Research themes 

• Coarse-graining of stochastic dynamics and associated evolution equations

• Large deviations and variational structures beyond gradient flows

• Sampling algorithms for molecular dynamics  

Preprints

• Alberto Montefusco, Upanshu Sharma, Oliver Tse, Fourier-Cattaneo equation: stochastic origin, variational formulation, and asymptotic limits (arXiv:2211.07265), submitted (2022).

Publications

• Robert Patterson, Michiel Renger, Upanshu Sharma, Variational structures beyond gradient flows: a macroscopic fluctuation-theory perspective (arXiv:2103.14384), Journal of Statistical Physics, 191:18 (2024) .

• Bastian Hilder, Upanshu Sharma, Quantitative coarse-graining of Markov chains (arXiv:2201.10256), SIAM Journal on Mathematical Analysis, 56(1), 913-954 (2024).

• Michiel Renger, Upanshu Sharma, Untangling Dissipative and Hamiltonian effects in bulk and boundary driven systems (arXiv:2205.05327), Physical Review E, 108(5), 054123 (2023).

• Frédéric Legoll, Tony Lelièvre, Upanshu Sharma, An adaptive parareal algorithm: application to the simulation of molecular dynamics trajectories (hal-03189428), SIAM Journal on Scientific Computing, 44(1), B146-B176 (2022). 

• Tobias Breiten, Carsten Hartmann, Lara Neureither, Upanshu Sharma, Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach (arXiv:2103.05096), Journal of Mathematical Physics, 62, 123302 (2021).

• Upanshu Sharma, Wei Zhang, Non-reversible sampling schemes on submanifolds (arXiv:2011.02835), SIAM Journal on Numerical Analysis, 59(6), 2989-3031 (2021).   

• Carsten Hartmann, Lara Neureither, Upanshu Sharma, Coarse-graining of non-reversible stochastic differential equations: quantitative results and connections to averaging (arXiv:191106081), SIAM Journal on Mathematical Analysis, 52(3), 2689-2733 (2020). 

• Bastian Hilder, Mark Peletier, Upanshu Sharma, Oliver Tse, An inequality connecting entropy distance, Fisher Information and large deviations (arXiv:1812.04358), Stochastic Processes and their Applications, 130(5), 2596-2638 (2020). 

• Frédéric Legoll, Tony Lelièvre, Upanshu Sharma, Effective dynamics for non-reversible stochastic differential equations: a quantitative study (arXiv:1809.10498), Nonlinearity, 32(12), 4779-4816 (2019). 

• Manh Hong Duong, Agnes Lamacz-Keymling, Mark Peletier, André Schlichting, Upanshu Sharma, Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics (arXiv:1712.09920), Nonlinearity, 31(10), 4517-4566 (2018). 

• Manh Hong Duong, Agnes Lamacz-Keymling, Mark Peletier, Upanshu Sharma, Variational approach to coarse-graining of generalized gradient flows (arXiv:1507.03207), Calculus of Variations and Partial Differential Equations, 56:100 (2017). 

• Upanshu Sharma, Remco Duits, Left-invariant  evolutions of wavelet transforms on the similitude group, Applied and Computational Harmonic Analysis, 39(1), 110-137 (2015). 

Proceedings

• Robert Patterson, Michiel Renger, Upanshu Sharma, Interpreting LDPs without detailed balance, Oberwolfach Reports 2020/29.

• Mark A. Peletier, Manh Hong Duong, Upanshu Sharma. Coarse-graining and fluctuations: Two birds with one stone, Oberwolfach Reports 2013/59 (arxiv:1404.1466). 

Thesis

• Coarse-graining of Fokker-Planck equations, 2017. PhD Thesis, Technische Universiteit Eindhoven (interview on my PhD work published in Nieuw Archief voor Wiskunde).

• Left-invariant evolutions of wavelet transforms on the similitude group, 2012. Masters Thesis, Technische Universiteit Eindhoven.