James-Michael Leahy

Research Associate
Department of Mathematics
Imperial College London

Email: j.leahy@imperial.ac.uk
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I am currently a research associate at the Department of Mathematics of Imperial College London. My research lies at the intersection of stochastic analysis, partial differential equations, and fluid dynamics. I am interested in developing, analyzing, and calibrating stochastic reduced models of fluids in order to improve ensemble forecasts for weather or climate prediction.

Darryl D. Holm and I have recently received a US AFOSR Grant (FA8655-21-1-7034) entitled Rough-Path Fluid Dynamics in which we are investigating a class of stochastic fluid models that arise from a pathwise stochastic variational principle.

I am also excited about reinforcement learning and stochastic control, and especially their connection to data-driven approaches to dynamical systems and control.

You can download my CV here.


arXiv, Google Scholar, ORCID, Scopus, MATHSCINET, Research Gate
Convergence of policy gradient for entropy regularized MDPs with neural network approximation in the mean-field regime
with Bekzhan Kerimkulov, David Siska, and Lukasz Szpruch
arXiv:2201.07296, to appear in ICML, 2022
Solution properties of the incompressible Euler system with rough path advection
with Dan Crisan, Darryl D. Holm, and Torstein Nilssen.
arXiv:2004.07829, 2021
Variational principles for fluid dynamics on rough paths
with Dan Crisan, Darryl D. Holm, and Torstein Nilssen.
Adv. Math., Volume 404, Part A, 2022,
Lagrangian averaged stochastic advection by Lie transport for fluids
with Theodore D. Drivas and Darryl D. Holm
J. Stat. Phys., 179:1304-1342, 2020
On a rough perturbation of the Navier-Stokes system and its vorticity formulation
with M. Hofmanova and T. Nilssen
Ann. Appl. Prob., 31(2):736-777, 2021
On the Navier-Stokes equation perturbed by rough transport noise
with M. Hofmanova and T. Nilssen
J. Evol. Equ., 19:203-247, 2019
On classical solutions of linear stochastic integro-differential equations
with Remigijus Mikulevicus
SPDEs: Anal. and Comp., 4:535-591, 2016
Finite difference schemes for linear stochastic integro-differential equations
with Konstantinos Dareiotis
Stoch. Anal. Appl., 126(10):3202-3234, 2016
On degenerate linear stochastic evolution equations driven by jump processes
with Remigijus Mikulevicus
Stoch. Anal. Appl., 125(10):3748-3784, 2015
On some properties of space inverses of stochastic flows
with R. Mikulevicius
SPDEs: Anal. and Comp., 3(4):445-478, 2015