I am interested in developing and applying analytic methods in game theory, economics, data science, machine learning, optimal control, partial differential equations, and related fields. I am also interested in developing and analyzing computational methods for high-dimensional problems arising in these areas using advanced machine learning techniques.

Publication List

Preprints

1. Monotone inclusion methods for a class of second-order non-potential mean-field games (with S. Liu and Y. T. Chow), arXiv:2403.20290, 2024

2. A note on the convergence of the monotone inclusion version of the primal-dual hybrid gradient algorithm, arXiv:2311.03689, 2023

3. Adaptive preconditioned gradient descent with energy (with H. Liu, X. Tian, and Y. Yang), arXiv:2310.06733, 2023

Journal articles

1. Applications of no-collision transportation maps in manifold learning (with E. Negrini), arXiv:2304.00199, to appear in SIAM Journal on Mathematics of Data Science, 2023

2. Taming hyperparameter tuning in continuous normalizing flows using the JKO scheme (with A. Vidal, S. Wu Fung, L Tenorio, and S. Osher), to appear in Nature Scientific Reports, 2022

3. Efficient natural gradient descent method for large-scale optimization problems (with W. Lei and Y. Yang), to appear in SIAM Journal on Scientific Computing, 2022

4. A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem (with Y.T. Chow, S. Wu Fung, S. Liu, and S. Osher), to appear in Inverse Problems, 2022

5. Optimal transport for parameter identification of chaotic dynamics via invariant measures (with Y. Yang, E. Negrini, R. Martin, and M. Pasha), to appear in SIAM Journal on Applied Dynamical Systems, 2022

6. A neural network approach for high-dimensional optimal control applied to multiagent path finding (with D. Onken, X. Li, S. Wu Fung, S. Osher, and L. Ruthotto), IEEE Transactions on Control Systems Technology, 2022

7. Random features for high-dimensional nonlocal mean-field games (with S. Agrawal, W. Lee, and S. Wu Fung), Journal of Computational Physics, 459, 2022

8. Computational methods for first-order nonlocal mean field games with applications (with S. Liu, M. Jacobs, W. Li, and S. Osher), SIAM Journal on Numerical Analysis, 59 (5), 2021

9. Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games (with A. T. Lin, S. Wu Fung, W. Li, and S. Osher), Proceedings of the National Academy of Sciences, 118 (31), 2021

10. Splitting methods for a class of non-potential mean field games (with S. Liu), Journal of Dynamics & Games, 2020

11. A machine learning framework for solving high-dimensional mean field game and mean field control problems (with L. Ruthotto, S. Osher, W. Li, and S. Wu Fung), Proceedings of the National Academy of Sciences 117 (17), 2020

12. No-collision transportation maps (with A. Iannantuono and A. M. Oberman), Journal of Scientific Computing 82 (2), 2020

13. Fourier approximation methods for first-order nonlocal mean-field games (with J. Saúde), Portugaliae Mathematica 75 (3), 2019

14. The variational structure and time-periodic solutions for mean-field games systems (with M. Cirant), Minimax Theory and its Applications 3 (2), 2018

15. One-dimensional, non-local, first-order, stationary mean-field games with congestion: a Fourier approach, Discrete and Continuous Dynamical Systems - Series S, 11 (5), 2018

16. First-order, stationary mean-field games with congestion (with D. Evangelista, R. Ferreira, D. A. Gomes, and V. Voskanyan), Nonlinear Analysis, 173, 2018

17. One-dimensional, stationary mean-field games with local coupling (with D. A. Gomes and M. Prazeres), Dynamic Games and Applications, 2017

18. Regularity of solutions in semilinear elliptic theory (with E. Indrei and A. Minne), Bulletin of Mathematical Sciences, 7 (1), 2017 

19. Existence of positive solutions for an approximation of stationary mean-field games (with D. A. Gomes et al.), Involve, a Journal of Mathematics, 10 (3), 2017

20. One-dimensional forward-forward mean-field games (with D. A. Gomes and M. Sedjro), Applied Mathematics and Optimization, 74 (3), 2016

21. Regularity of shadows and the geometry of the singular set associated to a Monge-Ampère equation (with E. Indrei), Communications in Analysis and Geometry, 24 (4), 2016

22. An infinite-dimensional weak KAM theory via random variables (with D. A. Gomes), Discrete and Continuous Dynamical Systems - Series A, 36 (11), 2016

23. On the stability of the polygonal isoperimetric inequality (with E. Indrei), Advances in Mathematics, 276, 2015

24. On the minimizers of calculus of variations problems in Hilbert spaces (with D. A. Gomes), Calculus of Variations and Partial Differential Equations, 52 (1-2), 2015

25. Lagrangian dynamics and a weak KAM theorem on the d-infinite dimensional torus (with D. A. Gomes), Doklady. Natsional'naya Akademiya Nauk Armenii, 112 (2), 2012

26. Calculus of variations in Hilbert spaces, Journal of Contemporary Mathematical Analysis, 47 (3), 2012

27. On analytic continuation of the power series outside of the convergence disc, Armenian Journal of Mathematics, 4 (1), 2012

28. Uniform approximations by rational functions of the simplest form, Anniversary Scientific Session Dedicated to the 90th Anniversary of Yerevan State University, Physics and Mathematical Sciences, 2009

29. Cayley's theorem for De Morgan algebras (in Russian), Proceedings of Yerevan State University, 211 (3), 2006

Peer-reviewed conference proceedings

1. A neural network approach applied to multi-agent optimal control (with D. Onken, X. Li, S. Wu Fung, S. Osher, and L. Ruthotto), European Control Conference, 2021

2. How to train your neural ODE: the world of Jacobian and kinetic regularization (with C. Finlay, J.-H. Jacobsen, and A. M. Oberman), 37th International Conference on Machine Learning, 2020

3. Radially symmetric mean-field games with congestion (with D. Evangelista and D. A. Gomes), 56th Conference on Decision and Control, Melbourne, 2017

4. Conservation laws arising in the study of forward-forward mean-field games (with D. A. Gomes and M. Sedjro), Theory, Numerics and Applications of Hyperbolic Problems I, 2016

5. Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion (with D. A. Gomes and M. Prazeres), 55th Conference on Decision and Control, Las Vegas, 2016

6. A mean-field game economic growth model (with D. A. Gomes and L. Lafleche), American Control Conference, Boston, 2016

Books

1. Economic models and mean-field games theory (with D. A. Gomes and E. A. Pimentel), 30th Brazilian Mathematics Colloquium, IMPA, Rio de Janeiro, iv+127 pp, 2015