1. (with T. Costa, J. Cummings, M. Jenkinson, J. Martinez, N. Olivares, A. Sezginer) Fast calculation of diffraction by photomasks, University of Minnesota. IMA, 2014

2. Constrained Hamilton--Jacobi equations and further applications via optimal control theory, Ph.D thesis, 2019

3.  Well-posedness for constrained Hamilton--Jacobi equations, Acta Applicandae Mathematicae, 2020

4.  On uniqueness for one-dimensional constrained Hamilton--Jacobi equation, Minimax Theory and its Applications, 2020

5. (with H. V. Tran and S. N.T. Tu) State-constraint static Hamilton-Jacobi equations in nested domains, SIAM Journal on Mathematical Analysis, 2020

6. (with K. Jun, I. Yang) Improved Regret Analysis for Variance-Adaptive Linear Bandits and Horizon-Free Linear Mixture MDPs, Advances in Neural Information Processing Systems (NeurIPS), 2022

7. (with J. Shin, A. Hakobyan, M. Park, G. Kim, I. Yang) Infusing model predictive control into meta-reinforcement learning for mobile robots in dynamic environments, IEEE Robotics and Automation Letters, 2022

8. (with I. Yang) On Representation Formulas for Optimal Control: A Lagrangian Perspective, IET Control Theory & Applications, 2022

9. (with K. Kim, I. Yang) On concentration bounds for Bayesian identification of linear non-Gaussian systems, Proceedings of the 62th IEEE Conference on Decision and Control (CDC), 2023

10. (with K. Kim, I. Yang) Approximate Thompson sampling for learning linear quadratic regulators with O(\sqrt{T}) regret, Leraning for Control and Decision Conference (L4DC), 2025

11. (with J. Jang) On a minimum eradication time for the SIR model with time-dependent coefficients,  Proceedings of the AMS, 2025

12. (with Y. Park, M. Kim) Acceleration of grokking in learning arithmetic operations via Kolmogorov-Arnold representation, Neurocomputing, 2025

13. (with Y. Choi, K. Park) Deep reinforcement learning for the design of metamaterial mechanisms with functional compliance control, Engineering Applications of Artificial Intelligence, 2025

14. (with Y. Kim, M. Kim) Physics-Informed Neural Networks for optimal vaccination plan in SIR epidemic models, Mathematical Biosciences and Engineering, 2025

15. (with J. Lee) Hamilton--Jacobi based policy-iteration via deep operator learning, Neurocomputing, 2025

16. (with Y. Kim. K. Jun) Instance-dependent fixed-budget pure exploration in reinforcement Learning, ICML 2025 EXAIT Workshop

(For the prospective students or potential collaborators) The following is a list of projects I have been working on. 

Preprints and projects in progress 

17. (with D. Kwon, G. Montufar, I. Yang) Training Wasserstein GANs without gradient penalties

18. (with N. Cho) On the stability of Lipschitz continuous control problems and its application to reinforcement learning

19. (with M. Gim, H. Yang) Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration

20. (with S. Choi, K. Kim) A diffusion-based generative model for financial time-series via geometric Brownian motion

21. (with N. Cho, Y. Kim) Neural Policy Iteration for Stochastic Optimal Control: A Physics-Informed Approach

22. (with N. Cho, Y. Kim) Physics-informed approach for exploratory Hamilton--Jacobi--Bellman equations via policy iterations

23. (with K. Park, E. Kim) Censored Sampling for Topology Design: Guiding Diffusion with Human Preferences

24. (with N. Cho, M. Kim) Physics-informed neural network for model-based reinforcement learning

25. (with D. Lee, M. Kim, S. Son) Physics-informed approach for solving the space-homogeneous Landau equation

26. (with K. Park, Y. Choi) Flexible functional graded lattice structure via reinforcement learning

27. (with Y. Park, J. Kim) Heterogeneous controlled SIR model

28. (with M. Gim, H. Yang) Stochastic reachability 

29. (with M. Gim, H. Yang) FDE-PINN for stochastic differential game and Hamilton--Jacobi--Iassacs equations

30. (with Y. Kim, N. Cho) Physics-informed approach for solving state-constraint Hamilton--Jacobi equations

31. (with S. Choi, K. Kim)  Generation of financial time-series via CEV process

32. (with M. Kim, Y. Kim)  Physics-informed approach for solving the time-varying minimum eradication problem of SIR model

33. (with M. Yoo) TBA