Xiao Liu - On-Going Research I: Statistical Learning for Dynamical Systems

On-Going Research Area I

Statistical Learning for Dynamical Systems

Research Objectives

To create a domain-aware statistical learning framework that enables the integration of governing physics and fundamental engineering domain knowledge into data-driven models.
To innovate new methodologies for inherently interpretable domain-aware modeling, data-driven discovery of governing physics, adaptive reduced-order modeling, and optimal dynamic sampling for dynamical engineering/scientific processes.

Wildfires smoke modeling using remote sensing data

Airborne collisions

inverse modeling: emission source detection

Urban environmental processes (air pollution)

Selected Publications:

Yeo, K.M., Hwang, Y.D., Liu, X., and Kalagnanam, J. (2019), "Development of hp-inverse model by using generalized polynomial chaos", Computer Methods in Applied Mechanics and Engineering, 347, 1-20. Article Link.
Liu, X., Yeo, K. M., Lu, S. Y. (2022), “Statistical Modeling for Spatio-Temporal Data from Stochastic Convection-Diffusion Processes”, Journal of the American Statistical Association (Theory and Methods), 117, 1482-1499. Article Link. code. (also on arXiv: 1910.10375).
Liu, X., and Yeo, K.M. (2023), “Inverse Model for Estimating the Initial Condition of Spatio-Temporal Advection-Diffusion Processes”, Technometrics, 65, 432-445. Article Link. code. (also on arXiv: 2302.04134).
Liu, X.C., Liu, X., Kaman, T, Lu, X., and Lin, G. (2023), “Statistical Learning for Nonlinear Dynamical Systems with Applications to Aircraft-UAV Collisions”, Technometrics, 65, 564-578. Article Link.
Wei, G.Z., Liu, X., and Barton, R. (2024), “An extended PDE-based statistical spatio-temporal model that suppresses the Gibbs phenomenon”, Environmetrics, 35, e2831. Article Link.
Wei, G.Z., Krishnan, V., Xie, Y., Sengupata, M., Zhang, Y.C., Liao, H.T., and Liu, X., (2024), "A Statistical Model for Multi-Source Remote-Sensing Data Streams of Wildfire Aerosols Optical Depth," INFORMS Journal on Data Science, 3, 162-178. Article Link. (also on arXiv: 2206.11766).
Liu, X.C., Hwang, Y., Phan, D., Klein, L. Liu, X., Yeo, K., (2025), "Sparse Sensor Allocation for Inverse Problems of Detecting Sparse Leaking Emission Sources", IISE Transactions, arXiv:2509.05559. Article Link.
Liu, X., Feng, J.Y., and Liu, X.C., (2025), "Adapting Projection-Based Reduced-Order Models using Projected Gaussian Process", under revision. arXiv: 2410.14090. Article Link.

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