Wangtao Lu

Yufei Wei, Chenxiao Hu, Wangtao Lu et al.

Scale-consistent ego-motion estimation is fundamental for autonomous ground robots. Bird's-Eye-View (BEV) representation naturally addresses the scale drift problem of monocular visual odometry (MVO) by providing a metric-scaled planar workspace, enabling the simplification of 6-DoF ego-motion to a more robust 3-DoF model. However, existing BEV-based methods suffer from two key limitations: sparse supervision signals from pose-only training, and information loss during perspective-to-BEV projection. We present BEV-ODOM2, an enhanced framework that addresses both limitations without requiring additional annotations. Our approach introduces (1) dense BEV optical flow supervision constructed directly from 3-DoF pose ground truth for pixel-level guidance, and (2) Perspective View (PV)-BEV fusion that computes correlation volumes before projection to preserve 6-DoF motion cues. An enhanced rotation sampling strategy further balances diverse motion patterns during training. We evaluate on four datasets with varied spatial scales: KITTI, Oxford, NCLT, and our newly collected ZJH-VO benchmark. BEV-ODOM2 achieves a 40\% RTE improvement over prior BEV-based methods, with real-time inference on an NVIDIA Jetson AGX Orin confirming edge deployment feasibility. The source code and the ZJH-VO dataset are publicly released to facilitate future research.

Wangtao Lu, Ya Yan Lu, Jianliang Qian

For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation conditions. For scattering problems in a layered medium, standard BIE methods based on the Green's function of the background medium must evaluate the expensive Sommefeld integrals. Alternative BIE methods based on the free-space Green's function give rise to integral equations on unbounded interfaces which are not easy to truncate, since the wave fields on these interfaces decay very slowly. We develop a BIE method based on the perfectly matched layer (PML) technique. The PMLs are widely used to suppress outgoing waves in numerical methods that directly discretize the physical space. Our PML-based BIE method uses the Green's function of the PML-transformed free space to define the boundary integral operators. The method is efficient, since the Green's function of the PML-transformed free space is easy to evaluate and the PMLs are very effective in truncating the unbounded interfaces. Numerical examples are presented to validate our method and demonstrate its accuracy.

Wangtao Lu, Ya Yan Lu, Dawei Song

Numerical mode matching (NMM) methods are widely used for analyzing wave propagation and scattering in structures that are piece-wise uniform along one spatial direction. For open structures that are unbounded in transverse directions (perpendicular to the uniform direction), the NMM methods use the perfectly matched layer (PML) technique to truncate the transverse variables. When incident waves are specified in homogeneous media surrounding the main structure, the total field is not always outgoing, and the NMM methods rely on reference solutions for each uniform segment. Existing NMM methods have difficulty handing gracing incident waves and special incident waves related to the onset of total internal reflection, and are not very efficient at computing reference solutions for non-plane incident waves. In this paper, a new NMM method is developed to overcome these limitations. A Robin-type boundary condition is proposed to ensure that non-propagating and non-decaying wave field components are not reflected by truncated PMLs. Exponential convergence of the PML solutions based on the hybrid Dirichlet-Robin boundary condition is established theoretically. A fast method is developed for computing reference solutions for cylindrical incident waves. The new NMM is implemented for two-dimensional structures and polarized electromagnetic waves. Numerical experiments are carried out to validate the new NMM method and to demonstrate its performance.

Wangtao Lu, Guanghui Hu

This paper is concerned with acoustic scattering from a sound-soft trapezoidal surface in two dimensions. The trapezoidal surface is supposed to consist of two horizontal half-lines pointing oppositely, and a single finite vertical line segment connecting their endpoints, which can be regarded as a non-local perturbation of a straight line. For incident plane waves, we enforce that the scattered wave, post-subtracting reflected plane waves by the two half lines of the scattering surface in certain two regions respectively, satisfies an integral form of Sommerfeld radiation condition at infinity. With this new radiation condition, we prove uniqueness and existence of weak solutions by a coupling scheme between finite element and integral equation methods. This consequently indicates that our new radiation condition is sharper than the Angular Spectrum Representation, and has generalized the radiation condition for scattering problems in a locally perturbed half-plane. Furthermore, we develop a numerical mode matching method based on this new radiation condition. A perfectly matched layer is setup to absorb outgoing waves at infinity. Since the medium composes of two horizontally uniform regions, we expand, in either uniform region, the scattered wave in terms of eigenmodes and match the mode expansions on the common interface between the two uniform regions, which in turn gives rise to numerical solutions to our problem. Numerical experiments are carried out to validate the new radiation condition and to show the performance of our numerical method.

Zhiming Yu, Wangtao Lu, Xin Lai

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.