Research Highlights

K. Course and P. B. Nair. State estimation of a physical system with unknown governing equations. Nature 622, 261–267 (2023). https://doi.org/10.1038/s41586-023-06574-8

K. Course and P. B. Nair. Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs. In Proc. Advances in Neural Information Processing Systems, 2023.

C. Audouze, A. Klein, A. Butscher, N. Morris, P. B. Nair, and M. Yano. Robust level-set-based topology optimization under uncertainties using anchored ANOVA Petrov-Galerkin method. SIAM/ASA Journal on Uncertainty Quantification, 11(3): 877-905, 2023. doi:10.1137/22M1524722

R. Bryan, P. S. Mohan, A. Hopkins, F. Galloway, M. Taylor, P. B. Nair, ''Statistical modelling of the whole human femur incorporating geometric and material properties, Medical Engineering and Physics, Vol. 32, No. 1, 2010, pp. 57-65.

Coming soon -- Khatri-Rao neural operators

❮ ❯

Prasanth Nair is a Professor at the University of Toronto Institute for Aerospace Studies (UTIAS) where he leads the Decision Analytics for Computational Engineering (DACE) research group. He obtained his doctorate degree from the University of Southampton in 2000, and his Bachelor’s and Master’s degrees from the Indian Institute of Technology, Mumbai in 1995 and 1997, respectively. After completing his PhD, he held the positions of Research Fellow, University Senior Research Fellow and Senior Lecturer in the School of Engineering Sciences at the University of Southampton. Professor Nair joined UTIAS in March 2011. He was a Tier-II Canada Research Chair in Computational Modeling and Design Optimization Under Uncertainty from 2011-2021 and he served as the Associate Director, Graduate Studies at UTIAS from 2020-2023.

Professor Nair's current research interests lie in the following areas:

1. Scalable numerical methods for learning from large datasets with applications to
   1. approximation of functions, low-dimensional manifolds, and operators,
   2. state estimation and control,
   3. Bayesian model calibration,
   4. discovery of continuous operator equations from temporal and spatio-temporal data streams, and
   5. accelerated calculation of decision analytics.
2. Optimization under uncertainty.
3. Numerical methods for stochastic differential equations.
4. Variational methods for learning reduced-complexity representations of parametrized operator equations.

Selected Publications

1. K. Course and P. B. Nair. State estimation of a physical system with unknown governing equations. Nature 622, 261–267 (2023). https://doi.org/10.1038/s41586-023-06574-8
2. R. Baptista, V. Stolbunov and P. B. Nair, ``Some greedy algorithms for sparse polynomial chaos expansions,” Journal of Computational Physics, Vol. 387, 2019, pp. 303–325. https://doi.org/10.1016/j.jcp.2019.01.035
3. C. Audouze and P. B. Nair, ``Sparse low-rank separated representation models for learning from data,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2221), 2019. https://doi.org/10.1098/rspa.2018.0490
4. C. Audouze and P. B. Nair, ``Anchored ANOVA Petrov-Galerkin projection schemes for parabolic stochastic partial differential equations,'' Computer Methods in Applied Mechanics and Engineering, Vol. 276, 2014, pp. 362-395. DOI: 10.1016/j.cma.2014.02.023 .
5. R. Bryan, P. S. Mohan, A. Hopkins, F. Galloway, M. Taylor, P. B. Nair, ''Statistical modelling of the whole human femur incorporating geometric and material properties, Medical Engineering and Physics, Vol. 32, No. 1, 2010, pp. 57-65. DOI:10.1016/j.medengphy.2009.10.008
6. A. J. Keane and P. B. Nair, ``Computational Approaches for Aerospace Design,'' John-Wiley and Sons, 602 pages, June 2005.
7. P. B. Nair, A. Choudhury and A. J. Keane, ``Some greedy learning algorithms for sparse regression and classification with Mercer kernels,'' Journal of Machine Learning Research, Vol. 3, 2002, pp. 781-801. http://www.ai.mit.edu/projects/jmlr/papers/v3/nair02a.html
8. P. B. Nair, ``Physics-Based Surrogate Modeling of Parameterized PDEs for Optimization and Uncertainty Analysis,'' Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, 2002, AIAA Paper 2002-1586.

News