Research
Mathematical modeling, scientific computing, and machine learning for physical and materials systems.
Scalable algorithms for long-range interactions
Research overview and future directions
Electrostatic and hydrodynamic computations pose significant challenges in confined, partially periodic, and heterogeneous systems. We develop Ewald-type decompositions, random-batch algorithms, boundary-integral formulations, and hybrid solvers tailored to these complex settings. Our work emphasizes rigorous error analysis, computational efficiency, and the accurate treatment of boundary and interface effects.
Future directions
Robust error control in high-contrast dielectric environments, scalable algorithms for strongly confined and heterogeneous geometries, and unified computational frameworks for electrostatic and hydrodynamic interactions.
Selected publications
- An O(N) quasi-Ewald splitting method for nanoconfined electrostatics, SIAM Multiscale Modeling and Simulation, 2026, Accepted
- Accurate error estimates and optimal parameter selection in Ewald summation for dielectrically confined Coulomb systems, Journal of Chemical Theory and Computation 21, 5890-5904, 2025, Published
- Random batch Ewald method for dielectrically confined Coulomb systems, SIAM Journal on Scientific Computing 47, B846-B874, 2025, Published
- Fast algorithm for quasi-2D Coulomb systems, Journal of Computational Physics 524, 113733, 2025, Published
- Computing hydrodynamic interactions in confined doubly periodic geometries in linear time, Journal of Chemical Physics 158, 154101, 2023, Published
Physical mechanisms in soft and active matter systems
Research overview and future directions
We model how dielectric contrast, confinement, activity, and memory govern attraction, packing, symmetry breaking, and collective motion. We combine continuum and statistical-mechanical theories with reduced models to interpret numerical observations and identify the regimes in which different mechanisms dominate.
Future directions
Emergent interactions and competing mechanisms in asymmetric polarizable systems, the roles of memory and hydrodynamic coupling in collective active dynamics, and how confinement and cohesion drive symmetry breaking and chiral or helical organization.
Selected publications
- Designing Coulombic contact interactions between polarizable particles through asymmetry, Journal of Chemical Theory and Computation, 2026, Published
- Dipolar cohesion in densely packed confined columns, Journal of Chemical Physics 164, 064905, 2026, Published
- Mechanisms of electrostatic interactions between two charged dielectric spheres inside a polarizable medium: an effective-dipole analysis, Soft Matter 21, 1860-1872, 2025, Published
- Quantitative theory for critical conditions of like-charge attraction between polarizable spheres, Journal of Chemical Theory and Computation 21, 2822-2828, 2025, Published
- Broken symmetries in quasi-2D charged systems via negative dielectric confinement, Journal of Chemical Physics 161, 011102, 2024, Published
- Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets, Journal of Chemical Physics 161, 014904, 2024, Published
Machine learning for PDEs and materials science
Research overview and future directions
We develop scientific machine-learning and reduced-order methods for complex physical systems, with a focus on operator learning, physics-informed computation, and model reduction for PDEs. Current applications span pattern formation, nonlinear fluid dynamics, parametrized PDEs, and strongly coupled plasmonic systems. We also extend these approaches to materials science through machine-learning potentials and AI-assisted materials modeling and discovery.
Future directions
Out-of-distribution generalization, long-time stability and error accumulation, and the accuracy–efficiency tradeoffs between learning-based and classical numerical methods.
Selected publications
- LSR-Net: Learning the forward evolution operator for nonlinear fluid dynamics, 15th Asian Control Conference, 2026, Accepted
- LSR-Net: Long-short-range operator learning for pattern dynamics on manifolds, Under review
- Inferring pattern formation from early-stage snapshots via long-short-range neural network, Under review
- A spectral-subspace-augmented POD-Galerkin method for parametrized PDEs with limited snapshot data, Under review
- RCIP-based reduced-basis modeling for frequency sweeps in nearly touching plasmonic disks, Preprint