Juan M. Restrepo

Juan Mario Restrepo (born 4 September 1961) is an American mathematician known for his contributions to ocean dynamics, data assimilation, and computational statistical mechanics.
Restrepo's work on wave-generated transport is a collaboration with James McWilliams (UCLA) and. later, with his former student, Dr. Emily Lane (NIWA). In "The Wave Driven Circulation" (McWilliams, Restrepo, 1999)
https://doi.org/10.1175/1520-0485(1999)029<2523:TWDOC>2.0.CO;2 
 https://doi.org/10.1016/s0278-4343(01)00016-4 the conservative dynamics of wave-generated transport and basin scale quasigeostropic current dynamics are worked out for well-posedness. Wave generated transport is
more dramatic in its interactions with currents in shallow waters and in (McWilliams, Restrepo, Lane, 2004) https://doi.org/10.1017/s0022112004009358 the interaction of waves, long waves and currents in conservative dynamics is completely laid out. The work is based upon the Craik-Leibovich vortex force, who developed a theory for the generation of ocean windrows. A comprehensive comparison between the radiation stress and vortex force formulations appears in Lane, Restrepo, McWilliams (2007) https://doi.org/10.1175/jpo3043.1 . Restrepo went on to formulate the inclusion of wave breaking in wave generated transport via stochastic parametrizations in Restrepo (2007) https://doi.org/10.1175/jpo3099.1 and in Restrepo, Ramirez, McWilliams, Banner (2011) https://doi.org/10.1175/2010jpo4298.1 . Transient wave generated transport, largely unexplored, was considered in Restrepo and Ramirez (2019) https://doi.org/10.1175/jpo-d-19-0087.1 .
In Restrepo, Venkataramani, Dawson (2014) https://doi.org/10.1016/j.ocemod.2014.06.003 it is theorized that
the phenomenon of nearshore "sticky waters," that is, 
the parking of shoreward propagating oil and debris in coastal waters, is the result of the transition of advective to diffusive transport in the nearshore.
Another major research program of his is concerned with the Bayesian estimation of time dependent model and observation predictions in the presence of uncertainties. Restrepo has focused on creating new methods, capable of handling nonlinear/non-Gaussian problems, mostly by adapting constructs from statistical mechanics (see Eyink et al., 2004 https://doi.org/10.1016/j.physd.2004.04.003 , Alexander et al., 2005 https://doi.org/10.1007/s10955-005-3770-1 , Restrepo, 2008 https://doi.org/10.1016/j.physd.2007.07.020 ). He made use of homotopy methods that circumvent particle filter collapse and has created specialized estimation methods (Restrepo, Ramirez 2021)https://doi.org/10.1615/int.j.uncertaintyquantification.2022038553 , such as a structure-preserving assimilation technique (Rosenthal et al., 2017) https://doi.org/10.1016/j.jcp.2016.10.025 , where area preserving maps are used to inform the likelihood, or the dynamic likelihood filter, that assimilates data and model outcomes in wave problems by allowing the likelihood to move in space-time along characteristics (Restrepo, 2017) https://doi.org/10.1002/qj.3143 . In the context of climate science, he has focused on the implications of ocean modeling on thermohaline circulation. A general audience presentation of his work in climate predictability is in: 
==Career==
Juan M. Restrepo is the Section Head of the Mathematics in Computation Section at Oak Ridge National Laboratory, a position that is a mix of scientific management and research. His research is devoted to the application of statistical physics ideas to systems biology, artificial intelligence, and learning to Bayesian estimation, sampling and probabilistic methods for artificial intelligence.
He is also Joint Faculty Professor in the Mathematics Department at the University of Tennessee, Knoxville.
Restrepo grew up in New Jersey/New York, and in Bogota Colombia, he is the son of the Colombian artist Pedro Restrepo and the Italian/Armenian Pianist and TV Producer Ilda Pace Restrepo.
Restrepo studied music theory and composition, starting in grade school, continuing at New York University. In his search for a quiet place to study he discovered the library at Courant Institute of Mathematical Sciences, where he rekindled his love for mathematics. He also met 
several mathematicians (George C. Papanicolaou, and Joseph Keller) who encouraged him to study applied mathematics. After earning a BS in music he enrolled at Columbia University where he trained in applied mathematics in their Applied Physics Department. At the same time he worked in the music industry, and as a support engineer for Record Plant, NYC, and the Columbia-Princeton Electronic Music Center. Cyril M. Harris encouraged him to apply to Pennsylvania State University Engineering, from which he obtained an MS in Acoustics, under a research assistantship from the Office of Naval Research. 
He joined what became the Pritchard Fluid Mechanics Laboratory at Penn State. He earned his PhD
in Physics, under the supervision of Jerry L. Bona and T. Brooke Benjamin, working on mathematical
aspects of solitary waves and the dynamics of sediment under the action of nonlinear dispersive waves. As a post-doctoral fellow he developed skills in parallel computing, and with Sever Tipei and Hans Kaper, created the first ever music on a parallel computer, the IBM SP-1 computer, and developed wavelet-based numerical methods and back propagation methods. Restrepo has made contributions, as intellectual lead, in Bayesian estimation methods, filtering, ocean dynamics, oil spill dynamics, solitary waves, acoustics scattering, bone and cell dynamics, climate dynamics, numerical methods in partial differential equations and back propagation, in voting and public choice. He had an acoustics consulting company (AEP Acoustics, LLC), designing the acoustics of the Advanced Photon Source Auditorium at Argonne National Laboratory.
He has served as vice chair of SIAM Geosciences Section, chair of the APS Focus Group on Climate, President of the Nonlinear Geophysics Section at AGU, and many committee assignments in SIAM. He is an associate editor at the International Journal of Uncertainty Quantification, Nonlinear Processes in Geophysics, and Foundations of Data Sciences.
==Recognition==
Restrepo's awards include the Society of Industrial and Applied Mathematics, SIAM, Geosciences Career Prize 2017 and a Department of Energy Young Investigator Award, 2003. He is a fellow of SIAM, and a fellow of 
the American Physical Society. 
==References==
#J. C. McWilliams, J. M. Restrepo, “The Wave-Driven Ocean Circulation”, Journal of Physical Oceanography, 29, pp 2523-2540 (1999).
#J. M. Restrepo, “Wave-Current Interactions in Shallow Waters and Shore-Connected Ridges,” Continental Shelf Research, 21, pp. 1331-1360 (2001).
#J. McWilliams, J. M. Restrepo, Emily Lane, “An Asymptotic Theory for the Interaction of Waves and Currents in Shallow Coastal Waters,” Journal of Fluid Mechanics, 511, pp. 135-178 (2004).
#E. Lane, J. M. Restrepo, J. McWilliams, “Wave-Current Interaction: A Comparison of Radiation Stress and Vortex-Force Representations,” Journal of Physical Oceanography, 37 pp.1122-1141 (2007).
#J. M. Restrepo, “Wave Breaking Dissipation in a Wave-driven Circulation,” Journal of Physical Oceanography, 37, pp. 1749-1763 (2007).
#J.M. Restrepo, J. Ramírez, J.C. McWilliams, M. Banner, ” Multiscale Momentum Flux and Diffusion due to Whitecapping in Wave-Current Interactions,” Journal of Physical Oceanography, 41, pp 837- 856 (2011).
#J, M. Restrepo, S. Venkataramami, C Dawson, ”Nearshore Sticky Waters,” Ocean Modelling, 80, pp. 49-58, (2014).
#J. M. Restrepo, J. Ramírez, “Transport due to Transient Progressive Waves,” Journal of Physical Oceanography, 49, pp. 2323-2336, (2019).
#G. E. Eyink, J. M. Restrepo, J. F. Alexander, “A Mean Field Approximation in Data Assimilation for Nonlinear Dynamics,” Physica D, 195, pp. 347-368 (2004). 
#J. F. Alexander, G. E. Eyink, J. M. Restrepo, “Accelerated Monte-Carlo for Optimal Estimation of Time Series,” Journal of Statistical Physics, 119, pp.1331-1345 (2005).
#J. M. Restrepo, “A Path Integral Method for Data Assimilation,” Physica D, 237, pp. 14–27 (2008).
#S. Rosenthal, S. Venkataramani, J. M. Restrepo, A. Mariano, ”Displacement Data Assimilation,” Journal of Computational Physics, 330, pp. 594-614, (2017).
#J. M. Restrepo, ”A Dynamic Likelihood Approach to Filtering” Quarterly Journal of the Royal Society of Meteorology, 10.1002/qj.3143 (2017).
#J.M. Restrepo, J. M. Ramírez, ”Calculating Probability Densities with Homotopy and Applications to Particle Filters,” International Journal of Uncertainty Quantification, 12, pp 71-89 (2021). 
Category:1961 births
Category:American mathematicians
Category:University of Arizona alumni
Category:Oregon State University alumni
Category:University of Tennessee alumni 
Category:American people