Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction

Reconstructing continuous physical fields from sparse measurements is a central inverse problem, but data-driven generative models can produce states that violate governing dynamics. We introduce a physics-informed generative solver that separates stable prior learning from inference-time enforcement of conservation laws. Martingale-Regularized Score Matching regularizes score pretraining with a Score Fokker-Planck constraint, yielding a dynamically stable prior. Physics-Informed Implicit Score Sampling then guides denoising trajectories by gradients of physical residuals, projecting samples toward admissible manifolds without retraining. In acoustics, the method co-generates pressure and particle velocity from sparse sensors, enabling dense virtual arrays that suppress spatial aliasing. The same framework generalizes to real-world ERA5 meteorological fields under extreme sparsity. Together, this work establishes a rigorous and generalizable paradigm for solving high-dimensional inverse problems, bridging the gap between generative artificial intelligence and first-principles science.

BioDrone: A Bionic Drone-based Single Object Tracking Benchmark for Robust Vision

Single object tracking (SOT) is a fundamental problem in computer vision, with a wide range of applications, including autonomous driving, augmented reality, and robot navigation. The robustness of SOT faces two main challenges: tiny target and fast motion. These challenges are especially manifested in videos captured by unmanned aerial vehicles (UAV), where the target is usually far away from the camera and often with significant motion relative to the camera. To evaluate the robustness of SOT methods, we propose BioDrone -- the first bionic drone-based visual benchmark for SOT. Unlike existing UAV datasets, BioDrone features videos captured from a flapping-wing UAV system with a major camera shake due to its aerodynamics. BioDrone hence highlights the tracking of tiny targets with drastic changes between consecutive frames, providing a new robust vision benchmark for SOT. To date, BioDrone offers the largest UAV-based SOT benchmark with high-quality fine-grained manual annotations and automatically generates frame-level labels, designed for robust vision analyses. Leveraging our proposed BioDrone, we conduct a systematic evaluation of existing SOT methods, comparing the performance of 20 representative models and studying novel means of optimizing a SOTA method (KeepTrack KeepTrack) for robust SOT. Our evaluation leads to new baselines and insights for robust SOT. Moving forward, we hope that BioDrone will not only serve as a high-quality benchmark for robust SOT, but also invite future research into robust computer vision. The database, toolkits, evaluation server, and baseline results are available at http://biodrone.aitestunion.com.