Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures

2025-05-26

AI Summary

Learning continuous dynamics under unknown, locally measurable, and uncertain environmental constraints remains challenging. Method: This paper proposes a geometric modeling framework based on fiber bundles. It is the first to naturally induce a fiber bundle structure directly from sensor measurements, unifying local constraints, perception data, and dynamics modeling; further, it designs measurement-aware adaptive Control Barrier Functions (CBFs) that theoretically guarantee both constraint satisfaction and learning convergence—dynamically adjustable according to perception quality. The approach integrates fiber bundle differential geometry, Neural ODEs, and uncertainty-aware embedding. Results: Experiments demonstrate that, under limited or uncertain perception, the method improves dynamics learning efficiency by over 40% and reduces constraint violation rates by more than 90%, significantly outperforming conventional filtering and global-constraint-based methods.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Learning unknown dynamics under environmental (or external) constraints is fundamental to many fields (e.g., modern robotics), particularly challenging when constraint information is only locally available and uncertain. Existing approaches requiring global constraints or using probabilistic filtering fail to fully exploit the geometric structure inherent in local measurements (by using, e.g., sensors) and constraints. This paper presents a geometric framework unifying measurements, constraints, and dynamics learning through a fiber bundle structure over the state space. This naturally induced geometric structure enables measurement-aware Control Barrier Functions that adapt to local sensing (or measurement) conditions. By integrating Neural ODEs, our framework learns continuous-time dynamics while preserving geometric constraints, with theoretical guarantees of learning convergence and constraint satisfaction dependent on sensing quality. The geometric framework not only enables efficient dynamics learning but also suggests promising directions for integration with reinforcement learning approaches. Extensive simulations demonstrate significant improvements in both learning efficiency and constraint satisfaction over traditional methods, especially under limited and uncertain sensing conditions.

Problem

• Learning unknown dynamics under local uncertain environmental constraints
• Exploiting geometric structure in local measurements for dynamics learning
• Ensuring constraint satisfaction and learning convergence with limited sensing

Innovation

• Fiber bundle structure unifies measurements and constraints
• Measurement-aware Control Barrier Functions adapt locally
• Neural ODEs preserve geometric constraints continuously