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Computational Mathematics and Data Science

Interpretable models, Data driven Modelling, Artificial Intelligence, Fast Computing, Statistical Learning, computational methods, stochastic evolution.

In the era of digitalization, data is the main source of information. If this information is processed correctly then it helps authorities to frame the efficient policies and implement them successfully. Therefore, processing the data is the most crucial and inevitable intermediate step for the formulation of efficient policies.

  • At the same time processing the data is a big challenge and we need technology and skilled human resources to achieve this.

  • Also, we need to update and innovate our skills to understand and comprehend the available data in a better way.

  • To achieve this we need a dedicated workforce that strives for continuous improvement in tools and techniques used for analyzing the data.

  • It is also important that we must understand and develop the mathematical theory to support our modeling.

  • Our project will mainly focus on mathematical aspects of the data-driven problem and design a new mathematical theory, if required, to arrive at a solution to the given research problem. The detailed list of problems is given next.

Computational Mathematics and Data Science

Neelesh S Upadhye

Principal Investigator

People

Neelesh S Upadhye

Area of Interest

Neelesh S Upadhye

Principal investigator

Mathematics

Website Google Scholar
neelesh@iitm.ac.in
Time Series , Data Science, Applied Probability
S.Sundar

Area of Interest

S.Sundar

Co-Principal investigator

Mathematics

Website
slnt@iitm.ac.in
Numerics for PDEs, Mathematical Modeling & Numerical Simulation.

Project

Research Areas/Problems

Any practical (data-driven) problem can be modeled using the following broadly classified areas in mathematics:

  • Statistics (classical or Bayesian)

  • Differential equations (Deterministic or Stochastic)

  • Optimization or Game theory

  • Computational mathematics

It may also need expertise from all the areas listed above. At present, we have an expertise in these areas, and with this proposed center, we can increase our collaboration with industries and an academic world which in turn has potential to produce cutting edge research and new theories in mathematics along with a practical (mathematically viable) solution to a data-driven problem.

Expected deliverables of the research

Keeping this wide spectrum in mind, the center will strive to achieve the following goals

  • Data-Driven Mathematical Modelling. Develop the models using data that will be mathematically viable. Once the viability of the model is established, use/design theory to establish the existence and uniqueness/nonuniqueness of the solution. In case, the solution to the problem is unique the optimality is assured, otherwise find the most optimal solution among the set of available solutions to the problem.

  • Human Resource Development. Organize short term courses on these topics to spread awareness in the academic neighborhood. Develop human resources through our academic programs for the demand in this field. Start MOOC based certification programs for Data Scientists, Data Analysts, and related fields.

  • Continuous Upgradation of Skills and Industry-Academia Connect. Organize international/national meetings among the world mathematics community to update and share our knowledge about data-driven mathematical modeling. Resolve the problems faced by the industry.

    Current status

Collaborations

International Collaborations

Prof.Dr. Axel Klar link

Dr. Sudarshan Tiwari link

Prof. Thomas Goetz link

Prof. Agnieska Wylomanska link

Prof. Jorg Kuhnert link

Prof. Vydas Cekanavicius link

Prof. Nicolas Privault link

Societal impact

Technical/ Scientific Progress

New work done in the project

  1. Estimation procedures for VARMA with stable noise is established.

  2. Estimation procedures for PAR(1) with stable noise is develped.

  3. A mathematical model governing the short-range transport of microplastic particles in a lid-driven cavity with an obstacle is established.

  4. Numerical methods for particle Agglomeration and breakage in lid-driven cavity ows at low Reynolds numbers are derived.

  5. Methodology for Transport of ellipsoidal microplastic particles in a 3D lid-driven cavity under size and aspect ratio variation is developed.

  6. A theory on Bifurcation, uniqueness and multiplicity results for classes of reaction diffusion equations arising in ecology with nonlinear boundary conditions is developed.

Infrastructure developments

We have upgraded Department Computing Facility with new furnture and computing nodes. (5 PCs, 1 Server class machine, 4 Server class machines (yet to come)).

Output

  1. A mathematical model governing the short-range transport of microplastic particles in a lid-driven cavity with an obstacle. Communications in Nonlinear Science and Numerical Simulation (S. Sundar, Nityananda Roy, Thomas Goetz and K.W.Putra).

  2. Fractional lower-order covariance (FLOC)-based estimation for multidimensional PAR(1) model with α−stable noise, International Journal of Advances in Engineering Sciences and Applied Mathematics, Springer,link (S. Sundar, Agnieszka Wylomanska and Prashant Giri).

  3. Numerical methods for particle Agglomeration and breakage in lid-driven cavity ows at low Reynolds numbers, Mathematics and Computers in Simulation,(S. Sundar, Robert Duerr, Andreas Bueck, Jitendra Kumar, Nityananda Roy)

  4. Transport of ellipsoidal microplastic particles in a 3D lid-driven cavity under size and aspect ratio variation, Applied Mathematics and Computation, (with Nityananda Roy, Thomas Goetz and K.W.Putra)

  5. Bifurcation, uniqueness and multiplicity results for classes of reaction diffusion equations arising in ecology with nonlinear boundary conditions, Communications on Pure and Applied Analysis. doi: 10.3934/cpaa.2021195 (S. Sundar, Mohan Mallick, Sarath Sasi, Ratnasingham Shivaji).

  6. Estimation of the parameters of vector autoregressive moving average (VARMA) time series model with symmetric stable noise. Int J Adv Eng Sci Appl Math 13, 206–214 (2021). Join (Sathe, A.M., Chowdhury, R. & Upadhye, N.S.)

  7. Special issues on the topic “Time Series Modeling, Data Science and Statistical Learning” have been brought out in the International Journal of Advances in Engineering Sciences and Applied Mathematics, Volume 13, Issues 2 -3, September 2021, Springer. (Guest Editors: Prof.S.Sundar, IIT Madras, Prof.Agnieszka Wylomanska, WUST, Poland and Prof.Januz Gajda, University of Warsaw, Poland.

  8. Webinar in IRIS Webinar Series

Mobility

Visits planned for PI, co-PIs, international collaborators and students (both inbound and outbound)

 

Relationship

Industrial Engagement

We will soon receive two projects from MPM Private LTD. Also, received on CSR Project form the same company.

University Engagement

Joint PhD Degree Memorandum of Understanding (MoU) between IIT Madras and TU Kaiserslautern, Germany has been signed in the month of December 2021 by the Director of IIT Madras and President of the TU Kaiserslautern for the student Ms.A. Parveena Shamim (MA17D003) jointly guided by Prof.S.Sundar of IIT Madras and Prof.Axel Klar of AG Technomathematik, TU Kaiserslautern, Germany.

Updates

Relevant Updates

Ph.D.s Awarded

  1. Dr. Nityananda Roy, MA16D018, “Modeling Studies on the Transport of Particles in Fluid”, September 2021. (Guide: Prof.S.Sundar, IIT Madras, Co-Guide: Prof.Thomas Goetz, University of Koblenz-Landau, Germany).

  2. Dr. Prashant Giri, MA16D038, “Estimation of Multidimensional Autoregressive (AR) and Periodic Autoregressive (PAR) Time Series Models with α-Stable Distribution”, December 2021(Guide: Prof.S.Sundar, IIT Madras, Co-Guide: Prof.Agneiszka Wylomanska, Wroclaw University of Science and Technology, Poland).

  3. Dr. Aastha M Sathe, MA15D200, “Estimation Problems related to Stable Distributions”, December 2021 (Guide: Dr. Neelesh S Upadhye, IIT Madras)