Research areas:
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Reduced order modeling (ROM)
Deriving reduced order models (ROMs) for fluid systems governed by partial differential equations is particularly challenging when the underlying flow manifolds exhibit strong nonlinear behavior, making classical reduced spaces inadequate. Fluid problems involving turbulence, multiscale interactions, convection–dominated transport, shocks, or sharp gradients typically generate such complex dynamics. I aim to develop advanced ROM techniques that capture these nonlinear fluid behaviors through approaches such as data-driven closure methods, stochastic parametrization techniques, and machine/deep learning architectures.
Related publications:
Mou, C., Merzari, E., San, O., & Iliescu, T. (2023). An energy-based lengthscale for reduced order models of turbulent flows. Nuclear Engineering and Design, 412, 112454.
Snyder, W., McGuire, J. A., Mou, C., Dillard, D. A., Iliescu, T., & De Vita, R. (2022). Data‐Driven Variational Multiscale Reduced Order Modeling of Vaginal Tissue Inflation. International Journal for Numerical Methods in Biomedical Engineering, e3660.
Mou, C., Koc, B., San, O., Rebholz, L. G., & Iliescu, T. (2021). Data-Driven Variational Multiscale Reduced Order Models. Computer Methods in Applied Mechanics and Engineering, 373, 113470.
Xie, X., Nolan, P. J., Ross, S. D., Mou, C., & Iliescu, T. (2020). Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents. Fluids, 5(4), 189.
Mou, C., Liu, H., Wells, D. R., & Iliescu, T. (2020). Data-Driven Correction Reduced Order Models for the Quasi-Geostrophic Equations: A Numerical Investigation. International Journal of Computational Fluid Dynamics, 34(2), 147-159.
Geophysical fluid dynamics (GFD) and data assimilation (DA)
Geophysical fluid dynamics (GFD) investigates the motion of the atmosphere, ocean, and cryosphere under the influence of Earth’s rotation, with the Coriolis force playing a central role. The governing equations exhibit strong nonlinearities and multiscale interactions, which makes accurate prediction and state estimation particularly challenging. My research has two complementary directions. First, I develop mathematical models to better understand the fundamental dynamics of geophysical systems. Second, I design data assimilation algorithms that leverage reduced-order models (ROMs) to efficiently combine observations with high-dimensional numerical simulations.
Related publications:
Chen, N., Mou, C.*, Smith, L. M., & Zhang, Y. (2024). A Stochastic Precipitating Quasi-Geostrophic Model. Physics of Fluids, 36, 116618.
Popov, A. A., Mou, C., Sandu, A., & Iliescu, T. (2021). A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates. SIAM Journal on Scientific Computing, 43(2), A1134-A1162.
Scientific machine learning (SciML)
Scientific machine learning (SciML) integrates principles from applied mathematics, physics, and computer science to build data-driven models that retain physical interpretability while exploiting modern advances in machine learning. Many scientific problems are governed by partial differential equations or other complex dynamical systems, which are often too expensive to simulate at scale or to use directly in forecasting and control. SciML seeks to bridge this gap by embedding physical structure into learning algorithms, thereby improving efficiency, stability, and generalizability. I focus on two complementary approaches: physics-informed neural networks (PINNs), which embed governing equations into the training process to approximate PDE solutions, and operator learning, which constructs neural surrogates that map input functions to solution operators.
Related publications:
Lu, B.†, Mou, C., & Lin, G. (2025). MOREPHY-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Operator Learning Network. Submitted; preprint, arXiv:2509.00663.
Lu, B.†, Mou, C., & Lin, G. (2025). MoPINNEnKF: Iterative Model Inference using generic-PINN-based ensemble Kalman filter. Submitted; preprint, arXiv:2506.00731.
Lin, G., Mou, C., & Zhang, J. (2025). Energy-Dissipative Evolutionary Kolmogorov-Arnold Networks for Complex PDE Systems. Journal of Computational Physics, 114326.
Numerical analysis (NA)
Numerical analysis (NA) provides the mathematical foundation for approximating solutions of problems that are otherwise intractable to solve analytically. The field develops and analyzes algorithms for differential equations, linear algebra, optimization, and approximation, with a central focus on accuracy, stability, and efficiency. By developing and analyzing error bounds, I aim to provide mathematical foundations that guide the construction of accurate, stable, and efficient ROMs.
Related publications:
Koc, B., Mohebujjaman, M., Mou, C., & Iliescu, T. (2019). Commutation Error in Reduced Order Modeling of Fluid Flows. Advances in Computational Mathematics, 45(5), 2587-2621.
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