arXiv subjects

Yong Shang

Publications and source records attributed to Yong Shang.

4 recordsLinked to original sources

arXiv2026

LightGTS-Cov: Covariate-Enhanced Time Series Forecasting

Time series foundation models are typically pre-trained on large, multi-source datasets; however, they often ignore exogenous covariates or incorporate them via simple concatenation with the target series, which limits their effectiveness in covariate-rich applications such as electricity price forecasting and renewable energy forecasting. We introduce LightGTS-Cov, a covariate-enhanced extension of LightGTS that preserves its lightweight, period-aware backbone while explicitly incorporating both past and future-known covariates. Built on a $\sim$1M-parameter LightGTS backbone, LightGTS-Cov adds only a $\sim$0.1M-parameter MLP plug-in that integrates time-aligned covariates into the target forecasts by residually refining the outputs of the decoding process. Across covariate-aware benchmarks on electricity price and energy generation datasets, LightGTS-Cov consistently outperforms LightGTS and achieves superior performance over other covariate-aware baselines under both settings, regardless of whether future-known covariates are provided. We further demonstrate its practical value in two real-world energy case applications: long-term photovoltaic power forecasting with future weather forecasts and day-ahead electricity price forecasting with weather and dispatch-plan covariates. Across both applications, LightGTS-Cov achieves strong forecasting accuracy and stable operational performance after deployment, validating its effectiveness in real-world industrial settings.

cs.LG↗

arXiv2024

Overlapping Schwarz Preconditioners for Randomized Neural Networks with Domain Decomposition

Randomized neural networks (RaNNs), in which hidden layers remain fixed after random initialization, provide an efficient alternative for parameter optimization compared to fully parameterized networks. In this paper, RaNNs are integrated with overlapping Schwarz domain decomposition in two (main) ways: first, to formulate the least-squares problem with localized basis functions, and second, to construct overlapping preconditioners for the resulting linear systems. In particular, neural networks are initialized randomly in each subdomain based on a uniform distribution and linked through a partition of unity, forming a global solution that approximates the solution of the partial differential equation. Boundary conditions are enforced through a constraining operator, eliminating the need for a penalty term to handle them. Principal component analysis (PCA) is employed to reduce the number of basis functions in each subdomain, yielding a linear system with a lower condition number. By constructing additive and restricted additive Schwarz preconditioners, the least-squares problem is solved efficiently using the Conjugate Gradient (CG) and Generalized Minimal Residual (GMRES) methods, respectively. Our numerical results demonstrate that the proposed approach significantly reduces computational time for multi-scale and time-dependent problems. Additionally, a three-dimensional problem is presented to demonstrate the efficiency of using the CG method with an AS preconditioner, compared to an QR decomposition, in solving the least-squares problem.

math.NA↗

arXiv2023

Randomized Neural Networks with Petrov-Galerkin Methods for Solving Linear Elasticity Problems

We develop the Randomized Neural Networks with Petrov-Galerkin Methods (RNN-PG methods) to solve linear elasticity problems. RNN-PG methods use Petrov-Galerkin variational framework, where the solution is approximated by randomized neural networks and the test functions are piecewise polynomials. Unlike conventional neural networks, the parameters of the hidden layers of the randomized neural networks are fixed randomly, while the parameters of the output layer are determined by the least square method, which can effectively approximate the solution. We also develop mixed RNN-PG methods for linear elasticity problems, which ensure the symmetry of the stress tensor and avoid locking effects. We compare RNN-PG methods with the finite element method, the mixed discontinuous Galerkin method, and the physics-informed neural network on several examples, and the numerical results demonstrate that RNN-PG methods achieve higher accuracy and efficiency.

math.NA↗

arXiv2022

Deep Petrov-Galerkin Method for Solving Partial Differential Equations

Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural network-based numerical method to solve partial differential equations. In this new framework, the method is designed on weak formulations, and the unknown functions are approximated by deep neural networks and test functions can be chosen by different approaches, for instance, basis functions of finite element methods, neural networks, and so on. Because the spaces of trial function and test function are different, we name this new approach by Deep Petrov-Galerkin Method (DPGM). The resulted linear system is not necessarily to be symmetric and square, so the discretized problem is solved by a least-square method. Take the Poisson problem as an example, mixed DPGMs based on several mixed formulations are proposed and studied as well. In addition, we apply the DPGM to solve two classical time-dependent problems based on the space-time approach, that is, the unknown function is approximated by a neural network, in which temporal variable and spatial variables are treated equally, and the initial conditions are regarded as boundary conditions for the space-time domain. Finally, several numerical examples are presented to show the performance of the DPGMs, and we observe that this new method outperforms traditional numerical methods in several aspects.

math.NA↗