Magnetic-anomaly navigation, leveraging small-scale variations in the Earth's magnetic field, is a promising alternative when GPS is unavailable or compromised. Airborne systems face a key challenge in extracting geomagnetic field data: the aircraft itself induces magnetic noise. Although the classical Tolles-Lawson model addresses this, it inadequately handles stochastically corrupted magnetic data required for navigation. To handle stochastic noise, we propose using two physics-based constraints: divergence-free vector fields and E(3)-equivariance. These ensure the learned magnetic field obeys Maxwell's equation and that outputs transform correctly with sensor position and orientation. The divergence-free constraint is implemented by training a neural network to output a vector potential A, with the magnetic field defined as its curl. For E(3)-equivariance, we use tensor products of geometric tensors represented via spherical harmonics with known rotational transformations. Enforcing physical consistency and restricting the admissible function space acts as an implicit regularizer that improves spatiotemporal performance. We present ablation studies evaluating each constraint alone and jointly across CNNs, MLPs, LTCs, and Contiformers. Continuous-time dynamics and long-term memory are critical for modelling magnetic time series; the Contiformer, which provides both, outperforms existing methods. To mitigate data scarcity, we generate synthetic datasets using the World Magnetic Model (WMM) and time-series conditional GANs, producing realistic, temporally consistent magnetic sequences across varied trajectories and environments. Experiments show that embedding these constraints significantly improves predictive accuracy and physical plausibility, outperforming classical and unconstrained deep learning approaches.
Acknowledgement: This work was done in collaboration with Dirac Labs.
Denoising-GS: Gaussian Splatting with Spatial-aware Denoising
School of Computer Science and Artificial Intelligence（计算机科学与人工智能学院）；Fudan University（复旦大学）；Software of Engineering（软件工程系）；Dalian University of Technology（大连理工大学）；Department of Information Engineering（信息工程系）；The Chinese University of Hong Kong（香港中文大学）；College of Computing and Data Science（计算与数据科学学院）；Nanyang Technological University（南洋理工大学）
Human-Aware Robot Navigation via Reinforcement Learning with Hindsight Experience Replay and Curriculum Learning
The Chinese University of Hong Kong（香港中文大学）；Southern University of Science and Technology（南方科技大学）；Shenzhen Research Institute of the Chinese University of Hong Kong（香港中文大学深圳研究院）
