arXiv subjects

Yingjie Shao

Publications and source records attributed to Yingjie Shao.

7 recordsLinked to original sources

arXiv2026

Frequency-dependent capacitance matrix formulation for Fabry-Perot resonances in two and three dimensional systems

We study scattering resonances of finite and infinite periodic two- and three-dimensional systems of high-contrast resonators beyond the subwavelength regime. At each fixed admissible nonzero reference frequency, we introduce frequency-dependent capacitance matrices and derive quantitative asymptotic expansions of hybridized Fabry--Pérot resonant frequencies and their corresponding eigenmodes in terms of the material contrast parameter. We provide a partial differential equation (PDE) formulation of the frequency-dependent capacitance matrix analogous to the one for the capacitance matrix in the subwavelength regime. Based on this PDE formulation, we establish key properties of the frequency-dependent capacitance matrix and estimate its norm at high frequencies for a single smooth resonator with nontrapping exterior in three dimensions, identifying a regime in which the reduced residual remains perturbative. For infinite periodic resonator arrays, we prove bandgap opening under a uniform exterior non-resonance condition and generic Dirac cones for a honeycomb scaling family. Our results extend the use of discrete approximations as a powerful tool for characterizing the resonant properties of finite and infinite periodic systems of high-contrast resonators at arbitrarily high frequencies and understanding their anomalous localization and transport properties arising from strong coupling to a discrete set of eigenfrequencies.

math.AP↗

arXiv2026

Curvature-aware dynamic precision approach for physics-informed neural networks

Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, recent studies show that PINN optimisation is sensitive to numerical precision. Existing implementations commonly use either single precision (FP32), which is computationally efficient but prone to failure modes, or double precision (FP64), which is robust but substantially expensive. This creates a trade-off between computational efficiency and numerical accuracy. To reduce the computational cost of double-precision training while retaining prediction accuracy, we propose a curvature-aware precision controller that adapts numerical precision during training rather than treating it as a fixed implementation choice. The proposed method reuses curvature information derived from the limited-memory BFGS (L-BFGS) optimiser to construct a precision controller, retaining FP32 when lower precision is sufficient and promoting computation to FP64 when the training dynamics indicate numerical sensitivity or precision-limited stagnation. We evaluate the proposed approach on four canonical PINN failure-mode benchmarks and an irradiance-driven ordinary differential equation example. We further test the proposed approach across different neural network architectures. The method consistently matches or even slightly exceeds full FP64 solution accuracy while reducing training time relative to full double-precision training on all benchmark equations. The obtained results indicate that precision sensitivity in PINN optimisation is phase-dependent, and that selectively applying higher precision only during numerically critical stages can lower computational cost without sacrificing predictive accuracy.

cs.LG↗

arXiv2026

Frequency-dependent capacitance matrix formulation for Fabry-Pérot resonances. Part I: One-dimensional finite systems

We study scattering resonances of finite one-dimensional systems of high-contrast resonators beyond the subwavelength regime. Introducing a novel tridiagonal frequency-dependent capacitance matrix, we derive quantitative asymptotic expansions of the hybridized Fabry-Pérot resonant frequencies in terms of the material contrast parameter. The leading-order shifts are governed by the eigenvalues of this matrix, while the corresponding eigenmodes are approximated, to leading order, by trigonometric functions on selected spacings between resonators. Our results extend the use of discrete approximations as a powerful tool for characterizing the resonant properties of a system of high-contrast resonators at arbitrarily high frequencies.

math.AP↗

arXiv2026

Non-Hermitian Fabry-Pérot Resonances

We characterise non-Hermitian Fabry-Pérot resonances in high-contrast resonator systems and study the properties of their associated resonant modes from continuous differential models. We consider two non-Hermitian effects: the exceptional point degeneracy and the skin effect induced by imaginary gauge potentials. Using the propagation matrix formalism, we characterise these two non-Hermitian effects beyond the subwavelength regime. This analysis allows us to (i) establish the existence of exceptional points purely from radiation conditions and to (ii) prove that the non-Hermitian skin effect applies uniformly across resonant modes, yielding broadband edge localisation.

math-ph↗

arXiv2025

Resonance analysis of one-dimensional acoustic media: a propagation matrix approach

This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric polynomial. Leveraging Nevanlinna's value distribution theory, we establish the distribution properties of the resonances and demonstrate that their imaginary parts are uniformly bounded, which contrasts with the three-dimensional case. In two classes of high-contrast regimes, we derive the asymptotics of both subwavelength and non-subwavelength resonances with respect to the contrast parameter. Furthermore, by applying the Newton polygon method, we recover the discrete capacitance matrix approximation for subwavelength Minnaert resonances in both Hermitian and non-Hermitian cases, thereby establishing its connection to the propagation matrix framework.

math.AP↗

arXiv2021

Real-Time Wave Mitigation for Water-Air OWC Systems Via Beam Tracking

In a water-air optical wireless communication (OWC) channel, dynamic ocean waves may significantly deflect the light beam from its original direction, thus deteriorating the communication performance. In this letter, a beam tracking system to mitigate wave-induced communication degradation is experimentally demonstrated. By employing the beam tracking on the PAM6 system, a maximum of 486% improvement (from 140 Mb/s to 820 Mb/s) in throughput is realized at a 1.2-m air distance for an average wave slope changing rate of 0.34 rad/s. For PAM4 signals, the packet loss rate reduces significantly from 75% to 11%, and a maximum throughput of 1.25 Gb/s is achieved.

eess.SP↗

arXiv2019

Robust UOWC systems against bubble-induced impairments via transmit/receive diversities

We systematically investigate the bubble-induced performance degradation for underwater wireless optical communication (UOWC) with different bubble sizes and positions. By using different transmit and receive diversities, we investigate the effectiveness of transmit/receive diversity on the mitigation of the bubble-induced impairment to the UOWC link. With the help of a 2 by 2 MIMO using repetition coding (RC) and maximum ratio combining (MRC), a robust 780-Mbit/s UOWC transmission is achieved. The corresponding outage probability can be significantly reduced from 34.6% for the system without diversity to less than 1%.

eess.SP↗