Research
Scientific computing for long-range interactions, soft matter, and machine learning
I develop mathematical models and scalable computational methods for soft and active materials. My work connects numerical analysis with physically specific models of long-range interactions, collective dynamics, and scientific machine learning.
Scalable algorithms for long-range interactions
Electrostatic and hydrodynamic calculations become more difficult in confined, partly periodic, and heterogeneous systems. We develop Ewald-type decompositions, random-batch methods, boundary-integral formulations, and hybrid solvers for these settings.
We study parameter-dependent error, computational cost, and the treatment of boundary and interface effects.
Selected publications
- 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
- An O(N) quasi-Ewald splitting method for nanoconfined electrostatics, SIAM Multiscale Modeling and Simulation, 2026, Accepted
Current questions
Error control under stronger dielectric contrast, scalable solvers for confined geometries, and links between electrostatic and hydrodynamic algorithms.
Physical mechanisms in soft and active matter systems
We model how dielectric contrast, confinement, activity, and memory shape attraction, packing, broken symmetry, and collective motion.
We test numerical observations against electrostatic theory and reduced physical models, and specify the regime for each explanation.
Selected publications
- 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
- Dipolar cohesion in densely packed confined columns, Journal of Chemical Physics 164, 064905, 2026, 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
Current questions
Contact interactions between asymmetric polarizable particles, memory in chemotactic motion, and the relation between confinement, cohesion, and helicity.
Machine learning for PDEs and materials science
We study operator learning, physics-informed methods, and reduced-order models for complex PDE systems. Current work covers pattern dynamics, nonlinear fluid evolution, parametrized PDEs, and nearly touching plasmonic structures. Machine-learning methods for materials science form part of this research direction.
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
- 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
Current questions
Generalization outside the training regime, error growth over time, and comparisons with standard numerical baselines.