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Junjun Wang

Publications and source records attributed to Junjun Wang.

8 recordsLinked to original sources

A Linearized and structure-preserving mixed virtual element method for the extended Fisher-Kolmogorov equation

In thsi paper, based on the leap-frog discretization in time and the mixed virtual element discretization in space, we developed a linearized and structure-preserving numerical algorithm. The main contributions of this work lie in that we not only provide a rigorous proof of the energy dissipation property of the fully discrete numerical scheme, but also establish the unconditionally optimal convergence analysis by means of a inverse inequality. The core of the proof lies in the classified discussion of the relationship between \(\tau\) and $h$. Finally, two numerical examples are provided to validate the correctness of the theoretical analysis as well as the energy dissipation property of the proposed scheme.

math.NA

ECTO: Exogenous-Conditioned Temporal Operator for Ultra-Short-Term Wind Power Forecasting

Accurate ultra-short-term wind power forecasting is critical for grid dispatch and reserve management, yet remains challenging due to the non-stationary, condition-dependent nature of wind generation. Meteorological exogenous variables carry substantial predictive information, but the most informative variable combination varies across sites, operating conditions, and prediction horizons. Existing deep learning approaches either treat exogenous inputs as generic auxiliary channels through uniform mixing or soft gating, or rely on fixed preprocessing steps such as PCA, without exploiting the physical structure of meteorological variables. We propose ECTO (Exogenous-Conditioned Temporal Operator), a unified framework that decomposes exogenous variable modeling into two complementary modules. Physically-Grounded Variable Selection (PGVS) performs hierarchical, group-aware sparse selection over exogenous variables using a domain-informed physical prior and sparsemax activations, producing a compact, condition-adaptive exogenous context. Exogenous-Conditioned Regime Refinement (ECRR) routes the forecast through learned regime experts that apply gain--bias calibration and horizon-specific corrections via a mixture-of-experts paradigm. Experiments on three wind farms spanning different climates, capacities (66--200 MW), and exogenous dimensions (11--13 variables) demonstrate that ECTO achieves the lowest MSE across all sites, with relative improvements over the strongest baseline ranging from 2.2% to 5.2%, widening to 8.6% at the longer prediction horizon ($H=32$). Ablation analysis confirms that each exogenous-related component contributes positively (PGVS +1.84%, ECRR +2.86%), and interpretability analysis reveals that PGVS learns physically meaningful, site-specific variable selection patterns, while ECRR converges to well-separated calibration strategies consistent across sites.

cs.LG

A semi-implicit DLN Galerkin finite element method for coupled Ginzburg-Landau equations with general nonlinearity

In this paper, based on the two-step discretization scheme proposed by Dahlquist, Liniger and Nevanlinna (DLN), we develop a semi-implicit Galerkin finite element method for solving the coupled generalized Ginzburg-Landau equations. By virtue of a novel analytical technique, the boundedness of the numerical solution in the infinity norm is established, upon which the unconditionally optimal error estimates in the $L^2$ and $H^1$-norms are further derived. Compared with the space-time error splitting technique commonly adopted in the literature, the analytical method proposed in this paper does not require the introduction of an additional temporal discretization system, thus greatly simplifying the theoretical argument. The core point of the argument lies in the skillful application of the inverse inequality and discrete Agmon inequality to analyze the two cases, namely $\tau \leq h$ and $\tau>h$, respectively. Three numerical examples covering both two- and three-dimensional scenarios are eventually provided for the validation of the theoretical findings.

math.NA

A new analytical technique of the fully implicit Crank-Nicolson discontinuous Galerkin method for the Ginzburg-Landau Model

In this paper, a fully implicit Crank-Nicolson discontinuous Galerkin method is proposed for solving the Ginzburg-Landau equation. By leveraging a novel analytical technique, we rigorously establish the unique solvability of the constructed numerical scheme, as well as its unconditionally optimal error estimates under both the \(L^2\)-norm and the energy norm. The core of the proof hinges on the \(L^2\)-norm boundedness of the numerical solution and the refined estimation of the cubic nonlinear term. Finally, two numerical examples are presented to validate the theoretical findings.

math.NA

On the rotating nonlinear Klein-Gordon equation with multiscale effects: structure-preserving methods and applications to vortex dynamics

We study numerical methods for the rotating nonlinear Klein-Gordon (RKG) equation, a fundamental model in relativistic quantum physics, which exhibits highly oscillatory multiscale behavior due to the presence of a small parameter {\epsilon}. The RKG equation models rotating galaxies under the Minkowski metric and also provides an effective description of phenomena such as cosmic superfluids. This work focuses on the development and rigorous analysis of structure-preserving Galerkin finite element methods (FEMs) for the RKG equation. A central challenge is that the rotational terms prevent traditional nonconforming FEMs from simultaneously conserving energy and charge. By employing a conservation-adjusting technique, we construct a consistent structure-preserving algorithm applicable to both conforming and nonconforming FEMs. Moreover, we provide a comprehensive convergence analysis, establishing unconditional optimal and high-order accuracy error estimates. These theoretical results are further validated through extensive numerical experiments, which demonstrate the accuracy, efficiency, and robustness of the structure-preserving schemes. Finally, simulations of vortex dynamics, ranging from the relativistic to the nonrelativistic regimes, are presented to illustrate vortex creation, relativistic effects on bound states, and interactions of vortex pairs.

math.NA

LLM-Powered Ensemble Learning for Paper Source Tracing: A GPU-Free Approach

We participated in the KDD CUP 2024 paper source tracing competition and achieved the 3rd place. This competition tasked participants with identifying the reference sources (i.e., ref-sources, as referred to by the organizers of the competition) of given academic papers. Unlike most teams that addressed this challenge by fine-tuning pre-trained neural language models such as BERT or ChatGLM, our primary approach utilized closed-source large language models (LLMs). With recent advancements in LLM technology, closed-source LLMs have demonstrated the capability to tackle complex reasoning tasks in zero-shot or few-shot scenarios. Consequently, in the absence of GPUs, we employed closed-source LLMs to directly generate predicted reference sources from the provided papers. We further refined these predictions through ensemble learning. Notably, our method was the only one among the award-winning approaches that did not require the use of GPUs for model training. Code available at https://github.com/Cklwanfifa/KDDCUP2024-PST.

cs.LG

Structure-preserving finite element methods for computing dynamics of rotating Bose-Einstein condensate

This work is concerned with the construction and analysis of structure-preserving Galerkin methods for computing the dynamics of rotating Bose-Einstein condensate (BEC) based on the Gross-Pitaevskii equation with angular momentum rotation. Due to the presence of the rotation term, constructing finite element methods (FEMs) that preserve both mass and energy remains an unresolved issue, particularly in the context of nonconforming FEMs. Furthermore, in comparison to existing works, we provide a comprehensive convergence analysis, offering a thorough demonstration of the methods' optimal and high-order convergence properties. Finally, extensive numerical results are presented to check the theoretical analysis of the structure-preserving numerical method for rotating BEC, and the quantized vortex lattice's behavior is scrutinized through a series of numerical tests.

math.NA

Unconditional superconvergence analysis of a linearized Crank-Nicolson Galerkin FEM for generalized Ginzburg-Landau equation

In this paper, a linearized Crank-Nicolson Galerkin finite element method (FEM) for generalized Ginzburg-Landau equation (GLE) is considered, in which, the difference method in time and the standard Galerkin FEM are employed. Based on the linearized Crank-Nicolson difference method in time and the standard Galerkin finite element method with bilinear element in space, the time-discrete and space-time discrete systems are both constructed. We focus on a rigorous analysis and consideration of unconditional superconvergence error estimates of the discrete schemes. Firstly, by virtue of the temporal error results, the regularity for the time-discrete system is presented. Secondly, the classical Ritz projection is used to obtain the spatial error with order $O(h^2)$ in the sense of $L^2-$norm. Thanks to the relationship between the Ritz projection and the interpolated projection, the superclose estimate with order $O(\tau^2 + h^2)$ in the sense of $H^1-$norm is derived. Thirdly, it follows from the interpolated postprocessing technique that the global superconvergence result is deduced. Finally, some numerical results are provided to confirm the theoretical analysis.

math.NA