* indicates the corresponding author.

2026

• Well-posedness and averaging principle for non-Gaussian McKean-Vlasov stochastic differential equations with locally Lipschitz coefficients
  Y. Chao, J. Duan, T. Gao, P. Wei* (alphabetical order)
  Advances in Applied Probability, 58(1), 301-344, 2026.

• Artificial intelligence as a surrogate brain: bridging neural dynamical models and data
  Y. Zhang, D. Liu, Z. Liang, J. Cheng, K. Lou, J. Duan, T. Gao*, B. Hu*, Q. Liu*
  National Science Review, 13(3), nwaf457, 2026.

• Learning Lévy density via adaptive RKHS regression with bi-level optimization
  L. Yang, F. Lu*, T. Gao, W. Wei, J. Duan
  Inverse Problems, 2026. DOI: 10.1088/1361-6420/ae9001.

• Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport
  Y. Wang, T. Gao*, J. Duan
  Philosophical Transactions of the Royal Society A, 384(2322), 20250375, 2026.

• Adaptive control for multi-scale stochastic dynamic systems with stochastic next generation reservoir computing
  J. Cheng, T. Gao*, J. Duan
  Physica D: Nonlinear Phenomena, Vol. 492, 135206, 2026.

• Predicting the onset of period-doubling bifurcations via dominant eigenvalue extracted from autocorrelation
  Z. Ma, C. Zeng, T. Gao, J. Duan
  Chaos, Solitons & Fractals, 207, 118010, 2026.

• Early warning prediction: Onsager-Machlup versus Schrödinger
  X. Xu, Y. Zhou, X. Zhou, J. Duan, T. Gao
  Stochastics and Dynamics, 2650011, 2026.

• Geometric Methods for Stochastic Dynamical Systems
  J. Duan, T. Gao, Q. Huang, Y. Huang
  arXiv preprint, 2026.

• Joint Discovery of Graph Structure and Dynamics in Stochastic Interacting Particle Systems
  D. Liu, T. Gao, J. Duan
  arXiv:2606.18279, 2026.

• A Jacobi Field Approach to Splitting Detection in Schrödinger Bridge
  C. Jiao, J. Guo, H. Zhang, J. Duan, T. Gao
  arXiv:2603.16618, 2026.

• Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics
  M. Li, T. Gao, J. Duan
  arXiv:2603.18035, 2026.

• Efficient Encrypted Computation in Convolutional Spiking Neural Networks with TFHE
  L. Guo, P. Li, T. Gao, Y. Zhong, H. Fan, J. Duan
  arXiv:2603.26781, 2026.

2025

• Analysis of influencing factors and the most probable transition pathway in the narrow escape problem for molecular systems based on deep learning method
  J. Liu, M. Yi, T. Gao, X. Chen
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(9), 2025.

• Action Functional as Early Warning Indicator in the Space of Probability Measures via Schrödinger Bridge
  P. Zhang, T. Gao*, J. Guo, J. Duan
  Quantitative Biology, Vol. 13, No. 3, e86, 2025.

• Early warning prediction with automatic labelling in epilepsy patients
  P. Zhang, T. Gao*, J. Guo, J. Duan, S. Nikolenko
  The ANZIAM Journal, 2025.

• Early heart rate predicts 3-month outcomes in acute ischemic stroke patients receiving intravenous thrombolysis: a machine learning approach
  M. Yao, M. Yao, J. Gu, T. Gao, Y. Yuan, Y. Chen, Y. Liu
  Frontiers in Neurology, 16: 1668901, 2025.

• Correspondence Research of the Most Probable Transition Paths between a Stochastic Interacting Particle System and its Mean Field Limit System
  X. Chen, Y. Hu, Y. Wang, T. Gao*, J. Duan
  arXiv:2404.07552, 2025.

• Latent Iterative Refinement Flow: A Geometric Constrained Approach for Few-Shot Generation
  S. Li, Z. Liao, T. Hou, T. Gao*
  arXiv:2509.19903, 2025.

• Hedging with Sparse Reward Reinforcement Learning
  Y. Ding, G. Yuan, D. Zuo, T. Gao*
  arXiv:2503.04218, 2025.

• NeuronSeek: On Stability and Expressivity of Task-driven Neurons
  H. Pei, J.-X. Liao, Q. Zhao, T. Gao, S. Zhang, X. Zhang, F.-L. Fan
  arXiv:2506.15715, 2025.

2024

• Multi-task meta label correction for time series prediction
  L. Yang, T. Gao*, W. Wei, M. Dai, C. Fang, J. Duan
  Pattern Recognition, Vol. 150, 110319, 2024.

• Early warning via transitions in latent stochastic dynamical systems
  L. Feng, T. Gao*, W. Xiao, J. Duan
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(3), 031101, 2024.

• Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics
  W. Xiao, T. Gao*, K. Liu, J. Duan, M. Zhao
  Physica D: Nonlinear Phenomena, 134145, 2024.

• Deep Reinforcement Learning in Finite-Horizon to Explore the Most Probable Transition Pathway
  J. Guo, T. Gao*, P. Zhang, J. Duan
  Physica D: Nonlinear Phenomena, 458, 133955, 2024.

• Detecting the Most Probable High Dimensional Transition Pathway Based on Optimal Control Theory
  J. Chen, T. Gao*, Y. Li, J. Duan
  Applied Mathematical Modelling, 127, 217-236, 2024.

2023

• Stochastic Dynamics and Data Science
  T. Gao, J. Duan*
  Stochastics and Dynamics, Vol. 23, No. 08, 2340003, 2023.

• Model Based Reinforcement Learning with Non-Gaussian Environment Dynamics and its Application to Portfolio Optimization
  H. Huang, T. Gao*, P. Li, J. Guo, P. Zhang, N. Du, J. Duan
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(8), 083129, 2023.

• Learning reduced effective dynamics from data-driven stochastic dynamical systems
  L. Feng, T. Gao*, M. Dai, J. Duan
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(4), 043131, 2023.

• Neural network stochastic differential equation models with applications to financial data forecasting
  L. Yang, T. Gao*, Y. Lu, J. Duan, T. Liu
  Applied Mathematical Modelling, 115, 279-299, 2023.

• Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems
  C. Fang, Y. Lu*, T. Gao, J. Duan
  Physica D: Nonlinear Phenomena, Vol. 456, 133919, 2023.

• Approximations of Lévy processes by integrated fast oscillating Ornstein-Uhlenbeck processes
  L. Feng, T. Gao, T. Li*, Z. Lin, X. Liu
  Stochastics and Dynamics, Vol. 23, No. 08, 2340005, 2023.

• Learning Stochastic Dynamical Systems as an Implicit Regularization with Graph Neural Network
  J. Guo, T. Gao*, Y. Lan, P. Zhang, S. Yang, J. Duan
  ICML 2023 Workshop on High-dimensional Learning Dynamics.

• Privacy-Preserving Discretized Spiking Neural Networks with TFHE
  P. Li, T. Gao*, H. Huang, J. Cheng, S. Gao, Z. Zeng, J. Duan
  ICNC 2023.

2022 and earlier

• An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable Lévy noise
  C. Fang, Y. Lu, T. Gao*, J. Duan
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(6), 063112, 2022.

• An Optimal Control Method to Compute the Most Likely Transition Path for Stochastic Dynamical Systems with Jumps
  W. Wei, T. Gao, X. Chen*, J. Duan
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(5), 051102, 2022.

• Learning the temporal evolution of multivariate densities via normalizing flows
  Y. Lu, R. Maulik*, T. Gao, F. Dietrich, I. G. Kevrekidis, J. Duan
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(3), 033121, 2022.

• Detecting the maximum likelihood transition path from data of stochastic dynamical systems
  M. Dai, T. Gao*, Y. Lu, Y. Zheng, J. Duan
  Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(11), 113124, 2020.

• Fokker-Planck Equations for Stochastic Dynamical Systems with Symmetric Lévy Motions
  T. Gao, J. Duan, X. Li*
  Applied Mathematics and Computation, 278, 1-20, 2016.

• Quantifying model uncertainty in dynamical systems driven by non-Gaussian Lévy stable noise with observations on mean exit time or escape probability
  T. Gao, J. Duan*
  Communications in Nonlinear Science and Numerical Simulation, 39, 1-6, 2016.

• Dynamical inference for transitions in stochastic systems with α-stable Lévy noise
  T. Gao, J. Duan*, X. Kan, Z. Cheng
  Journal of Physics A: Mathematical and Theoretical, 49(29), 294002, 2016.

• Mean exit time and escape probability for dynamical systems driven by Lévy noise
  T. Gao, J. Duan, X. Li*, R. Song
  SIAM Journal on Scientific Computing, 36(3), A887-A906, 2014.

• Non-Gaussian dynamics of a tumor growth system with immunization
  M. Hao, T. Gao, J. Duan*, W. Xu
  Inverse Problems and Imaging, 7(3), 2013.

• Quantifying Model Uncertainties in the Space of Probability Measures
  J. Duan, T. Gao, G. He
  Interdisciplinary Mathematical Sciences, Vol. 13, 99-110, 2012.

• Mean Exit Time and Escape Probability for a Tumor Growth System under Non-Gaussian Noise
  J. Ren, C. Li, T. Gao, X. Kan, J. Duan
  International Journal of Bifurcation and Chaos, 22(4), 1250090, 2012.

• Mathematical analysis of an HIV model with impulsive antiretroviral drug doses
  T. Gao, W. Wang*, X. Liu
  Mathematics and Computers in Simulation, 82(4), 653-665, 2011.

• Global analysis of a viral model with delayed intracellular immune response
  T. Gao, W. Wang
  Journal of Southwest University (Natural Science), 2009.

Patents

• 一种基于全同态加密的跨医院脑疾病预警机制和方法
  高婷，李鹏博等
  2023113108808, 2023-10-10.

• 一种基于电路自举和SNN的脑肿瘤分类方法及系统
  樊浩杰，高婷等
  202510568325.8.

• 多模态脑卒中智能预警方法及系统
  郭龙飞，高婷等
  2025109460333.

• Homomorphic Ciphertext-PC
  R. Wang, J. Zhou, Z. Cheng, J. Duan, T. Gao, Y. Jiao, Y. Liu, B. Zeng, P. Li
  PCT/SE2022/050900, 2022-10-06.

• Homomorphic recommendation-PC
  Z. Cheng, S. Jin, R. Wang, T. Gao, J. Duan, Y. Jiao, Y. Liu, B. Zeng, P. Li
  PCT/SE2022/050898, 2022-10-06.

• Sales inflation recommendation based on DDPG
  T. Gao, C. Lam, et al.
  US Application 62/856,536, 2019.