arXiv subjects

Zhenyi Zhu

Publications and source records attributed to Zhenyi Zhu.

8 recordsLinked to original sources

arXiv2026

When GNNs Fail: Quantifying and Overcoming Temporal Correlation Volatility in Time Series

Modeling multivariate time series by representing them as graphs, where individual series act as nodes and pairwise temporal corre- lations serve as edges, has gained significant traction. Recent advances in Graph Neural Networks (GNNs) have demonstrated strong perfor- mance by assuming a static graph topology and aggregating information from neighboring series. In this work, we investigate the representa- tional power of GNNs for forecasting under both static and dynamic settings (i.e., when pairwise correlations evolve drastically over time) and identify critical limitations in current architectures. To formalize this, we first propose Temporal Correlation Volatility (TCV), a model- agnostic metric designed to quantify the distributional evolution of these latent structures. We establish a clear connection between TCV and performance degradation, demonstrating that many popular models, including Transformers, generalize poorly in high-TCV settings and are often outperformed by simple structure-agnostic baselines. To address these limitations, we propose Graph Layer for Inference in Dynamic En- vironments (GLIDE), a novel GNN layer enhanced by two theoretically grounded design mechanisms: (D1) Path-based Message Passing, which captures path-based neighborhoods and (D2) Static and Dynamic Propagation Separation, which identifies optimal dynamics via local static approximation. These components significantly improve learning under dynamic topology while preserving robustness in static scenarios. Ex- tensive experiments on synthetic and real-world benchmarks show that GLIDE improves average performance by up to 45.6% across static and dynamic settings, with the largest gain reaching 85.7%. The source code is available at https://github.com/ChenS676/GLIDE.

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arXiv2026

Dynamical low-rank approximation for the semiclassical Schrodinger equation with uncertainties

In this paper, we propose a dynamical low-rank (DLR) approximation framework for solving the semiclassical Schrodinger equation with uncertainties. The primary numerical challenges arise from the dual nature of the oscillations: the spatial oscillations inherent in the semiclassical limit and the high-frequency oscillations in the random space induced by uncertainties. We extend two robust integrators -- the projector-splitting integrator and the unconventional integrator -- to the semiclassical regime to evolve the solution on a low-rank manifold. Through extensive numerical experiments, we demonstrate that the DLR method is significantly more computationally efficient than the standard stochastic Galerkin method, as it captures the essential quantum dynamics using a much smaller number of basis functions. Our findings reveal that despite the complex oscillatory patterns of the wave function, its evolution remains concentrated in a low-rank subspace for the cases investigated. Specifically, we observe that the DLR method achieves high fidelity with a remarkably small numerical rank, which remains robust even as the semiclassical parameter $\varepsilon$ decreases. Within our problem settings, the results further suggest that the rank growth is primarily driven by the randomness and regularity of the potential. These results provide practical insights into the low-rank structure of uncertain quantum systems and offer an efficient approach for high-dimensional uncertainty quantification in the semiclassical regime.

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arXiv2025

A Bi-fidelity based asymptotic-preserving neural network for the semiconductor Boltzmann equation and its inverse problem

This paper introduces a Bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the semiconductor Boltzmann equation. Our approach builds upon the Asymptotic-Preserving Neural Network (APNNs) methodology \cite{APNN-transport}, which employs a micro-macro decomposition to handle the model's multiscale nature. We specifically address a key bottleneck in the original APNNs: the slow convergence of the macroscopic density $ρ$ in the near fluid-dynamic regime, i.e., for small Knudsen numbers $\varepsilon$. The core innovation of BI-APNNs is a novel bi-fidelity decomposition of the macroscopic quantity $ρ$, which accurately approximates the true density at small $\varepsilon$, and can be efficiently pre-trained. A separate and more compact neural network is then tasked with learning only the minor correction term, $ρ_{\text{corr}}$. This strategy not only significantly {\it accelerates} the training convergence but also improves the accuracy of the forward problem solution, particularly in the challenging fluid-dynamic limit. Meanwhile, we demonstrate through extensive numerical experiments that our new BI-APNNs yields substantially more accurate and robust results for inverse problems compared to the standard APNNs. Validated on both the semiconductor Boltzmann and the Boltzmann-Poisson systems, our work shows that the bi-fidelity formulation is a powerful enhancement for tackling multiscale kinetic equations, especially when dealing with inverse problems constrained by partial observation data.

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arXiv2025

Real-E: A Foundation Benchmark for Advancing Robust and Generalizable Electricity Forecasting

Energy forecasting is vital for grid reliability and operational efficiency. Although recent advances in time series forecasting have led to progress, existing benchmarks remain limited in spatial and temporal scope and lack multi-energy features. This raises concerns about their reliability and applicability in real-world deployment. To address this, we present the Real-E dataset, covering over 74 power stations across 30+ European countries over a 10-year span with rich metadata. Using Real- E, we conduct an extensive data analysis and benchmark over 20 baselines across various model types. We introduce a new metric to quantify shifts in correlation structures and show that existing methods struggle on our dataset, which exhibits more complex and non-stationary correlation dynamics. Our findings highlight key limitations of current methods and offer a strong empirical basis for building more robust forecasting models

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arXiv2025

PhysicsSolver: Transformer-Enhanced Physics-Informed Neural Networks for Forward and Forecasting Problems in Partial Differential Equations

Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the solution outside the given temporal region. Most traditional numerical methods are applied to a given time-space region and can only accurately approximate the solution of the given region. To address this problem, many deep learning-based methods, basically data-driven and data-free approaches, have been developed to solve these problems. However, most data-driven methods require a large amount of data, which consumes significant computational resources and fails to utilize all the necessary information embedded underlying the partial differential equations (PDEs). Moreover, data-free approaches such as Physics-Informed Neural Networks (PINNs) may not be that ideal in practice, as traditional PINNs, which primarily rely on multilayer perceptrons (MLPs) and convolutional neural networks (CNNs), tend to overlook the crucial temporal dependencies inherent in real-world physical systems. We propose a method denoted as \textbf{PhysicsSolver} that merges the strengths of two approaches: data-free methods that can learn the intrinsic properties of physical systems without using data, and data-driven methods, which are effective at making predictions. Extensive numerical experiments have demonstrated the efficiency and robustness of our proposed method. We provide the code at \href{https://github.com/PhysicsSolver/PhysicsSolver}{https://github.com/PhysicsSolver}.

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arXiv2025

Deep learning-based moment closure for multi-phase computation of semiclassical limit of the Schrödinger equation

We present a deep learning approach for computing multi-phase solutions to the semiclassical limit of the Schrödinger equation. Traditional methods require deriving a multi-phase ansatz to close the moment system of the Liouville equation, a process that is often computationally intensive and impractical. Our method offers an efficient alternative by introducing a novel two-stage neural network framework to close the $2N\times 2N$ moment system, where $N$ represents the number of phases in the solution ansatz. In the first stage, we train neural networks to learn the mapping between higher-order moments and lower-order moments (along with their derivatives). The second stage incorporates physics-informed neural networks (PINNs), where we substitute the learned higher-order moments to systematically close the system. We provide theoretical guarantees for the convergence of both the loss functions and the neural network approximations. Numerical experiments demonstrate the effectiveness of our method for one- and two-dimensional problems with various phase numbers $N$ in the multi-phase solutions. The results confirm the accuracy and computational efficiency of the proposed approach compared to conventional techniques.

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arXiv2024

Asymptotic-preserving neural networks for the semiconductor Boltzmann equation and its application on inverse problems

In this paper, we develop the Asymptotic-Preserving Neural Networks (APNNs) approach to study the forward and inverse problem for the semiconductor Boltzmann equation. The goal of the neural network is to resolve the computational challenges of conventional numerical methods and multiple scales of the model. To guarantee the network can operate uniformly in different regimes, it is desirable to carry the Asymptotic-Preservation (AP) property in the learning process. In a micro-macro decomposition framework, we design such an AP formulation of loss function. The convergence analysis of both the loss function and its neural network is shown, based on the Universal Approximation Theorem and hypocoercivity theory of the model equation. We show a series of numerical tests for forward and inverse problems of both the semiconductor Boltzmann and the Boltzmann-Poisson system to validate the effectiveness of our proposed method, which addresses the significance of the AP property when dealing with inverse problems of multiscale Boltzmann equations especially when only sparse or partially observed data are available.

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arXiv2023

Laugh Betrays You? Learning Robust Speaker Representation From Speech Containing Non-Verbal Fragments

The success of automatic speaker verification shows that discriminative speaker representations can be extracted from neutral speech. However, as a kind of non-verbal voice, laughter should also carry speaker information intuitively. Thus, this paper focuses on exploring speaker verification about utterances containing non-verbal laughter segments. We collect a set of clips with laughter components by conducting a laughter detection script on VoxCeleb and part of the CN-Celeb dataset. To further filter untrusted clips, probability scores are calculated by our binary laughter detection classifier, which is pre-trained by pure laughter and neutral speech. After that, based on the clips whose scores are over the threshold, we construct trials under two different evaluation scenarios: Laughter-Laughter (LL) and Speech-Laughter (SL). Then a novel method called Laughter-Splicing based Network (LSN) is proposed, which can significantly boost performance in both scenarios and maintain the performance on the neutral speech, such as the VoxCeleb1 test set. Specifically, our system achieves relative 20% and 22% improvement on Laughter-Laughter and Speech-Laughter trials, respectively. The meta-data and sample clips have been released at https://github.com/nevermoreLin/Laugh_LSN.

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