FePySR: A Neural Feature Extraction Framework for Efficient and Scalable Symbolic Regression

A fundamental challenge in symbolic regression (SR) is efficiently recovering complex mathematical expressions from observational data. Although this problem is NP-hard, many expressions of practical interest decompose naturally into combinations of nonlinear feature modules, concentrating structural complexity into a small number of reusable components. Here, we introduce FePySR, a two-stage framework that reduces the SR search space by extracting valid features prior to equation search. FePySR first employs a heterogeneous neural network to constrain observational data to a set of candidate expressions, then performs structural optimization within this refined expression space using PySR. Across five standard benchmarks, FePySR outperforms state-of-the-art methods by achieving higher equation recovery rates. On a set of 75 highly complex synthesized equations, FePySR recovers 36 equations, while producing substantially smaller mean squared errors on the remaining unrecovered cases, with reduced computation time compared to PySR. FePySR's first stage also maintains consistent performance under varying numbers of selected top features and increasing levels of noise in the observational data. Applied to ordinary differential equations governing biological systems, FePySR successfully identifies governing equations in 24 out of 100 tests where PySR recovers none. Taken together, FePySR is a generalizable framework that can enhance the SR solvers, enabling the efficient and reliable recovery of symbolic expressions across scientific domains.

BEV-ODOM2: Enhanced BEV-based Monocular Visual Odometry with PV-BEV Fusion and Dense Flow Supervision for Ground Robots

Bird's-Eye-View (BEV) representation offers a metric-scaled planar workspace, facilitating the simplification of 6-DoF ego-motion to a more robust 3-DoF model for monocular visual odometry (MVO) in intelligent transportation systems. However, existing BEV methods suffer from sparse supervision signals and information loss during perspective-to-BEV projection. We present BEV-ODOM2, an enhanced framework addressing both limitations without additional annotations. Our approach introduces: (1) dense BEV optical flow supervision constructed from 3-DoF pose ground truth for pixel-level guidance; (2) PV-BEV fusion that computes correlation volumes before projection to preserve 6-DoF motion cues while maintaining scale consistency. The framework employs three supervision levels derived solely from pose data: dense BEV flow, 5-DoF for the PV branch, and final 3-DoF output. Enhanced rotation sampling further balances diverse motion patterns in training. Extensive evaluation on KITTI, NCLT, Oxford, and our newly collected ZJH-VO multi-scale dataset demonstrates state-of-the-art performance, achieving 40 improvement in RTE compared to previous BEV methods. The ZJH-VO dataset, covering diverse ground vehicle scenarios from underground parking to outdoor plazas, is publicly available to facilitate future research.

Capsizing-Guided Trajectory Optimization for Autonomous Navigation with Rough Terrain

It is a challenging task for ground robots to autonomously navigate in harsh environments due to the presence of non-trivial obstacles and uneven terrain. This requires trajectory planning that balances safety and efficiency. The primary challenge is to generate a feasible trajectory that prevents robot from tip-over while ensuring effective navigation. In this paper, we propose a capsizing-aware trajectory planner (CAP) to achieve trajectory planning on the uneven terrain. The tip-over stability of the robot on rough terrain is analyzed. Based on the tip-over stability, we define the traversable orientation, which indicates the safe range of robot orientations. This orientation is then incorporated into a capsizing-safety constraint for trajectory optimization. We employ a graph-based solver to compute a robust and feasible trajectory while adhering to the capsizing-safety constraint. Extensive simulation and real-world experiments validate the effectiveness and robustness of the proposed method. The results demonstrate that CAP outperforms existing state-of-the-art approaches, providing enhanced navigation performance on uneven terrains.

BEV-DWPVO: BEV-based Differentiable Weighted Procrustes for Low Scale-drift Monocular Visual Odometry on Ground

Monocular Visual Odometry (MVO) provides a cost-effective, real-time positioning solution for autonomous vehicles. However, MVO systems face the common issue of lacking inherent scale information from monocular cameras. Traditional methods have good interpretability but can only obtain relative scale and suffer from severe scale drift in long-distance tasks. Learning-based methods under perspective view leverage large amounts of training data to acquire prior knowledge and estimate absolute scale by predicting depth values. However, their generalization ability is limited due to the need to accurately estimate the depth of each point. In contrast, we propose a novel MVO system called BEV-DWPVO. Our approach leverages the common assumption of a ground plane, using Bird's-Eye View (BEV) feature maps to represent the environment in a grid-based structure with a unified scale. This enables us to reduce the complexity of pose estimation from 6 Degrees of Freedom (DoF) to 3-DoF. Keypoints are extracted and matched within the BEV space, followed by pose estimation through a differentiable weighted Procrustes solver. The entire system is fully differentiable, supporting end-to-end training with only pose supervision and no auxiliary tasks. We validate BEV-DWPVO on the challenging long-sequence datasets NCLT, Oxford, and KITTI, achieving superior results over existing MVO methods on most evaluation metrics.