Kang Jiayi

Personal Profile

Kang Jiayi obtained a PhD in Mathematics from Tsinghua University in 2024. In July of the same year, he joined the Beijing Institute of Mathematical Sciences (BIMSA) as an Assistant Research Fellow. From November 2025, he has served as Assistant Professor at the Hetao Institute of Mathematics and Interdisciplinary Sciences (HIMIS). His research focuses on the interdisciplinary field of deep learning, nonlinear filtering, and computational biology. Primary research interests include: neural network-based filtering algorithms and their mathematical foundations; sampling methods in Wasserstein geometry; nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other domains; computational genomics and evolutionary systems modelling. He is dedicated to addressing complex problems in science and engineering through mathematical and machine learning approaches.

Research Interests

Deep learning

Neural Network-Based Filtering: Novel neural network algorithms have been developed for state estimation in complex noisy systems, such as robotics and climate modelling. Scalable decentralised filters suitable for large-scale distributed systems have been designed. Sampling in Wasserstein Geometry: Efficient sampling methods have been devised using Wasserstein geometry to explore complex probability distributions for Bayesian inference and generative modelling.

Mathematical Foundations of Deep Learning: Employing control theory to analyse the expressive power, generalisability, and optimisation algorithms of neural networks.

Filtering

Nonlinear filtering theory: Advancing nonlinear filtering theory (including the Yau-Yau method) and developing novel algorithms for stochastic systems on manifolds and under general noise conditions.

Scientific applications: Applying nonlinear filtering to address critical challenges in climate science and engineering, such as carbon data assimilation and real-time data analysis.

Bioinformatics

Computational genomics: Utilising machine learning models to classify genomic and protein data.

Evolutionary systems modelling: Developing and interpreting stochastic/deterministic dynamical systems to model processes in evolutionary biology.

Educational Background

PhD/2019–2024         Tsinghua University      Mathematics

Bachelor's Degree/2015–2019 Sichuan University Mathematics and Applied Mathematics

Work Experience

2024–2025           Beijing Yanqi Lake Institute for Applied Mathematics (BIMSA)         Assistant Research Fellow

Publications

Journal article

1. X. Chen*, J. Kang*, and S. S.-T. Yau. Continuous discrete optimal transportation particle filter. Asian Journal of Mathematics, vol. 29, no. 1, pp. 51–76, 2025. DOI: 10.4310/AJM.250429054646.

2. J. Kang*, X. Jiao*, and S. S.-T. Yau. Estimation of the linear system via optimal transportation and its application for missing data observations. IEEE Transactions on Automatic Control, vol. 70, no. 9, pp. 5644–5659, 2025. DOI: 10.1109/TAC.2025.3544144.

3. J. Kang, X. Chen, and S. S.-T. Yau. Explicit convergence analyses of pde-based filtering algorithms. SIAM Journal on Control and Optimization, vol. 63, no. 5, pp. 3356–3377, 2025. DOI: https://doi.org/10.1137/24M166704X.

4. Y. Li, J. Kang, T. Guo, W. Xia, and Y. Mao. On extended state based maximum correntropy kalman filter. IEEE Control Systems Letters, 2025. DOI: 10.1109/LCSYS.2025.3613560.

5. X. Chen, J. Kang, and S. S.-T. Yau. Time-varying feedback particle filter. Automatica, vol. 167, p. 111740, 2024, ISSN: 0005-1098. DOI: https://doi.org/10.1016/j.automatica.2024.111740.

6. Y. Tao, J. Kang, and S. S.-T. Yau. Neural projection filter: Learning unknown dynamics driven by noisy observations. IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 7, pp. 9508–9522, 2024. DOI: 10.1109/TNNLS.2022.3233888.

7. Y. Tao, J. Kang, and S. S.-T. Yau. The stochastic stability analysis for outlier robustness of kalman-type filtering framework based on correntropy-induced cost. IEEE Transactions on Automatic Control, 2024.

8. J. Kang, X. Jiao, and S. S.-T. Yau. Finite dimensional estimation algebra for time-varying filtering system and optimal transport particle filter: A tangent flow point of view. IEEE Transactions on Aerospace and Electronic Systems, vol. 59, no. 6, pp. 8005–8021, 2023. DOI: 10.1109/TAES.2023.3299916.

9. J. Kang, A. Salmon, and S. S.-T. Yau. Log-concave posterior densities arising in continuous filtering and a maximum a posteriori algorithm. SIAM Journal on Control and Optimization, vol. 61, no. 4, pp. 2407–2424, 2023. DOI: https://doi.org/10.1137/22M1508352.

10. J. Kang, X. Chen, Y. Tao, and S. S.-T. Yau. Optimal transportation particle filter for linear filtering systems with correlated noises. IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 6, pp. 5190–5203, 2022. DOI: 10.1109/TAES.2022.3166863.

11. X. Chen*, J. Kang*, M. Teicher, and S. S.-T. Yau. A new linear regression kalman filter with symmetric samples. Symmetry, vol. 13, no. 11, pp. 2139–2151, 2021. DOI: https://doi.org/10.3390/sym13112139.

12. X. Jiao, S. Pei, Z. Sun, J. Kang, and S. S.-T. Yau. Determination of the nucleotide or amino acid composition of genome or protein sequences by using natural vector method and convex hull principle. Fundamental Research, vol. 1, no. 5, pp. 559–564, 2021. DOI: https://doi.org/10.1016/j.fmre.2021.08.010.

Conference paper

1. Y. Tao, J. Kang, and S. S.-T. Yau. Maximum correntropy ensemble kalman filter. In Proceedings of the 2023 62nd IEEE Conference on Decision and Control, 2023, pp. 8659–8664. DOI: 10.1109/CDC49753.2023.10384142.

monograph

1. S. S.-T. Yau, X. Chen, X. Jiao, J. Kang, Z. Sun, and Y. Tao. Principles of Nonlinear Filtering Theory (Algorithms and Computation in Mathematics (Vol. 33)). Springer Nature Switzerland, 2024. DOI: https://doi.org/10.1007/978-3-031-77684-7.

preprint

1. Y. Hu, J. Kang, L. Ma, and X. Zhang. A novel implementation of yau-yau filter for time-variant nonlinear problems. Preprint, arXiv, 2025. eprint: arXiv:2505.03240.

2. J. Kang, A. Salmon, and S. S.-T. Yau. Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds. Preprint, arXiv, 2024. eprint: arXiv:2410.08689.

Introduction

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025.

His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.

Research Interests Deep Learning

Neural Network-Based Filtering: Developed novel neural network algorithms for state estimation in complex, noisy systems (e.g., robotics, climate modeling). Engineered scalable, decentralized filters for large-scale distributed systems.

Wasserstein Geometry in Sampling: Designed efficient sampling methods using Wasserstein geometry to explore complex probability distributions for Bayesian inference and generative modeling.

Mathematical Foundations of Deep Learning: Leveraged control theory to analyze the expressivity, generalization, and optimization algorithms of neural networks. 

Filtering 

Nonlinear Filtering Theory: Advanced nonlinear filtering theories, including the Yau-Yau method, and developed novel algorithms for systems on manifolds and under general noise conditions.

Scientific Applications: Applied nonlinear filtering to solve key problems in climate science and engineering, such as carbon data assimilation and real-time data analysis.

Bioinformatics

Computational Genomics: Utilized machine learning models for the classification of genomic and protein data.

Evolutionary Systems Modeling: Developed and interpreted stochastic/ deterministic dynamical systems to model processes in evolutionary biology.

Education

Employment History

Publications

Journal Articles

1. X. Chen*, J. Kang*, and S. S.-T. Yau. Continuous discrete optimal transportation particle filter. Asian Journal of Mathematics, vol. 29, no. 1, pp. 51–76, 2025. DOI: 10.4310/AJM.250429054646.

2. J. Kang*, X. Jiao*, and S. S.-T. Yau. Estimation of the linear system via optimal transportation and its application for missing data observations. IEEE Transactions on Automatic Control, vol. 70, no. 9, pp. 5644–5659, 2025. DOI: 10.1109/TAC.2025.3544144.

3. J. Kang, X. Chen, and S. S.-T. Yau. Explicit convergence analyses of pde-based filtering algorithms. SIAM Journal on Control and Optimization, vol. 63, no. 5, pp. 3356–3377, 2025. DOI: https://doi.org/10.1137/24M166704X.

4. Y. Li, J. Kang, T. Guo, W. Xia, and Y. Mao. On extended state based maximum correntropy kalman filter. IEEE Control Systems Letters, 2025. DOI: 10.1109/LCSYS.2025.3613560.

5. X. Chen, J. Kang, and S. S.-T. Yau. Time-varying feedback particle filter. Automatica, vol. 167, p. 111740, 2024, ISSN: 0005-1098. DOI: https://doi.org/10.1016/j.automatica.2024.111740.

6. Y. Tao, J. Kang, and S. S.-T. Yau. Neural projection filter: Learning unknown dynamics driven by noisy observations. IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 7, pp. 9508–9522, 2024. DOI: 10.1109/TNNLS.2022.3233888.

7. Y. Tao, J. Kang, and S. S.-T. Yau. The stochastic stability analysis for outlier robustness of kalman-type filtering framework based on correntropy-induced cost. IEEE Transactions on Automatic Control, 2024.

8. J. Kang, X. Jiao, and S. S.-T. Yau. Finite dimensional estimation algebra for time-varying filtering system and optimal transport particle filter: A tangent flow point of view. IEEE Transactions on Aerospace and Electronic Systems, vol. 59, no. 6, pp. 8005–8021, 2023. DOI: 10.1109/TAES.2023.3299916.

9. J. Kang, A. Salmon, and S. S.-T. Yau. Log-concave posterior densities arising in continuous filtering and a maximum a posteriori algorithm. SIAM Journal on Control and Optimization, vol. 61, no. 4, pp. 2407–2424, 2023. DOI: https://doi.org/10.1137/22M1508352.

10. J. Kang, X. Chen, Y. Tao, and S. S.-T. Yau. Optimal transportation particle filter for linear filtering systems with correlated noises. IEEE Transactions on Aerospace and Electronic Systems, vol. 58, no. 6, pp. 5190–5203, 2022. DOI: 10.1109/TAES.2022.3166863.

11. X. Chen*, J. Kang*, M. Teicher, and S. S.-T. Yau. A new linear regression kalman filter with symmetric samples. Symmetry, vol. 13, no. 11, pp. 2139–2151, 2021. DOI: https://doi.org/10.3390/sym13112139.

12. X. Jiao, S. Pei, Z. Sun, J. Kang, and S. S.-T. Yau. Determination of the nucleotide or amino acid composition of genome or protein sequences by using natural vector method and convex hull principle. Fundamental Research, vol. 1, no. 5, pp. 559–564, 2021. DOI: https://doi.org/10.1016/j.fmre.2021.08.010.

Conference

13. Y. Tao, J. Kang, and S. S.-T. Yau. Maximum correntropy ensemble kalman filter. In Proceedings of the 2023 62nd IEEE Conference on Decision and Control, 2023, pp. 8659–8664. DOI: 10.1109/CDC49753.2023.10384142.

BOOK

14. S. S.-T. Yau, X. Chen, X. Jiao, J. Kang, Z. Sun, and Y. Tao. Principles of Nonlinear Filtering Theory (Algorithms and Computation in Mathematics (Vol. 33)). Springer Nature Switzerland, 2024. DOI: https://doi.org/10.1007/978-3-031-77684-7.

Preprint

15. Y. Hu, J. Kang, L. Ma, and X. Zhang. A novel implementation of yau-yau filter for time-variant nonlinear problems. Preprint, arXiv, 2025. eprint: arXiv:2505.03240.

16. J. Kang, A. Salmon, and S. S.-T. Yau. Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds. Preprint, arXiv, 2024. eprint: arXiv:2410.08689.