康家熠，2024年获清华大学数学博士学位，同年7月加入北京雁栖湖应用数学研究院(BIMSA)担任助理研究员，2025年11月起任河套数学与交叉科学研究院（HIMIS）助理教授。研究方向聚焦于深度学习、非线性滤波与计算生物学的交叉领域。主要研究兴趣包括:基于神经网络的滤波算法及其数学基础、Wasserstein几何中的采样方法、非线性滤波理论(含Yau-Yau方法)及其在气候科学等领域的应用、计算基因组学与进化系统建模。致力于用数学和机器学习方法解决科学与工程中的复杂问题。
基于神经网络的滤波：开发了用于复杂噪声系统（如机器人、气候建模）状态估计 的新型神经网络算法。设计了适用于大规模分布式系统的可扩展去中心化滤波器。 Wasserstein 几何中的采样：利用Wasserstein几何设计高效采样方法，以探索用于 贝叶斯推断和生成建模的复杂概率分布。
深度学习的数学基础：利用控制理论分析神经网络的表达能力、泛化性和优化算法。
非线性滤波理论：推进非线性滤波理论（包括Yau-Yau方法），并为流形上以及一般噪声条件下的随机系统开发新算法。
科学应用：将非线性滤波应用于解决气候科学和工程学学中的关键问题，如碳数据同化和实时数据分析。
计算基因组学：利用机器学习模型对基因组和蛋白质数据进行分类。
进化系统建模：开发和解释随机/确定性动力系统，以建模进化生物学中的过程。
博士/2019-2024 本科/2015-2019 | 清华大学 四川大学 | 数学 数学与应用数学 |
2024-2025 | 北京雁栖湖应用数学研究院（BIMSA） | 助理研究员 |
期刊论文
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.
会议论文
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.
专著
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.
预印本
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.
1 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.
2 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.
3 Education
Ph.D./2019-2024 B.Sc./2015-2019 | Tsinghua University Sichuan University | Mathematics Mathematics and applied Mathematics. |
4Employment History
2024-2025 | Beijing Institute of Mathematical Sciences and Applications (BIMSA). | Assistant Professor |
5 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.