Time-periodic quasigeostrophic motion under dissipation and forcing. - Jinqiao Duan (Appl. Math. Comput., 1999)

A remark on the three dimensional baroclinic quasi-geostrophic dynamics. - Jinqiao Duan (Appl. Math. Comput., 1999)

Probabilistic structural dynamics of protein folding. - Jinqiao Duan (Appl. Math. Comput., 2000)

On nonlinear amplitude evolution under stochastic forcing. - Jinqiao Duan; Vincent J. Ervin (Appl. Math. Comput., 2000)

Chaotic Properties of Subshifts Generated by a Nonperiodic Recurrent Orbit. - Xin-Chu Fu; Yibin Fu; Jinqiao Duan; Robert S. MacKay (Int. J. Bifurc. Chaos, 2000)

The effect of changing the Coriolis force gradient parameter on the escape probability and mean residence time. - David Szurley; Jinqiao Duan (Appl. Math. Comput., 2001)

Time-periodically forced amplitude evolution in spatially extended nonlinear systems. - Jinqiao Duan; Xin-Chu Fu (Appl. Math. Comput., 2002)

Effective Macroscopic Dynamics of Stochastic Partial Differential Equations in Perforated Domains. - Wei Wang; Daomin Cao; Jinqiao Duan (SIAM J. Math. Anal., 2006)

Uniform Attractors for Nonautonomous Wave Equations with Nonlinear Damping. - Chunyou Sun; Daomin Cao; Jinqiao Duan (SIAM J. Appl. Dyn. Syst., 2007)

Bridging the Boussinesq and primitive equations through spatio-temporal filtering. - Jinqiao Duan; Paul F. Fischer; Traian Iliescu; Tamay M. Özgökmen (Appl. Math. Lett., 2010)

A computational analysis for mean exit time under non-Gaussian Lévy noises. - Huiqin Chen; Jinqiao Duan; Xiaofan Li 003; Chengjian Zhang (Appl. Math. Comput., 2011)

A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions. - Shengqiang Xu; Jinqiao Duan (Appl. Math. Comput., 2011)

Mean Exit Time and Escape Probability for a Tumor Growth System under Non-Gaussian noise. - Jian Ren; Chujin Li; Ting Gao; Xingye Kan; Jinqiao Duan (Int. J. Bifurc. Chaos, 2012)

Upper semicontinuity of Global attractors for 2D Navier-Stokes equations. - Caidi Zhao; Jinqiao Duan (Int. J. Bifurc. Chaos, 2012)

State estimation under non-Gaussian Levy noise: A modified Kalman filtering method - Xu Sun; Jinqiao Duan; Xiaofan Li 003; Xiangjun Wang (CoRR, 2013)

Simulating Stochastic Inertial Manifolds by a Backward-Forward Approach. - Xingye Kan; Jinqiao Duan; Ioannis G. Kevrekidis; Anthony J. Roberts (SIAM J. Appl. Dyn. Syst., 2013)

Approximating Dynamics of a Singularly Perturbed Stochastic Wave Equation with a Random Dynamical Boundary Condition. - Guanggan Chen; Jinqiao Duan; Jian Zhang (SIAM J. Math. Anal., 2013)

Mean Exit Time and Escape Probability for Dynamical Systems Driven by Lévy Noises. - Ting Gao; Jinqiao Duan; Xiaofan Li 003; Renming Song (SIAM J. Sci. Comput., 2014)

Numerical methods for the mean exit time and escape probability of two-dimensional stochastic dynamical systems with non-Gaussian noises. - Xiao Wang 010; Jinqiao Duan; Xiaofan Li 003; Yuanchao Luan (Appl. Math. Comput., 2015)

A nonlocal Fokker-Planck equation for non-Gaussian stochastic dynamical systems. - Jinchun He; Jinqiao Duan; Hongjun Gao (Appl. Math. Lett., 2015)

Fokker-Planck equations for stochastic dynamical systems with symmetric Lévy motions. - Ting Gao; Jinqiao Duan; Xiaofan Li 003 (Appl. Math. Comput., 2016)

Approximation representation of parameterizing manifold and non-Markovian reduced systems for a stochastic Swift-Hohenberg equation. - Yanfeng Guo; Jinqiao Duan (Appl. Math. Lett., 2016)

Smooth solution of a nonlocal Fokker-Planck equation associated with stochastic systems with Lévy noise. - Ming Wang 003; Jinqiao Duan (Appl. Math. Lett., 2016)

Most probable dynamics of some nonlinear systems under noisy fluctuations. - Zhuan Cheng; Jinqiao Duan; Liang Wang 032 (Commun. Nonlinear Sci. Numer. Simul., 2016)

Quantifying model uncertainty in dynamical systems driven by non-Gaussian Lévy stable noise with observations on mean exit time or escape probability. - Ting Gao; Jinqiao Duan (Commun. Nonlinear Sci. Numer. Simul., 2016)

Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion. - Xiao Wang 010; Jinqiao Duan; Xiaofan Li 003; Renming Song (Appl. Math. Comput., 2018)

Stability and convergence of compact finite difference method for parabolic problems with delay. - Fengyan Wu; Dongfang Li; Jinming Wen; Jinqiao Duan (Appl. Math. Comput., 2018)

Linearized compact ADI schemes for nonlinear time-fractional Schrödinger equations. - Xiaoli Chen; Yana Di; Jinqiao Duan; Dongfang Li (Appl. Math. Lett., 2018)

A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations. - Fengyan Wu; Xiujun Cheng; Dongfang Li; Jinqiao Duan (Comput. Math. Appl., 2018)

A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits. - Hui Wang; Xiaoli Chen; Jinqiao Duan (Int. J. Bifurc. Chaos, 2018)

Kinetic Solutions for Nonlocal Scalar Conservation Laws. - Jinlong Wei; Jinqiao Duan; Guangying Lv (SIAM J. Math. Anal., 2018)

Fokker-Planck equation driven by asymmetric Lévy motion. - Xiao Wang 010; Wenpeng Shang; Xiaofan Li 003; Jinqiao Duan; Yanghong Huang (Adv. Comput. Math., 2019)

Most probable dynamics of a genetic regulatory network under stable Lévy noise. - Xiaoli Chen; Fengyan Wu; Jinqiao Duan; Jürgen Kurths; Xiaofan Li 003 (Appl. Math. Comput., 2019)

A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations. - Xiujun Cheng; Jinqiao Duan; Dongfang Li (Appl. Math. Comput., 2019)

A parameter estimator based on Smoluchowski-Kramers approximation. - Ziying He; Jinqiao Duan; Xiujun Cheng (Appl. Math. Lett., 2019)

Stochastic nonlocal conservation laws on whole space. - Guangying Lv; Jinqiao Duan; Hongjun Gao (Comput. Math. Appl., 2019)

Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements. - Xiaoli Chen; Jinqiao Duan; George Em Karniadakis (CoRR, 2019)

Transitions between metastable states in a simplified model for the thermohaline circulation under random fluctuations. - Daniel Tesfay; Pingyuan Wei; Yayun Zheng; Jinqiao Duan; Jürgen Kurths (Appl. Math. Comput., 2020)

Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation. - Jintao Wang; Lu Yang; Jinqiao Duan (Appl. Math. Comput., 2020)

Mean exit time for stochastic dynamical systems driven by tempered stable Lévy fluctuations. - Yanjie Zhang; Xiao Wang 010; Jinqiao Duan (Appl. Math. Lett., 2020)

Mean escape time for randomly switching narrow gates in a steady flow. - Hui Wang; Jinqiao Duan; Xianguo Geng; Ying Chao (Comput. Math. Appl., 2020)

Identifying stochastic governing equations from data of the most probable transition trajectories. - Jian Ren; Jinqiao Duan (CoRR, 2020)

A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise. - Yang Li; Jinqiao Duan (CoRR, 2020)

Extracting Non-Gaussian Governing Laws from Data on Mean Exit Time. - Yanxia Zhang; Jinqiao Duan; Yanfei Jin; Yang Li (CoRR, 2020)

Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise. - Qingyi Zhan; Jinqiao Duan; Xiaofan Li 003 (CoRR, 2020)

Symplectic method for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus. - Qingyi Zhan; Jinqiao Duan; Xiaofan Li 003; Yuhong Li (CoRR, 2020)

Bifurcation in Mean Phase Portraits for Stochastic Dynamical Systems with Multiplicative Gaussian Noise. - Hui Wang 102; Athanasios Tsiairis; Jinqiao Duan (Int. J. Bifurc. Chaos, 2020)

Maximum likelihood estimation of stochastic differential equations with random effects driven by fractional Brownian motion. - Min Dai; Jinqiao Duan; Junjun Liao; Xiangjun Wang (Appl. Math. Comput., 2021)

Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance. - Yayun Zheng; Fang Yang; Jinqiao Duan; Jürgen Kurths (Commun. Nonlinear Sci. Numer. Simul., 2021)

Learning the temporal evolution of multivariate densities via normalizing flows. - Yubin Lu; Romit Maulik; Ting Gao; Felix Dietrich; Ioannis G. Kevrekidis; Jinqiao Duan (CoRR, 2021)

Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations. - Gangnan Yuan; Ding Deng; Jinqiao Duan; Weiguo Lu; Fengyan Wu (CoRR, 2021)

Extracting stochastic dynamical systems with $α$-stable Lévy noise from data. - Yang Li; Yubin Lu; Shengyuan Xu; Jinqiao Duan (CoRR, 2021)

Most Probable Transitions from Metastable to Oscillatory Regimes in a Carbon Cycle System. - Wei Wei; Jianyu Hu; Jianyu Chen; Jinqiao Duan (CoRR, 2021)

The Most Likely Transition Path for a Class of Distribution-Dependent Stochastic Systems. - Wei Wei; Jianyu Hu; Jinqiao Duan (CoRR, 2021)

Data-driven method to learn the most probable transition pathway and stochastic differential equations. - Jianyu Hu; Dongfang Li; Jinqiao Duan; Xiaoli Chen (CoRR, 2021)

Time Series Forecasting with Ensembled Stochastic Differential Equations Driven by Lévy Noise. - Luxuan Yang; Ting Gao; Yubin Lu; Jinqiao Duan; Tao Liu (CoRR, 2021)

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-Informed Neural Networks. - Xiaoli Chen; Liu Yang; Jinqiao Duan; George Em Karniadakis (SIAM J. Sci. Comput., 2021)

An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable Lévy noise. - Cheng Fang; Yubin Lu; Ting Gao; Jinqiao Duan (CoRR, 2022)

An Optimal Control Method to Compute the Most Likely Transition Path for Stochastic Dynamical Systems with Jumps. - Wei Wei; Xiaoli Chen; Ting Gao; Jinqiao Duan (CoRR, 2022)

Auto-SDE: Learning effective reduced dynamics from data-driven stochastic dynamical systems. - Lingyu Feng; Ting Gao; Min Dai; Jinqiao Duan (CoRR, 2022)

Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle. - Qingyi Zhan; Jinqiao Duan; Xiaofan Li 003; Yuhong Li (CoRR, 2022)

Analysis of multiscale methods for stochastic dynamical systems driven by α-stable processes. - Yanjie Zhang; Xiao Wang 010; Zibo Wang; Jinqiao Duan (Appl. Math. Lett., 2023)

Meta contrastive label correction for financial time series. - Luxuan Yang; Ting Gao; Min Dai; Yubin Lu; Wei Wei; Cheng Fang; Yufu Lan; Jinqiao Duan (CoRR, 2023)

Learning Stochastic Dynamical Systems as an Implicit Regularization with Graph Neural Networks. - Jin Guo; Ting Gao; Yufu Lan; Peng Zhang 001; Sikun Yang; Jinqiao Duan (CoRR, 2023)

Privacy-Preserving Discretized Spiking Neural Networks. - Pengbo Li; Ting Gao; Huifang Huang; Jiani Cheng; Shuhong Gao; Zhigang Zeng; Jinqiao Duan (CoRR, 2023)

Early warning via transitions in latent stochastic dynamical systems. - Lingyu Feng; Ting Gao; Xiao Wang 010; Jinqiao Duan (CoRR, 2023)

Efficient Privacy-Preserving Convolutional Spiking Neural Networks with FHE. - Pengbo Li; Huifang Huang; Ting Gao; Jin Guo; Jinqiao Duan (CoRR, 2023)

Early Warning via tipping-preserving latent stochastic dynamical system and meta label correcting. - Peng Zhang 001; Ting Gao; Jin Guo; Jinqiao Duan (CoRR, 2023)

Homogenization of Dissipative Hamiltonian Systems Under Lévy Fluctuations. - Zibo Wang; Li Lv; Jinqiao Duan (J. Nonlinear Sci., 2023)

Analysis for a class of stochastic fractional nonlinear Schrödinger equations. - Yanjie Zhang; Ao Zhang; Pengde Wang; Xiao Wang 010; Jinqiao Duan (CoRR, 2024)

Stochastic parameter reduced-order model based on hybrid machine learning approaches. - Cheng Fang; Jinqiao Duan (CoRR, 2024)

Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation. - Qingyi Zhan; Jinqiao Duan; Xiaofan Li 003; Lijin Wang (CoRR, 2024)

Multi-task meta label correction for time series prediction. - Luxuan Yang; Ting Gao; Wei Wei; Min Dai; Cheng Fang; Jinqiao Duan (Pattern Recognit., 2024)

Symplectic numerical integration for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus. - Qingyi Zhan; Jinqiao Duan; Xiaofan Li 003; Yuhong Li (Math. Comput. Simul., 2024)

Small-Noise-Induced Metastable Transition of Periodically Perturbed Systems. - Ying Chao; Jinqiao Duan; Pingyuan Wei (SIAM J. Appl. Dyn. Syst., 2024)

Modulation Analysis of the Stochastic Camassa-Holm Equation with Pure Jump Noise. - Yong Chen; Jinqiao Duan; Hongjun Gao; Xingyu Guo (J. Nonlinear Sci., 2024)

Euler-Maruyama Method Based Channel Prediction: An LDE-Net Implementation and Field Evaluation. - Tianci Wang; Xianling Wang; Yi Shi 004; Wenbo Xin; Zhiyuan Jiang; Ting Gao; Jinqiao Duan (IEEE Trans. Veh. Technol., 2024)

An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas. - Yang Li; Shengyuan Xu; Jinqiao Duan (Commun. Nonlinear Sci. Numer. Simul., 2025)

Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation. - Qingyi Zhan; Jinqiao Duan; Lijin Wang (Commun. Nonlinear Sci. Numer. Simul., 2025)

Diffusion model conditioning on Gaussian mixture model and negative Gaussian mixture gradient. - Weiguo Lu; Xuan Wu; Deng Ding; Jinqiao Duan; Jirong Zhuang; Gangnan Yuan (Neurocomputing, 2025)

Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. - Peng Zhang 001; Ting Gao; Jin Guo; Jinqiao Duan (Quant. Biol., 2025)

Probability Flow Approach to the Onsager-Machlup Functional for Jump-Diffusion Processes. - Yuanfei Huang; Xiang Zhou 001; Jinqiao Duan (SIAM J. Appl. Math., 2025)

Adaptive control for multi-scale stochastic dynamical systems with stochastic next generation reservoir computing. - Jiani Cheng; Ting Gao; Jinqiao Duan (CoRR, 2025)