arXiv subjects

Xiaoling Peng

Publications and source records attributed to Xiaoling Peng.

3 recordsLinked to original sources

arXiv2024

A novel number-theoretic sampling method for neural network solutions of partial differential equations

Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling points, which is a robust approach specifically designed to handle partial differential equations with rough solutions or in high dimensions. The sample points are generated by the generating vector to achieve the smallest discrepancy. The architecture integrates Physics-Informed Neural Networks (PINNs) with rigorous mathematical guarantees demonstrating lower error bounds compared to conventional uniform random sampling. Numerical validation includes low-regularity Poisson equations, two-dimensional inverse Helmholtz problems, and high-dimensional linear/nonlinear PDEs, systematically demonstrating the algorithm's superior performance and generalization capabilities.

math.NA↗

arXiv2023

Chiral photonic topological states in Penrose quasicrystals

Electromagnetic topological edge states typically are created in photonic systems with crystalline symmetry and these states emerge because of the topological feature of bulk Bloch bands in momentum space according to the bulk-edge correspondence principle. In this work, we demonstrate the existence of chiral topological electromagnetic edge states in Penrose-tiled photonic quasicrystals made of magneto-optical materials, without relying on the concept of bulk Bloch bands in momentum space. Despite the absence of bulk Bloch bands, which naturally defiles the conventional definition of topological invariants in momentum space characterizing these states, such as the Chern number, we show that some bandgaps in these photonic quasicrystals still could host unidirectional topological electromagnetic edge states immune to backscattering in both cylinders-in-air and holes-in-slab configurations. Employing a real-space topological invariant based on the Bott index, our calculations reveal that the bandgaps hosting these chiral topological edge states possess a nontrivial Bott index of $\pm 1$, depending on the direction of the external magnetic field. Our work opens the door to the study of topological states in photonic quasicrystals.

physics.optics↗

arXiv2023

Construction of Uniform Designs over Continuous Domain in Computer Experiments

The construction of uniform designs (UDs) has received much attention in computer experiments over the past decades, but most of the previous works obtain uniform designs over a U-type by lattice domain. Due to increasing demands for continuous factors, UDs over the continuous domain is in lack. Moreover, the uniformity can be further improved over a continuous domain. In this paper, we use coordinate descent methods with an initialization derived by threshold accepting (TA) algorithm to construct UDs over a continuous domain with Centered $L_2$-discrepancy. The new UDs perform better than the recorded ones in several computer experiments by the Kriging modeling.

stat.CO↗