Professor Prasanth B. Nair

Decision Analytics for Computational Engineering Research Group
Institute for Aerospace Studies
University of Toronto
Professor Prasanth Nair

Research Interests

My current research lies at the intersection of deep learning, stochastic operator equations, and scientific computing, with a focus on continuous-time perspectives on sequence models and simulator-free variational methods for generative modeling. Across these areas, I study how transport identities, path-space principles, and coordinate transformations reveal structure that improves learning, inference, and computation.

Draft Lecture Notes

Mathematical Foundations of Inference & Learning with Continuous-Time Stochastic Differential Equations: Variational Inference, Gauss–Markov Reparametrization, & Diffusion-Based Generative Modeling (PDF)

These lecture notes are being made available in draft form and will continue to be revised.

Recent Papers/Preprints

  1. S. Maharaj and P. B. Nair, “Deep Learning with Learnable Product-Structured Activations,” to appear in ICLR 2026. https://openreview.net/pdf?id=EB2Qgp5Vb0
  2. S. Dama and P. B. Nair, “Scalable Gaussian process modeling of parametrized spatio-temporal fields,” arXiv:2603.00290. https://doi.org/10.48550/arXiv.2603.00290
  3. A. F. Ilersich, K. Course, and P. B. Nair, “Data-driven stochastic reduced-order modeling of parametrized dynamical systems,” arXiv preprint arXiv:2601.10690, 2026. https://arxiv.org/abs/2601.10690
  4. A. F. Ilersich and P. B. Nair, “Learning Stochastic Multiscale Models,” NeurIPS 2025. https://openreview.net/pdf?id=Oir5nKRKVP
  5. S. Dama, K. Course, and P. B. Nair, “Shifting time: time-series forecasting with Khatri-Rao neural operators,” ICML 2025. https://proceedings.mlr.press/v267/dama25a.html
  6. K. Course and P. B. Nair, “Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs,” NeurIPS 2023. https://proceedings.neurips.cc/paper_files/paper/2023/file/f72d4fdfd5eb425cd81df9fe6272a533-Paper-Conference.pdf
  7. K. Course and P. B. Nair, “State estimation of a physical system with unknown governing equations,” Nature 622, 2023, pp. 261–267. https://doi.org/10.1038/s41586-023-06574-8

Selected Older Publications

  1. 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
  2. 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
  3. C. Audouze and P. B. Nair, ``A priori error estimates for finite element approximations of parabolic stochastic partial differential equations with generalized random variables,'' Stochastics, Vol. 87, No. 4, 2015, pp. 537--561. DOI: 10.1080/17442508.2014.989526.
  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. P. B. Nair, ``Stochastic subspace projection schemes for dynamic analysis of uncertain systems," Vibration Analysis of Structures with Uncertainties, editors: A. Belyaev and R.S. Langley, Springer, 2011, pp. 347-360,
  6. 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
  7. A. J. Keane and P. B. Nair, “Computational Approaches for Aerospace Design,” John-Wiley and Sons, 602 pages, June 2005.
  8. P. B. Nair, ``Projection schemes in stochastic finite element analysis,'' Chapter 21 in CRC Engineering Design Reliability Handbook, editors: E. Nikolaidis, D.M. Ghiocel and S. Singhal, CRC Press, Boca Raton, FL, 2004.
  9. 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
  10. P. B. Nair, “Physics-Based Surrogate Modeling of Parameterized PDEs for Optimization and Uncertainty Analysis (PDF),” Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO, 2002, AIAA Paper 2002-1586.

News

11 November 2023 AI algorithm improves predictive models of complex dynamical systems, U of T News article.

12 October 2023 State-estimation method allows for efficient forecasts without details of underlying model, Phys.org

11 October 2023 B. Keith, The technique that can find a system's state through data alone, Nature, News and Views, Vol. 622, pp. 246-247.