Jie Qi

Jie Qi, Jing Zhang, Miroslav Krstic

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output or input. The PDE backstepping design produces gain functions that are outputs of a nonlinear operator, mapping functions on a spatial domain into functions on a spatial domain, and where this gain-generating operator's inputs are the PDE's coefficients. The operator is approximated with a DeepONet neural network to a degree of accuracy that is provably arbitrarily tight. Once we produce this approximation-theoretic result in infinite dimension, with it we establish stability in closed loop under feedback that employs approximate gains. In addition to supplying such results under full-state feedback, we also develop DeepONet-approximated observers and output-feedback laws and prove their own stabilizing properties under neural operator approximations. With numerical simulations we illustrate the theoretical results and quantify the numerical effort savings, which are of two orders of magnitude, thanks to replacing the numerical PDE solving with the DeepONet.

Shurong Mo, Nailong Wu, Jie Qi et al.

This study proposes a delay-compensated feedback controller based on proximal policy optimization (PPO) reinforcement learning to stabilize traffic flow in the congested regime by manipulating the time-gap of adaptive cruise control-equipped (ACC-equipped) vehicles.The traffic dynamics on a freeway segment are governed by an Aw-Rascle-Zhang (ARZ) model, consisting of $2\times 2$ nonlinear first-order partial differential equations (PDEs).Inspired by the backstepping delay compensator [18] but different from whose complex segmented control scheme, the PPO control is composed of three feedbacks, namely the current traffic flow velocity, the current traffic flow density and previous one step control input. The control gains for the three feedbacks are learned from the interaction between the PPO and the numerical simulator of the traffic system without knowing the system dynamics. Numerical simulation experiments are designed to compare the Lyapunov control, the backstepping control and the PPO control. The results show that for a delay-free system, the PPO control has faster convergence rate and less control effort than the Lyapunov control. For a traffic system with input delay, the performance of the PPO controller is comparable to that of the Backstepping controller, even for the situation that the delay value does not match. However, the PPO is robust to parameter perturbations, while the Backstepping controller cannot stabilize a system where one of the parameters is disturbed by Gaussian noise.

Zhuofan Xie, Zishan Lin, Jinliang Lin et al.

Active Learning (AL) reduces annotation costs in medical imaging by selecting only the most informative samples for labeling, but suffers from cold-start when labeled data are scarce. Vision-Language Models (VLMs) address the cold-start problem via zero-shot predictions, yet their temperature-scaled softmax outputs treat text-image similarities as deterministic scores while ignoring inherent uncertainty, leading to overconfidence. This overconfidence misleads sample selection, wasting annotation budgets on uninformative cases. To overcome these limitations, the Similarity-as-Evidence (SaE) framework calibrates text-image similarities by introducing a Similarity Evidence Head (SEH), which reinterprets the similarity vector as evidence and parameterizes a Dirichlet distribution over labels. In contrast to a standard softmax that enforces confident predictions even under weak signals, the Dirichlet formulation explicitly quantifies lack of evidence (vacuity) and conflicting evidence (dissonance), thereby mitigating overconfidence caused by rigid softmax normalization. Building on this, SaE employs a dual-factor acquisition strategy: high-vacuity samples (e.g., rare diseases) are prioritized in early rounds to ensure coverage, while high-dissonance samples (e.g., ambiguous diagnoses) are prioritized later to refine boundaries, providing clinically interpretable selection rationales. Experiments on ten public medical imaging datasets with a 20% label budget show that SaE attains state-of-the-art macro-averaged accuracy of 82.57%. On the representative BTMRI dataset, SaE also achieves superior calibration, with a negative log-likelihood (NLL) of 0.425.

Jiaqi Hu, Jie Qi, Jing Zhang

Control of distributed parameter systems affected by delays is a challenging task, particularly when the delays depend on spatial variables. The idea of integrating analytical control theory with learning-based control within a unified control scheme is becoming increasingly promising and advantageous. In this paper, we address the problem of controlling an unstable first-order hyperbolic PDE with spatially-varying delays by combining PDE backstepping control strategies and deep reinforcement learning (RL). To eliminate the assumption on the delay function required for the backstepping design, we propose a soft actor-critic (SAC) architecture incorporating a DeepONet to approximate the backstepping controller. The DeepONet extracts features from the backstepping controller and feeds them into the policy network. In simulations, our algorithm outperforms the baseline SAC without prior backstepping knowledge and the analytical controller.