Research

 Research interests

My research interests span a wide range of topics in the intersections of analysis, applied probability and computational mathematics. Most of my research are inspired from applications in statistical physics and biological/social/material sciences. Specifically, I have been working on:

Publications

Mathscinet   Google scholar    Arxiv      ORCID 

Our research on random evolutionary game theory  has been featured in Atlas of Science and in University of Birmingham's news.

Preprints

[8]. Matteo Colangeli, Manh Hong Duong, and Adrian Muntean. A hybrid approach to model reduction of Generalized Langevin Dynamics, arXiv:2405.16157, 2024. 

[7]. Zainab Alalawi, Paolo Bova, Theodor Cimpeanu, Alessandro Di Stefano, Manh Hong Duong, Elias Fernandez Domingos, The Anh Han, Marcus Krellner, Bianca Ogbo, Simon T. Powers, and Filippo Zimmaro. Trust AI Regulation? Discerning users are vital to build trust and effective AI regulation.  arXiv:2403.09510, 2024.

[6]. M. H. Duong, C. M. Durbac, and T. A. Han. Cost optimisation of individual-based institutional reward incentives for promoting cooperation in finite populations. arXiv:2402.07663, 2024.

[5]. B. van Rensburg, F. Spill, M. H. Duong. Adaptive Dynamics of Diverging Fitness Optima. arXiv:2311.00829, 2023.

[4]. M. H. Duong and A. Einav. Convergence to equilibrium for a degenerate McKean-Vlasov Equation. arXiv:2307.16677

[3]. M. Buze and M. H. Duong. Entropic regularisation of unbalanced optimal transportation problems. arXiv:2305.02410

[2]. M. H. Duong and T. A. Han. Random evolutionary games and random polynomials. arXiv:2304.13831

[1]. M. H. Duong, T. H. Dang-Ha, Q. B. Tang, H. M. Tran. Generalized potential games. arXiv:1908.06266

Published or forthcoming articles      

[47]. M. H. Duong and H. D. Nguyen. Asymptotic analysis for the generalized Langevin equation with singular potentials. Journal of Nonlinear Science, Volume 34, article number 62, 2024.

[46].  L. Chen, C. Deng, M. H. Duong, and T. A. Han. On the number of equilibria of the replicator-mutator dynamics for noisy social dilemmas. Chaos, Solitons and Fractals, Volume 180, March 2024, 114565 . 

[45]. M. H. Duong, C. M. Durbac, and T. A. Han. Cost optimisation of hybrid institutional incentives for promoting cooperation in finite populations. Journal of Mathematical Biology, Volume 87, Article 77 , 2023. 

 [44]. M. Colangeli, M. H. Duong, and A. Muntean.  Model reduction of Brownian oscillators: quantification of errors and long-time behaviour. Journal of Physics A: Mathematical and Theoretical,  56 345003, 2023.

[43]. P.- E. Chaudru de Raynal, M. H. Duong, P. Monmarché, M. Tomašević, and J. Tugaut. Reducing exit-times of diffusions with repulsive interactions. ESAIM: Probability and Statistics, Volume 27, page 723-748, 2023.

[42] T. C. Son, D. Q. Le, M. H. Duong. Rate of convergence in the Smoluchowski-Kramers approximation for mean-field stochastic differential equations, Potential Anal ysis 60, 1031–1065, 2024.

[41]. A. B. Duncan, M. H. Duong and G. A. Pavliotis. Brownian motion in an N-scale periodic potential. Journal of Statistical Physics, 190, Article number: 82, 2023.

[40]. M. H. Duong and J. Zimmer. On decomposition of non-reversible processes, Journal of Physics: Conference Series, volume 2514, number 1, pages 012007, 2023.

[39]. M. H. Duong and M. Ottobre. Non-reversible processes: GENERIC, Hypocoercivity and fluctuations. Nonlinearity,  volume 36, number 3, 2023.

[38]. M. Colangeli, M. H. Duong, A. Muntean.  A reduction scheme for coupled Brownian harmonic oscillators. Journal of Physics A: Mathematical and Theoretical, volume 55, number 50, pages 505002, 2022.

[37]. S. Kum, M. H. Duong, Y. Lim, S. Yun. A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures. Journal of Computational and Applied Mathematics, Volume 416, 114588, 2022. 

[36]. D. Adams, M. H. Duong and G. dos Reis. Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems. Discrete and Continuous Dynamical Systems-A, 42(11): 5453-5486,2022.

[35]. M. H. Duong and X. Shang. Accurate and robust splitting methods for the generalized Langevin equation with a positive Prony series memory kernel. Journal of Computational Physics, Volume 464, 111332, 2022. 

[34].  D. Adams, M. H. Duong and G. dos Reis. Entropic regularisation of non-gradient systems. SIAM Journal on Mathematical Analysis, 54:4, 4495-4535, 2022. 

[33]. V. H. Can, M. H. Duong, V. H. Pham. On the expected number of real roots of random polynomials arising from evolutionary game theory. Communications in Mathematical Sciences, Vol. 20, No. 6, pp. 1613-1636, 2022. 

[32]. M. H. Duong and T. A. Han. Cost efficiency of institutional incentives for promoting cooperation in finite populations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, volume 477, issue 2254, 2021.

[31]. Manh Hong Duong and The Anh Han. Statistics of the number of equilibria in random social dilemma evolutionary games with mutation. Eur. Phys. J. B 94, Article number: 171 (2021).

[30].  Julian Braun, Manh Hong Duong, and Christoph Ortner.  Thermodynamic Limit of the Transition Rate of a Crystalline Defect.  Archive for Rational Mechanics and Analysis,  238, 1413–1474, 2020. 

[29]. M. H. Duong and B. Jin. Wasserstein Gradient Flow Formulation of the Time-Fractional Fokker-Planck Equation. Communications in Mathematical Sciences, Volume 18, Number 7, Page 1949-1975, 2020.

[28]. Manh Hong Duong and The Anh Han. On equilibrium properties of the mutator-replicator equation in deterministic and random games, Dynamics Games and Applications, Volume 10, Issue 3, 641–663, 2020 (Special Issue on Evolutionary Games in memory of Chris Cannings).

[27]. Manh Hong Duong and Julian Tugaut. Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures, Stochastics: An International Journal of Probability and Stochastic Processes, Volume 92, Issue 6, Pages 900-943, 2020.

[26]. Van Hao Can, Manh Hong Duong and Viet Hung Pham. Persistence probability of a random polynomial arising from evolutionary game theory. Journal of Applied Probability, Volume 56, Issue 3, pp. 870-890, 2019.

[25]. Manh Hong Duong and Yulong Lu. An operator splitting scheme for the fractional kinetic Fokker-Planck equation. Discrete and Continuous Dynamical Systems-Series A,  39(10): 5707-5727, 2019.  

[24]. Manh Hong Duong, Hoang Minh Tran and The Anh Han. On the distribution of the number of internal equilibria in random evolutionary games. Journal of Mathematical Biology, Volume 78, Issue 1–2, pp 331–371, 2019.     

[23]. Manh Hong Duong, Hoang Minh Tran and The Anh Han. On the expected number of internal equilibria in random evolutionary games with correlated payoff matrix. Dynamic Games and Applications , Volume 9, Issue 2, pp 458–485, 2019.

[22]. M. H. Duong and G. A. Pavliotis. Mean field limits for non-Markovian interacting particles: convergence to equilibrium, GENERIC formalism, asymptotic limits and phase transitions, Communications in Mathematical Sciences, Volume 16, No.8, page 2199-2230, 2018.  

[21]. Manh Hong Duong, Agnes Lamacz, Mark A. Peletier, André Schlichting, and Upanshu Sharma. Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics.  Nonlinearity, 31(10), pp. 4517-4566, 2018.

[20]. Manh Hong Duong and Julian Tugaut. The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium. Electronic Communications in Probability, Vol. 23, paper no.19, 1-10, 2018.    

[19]. Manh Hong Duong and Hoang Minh Tran. On the fundamental solution and a variational formulation of a degenerate diffusion of Kolmogorov type. Discrete and Continuous Dynamical Systems- Series A (DCDS-A), 38(7): 3407-3438, 2018.

[18]. Matthew Dobson,  Manh Hong Duong and Christoph Ortner. On assessing the accuracy of defect free energy computations. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 52, Number 4, 1315 - 1352, 2018.

[17]. Joep H.M. Evers, Iason A. Zisis, Bas J. van der Linden, Manh Hong Duong. From continuum mechanics to SPH particle systems and back: Systematic derivation and convergence. ZAMM-Zeitschrift für Angewandte Mathematik und Mechanik, Volume 98, Issue 1, Pages 106-133, 2018. This paper was one of the most accessed papers in the ZAMM in 2018.

[16]. Manh Hong Duong and Hoang Minh Tran. Analysis of the mean squared derivative cost functions. Mathematical Methods in the Applied Sciences, Volume 40, Issue 14, Pages 5222–5240, 2017. 

[15]. Manh Hong Duong, Agnes Lamacz, Mark A.Peletier, and Upanshu Sharma. Variational approach to coarse-graining of generalized gradient flows. Calculus of Variations and Partial Differential Equations, 56 (4), 56:100, 2017.

[14]. Manh Hong Duong, Adrian Muntean and Omar Richardson. Discrete and continuum links to a nonlinear coupled transport problem of interacting populations. The European Physical Journal Special Topics, Volume 226, Issue 10, pp 2345–2357, 2017.

[13]. Manh Hong Duong, The Anh Han. Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games. Journal of Mathematical Biology, 73(6), 1727-1760, 2016.

[12]. Manh Hong Duong, Max Fathi. The two-scale approach to hydrodynamic limits for non-reversible dynamics. Markov Processes and Related Fields, Volume 22, Issue 1, 1-36, 2016.

[11]. Manh Hong Duong, The Anh Han. On the expected number of equilibria in a multi-player multi-strategy evolutionary game. Dynamic Games and Applications, Volume 6, Issue 3, Pages 324-346, 2016.

[10]. Manh Hong Duong, Julian Tugaut. Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition. Applied Mathematics Letters, Volume 52,  Pages 38–45, February 2016.

[9]. Manh Hong Duong. Comparison and maximum principles for a class of flux-limited diffusions with external force fields. Advances in Nonlinear Analysis, Volume 5, Issue 2, Pages 167-176, 2016.

[8]. Manh Hong Duong. Non-equilibrium thermodynamics of damped Timoshenko and damped Bresse systems. Nonlinear Phenomena in Complex Systems, Volume 18, Number 4, Page 410-428, 2015.

[7]. Manh Hong Duong. Formulation of the relativistic heat equation and the relativistic kinetic Fokker-Planck equation using GENERIC. Physica A, Volume 439, Pages 34–43, 2015.                   

[6]. Manh Hong Duong. Long time behaviour and particle approximation of a generalised Vlasov dynamic. Nonlinear Analysis: Theory, Methods & Applications, Vol. 127, Pages 1-16, 2015.

[5]. Manh Hong Duong. Asymptotic equivalence of the discrete variational functional and a rate-large-deviation-like functional in the Wasserstein gradient flow of the porous medium equation. Asymptotic Analysis, 92(1-2), 85-106, 2015.

[4]. Kiamars Vafayi, Manh Hong Duong.  Weakly non-equilibrium properties of symmetric inclusion process with open boundaries. Physical Review E, 90, 052143, 2014.

[3]. Manh Hong Duong, Mark A.Peletier, Johannes Zimmer. Conservative-dissipative approximation schemes for ageneralized Kramers equation. Mathematical Methods in the Applied Sciences, 37(16), 2517–2540, 2014.

[2]. Manh Hong Duong, Vaios Laschos, Michiel Renger. Wasserstein gradient flows from large deviations of thermodynamic limits. ESAIM: Control, Optimisation and Calculus of Variations, 19(4), 1166-1188, 2013.

[1]. Manh Hong Duong, Mark A.Peletier, Johannes Zimmer. GENERIC formalism of a Vlasov-Fokker-Planck equationand connection to Large Deviation Principle. Nonlinearity 26, 2951-2971, 2013. This paper has been selected by the journal for  ‘2013 Highlights Collection’.

Proceedings, technical reports and extended-abstracts

[13]. M. H. Duong, C. Durbac, and T. A. Han. Optimisation of hybrid institutional incentives for cooperation in finite populations. Proceedings of the 2023 Artificial Life Conference , MIT Press, 2023.

[12]. M. H. Duong and T. A. Han. The probability distribution of the number of equilibria in random replicator-mutator equations for social dilemmas,  4th International Workshop on Agent-Based Modelling of Human Behaviour (ABMHuB'22).

[11]. M. H. Duong and T. A. Han. Cost-efficiency of institutional reward and punishment in cooperation dilemmas. Proceedings of the Artificial Life Conference 2022, volume 34, 241-243, MIT Press, 2022. 

[10]. M. H. Duong and T. A. Han. Statistics of equilibria points in pairwise social dilemmas under replicator-mutator dynamics. Conference on Complex Systems 2021 (CSS 2021), Lyon.

[9]. M. H. Duong and T. A. Han. Institutional incentives for promotion of cooperation: a rigorous analysis. 3rd International Workshop on Agent-Based Modelling of Human Behaviour (ABMHuB'21).

[8]. M. H. Duong and T. A. Han. The effect of mutation on equilibrium properties of deterministic and random evolutionary games. Proceedings of  the Artificial Life Conference 2020,  No. 32, 248-250, MIT Press, 2020. 

[7]. M. H. Duong and T. A. Han. On the Expected Number and Distribution of Equilibria in Multi-player Evolutionary Games. Proceedings of  the Artificial Life Conference 2019, pages 143-144, MIT Press, 2019.

[6]. Joep H.M. Evers, Iason A. Zisis, Bas J. van der Linden, Manh Hong Duong. Recent results in the systematic derivation and convergence of SPH. Proceedings of 11th International SPHERIC (SPHERIC 2016) Workshop at Technische Universität München, June 2016.  See also SPHERIC Newsletter, Issue 22, July 2016. Iason Zisis has won the Libersky Student Prize for this paper and his accompanying presentation at the 2016 SPHERIC workshop.

[5]. Mark Peletier, Manh Hong Duong, Upanshu Sharma. Coarse-graining and fluctuations: Two birds with one stone. Oberwolfach report of the workshop Material Theories, OWR 2013/59, 2013     

[4]. Ted van der Aalst, Dee Denteneer, Hanna Doering, Manh Hong Duong, Ross J. Kang, Mike Keane, Janne Kool,Ivan Kryven, Thomas Meyfroyt, Tobias Mueller, Guus Regts and Jakub Tomczyk. Random disc thrower problem. Proceedings of the 90th European Study Group Mathematics with Industry, 2013.

[3]. Vaios Laschos, Manh Hong Duong, Michiel Renger. Wasserstein gradient flows from large deviations of thermodynamic limits. Oberwolfach report of the workshop Interplay of Analysis and Probability in Physics, OWR, 2012/06, 2012.

[2]. Manh Hong Duong. Finite-time blow-up and variational approximation scheme for a Wigner-Fokker-Planck equation with a nonlocal perturbation. CASA Report, No. 13-13, Technische Universiteit Eindhoven, 2013

[1]. Sylvestre Burgos, Manh Hong Duong, Laura Friis Frølich, Daniel Høyer Iversen, Bogna Pawlowska, Matthias Voigt, Mikalai Zhudro. How to enhance the exploratory power of Qlucore Omics Explorer? The 23rd ECMI Modelling Week on Mathematical Modelling in Industrial and Commerce, Wroclaw University of Technology, 2009.

Theses

[2]. Manh Hong Duong. Large deviation and variational approaches to generalized gradient flows. PhD thesis, Eindhoven University of Technology, September 2014. The thesis was awarded the best doctoral project completed in 2014 of the department of Mathematics and Computer Science and nominated for the Eindhoven University of Technology Doctoral Award 2015. Reserach of my PhD work has been featured TU/e website.

[1]. Manh Hong Duong. Numerical differentiation on irregular grids using finite pointset methods. Master thesis, Kaiserslautern University of Technology and Eindhoven University of Technology, August 2010.  

Lecture notes

[3] Collective dynamics of interacting particle systems. This was the lecture notes for the Karlstad Autumn PhD School "Interacting Particles meet Homogenization and Measure Theory", November  2021.

[2 Fundamental inequalities: techniques and applications.  This was taught for Warwick's team for International Mathematics Competition for University Students, 24th IMC 2017

[1] Particle systems, large-deviation and variational approaches to generalised gradient flows. This was lecture notes for a mini-course given at Department of Probability and Statistics, Hanoi Institute of Mathematics in Summer 2015.


Popular  Press (some are in Vietnamese)

[5]. Complexity and behavioral diversity in evolving populations under uncertainty. Atlas of Sciene, 2020.

[4]. Mathematician pairs two seemingly unrelated theories to boost understanding of distribution of equilibrium points in dynamical systems with multiple participants, University of Birmingham.

[3]. An interview with the alumni association of Department of Applied Mathematics and Informatics, Hanoi University of Science and Technology (In Vietnamese). 

[2]. Manh Hong Duong. About Abel prizes 2008. Bulletin of Vietnam mathematical society, Vol. 12, No. 2, 2008

[1]. Manh Hong Duong and Pham Tra An. The international mathematical Olympiad. Bulletin of Vietnam mathematical society, Vol. 11, No. 2, 2007   

In addition, during 2006-2010, I was co-in charge of editing news on international mathematical activities for the bulletin of Vietnam mathematical society.

Other media