arXiv subjects

Xiaojun Duan

Publications and source records attributed to Xiaojun Duan.

8 recordsLinked to original sources

arXiv2026

Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computing

Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical thresholds, known as tipping points, pose a prediction problem of both theoretical and practical significance, yet remain largely unresolved. To address this, we articulate a model-free framework that integrates the measures characterizing the stability and sensitivity of dynamical systems with the reservoir computing (RC), a lightweight machine learning technique, using only observational time series data. The framework consists of two stages. The first stage involves using RC to robustly learn local complex dynamics from observational data segmented into windows. The second stage focuses on accurately detecting early warning signals of tipping points by analyzing the learned autonomous RC dynamics through dynamical measures, including the dominant eigenvalue of the Jacobian matrix, the maximum Floquet multiplier, and the maximum Lyapunov exponent. Furthermore, when these dynamical measures exhibit trend-like patterns, their extrapolation enables ultra-early prediction of tipping points significantly prior to the occurrence of critical transitions. We conduct a rigorous theoretical analysis of the proposed method and perform extensive numerical evaluations on a series of representative synthetic systems and eight real-world datasets, as well as quantitatively predict the tipping time of the Atlantic Meridional Overturning Circulation system. Experimental results demonstrate that our framework exhibits advantages over the baselines in comprehensive evaluations, particularly in terms of dynamical interpretability, prediction stability and robustness, and ultra-early prediction capability.

cs.LG↗

arXiv2025

Human Mobility in Epidemic Modeling

Human mobility forms the backbone of contact patterns through which infectious diseases propagate, fundamentally shaping the spatio-temporal dynamics of epidemics and pandemics. While traditional models are often based on the assumption that all individuals have the same probability of infecting every other individual in the population, a so-called random homogeneous mixing, they struggle to capture the complex and heterogeneous nature of real-world human interactions. Recent advancements in data-driven methodologies and computational capabilities have unlocked the potential of integrating high-resolution human mobility data into epidemic modeling, significantly improving the accuracy, timeliness, and applicability of epidemic risk assessment, contact tracing, and intervention strategies. This review provides a comprehensive synthesis of the current landscape in human mobility-informed epidemic modeling. We explore diverse sources and representations of human mobility data, and then examine the behavioral and structural roles of mobility and contact in shaping disease transmission dynamics. Furthermore, the review spans a wide range of epidemic modeling approaches, ranging from classical compartmental models to network-based, agent-based, and machine learning models. And we also discuss how mobility integration enhances risk management and response strategies during epidemics. By synthesizing these insights, the review can serve as a foundational resource for researchers and practitioners, bridging the gap between epidemiological theory and the dynamic complexities of human interaction while charting clear directions for future research.

cs.SI↗

arXiv2025

Symbolic Neural Ordinary Differential Equations

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great significance. In this study, we propose a novel learning framework of symbolic continuous-depth neural networks, termed Symbolic Neural Ordinary Differential Equations (SNODEs), to effectively and accurately learn the underlying dynamics of complex systems. Specifically, our learning framework comprises three stages: initially, pre-training a predefined symbolic neural network via a gradient flow matching strategy; subsequently, fine-tuning this network using Neural ODEs; and finally, constructing a general neural network to capture residuals. In this process, we apply the SNODEs framework to partial differential equation systems through Fourier analysis, achieving resolution-invariant modeling. Moreover, this framework integrates the strengths of symbolism and connectionism, boasting a universal approximation theorem while significantly enhancing interpretability and extrapolation capabilities relative to state-of-the-art baseline methods. We demonstrate this through experiments on several representative complex systems. Therefore, our framework can be further applied to a wide range of scientific problems, such as system bifurcation and control, reconstruction and forecasting, as well as the discovery of new equations.

cs.LG↗

arXiv2024

CIM-PPO:Proximal Policy Optimization with Liu-Correntropy Induced Metric

As a popular Deep Reinforcement Learning (DRL) algorithm, Proximal Policy Optimization (PPO) has demonstrated remarkable efficacy in numerous complex tasks. According to the penalty mechanism in a surrogate, PPO can be classified into PPO with KL divergence (PPO-KL) and PPO with Clip (PPO-Clip). In this paper, we analyze the impact of asymmetry in KL divergence on PPO-KL and highlight that when this asymmetry is pronounced, it will misguide the improvement of the surrogate. To address this issue, we represent the PPO-KL in inner product form and demonstrate that the KL divergence is a Correntropy Induced Metric (CIM) in Euclidean space. Subsequently, we extend the PPO-KL to the Reproducing Kernel Hilbert Space (RKHS), redefine the inner products with RKHS, and propose the PPO-CIM algorithm. Moreover, this paper states that the PPO-CIM algorithm has a lower computation cost in policy gradient and proves that PPO-CIM can guarantee the new policy is within the trust region while the kernel satisfies some conditions. Finally, we design experiments based on six Mujoco continuous-action tasks to validate the proposed algorithm. The experimental results validate that the asymmetry of KL divergence can affect the policy improvement of PPO-KL and show that the PPO-CIM can perform better than both PPO-KL and PPO-Clip in most tasks.

cs.LG↗

arXiv2024

From Fourier to Neural ODEs: Flow Matching for Modeling Complex Systems

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a simulation-free framework, called Fourier NODEs (FNODEs), that effectively trains NODEs by directly matching the target vector field based on Fourier analysis. Specifically, we employ the Fourier analysis to estimate temporal and potential high-order spatial gradients from noisy observational data. We then incorporate the estimated spatial gradients as additional inputs to a neural network. Furthermore, we utilize the estimated temporal gradient as the optimization objective for the output of the neural network. Later, the trained neural network generates more data points through an ODE solver without participating in the computational graph, facilitating more accurate estimations of gradients based on Fourier analysis. These two steps form a positive feedback loop, enabling accurate dynamics modeling in our framework. Consequently, our approach outperforms state-of-the-art methods in terms of training time, dynamics prediction, and robustness. Finally, we demonstrate the superior performance of our framework using a number of representative complex systems.

cs.LG↗

arXiv2022

A Less Uncertain Sampling-Based Method of Batch Bayesian Optimization

This paper presents a method called sampling-computation-optimization (SCO) to design batch Bayesian optimization. SCO does not construct new high-dimensional acquisition functions but samples from the existing one-site acquisition function to obtain several candidate samples. To reduce the uncertainty of the sampling, the general discrepancy is computed to compare these samples. Finally, the genetic algorithm and switch algorithm are used to optimize the design. Several strategies are used to reduce the computational burden in the SCO. From the numerical results, the SCO designs were less uncertain than those of other sampling-based methods. As for application in batch Bayesian optimization, SCO can find a better solution when compared with other batch methods in the same dimension and batch size. In addition, it is also flexible and can be adapted to different one-site methods. Finally, a complex experimental case is given to illustrate the application value and scenario of SCO method.

math.OC↗

arXiv2019

Sliced Latin hypercube designs with arbitrary run sizes

Latin hypercube designs achieve optimal univariate stratifications and are useful for computer experiments. Sliced Latin hypercube designs are Latin hypercube designs that can be partitioned into smaller Latin hypercube designs. In this work, we give, to the best of our knowledge, the first construction of sliced Latin hypercube designs that allow arbitrarily chosen run sizes for the slices. We also provide an algorithm to reduce correlations of our proposed designs.

math.ST↗

arXiv2018

Feature analysis of multidisciplinary scientific collaboration patterns based on PNAS

The features of collaboration patterns are often considered to be different from discipline to discipline. Meanwhile, collaborating among disciplines is an obvious feature emerged in modern scientific research, which incubates several interdisciplines. The features of collaborations in and among the disciplines of biological, physical and social sciences are analyzed based on 52,803 papers published in a multidisciplinary journal PNAS during 1999 to 2013. From those data, we found similar transitivity and assortativity of collaboration patterns as well as the identical distribution type of collaborators per author and that of papers per author, namely a mixture of generalized Poisson and power-law distributions. In addition, we found that interdisciplinary research is undertaken by a considerable fraction of authors, not just those with many collaborators or those with many papers. This case study provides a window for understanding aspects of multidisciplinary and interdisciplinary collaboration patterns.

physics.soc-ph↗