Kunpeng Xu

Kunpeng Xu, Lifei Chen, Shengrui Wang

In the realm of time series analysis, tackling the phenomenon of concept drift poses a significant challenge. Concept drift -- characterized by the evolving statistical properties of time series data, affects the reliability and accuracy of conventional analysis models. This is particularly evident in co-evolving scenarios where interactions among variables are crucial. This paper presents CORAL, a simple yet effective method that models time series as an evolving ecosystem to learn representations of concept drift. CORAL employs a kernel-induced self-representation learning to generate a representation matrix, encapsulating the inherent dynamics of co-evolving time series. This matrix serves as a key tool for identification and adaptation to concept drift by observing its temporal variations. Furthermore, CORAL effectively identifies prevailing patterns and offers insights into emerging trends through pattern evolution analysis. Our empirical evaluation of CORAL across various datasets demonstrates its effectiveness in handling the complexities of concept drift. This approach introduces a novel perspective in the theoretical domain of co-evolving time series analysis, enhancing adaptability and accuracy in the face of dynamic data environments, and can be easily integrated into most deep learning backbones.

Yunpeng Gong, Sihan Lan, Can Yang et al.

Symbolic regression aims to find interpretable analytical expressions by searching over mathematical formula spaces to capture underlying system behavior, particularly in scientific modeling governed by physical laws. However, traditional methods lack mechanisms for extracting structured physical priors from time series observations, making it difficult to capture symbolic expressions that reflect the system's global behavior. In this work, we propose a structure-aware symbolic regression framework, called StruSR, that leverages trained Physics-Informed Neural Networks (PINNs) to extract locally structured physical priors from time series data. By performing local Taylor expansions on the outputs of the trained PINN, we obtain derivative-based structural information to guide symbolic expression evolution. To assess the importance of expression components, we introduce a masking-based attribution mechanism that quantifies each subtree's contribution to structural alignment and physical residual reduction. These sensitivity scores steer mutation and crossover operations within genetic programming, preserving substructures with high physical or structural significance while selectively modifying less informative components. A hybrid fitness function jointly minimizes physics residuals and Taylor coefficient mismatch, ensuring consistency with both the governing equations and the local analytical behavior encoded by the PINN. Experiments on benchmark PDE systems demonstrate that StruSR improves convergence speed, structural fidelity, and expression interpretability compared to conventional baselines, offering a principled paradigm for physics-grounded symbolic discovery.

Kunpeng Xu, Lifei Chen, Shengrui Wang

Dynamic concepts in time series are crucial for understanding complex systems such as financial markets, healthcare, and online activity logs. These concepts help reveal structures and behaviors in sequential data for better decision-making and forecasting. However, existing models often struggle to detect and track concept drift due to limitations in interpretability and adaptability. To address this challenge, inspired by the flexibility of the recent Kolmogorov-Arnold Network (KAN), we propose WormKAN, a concept-aware KAN-based model to address concept drift in co-evolving time series. WormKAN consists of three key components: Patch Normalization, Temporal Representation Module, and Concept Dynamics. Patch normalization processes co-evolving time series into patches, treating them as fundamental modeling units to capture local dependencies while ensuring consistent scaling. The temporal representation module learns robust latent representations by leveraging a KAN-based autoencoder, complemented by a smoothness constraint, to uncover inter-patch correlations. Concept dynamics identifies and tracks dynamic transitions, revealing structural shifts in the time series through concept identification and drift detection. These transitions, akin to passing through a \textit{wormhole}, are identified by abrupt changes in the latent space. Experiments show that KAN and KAN-based models (WormKAN) effectively segment time series into meaningful concepts, enhancing the identification and tracking of concept drift.

Kunpeng Xu, Lifei Chen, Shengrui Wang

Kolmogorov-Arnold Networks (KAN) is a groundbreaking model recently proposed by the MIT team, representing a revolutionary approach with the potential to be a game-changer in the field. This innovative concept has rapidly garnered worldwide interest within the AI community. Inspired by the Kolmogorov-Arnold representation theorem, KAN utilizes spline-parametrized univariate functions in place of traditional linear weights, enabling them to dynamically learn activation patterns and significantly enhancing interpretability. In this paper, we explore the application of KAN to time series forecasting and propose two variants: T-KAN and MT-KAN. T-KAN is designed to detect concept drift within time series and can explain the nonlinear relationships between predictions and previous time steps through symbolic regression, making it highly interpretable in dynamically changing environments. MT-KAN, on the other hand, improves predictive performance by effectively uncovering and leveraging the complex relationships among variables in multivariate time series. Experiments validate the effectiveness of these approaches, demonstrating that T-KAN and MT-KAN significantly outperform traditional methods in time series forecasting tasks, not only enhancing predictive accuracy but also improving model interpretability. This research opens new avenues for adaptive forecasting models, highlighting the potential of KAN as a powerful and interpretable tool in predictive analytics.