Dynamical Systems & Chaos
Nonlinear differential equations, single- and two-tier Lorenz-96 systems, RK4 integration, and the online numerical stability of data-driven subgrid closures.
Sumangalam Avtar Sharma
BS-MS student in Mathematics · IISER Pune
I am an undergraduate in the BS-MS dual degree program at the Indian Institute of Science Education and Research (IISER), Pune, studying mathematics. My interests include dynamical systems, atmospheric variability, and applied statistics. Here you will find my coursework, student projects, writeups, and code.
Academic Interests
The main areas of my coursework and computational work as an undergraduate at IISER Pune.
Atmospheric & Climate Variability
Indian monsoon rainfall, regional ENSO sensitivity, and spatial interpolation of multi-decadal gridded precipitation data.
Applied Statistics & ML
Bayesian estimation, time series analysis, regression, and hypothesis testing, applied to physical models and survey data.
Dynamical Systems · Independent Study
Aug 2026 – Present
Lorenz-96 Subgrid Parameterization & Online Stability
How much training data does a neural network need to parameterize the unresolved subgrid coupling $U_k$ without drift or blow-up when it is integrated online in the reduced Lorenz-96 model?
$$\frac{dX_k}{dt} = -X_{k-1}(X_{k-2} - X_{k+1}) - X_k + F - \hat{U}_k(X)$$
Mathematical Writing · Open Source
Oct 2026 – Present
Mathematical Methods Handbook
A website-book of the mathematics physicists and applied scientists use, split into small units you can read on their own, select, and download as a PDF. Written from 19 textbooks, with every block labeled and checked against its sources.
Monsoon Dynamics · IDEAS-TIH, ISI Kolkata
May 2026 – Jul 2026
Impact of ENSO on Kharif Crop Rainfall Variability
Summer project with IDEAS-TIH, ISI Kolkata: an interpolation pipeline that raises the resolution of IMD gridded rainfall data, and ENSO sensitivity indices across major kharif crop-growing states.
$$\text{ESI} = \frac{\bar{P}_{\text{El Niño}} - \bar{P}_{\text{La Niña}}}{\sigma_{\text{climatology}}}$$
Science Education · ProblemSolvers Lab, IISER Pune
Jun 2026 – Jul 2026
Patterns of Reasoning and Factors of Growth
Studied how students reason through pattern-recognition problems at IISER Pune: a literature review, cleaning of participant data, and a new conceptual framework for the reasoning patterns observed.
Applied Statistics · UC Berkeley REYES
Jun 2025 – Oct 2025
Statistical Instrument on Circular Economy
With the UC Berkeley REYES mentorship program: a public survey and a literature review of 300+ articles on circular economy awareness, analyzed with hypothesis tests, ANOVA, and regression.
Relevant Coursework
Courses completed or underway at IISER Pune in mathematics, physics, computing, and the earth sciences.
Mathematics
- MT1223 Linear Algebra
- MT2113 Introduction to Probability
- MT2223 Real Analysis I
- MT3124 Real Analysis II
- MT3134 Point Set Topology
Physics
- PH1113 Introductory Mechanics
- PH2113 Introductory Quantum Physics
- PH2123 Mathematical Methods for Physics
- PH2213 Classical Mechanics
- PH2223 Thermal & Statistical Physics
Computing & Data Science
- TD1113 Introduction to Computing
- TD2223 Data Analysis
- DS4144 Deep Learning
- DS4233 Time Series Analysis
- DS4244 Bayesian Theory and Practice
Climate & Earth Sciences
- EC1213 Evolution of Earth and Life
- EC1223 The Solid Earth
- EC2113 Introduction to Climate Science
- EC2213 Principles of Planetary Climate
- EC3124 Physics of the Atmosphere
Code & Repositories
Selected repositories on GitHub. Star counts and dates update from GitHub when the page loads.
Neural-network parameterizations of the two-tier Lorenz-96 model: offline training, online coupling, and a training-data volume sweep for long-horizon stability.
Source and verification tooling for the Mathematical Methods Handbook, a website-book of mathematical methods for physicists and applied scientists.
IDEAS-TIH internship project on how ENSO affects rainfall in major kharif crop-growing states of India, 2000–2025: data, report, and slides.
Notebooks for generating data from, simulating, and learning Markovian and non-Markovian systems.
Discord bot that ran the Maths Club treasure hunt at IISER Pune: team roles, clue verification, broadcasts, and a live leaderboard.
Everything else, including this website's source and my Linux dotfiles, is on my GitHub profile.
Contact
Feel free to reach out about coursework, code, or student projects. Email is the best way to reach me.
Institutional address
Department of MathematicsIndian Institute of Science Education and Research (IISER), Pune
Dr. Homi Bhabha Road, Pashan, Pune 411008, Maharashtra, India