My research lies at the intersection of computational mathematics, multiscale modeling, and scientific machine learning. I develop mathematical and computational methods for constructing partial differential equations and stochastic models from microscopic first-principles descriptions. A central issue is to identify reduced model classes with sufficient representation ability while preserving conservation laws, dissipative structure, and physical constraints. My work addresses the characterization and constructive representation of these classes, with the goal of establishing physically interpretable models that retain microscopic model fidelity and admit stable, efficient numerical approximation.

Research Interests

• Multi-scale and stochastic modeling
• Numerical methods for PDEs
• Scientific machine-learning
• Kinetic equations
• Fluid physics

Collisional Kinetic Equations

Collisional kinetic equations describe the transport and relaxation of many-particle systems, but their predictive accuracy depends on how the collision operator represents unresolved interactions and correlations. My work characterizes broader admissible classes of collision operators that preserve conservation laws, entropy production, and physical symmetries. These classes accommodate anisotropic interactions and heterogeneous energy transfer beyond the classical Landau form, enabling accurate predictions of microscopic relaxation and transport in correlated regimes. I develop learning algorithms to construct the generalized collision operator directly from microscopic molecular dynamics. The constructed model enables fast, scalable evaluations and structure-preserving discretizations, and achives accurate prediction of kinetic dynamics across the moderately coupled regimes.

Multiscale Fluids

Transferring microscopic physical laws into reliable macroscopic fluid equations remains a central challenge in multiscale modeling. My work develops an extendable variational approach in which the reduced description can be enriched while preserving physical constraints and free-energy dissipation. The variational structure generates constitutive dynamics and stress jointly beyond prescribed empirical closures. This approach establishes a pathway for passing microscopic physical laws across scales and constructing energy-stable macroscopic equations. My current work on polymeric fluids captures nonlinear viscoelastic responses and can be applied to multiscale fluids and kinetic–hydrodynamic reduction.

Mesoscopic Dynamics

Mesoscopic descriptions of molecular systems must account for the influence of unresolved dynamics, particularly when scale separation is insufficient. My research develops stochastic reduced models with state-dependent, non-Markovian dynamics to capture many-body memory and heterogeneous dissipation. A main contribution is the construction of extendable memory representations that preserve physical symmetries, fluctuation–dissipation consistency, and equilibrium statistics while admitting efficient simulation. These models provide a broader description of collective transport and molecular relaxation beyond conventional Markovian approximations.