PINNs & AI Simulations

Physics-Informed Neural Networks (PINNs) provide a powerful framework for solving differential equations and learning hidden dynamics from scientific data. My research focuses on combining PINNs, Bayesian learning, and mechanistic mathematical models for biological and ecological systems.

The research explores how AI-based scientific computing can enhance parameter estimation, reduce computational cost, and improve predictive accuracy for complex nonlinear systems. Applications include Alzheimer's disease dynamics, reaction-diffusion systems, ecological simulations, and inverse problems.

Core Methodologies

Physics-informed neural networks (PINNs)
Deep neural differential equations
Inverse problem solving
Bayesian PINNs
Hybrid scientific AI models
GPU-accelerated simulations
Data assimilation techniques

Research Directions

Neurodegenerative disease prediction
Ecological pattern simulations
AI-assisted parameter estimation
Scientific uncertainty quantification
Control and optimization in biological systems

Research Contributions

Recent work integrates Bayesian PINNs with mechanistic disease models to estimate hidden parameters and predict Alzheimer's disease progression. The framework combines scientific laws with neural networks, enabling robust predictions under sparse observational data.

Selected References

1. Pal, S., & Melnik, R. (2025). Adaptive modelling of anti-tau treatments using Bayesian PINNs.

2. Pal, S., Banerjee, M., & Melnik, R. (2024). Nonlocal Models in Biology and Life Sciences.

3. Raissi, M., Perdikaris, P., & Karniadakis, G. (2019). Physics-informed neural networks: A deep learning framework for solving differential equations.