest relative L2 error in 18 of 25 configurations and 14 of 15 sparse-sensing cases, while training 2.4 times faster than the extended PINN (XPINN) baseline under the evaluated implementations and training budgets. Non-neural comparisons show that the advantage over interpolation is concentrated under sparse sensing, whereas dense sensing often favors interpolation. A separate 250-run operational evaluation finds infrequent activation and motivates the Stage-1-preserving safeguard. The residual is treated as an indicator of model difficulty rather than a validated shock detector. The evidence supports a sensing-density-dependent operating range rather than uniform improvement.
Accurate modeling of nonlinear vehicle dynamics is essential for high-speed autonomous racing, where controllers operate at the handling limits. Model-based methods are interpretable but rely on simplifying assumptions, while purely learned models capture nonlinearities yet often lack physical consistency, generalization, and adaptability to changing operating conditions. This paper presents DynSSM, a physics-aware state-space memory framework that combines learned temporal representations with a structured vehicle dynamics model. The proposed approach integrates state-space sequence modeling and recurrent encoders to capture long- and short-term dynamic behavior. It simultaneously adapts tire and vehicle-dynamics parameters within bounded ranges to preserve physical plausibility. A residual correction mechanism compensates for remaining unmodeled dynamics while preserving the underlying physics-based structure. DynSSM is evaluated on both simulated small-scale racing data and real-world full-scale autonomous Indy racecar data. When evaluated on an unseen real-world track, DynSSM reduces one-step prediction RMSE by up to 27.2% in longitudinal velocity, 73.9% in lateral velocity, and 88.8% in yaw rate compared with the state-of-the-art (\sota{}) baselines. Component-wise ablation studies demonstrate the importance of temporal memory, parameter adaptation, and residual correction for predictive performance and robustness. Further, closed-loop simulations using nonlinear model predictive control demonstrate that DynSSM remains feasible across the evaluated tracks and achieves up to a 13.2% reduction in one-lap completion time compared with \sota{} baselines. These results indicate that combining temporal memory, bounded physics-guided parameter adaptation, and residual correction provides an accurate, interpretable, and control-ready dynamics model for autonomous racing.
Musabbir Ahmed Arrafi, Malik Ali, Nicholas M. Stiffler +1
Traffic prediction is difficult due to the complex interplay of temporal evolution, spatial interactions, and delayed spatio-temporal propagation over road networks. Existing methods either model spatial and temporal dependencies separately or employ unified spatio-temporal structures, but they often insufficiently characterize how neighboring sensors at historical timestamps influence a target node, while complex joint models may incur high computation. This paper proposes STEI-PCN, an efficient pure convolutional network based on spatio-temporal encoding and relation inference. It first builds a local causal joint spatio-temporal graph to restrict candidate interactions, then uses absolute position and relative distance encodings to infer dynamic edge weights. A single-layer graph convolution with a position-aware gated activation unit captures local joint dependencies, and temporal dilated causal convolutions complement long-range temporal patterns. A multi-view prediction module fuses raw, local propagation, and long-range temporal representations for direct multi-step forecasting. Experiments on PeMS03, PeMS04, PeMS07, PeMS08, and PeMS-Bay under multiple horizons show that STEI-PCN achieves competitive accuracy with moderate parameters and low training and inference costs. Ablation and fluctuation analyses further verify the contributions of the main components and empirically analyze the effects of the training-stage constraints under sharp speed changes. Our code is available at a GitHub link https://github.com/Jessez2/STEI-PCN.