Stable Accurate Fast Robust Algorithms & Numerics


Publications Research Software Funding

The SAFRAN lab was born in April 2016 and resides at Room 203, SERC building at IISc.

Publications

(16) Daniel Foreman-Mackey, Eric Agol, Ruth Angus, Sivaram Ambikasaran, "Fast and scalable Gaussian process modeling with applications to astronomical time series", Submitted to AAS journals. Preprint*
This relies on my earlier work "The Generalized Rybicki Press algorithm"

(15) Sivaram Ambikasaran, Krithika Narayanaswamy, "An accurate, fast, mathematically robust, universal, non-iterative algorithm for computing multi-component diffusion velocities", Proceedings of Combustion Institute. Preprint*/ Journal version

(14) Sivaram Ambikasaran, Carlos Borges, Lise-Marie Imbert-Gerard, Leslie Greengard, "Fast, adaptive, high order discretization of the Lippmann-Schwinger equation in two dimension", SIAM Journal of Scientific Computing. Preprint*/ Journal version

(13) Sivaram Ambikasaran, "Generalized Rybicki Press algorithm", Numerical Linear Algebra with Applications. Preprint*/ Journal version

(12) Sivaram Ambikasaran, Eric Darve, "The Inverse Fast Multipole Method" Preprint*

(11) Sivaram Ambikasaran, Michael O'Neil, Karan Raj Singh, "Fast symmetric factorization of hierarchical matrices with applications", Submitted Preprint*

(10) Jun Lai, Sivaram Ambikasaran, Leslie F. Greengard, "A fast direct solver for high frequency scattering from a large cavity in two dimensions", SIAM Journal of Scientific Computing. Preprint*/ Journal version
Here is a video of scattering from an engine shaped cavity. Fast direct solver is especially attractive in the present context, since it permits the computation of the scattered field for multiple incident angles in a negligible amount of time.

(9) Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard, David W. Hogg, Michael O'Neil, "Fast Direct Methods for Gaussian Processes and the Analysis of NASA Kepler Mission Data", Transactions on Pattern Analysis and Machine Intelligence. Preprint*/ Journal version

(8) Amirhossein Aminfar, Sivaram Ambikasaran, Eric Darve, "A fast block low-rank dense solver with applications to finite-element matrices", Journal of Computational Physics. Preprint*/ Journal version

(7) Judith Y Li, Sivaram Ambikasaran, Eric Darve, Peter K Kitanidis, "A Kalman filter powered by \(\mathcal{H}^2\)-matrices for quasi-continuous data assimilation problems", Water Resources Research. Preprint*/ Journal version

(6) Sivaram Ambikasaran, "Fast Algorithms for Dense Numerical Linear Algebra and Applications, Stanford Thesis" Official version

(5) Sivaram Ambikasaran, Arvind Krishna Saibaba, Eric Darve, Peter K Kitanidis, "Fast Algorithms for Bayesian Inversion", The IMA Volumes in Mathematics and its Applications Preprint*/ Book chapter

(4) Arvind Krishna Saibaba, Sivaram Ambikasaran, Judith Y Li, Peter K Kitanidis, Eric Darve, "Application of hierarchical matrices in geostatistics", Oil & Gas Science and Technology - Revue d'IFP Energies Nouvelles. Preprint*/ Journal version

(3) Sivaram Ambikasaran, Judith Y Li, Peter K Kitanidis, Eric Darve, "Large-scale stochastic linear inversion using hierarchical matrices", Computational Geosciences. Preprint*/ Journal version

(2) Sivaram Ambikasaran, and Eric Darve, "An \( \mathcal{O}(N \log N) \) fast direct solver for partially hierarchical semi-separable matrices", Journal of Scientific Computing. Preprint*/ Journal version

(1) K. Bhaskar and Sivaram Ambikasaran, "Untruncated infinite series superposition method for accurate flexural analysis of isotropic/orthotropic rectangular plates with arbitrary edge conditions", Composite Structures. Author copy*/ Journal version

*-Preprints/Author copy are provided for timely dissemination of scholarly and technical work. Also, be aware that the journal version might be little different from the preprint in some cases.

Research

The group works on theoretical & computational aspects of numerical linear algebra, approximation theory & functional analysis with a focus on constructing highly accurate fast stable algorithms for electromagnetics, elasticity, fluid mechanics, computational statistics, inverse problems and filtering. The overarching goal of the group is to develop robust algorithms founded in rigorous mathematics and convert them into technologies, which inturn can be used as blackbox tools for the aforementioned applications. The broad areas of research are enlisted below.

List of possible Research Projects

Below are some of the possible research projects, one can pursue as a member of our group. The list is only indicative and by no means exhaustive.

Software

All codes are made available in the hope that they will be useful, but without any warranty. All the codes can be redistributed and/or modified under the terms of the appropriate license.
BBFMM2D
- Black Box Fast Multipole Method in two dimensions. Available at: https://github.com/sivaramambikasaran/BBFMM2D
FLIPACK
- Fast Linear Inversion PACKage. Available at: https://github.com/sivaramambikasaran/FLIPACK
HODLR
- Fast Direct Solver for hierarchical off-diagonal low-rank matrices. Available at: https://github.com/sivaramambikasaran/HODLR
ESS
- Extended Semi-Separable algorithm and the generalized Rybicki Press algorithm. Available at: https://github.com/sivaramambikasaran/ESS
George
- fast and flexible Python library for Gaussian Process Regression. Availabe at: http://dan.iel.fm/george/current/
Celerite
- A scalable method for Gaussian Process regression. Available at: http://celerite.readthedocs.io/en/latest/

Funding