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新论文 · v1arXiv:2611.07395

Rigorously Certified Neural-Network Computation of Nonlinear Water Waves at Near-Machine Precision

Michal Shavit, Yongji Wang, Tristan Buckmaster

原文摘要

We present a computational framework that combines machine-learning-based discovery with rigorous computer-assisted numerical certification and formal verification for strongly nonlinear partial differential equations. We demonstrate the approach for periodic gravity-capillary traveling water waves. Physics-informed neural networks are used as a search mechanism, with the wave profile, wave speed and, in continuation experiments, surface tension learned directly from the governing equations without training data. Through a staged training and refinement procedure, the neural networks achieve near-machine-precision residuals of the governing equations, even in strongly nonlinear regimes. A single formulation recovers high-amplitude Stokes waves, Crapper waves and Wilton ripples. Continuation from a high-amplitude Wilton ripple in surface tension reveals new high-amplitude candidate solutions. We freeze one candidate as an explicit finite representation and rigorously certify a uniform bound on its governing-equation residual using interval arithmetic, accounting for floating-point roundoff, Fourier truncation, aliasing and grid-to-continuum errors. This independently validates the neural-network accuracy. We formalize the certification argument in Lean, which machine-checks the deductions from certified numerical bounds to the residual theorem. Both the interval certification and formalization were developed with substantial assistance from a large language model, while the validity of the result remains independent of the language model: the numerical bounds are rigorously enclosed by interval arithmetic and the subsequent mathematical deductions are checked by the Lean kernel. Together, these steps provide a pipeline from neural discovery to rigorous numerical certification and machine-checked verification with auditable mathematical guarantees.

math.AP · cs.LG · physics.flu-dyn

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.18099

Fluid Antenna-Aided Robust Secure Uplink Transmission in LEO Satellite Constellations

Suhong Luo, Pan Tang, Jianhua Zhang, Ji Wang, Yixuan Li, Xingwang Li

原文摘要

Secure uplink transmission in low-earth orbit (LEO) satellite constellations faces significant challenges due to the time-varying spatial distributions of serving and potential eavesdropping satellites, particularly when their angular separations are small and eavesdropper channel state information (CSI) is imperfect. To address these challenges, this paper investigates fluid antenna (FA)-aided robust secure uplink transmission in LEO satellite constellations. To avoid frequent antenna reconfiguration, the FA positions are optimized over an observation interval and remain fixed throughout the interval, while transmit beamforming dynamically adapts to the time-varying satellite channels. We formulate an average worst-case secrecy rate maximization problem by jointly optimizing FA positions and time-varying beamforming under norm-bounded eavesdropper CSI uncertainties and per-slot secrecy rate constraints. Two new alternating optimization (AO) algorithms are developed to solve the resulting non-convex problem. For robust beamforming optimization, the S-procedure, semidefinite relaxation (SDR), and first-order approximation are employed to construct a tractable convex problem, followed by Gaussian randomization for rank-one recovery. For FA position optimization, we derive concave surrogate functions for successive convex approximation (SCA) and develop a differential evolution (DE)-based search strategy to reduce computational complexity. Numerical results demonstrate that both FA-aided schemes consistently outperform conventional fixed-position antenna arrays across different constellation configurations and CSI uncertainty levels. Moreover, the two algorithms exhibit different performance-complexity tradeoffs as the number of FA elements increases, with DE offering a computational advantage for larger arrays while SCA can achieve higher secrecy rates.

cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.06204

CoSafe: Cooperative Runtime Safety Assurance for Mixed-Traffic Autonomous Driving

Dingji Wang, You Lu, Haowen Jiang, Yanggang Chen, Yuyang Bi, Bihuan Chen, Shenglin Bao, Xin Peng

原文摘要

With the rapid development of autonomous driving systems (ADSes), real-world roads are evolving into mixed-traffic environments where autonomous vehicles (AVs) and other traffic participants (e.g., human-driven vehicles (HDVs), cyclists, and pedestrians) coexist and interact with each other. However, current ADSes still incur various safety violations in mixed traffic scenarios, raising a strong demand for runtime safety assurance frameworks that can continuously monitor hazards and prevent potential violations. Existing ego-centric assurance approaches are insufficient for mixed traffic, where violations often arise from locally reasonable yet jointly incompatible decisions among multiple vehicles and cannot be reliably resolved through independent takeover. To bridge this gap, we propose CoSafe, a modular and ADS-agnostic cooperative runtime safety assurance framework for mixed-traffic autonomous driving to extend runtime safety assurance from ego-centric takeover to scene-level cooperative intervention. CoSafe leverages vehicle-to-everything (V2X) communication to enable roadside units (RSUs) to monitor scene-level hazards and jointly mitigate hazards involving multiple vehicles. We integrate CoSafe with seven state-of-the-art ADSes, and our evaluation on the InterDrive benchmark demonstrates that CoSafe improves the driving score of AVs by 70.03% on average, reduces safety violations by 87.80%, and accurately identifies unsafe AVs with an F3 score of 0.930, while satisfying real-time constraints.

cs.SE · cs.AI · cs.RO

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2608.16745

VicEdit: Learning to Edit Videos from Visual In-Context Examples

Yuji Wang, Teng Hu, Yuheng Chen, Ran Yi, Han Feng, Weijian Cao, Chengjie Wang, Lizhuang Ma 等 9 位作者

原文摘要

Despite remarkable progress in instruction-based video editing, textual descriptions remain limited in expressing fine-grained appearance, spatial transformations, and temporal dynamics. We introduce Visual In-context Editing, a new paradigm that shifts video editing from text-only instructions to visual demonstrations, where users specify desired edits through heterogeneous visual references including single images, image pairs, and video pairs. To establish this paradigm, we curate VicEdit-400K, the first large-scale dataset for visual in-context video editing, containing 400K high-quality samples across ten editing tasks with comprehensive semantic and visual consistency filtering. Building upon this foundation, we propose VicEdit, a unified framework that enables effective reasoning over diverse visual contexts and textual instructions. Specifically, we introduce Modality-Adaptive Semantic Distillation to extract modality-aware visual editing semantics and Dual-Context Injection to align visual contexts with textual editing intents. Extensive experiments on VicEdit-Bench demonstrate that VicEdit achieves state-of-the-art performance on both conventional instruction-based editing and visual in-context editing. Further controlled studies and human evaluations verify that VicEdit effectively leverages heterogeneous visual references, establishing visual in-context editing as a promising paradigm for controllable video editing.

cs.CV

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.05439

Learning Implicit Solves for Dynamic Simulations

Chawit Kaewnuratchadasorn, Jiaji Wang, Xin Nie

原文摘要

High-fidelity simulation of dynamical systems is central to scientific discovery and engineering design, yet remains computationally demanding. Here we introduce the Implicit Neural Operator Solver (INOS), which learns the implicit solve and encodes a time integrator. INOS pretrains a neural operator from static equilibrium solutions and reuses it within Newmark-$β$ integration. At each time increment, the integrator forms an effective equilibrium problem, the pretrained neural operator infers the next-step solution field, and the Newmark relations advance the dynamic state. Numerical examples in linear and nonlinear elastodynamics demonstrate accurate full-field predictions without dynamic trajectory supervision. Comparative results show that INOS, evaluated zero-shot, achieves higher predictive accuracy than neural solver baselines trained on dynamic simulations. In addition, INOS delivers over 4,600$\times$ speedup in nonlinear simulations over sequential classical finite-element solvers. INOS natively accommodates changes in dynamic conditions and enables reuse of the pretrained operator across spatial and temporal discretizations. Further evaluation demonstrates a stable million-step rollout. These findings establish INOS as a reusable neural implicit solver for accurate, efficient, and robust dynamic modeling.

cs.LG · cs.CE

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arXiv ↗PDF ↗