I am an Applied Mathematics researcher with a strong academic foundation in Partial Differential Equations (PDEs), Numerical Analysis, and Scientific Machine Learning (SciML).

I hold an M.Sc. in Applied Mathematics from the Indian Institute of Engineering Science and Technology (IIEST), Shibpur, with specialization in Fluid Mechanics and Numerical Methods.
My research interests focus on developing structure-preserving and interpretable learning frameworks that integrate classical mathematical modeling with modern machine learning.

My work spans:

• 📐 Physics-Informed Neural Networks (PINNs) for PDEs
• 🌊 Convection–diffusion and transport phenomena
• 📈 Time-dependent and dynamical system modeling
• 🧮 Uncertainty-aware mathematical frameworks
• 🔁 Statistical and learning-based solvers for physical systems

My goal is to contribute to reliable, mathematically grounded learning methods for scientific computing.

• Scientific Machine Learning (SciML)
• Physics-Informed Neural Networks (PINNs)
• Partial Differential Equations (PDEs)
• Computational Fluid Dynamics (CFD)
• Numerical Analysis for dynamical systems
• Time-series modeling for physical processes
• Constraint-based and uncertainty-aware modeling

Partial Differential Equations • Numerical Analysis • Linear Algebra •
Fluid Mechanics • Probability & Statistics • Fuzzy Logic

Python (NumPy, SciPy, Matplotlib) • LaTeX • MATLAB (basic)

PyTorch • TensorFlow • Physics-Informed Neural Networks (PINNs) • DeepXDE
LSTM • Statistical Time-Series Models

Git • GitHub • Jupyter Notebook • Google Colab • VS Code

Generalized Intuitionistic Fuzzy Soft Sets and Its Applications

Developed rigorous mathematical frameworks for modeling non-probabilistic uncertainty in decision-making problems, forming a theoretical basis for uncertainty-aware scientific computing and applied mathematics research.

I am building MLMathematics, an academic initiative focused on the
mathematical foundations of machine learning, SciML, and physics-informed modeling.

The platform aims to bridge rigorous mathematics with modern learning-based methods for research, education, and scientific dissemination.

🌍 https://mlmathematics.com

I am open to academic research collaboration in areas related to:

• Scientific Machine Learning & PINNs
• PDE-constrained learning
• Numerical methods for physical systems
• Mathematical modeling and uncertainty quantification

• 📧 Email: akhileshyadav.maths@gmail.com
• 💼 LinkedIn: https://www.linkedin.com/in/akhileshyadav1598
• 🌍 MLMathematics: https://mlmathematics.com

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”
— S. Gudder