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Researcher profile

Wangtao Lu

Wangtao Lu contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math-phmath.MPArtificial IntelligenceMachine Learningmath.NANumerical Analysisphysics.opticsSymbolic Computation

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Published work

4 published item(s)

preprint2026arXiv

Existence of Friedrich-Wintgen Bound States in the Continuum: Cavity with a Thin Waveguide Opening

Bound states in the continuum (BICs) are localized states embedded within a continuum of propagating waves. Perturbations that disrupt BICs typically induce ultra-strong resonances, a phenomenon enabling diverse applications in photonics. This work investigates the existence of BICs in two-dimensional electromagnetic cavities coupled to thin waveguides for H-polarized waves. Our focus is on Friedrich-Wintgen BICs (FW-BICs), which arise from destructive interference between two resonant modes and were identified numerically in rectangular cavities with waveguide openings by Lyapina et al. [J. Fluid Mech., 780 (2015), pp. 370--387]. Here, we rigorously establish the existence of FW-BICs in a broader class of cavity geometries by introducing perturbations to the refractive index under regularity constraints. We show that BICs correspond to intersections of two curves derived implicitly from the governing equations constructed via the mode-matching method. Crucially, we prove that such intersections are guaranteed for sufficiently small waveguide widths, provided that two eigenvalues of the cavity cross and the associated eigenfunctions exhibit non-vanishing coupling to the radiation channel at the cavity-waveguide interface. Furthermore, our approach remains applicable for studying the emergence of FW-BICs under parameter-dependent boundary perturbations to the cavity.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mathematical theory for electromagnetic scattering resonances and field enhancement in a subwavelength annular gap

This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width $h\ll1$. The model is representative among many 3D subwavelength hole structures, which are able to induce resonant scattering of electromagnetic wave and the so-called extraordinary optical transmission. We develop a multiscale framework for the underlying scattering problem based upon a combination of the integral equation in the exterior domain and the waveguide mode expansion inside the tiny hole. The matching of the electromagnetic field over the hole aperture leads to a sequence of decoupled infinite systems, which are used to set up the resonance conditions for the scattering problem. By performing rigorous analysis for the infinite systems and the resonance conditions, we characterize all the resonances in a bounded domain over the complex plane. It is shown that the resonances are associated with the TE and TEM waveguide modes in the annular hole, and they are close to the real axis with the imaginary parts of order ${\cal O}(h)$. We also investigate the resonant scattering when an incident wave is present. It is proved that the electromagnetic field is amplified with order ${\cal O}(1/h)$ at the resonant frequencies that are associated with the TE modes in the annular hole. On the other hand, one particular resonance associated with the TEM mode can not be excited by a plane wave but can be excited with a near-field electric dipole source, leading to field enhancement of order ${\cal O}(1/h)$.

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preprint2020arXiv

Mathematical analysis of wave radiation by a step-like surface

This paper proposes, for wave propagating in a globally perturbed half plane with a perfectly conducting step-like surface, a sharp Sommerfeld radiation condition (SRC) for the first time, an analytic formula of the far-field pattern, and a high-accuracy numerical solver. We adopt the Wiener-Hopf method to compute the Green function for a cracked half plane, a background for the perturbed half plane. We rigorously show that the Green function asymptotically satisfies a universal-direction SRC (uSRC) and radiates purely outgoing at infinity. This helps to propose an implicit transparent boundary condition for the scattered wave, by either a cylindrical incident wave due to a line source or a plane incident wave. Then, a well-posedness theory is established via an associated variational formulation. The theory reveals that the scattered wave, post-subtracting a known wave field, satisfies the same uSRC so that its far-field pattern is accessible theoretically. For a plane-wave incidence, asymptotic analysis shows that merely subtracting reflected plane waves, due to non-uniform heights of the step-like surface at infinity, from the scattered wave in respective regions produces a discontinuous wave satisfying the uSRC as well. Numerically, we adopt a previously developed perfectly-matched-layer (PML) boundary-integral-equation method to solve the problem. Numerical results demonstrate that the PML truncation error decays exponentially fast as thickness or absorbing power of the PML increases, of which the convergence relies heavily on the Green function exponentially decaying in the PML.

0 citations0 reviewsNo code linkedOpen access