arXiv subjects

Dingjiong Ma

Publications and source records attributed to Dingjiong Ma.

5 recordsLinked to original sources

arXiv2025

Meta-DSP: A Meta-Learning Approach for Data-Driven Nonlinear Compensation in High-Speed Optical Fiber Systems

Nonlinear effects in high-speed optical fiber systems fundamentally limit channel capacity. While traditional Digital Backward Propagation (DBP) with adaptive filters addresses these effects, its computational complexity remains impractical. Data-driven solutions like Filtered DBP (FDBP) reduce complexity but critically lack inherent generalization: Their nonlinear compensation capability cannot be naturally extended to new transmission rates or WDM channel counts without retraining on newly collected data. We propose Meta-DSP, a novel signal processing pipeline combining: (1) Meta-DBP, a meta-learning-based DBP model that generalizes across transmission parameters without retraining, and (2) XPM-ADF, a carefully engineered adaptive filter designed to address multi-channel nonlinear distortions. The system demonstrates strong generalization, learning from 40 Gbaud single-channel data and successfully applying this knowledge to higher rates (80/160 Gbaud) and multi-channel configurations (up to 21 channels). Experimental results show Meta-DSP improves Q-factor by 0.55 dB over CDC in challenging scenarios while reducing computational complexity 10$\times$ versus DBP. This work provides a scalable solution for nonlinear compensation in dynamic optical networks, balancing performance with practical computational constraints.

eess.SP↗

arXiv2024

A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation

In this paper, we combine the Smolyak technique for multi-dimensional interpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain a new Filon-Clenshaw-Curtis-Smolyak (FCCS) rule for oscillatory integrals with linear phase over the $d-$dimensional cube $[-1,1]^d$. By combining stability and convergence estimates for the FCC rule with error estimates for the Smolyak interpolation operator, we obtain an error estimate for the FCCS rule, consisting of the product of a Smolyak-type error estimate multiplied by a term that decreases with $\mathcal{O}(k^{-\tilde{d}})$, where $k$ is the wavenumber and $\tilde{d}$ is the number of oscillatory dimensions. If all dimensions are oscillatory, a higher negative power of $k$ appears in the estimate. As an application, we consider the forward problem of uncertainty quantification (UQ) for a one-space-dimensional Helmholtz problem with wavenumber $k$ and a random heterogeneous refractive index, depending in an affine way on $d$ i.i.d. uniform random variables. After applying a classical hybrid numerical-asymptotic approximation, expectations of functionals of the solution of this problem can be formulated as a sum of oscillatory integrals over $[-1,1]^d$, which we compute using the FCCS rule. We give numerical results for the FCCS rule and the UQ algorithm showing that accuracy improves when both $k$ and the order of the rule increase. We also give results for dimension-adaptive sparse grid FCCS quadrature showing its efficiency as dimension increases.

math.NA↗

arXiv2019

A multiscale reduced basis method for Schrödinger equation with multiscale and random potentials

The semiclassical Schrödinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both the physical space and the random space, which poses severe challenges for numerical methods. In this paper, we propose a multiscale reduced basis method, where we construct multiscale reduced basis functions using an optimization method and the proper orthogonal decomposition method in the physical space and employ the quasi-Monte Carlo method in the random space. Our method is verified to be efficient: the spatial gridsize is only proportional to the semiclassical parameter and the number of samples in the random space is inversely proportional to the same parameter. Several theoretical aspects of the proposed method, including how to determine the number of samples in the construction of multiscale reduced basis and convergence analysis, are studied with numerical justification. In addition, we investigate the Anderson localization phenomena for Schrödinger equation with correlated random potentials in both 1D and 2D.

math.NA↗

arXiv2019

A multiscale finite element method for the Schrödinger equation with multiscale potentials

In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantum dynamics of electrons can be described by the Schrödinger equation with multiscale potentials. The model, however, cannot be solved by asymptoics-based approaches where an additive form of different scales in the potential term is required to construct the prescribed approximate solutions. In this paper, we propose a multiscale finite element method to solve this problem in the semiclassical regime. The localized multiscale basis are constructed using sparse compression of the Hamiltonian operator, and thus are "blind" to the specific form of the potential term. After an one-shot eigendecomposition, we solve the resulting system of ordinary differential equations explicitly for the time evolution. In our approach, the spatial mesh size is $ H=\mathcal{O}(ε) $ where $ε$ is the semiclassical parameter and the time stepsize $ k$ is independent of $ε$. Numerical examples in one dimension with a periodic potential, a multiplicative two-scale potential, and a layered potential, and in two dimension with an additive two-scale potential and a checkboard potential are tested to demonstrate the robustness and efficiency of the proposed method. Moreover, first-order and second-order rates of convergence are observed in $H^1$ and $L^2$ norms, respectively.

math.NA↗

arXiv2018

A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach

In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized multiscale data-driven stochastic basis functions that give optimal approximation property of the solution operator. Our method consists of the offline and online stages. In the offline stage, we construct the localized multiscale data-driven stochastic basis functions by solving an optimization problem. In the online stage, using our basis functions, we can efficiently solve multiscale elliptic PDEs with random coefficients with relatively small computational costs. Therefore, our method is very efficient in solving target problems with many different force functions. The convergence analysis of the proposed method is also presented and has been verified by the numerical simulation.

math.NA↗