My research lies at the intersection of scientific machine learning, data-driven dynamical systems, and uncertainty quantification. It can be broadly categorized into the following areas:
Learning physical models from dynamical data: developing data-driven methods for discovering interaction kernels in collective dynamics, estimating composite functions nonparametrically, and building generalizable and interpretable predictive models.
Uncertainty quantification for predictive models: providing performance guarantees for models subject to aleatoric and epistemic uncertainties, developing sensitivity analysis methods, and identifying the model components that most strongly influence predictions in probabilistic graphical models.
Data-driven learning of interaction laws in multispecies particle systems with Gaussian processes: Convergence theory and applications, with C. Kulick and S. Tang, arXiv:2511.02053.
A sparse Bayesian learning algorithm for estimation of interaction kernels in Motsch–Tadmor model, with S. Tang, arXiv:2505.07068, to appear in Journal of Scientific Computing.
Scalable iterative data-adaptive RKHS regularization, with H. Li and F. Lu, arXiv:2401, to appear in SIAM Journal on Scientific Computing.
Data-driven model selections of second-order particle dynamics via integrating Gaussian processes with low-dimensional interacting structures, with C. Kulick and S. Tang, Physica D: Nonlinear Phenomena 461 (2024): 134097.
Learning particle swarming models from data with Gaussian processes, with C. Kulick, Y. Ren, and S. Tang, Mathematics of Computation 93, no. 349 (2024): 2391–2437.
Learning collective behaviors from observation, with M. Zhong, in Explorations in the Mathematics of Data Science: The Inaugural Volume of the Center for Approximation and Mathematical Data Analytics, edited by S. Foucart and S. Wojtowytsch, Cham: Springer Nature Switzerland, 2024, pp. 101–132.
Learning interaction variables and kernels from observations of agent-based systems, with M. Maggioni, P. Martin, and M. Zhong, IFAC-PapersOnLine 55, no. 30 (2022): 162–167.
Model uncertainty and correctability for directed graphical models, with P. Birmpa, M. A. Katsoulakis, and L. Rey-Bellet, SIAM/ASA Journal on Uncertainty Quantification 10, no. 4 (2022): 1461–1512.
Explainable and trustworthy artificial intelligence for correctable modeling in chemical sciences, with J. L. Lansford, M. A. Katsoulakis, and D. G. Vlachos, Science Advances 6, no. 42 (2020): eabc3204.
Non-parametric correlative uncertainty quantification and sensitivity analysis: Application to a Langmuir bimolecular adsorption model, with J. L. Lansford, A. Mironenko, D. B. Pourkargar, D. G. Vlachos, and M. A. Katsoulakis, AIP Advances 8, no. 3 (2018): 035021.