I am Woojeong Kim and a Ph.D. candidate in Indiana University Mathematics working at the intersection of scientific computing, AI-assisted modeling, and numerical simulation. My research and projects involve PDEs, PINNs, adaptive algorithms, Data assimilation and quantitative validation, with applications to phase transitions, biological systems, and engineering analysis.
Woojeong Kim, Local Well-Posedness of a Modified NSCH-Oldroyd System: PINN-Based Numerical Illustrations, arXiv preprint.
Kevin Buck and Woojeong Kim, Auto-Adaptive PINNs with Applications to Phase Transitions, Numerical Mathematics: Theory, Methods and Applications, Vol. 19, No. 2, pp. 510--534, 2026., (Link). (simulation results are in git pages Github)
Woojeong Kim and Roger Temam, A numerical scheme for a multi-scale model of thrombus in arteries (2025), processing preprint.
Woojeong Kim, Krutika Tawri, Roger Temam, Local well-posedness of a three-dimensional phase-field model for
thrombus and blood flow, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116 (4) (2022). SCIE publication.
Hyperbolicity equations for pseudo hyperbolic structures of knot complements, Woojeong Kim, thesis paper
for Master of Science degree, Seoul National University.
Auto-Adaptive PINNs with Applications to Phase Transitions, paper Github