Assistant Professor of Mathematics working at the intersection of numerical methods, hyperbolic PDEs, entropy-stable schemes, and AI-assisted scientific computing.
Assistant Professor of Mathematics
Amity University ยท HEC core capital area Nayasarai, Jharkhand, Ranchi, India, 835303
I am a researcher working on numerical methods for hyperbolic PDEs, integrating AI and machine learning techniques for robust solvers.
"Mathematics is the representation of the artistic feature of nature."โ Inspired by the beauty of numbers and equations
Numerical schemes for hyperbolic conservation laws and sharp solution features.
This thread connects finite volume ideas, shock capturing, limiter design, and robust computation for physically meaningful simulations.
Stability-aware discretizations for degenerate parabolic and hyperbolic models.
The goal is to preserve mathematical structure at the discrete level so simulations remain reliable under challenging regimes.
Machine learning tools that complement classical numerical analysis.
This includes data-driven viscosity, reduced models, neural surrogates, and careful hybrid methods that respect numerical constraints.
Computational ideas shaped by quantum algorithms and optimization viewpoints.
A forward-looking direction for exploring new computational paradigms while keeping the bridge to classical numerical methods clear.
Adaptive numerical viscosity selected through optimization and learning signals.
This direction asks how much dissipation is enough, where it should be placed, and how to tune it without washing away important dynamics.
Clear explanations, reading pathways, and academic notes for students and collaborators.
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I welcome conversations with researchers, PhD scholars, junior faculty, and motivated students around rigorous, reproducible scientific computing.
This lightweight canvas demo gives visitors a quick intuition for one of your research themes: too little viscosity creates oscillations, while too much viscosity smears important structure.
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Exploring how classical numerical schemes complement modern deep learning approaches for solving PDEs, and why the marriage of both is the future.
Read More โMy thoughts on integrating quantum-inspired algorithms into traditional numerical schemes and the potential paradigm shift it could bring.
Read More โA deep dive into why entropy-stable schemes are crucial for handling degenerate parabolic equations and ensuring physically meaningful solutions.
Read More โThe bible of quantum computing. Essential reading for anyone interested in quantum-inspired numerical algorithms.
45% completed ยท Chapter 5: Quantum Algorithms
The definitive textbook on deep learning. Revisiting key chapters to strengthen the theoretical foundations of my ML-PDE work.
72% completed ยท Chapter 14: Autoencoders
A theoretical physics approach to understanding why deep learning works. Perfect for bridging my math background with modern ML theory.
Comprehensive coverage of spectral methods โ directly relevant to my research on high-resolution solvers.
A rigorous mathematical foundation for ML. Want to use this as a reference for teaching and research.