My primary area of expertise is data-driven mathematical modeling, nonlinear partial differential equations and scientific computing. Using a mixture of analytical and numerical techniques, I study a wide range of nonlinear dynamics with applications in engineering, biological and physical systems. Focuses of my work include problems in fluid dynamics, dynamical systems, numerical analysis, and industrial applications.

I am grateful to have received support from

  • National Science Foundation, DMS-2309774, 2023 - 2026, PI
  • The Simons Foundation, MPS-TSM, 2023 - 2028, PI
  • North Carolina State University, FRPD, 2022 - 2023, PI

Free Surface Flows

Lubrication theory, interfacial instabilities, droplet dynamics, non-conservative effects, pattern formation, applications in heat and mass exchange, desalination, and vapor capture

1. H. Ji, T. P. Witelski, Coarsening of thin films with weak condensation. To appear in SIAM Journal on Applied Mathematics (2023)
2. W. Chu, H. Ji, Q. Wang, C-J Kim, A. L. Bertozzi, An electro-hydrodynamics modeling of droplet actuation on solid surface by surfactant-mediated electro-dewetting. Physical Review Fluids 8.7 (2023): 073701
3. H. Ji, C. Falcon, E. Sedighi, A. Sadeghpour, Y. S. Ju, A. L. Bertozzi, Thermally-driven coalescence in thin liquid film flowing down a fiber, Journal of Fluid Mechanics, 916, A19 (2021)
4. H. Ji, A. Sadeghpour, A. L. Bertozzi, Y. S. Ju, Modeling film flows down a fibre influenced by nozzle geometry, Journal of Fluid Mechanics Rapids, volume 901 (2020)
5. Y. Dukler, H. Ji, C. Falcon, A. L. Bertozzi, Theory for undercompressive shocks in tears of wine, Physical Review Fluids 5, 034002 (2020)
6. H. Ji, C. Falcon, A. Sadeghpour, Z. Zeng, Y. S. Ju, A. L. Bertozzi, Dynamics of thin liquid films on vertical cylindrical fibers, Journal of Fluid Mechanics 865: 303-327 (2019)
7. A. Sadeghpour, Z. Zeng, H. Ji, N. D. Ebrahimi, A. L. Bertozzi, Y. S. Ju, Water vapor capturing using an array of traveling liquid beads for desalination and water treatment, Science Advances 5, no. 4, eaav7662 (2019)
8. H. Ji, T. P. Witelski, Instability and dynamics of volatile thin films, Physical Review Fluids 3, no. 2: 024001 (2018)

Scientific Machine Learning

Physics-based data-driven modeling, image-based learning, radiotherapy treatment outcome prediction, porous media flow prediction, and other healthcare and engineering applications

1. D. Ko, H. Ji, Y. S. Ju, Prediction of pore-scale flow in heterogeneous porous media from periodic structures using deep learning, AIP Advances 13 (4): 045324 (2023)
2. D. Ko, H. Ji, Y. S. Ju, Prediction of 3D velocity field of reticulated foams using deep learning for transport analysis, Transport in Porous Media, 148, 577–604 (2023)
3. Z. Yang, Z. Hu, H. Ji, K. Lafata, E. Vaios, S. Floyd, F.-F. Yin, C. Wang, A Neural Ordinary Differential Equation Model for Visualizing Deep Neural Network Behaviors in Multi-Parametric MRI based Glioma Segmentation, Medical Physics (2023).
4. H. Ji, K. Lafata, Y. Mowery, D. Brizel, A. L. Bertozzi, F.-F. Yin, C. Wang, Post-Radiotherapy PET Image Outcome Prediction by Deep Learning under Biological Model Guidance: A Feasibility Study of Oropharyngeal Cancer Application, Frontiers in Oncology, Volume 12, (2022)
5. H. Xia, V. Suliafu, H. Ji, T. M. Nguyen, A. L. Bertozzi, S. Osher, B. Wang, Heavy Ball Neural Ordinary Differential Equations, Advances in Neural Information Processing Systems, 34 (2021)

Nonlinear Partial Differential Equations

Coherent structures, traveling waves, finite-time singularities, regularity of parabolic-type degenerate PDEs, numerical analysis for high-order PDEs

1. B. Kim, H. Ji, A. L. Bertozzi, A. Sadeghpour, Y. S. Ju, A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber. Journal of Computational Physics, 496, 112560 (2024).
2. L. Li, H. Ji , Q. Tang, Numerical methods for fourth-order PDEs on overlapping grids with application to Kirchhoff-Love plates. To appear in Journal of Scientific Computing (2024).
3. H. Ji, R. Taranets, M. Chugunova, Qualitative analysis of travelling wave solutions for a model of a liquid film flowing down a fiber, European Journal of Applied Mathematics, 1-30 (2021)
4. T. A. Nguyen, L. Li, H. Ji, Stable and accurate numerical methods for generalized Kirchhoff-Love plates, Journal of Engineering Mathematics, 130, 6 (2021)
5. H. Ji, L. Li, Numerical methods for thermally stressed shallow shell equations Journal of Computational and Applied Mathematics, Volume 362, 626-652 (2019)
6. Y. Gao, H. Ji, J. Liu, T. P. Witelski, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete & Continuous Dynamical Systems - B, 1771-1784 (2018)
7. H. Ji, T. P. Witelski, Finite-time thin film rupture driven by modified evaporative loss, Physica D: Nonlinear Phenomena, vol 342, pp. 1-15 (2017)
8. Y. Gao, H. Ji, J. Liu, T. P. Witelski, Global existence of solutions to a tear film model with locally elevated evaporation rates, Physica D: Nonlinear Phenomena, vol 350, pp. 13-25 (2017)

Optimization and Control

Optimal control of droplet dynamics, shape and topology optimization

1. S. Biswal, H. Ji, K. Elamvazhuthi, A. L. Bertozzi, Optimal Boundary Control of a Model Thin-Film Equation. Under review (2023)
2. X. Hu, Y. Li, H. Ji, A nodal-based finite element approximation of a phase field model for shape and topology optimization, Applied Mathematics and Computation, vol 339, Pages 675-684 (2018).