I treat well-engineered, open-source software as a first-class research output. All projects are on GitHub.
DAE-FINDER
github.com/mjayadharan/DAE-FINDER_dev · dae-finder on PyPI · Python
A model-agnostic scientific-ML package for discovering differential-algebraic equations from noisy data via sparse optimization. The package exposes a scikit-learn-compatible .fit()/.score() interface and supports any algorithm conforming to that API, making it a benchmarking substrate for the broader equation-discovery community (SINDy, Weak-SINDy, IDENT, and SODAs variants on a common footing). I led the design and open-source release, and I actively maintain it. Its method-agnostic architecture was inspired by the asset-agnostic pricing-library framework I worked on at Citigroup.
DAE-FINDER recovering power-grid algebraic relationships at 30dB signal-to-noise: larger perturbations carry more information, reaching reliable recovery with fewer experiments.
FluidLearn
github.com/mjayadharan/FluidLearn · Python, TensorFlow/Keras
A framework for solving fluid-flow PDEs using physics-informed neural networks (PINNs), packaged so that domain scientists can define geometry, boundary conditions, and physics without touching the underlying ML code.
FluidLearn approximates the solution and PDE operator with neural networks trained on boundary and initial-condition data.
SpaceTimeDD
github.com/mjayadharan/MMMFE-ST-DD · C++, deal.II
A parabolic-PDE solver using space-time multiscale mortar mixed finite elements with domain decomposition. Allows different spatial and temporal discretizations on different subdomains, which the time-dependent problems in the associated SIAM J. Numer. Anal. paper exploit.
Non-matching space-time grids across subdomains (left) and the computed pressure on the glued global grid (right).
BiotDDSolver
github.com/mjayadharan/BiotDD · C++, MPI, deal.II
A poroelastic fluid-flow simulator using MPI-based non-overlapping domain decomposition for the Biot system. Subdomain solves are independent and map naturally onto distributed-memory architectures.
A poroelastic flow simulation computed with BiotDD.
Contributions to deal.II
I am a contributor to deal.II, the widely used open-source C++ finite element library that powers most of my HPC packages.
In development
- An open, documented version of the electrochemical transport solver (coupled Poisson-Nernst-Planck with Butler-Volmer boundary conditions) developed at Northwestern’s Trienens Institute.
- A library of reusable agentic skill sets and validation protocols for AI-assisted scientific computing, growing out of my current research program and the Fall 2026 Northwestern course Agentic AI for Scientific Computing.