AI / ML
Computational Modeling — Physics & Epidemiology
Two independent research projects exploring computational approaches to complex systems — building neural PDE solvers with embedded physical laws and modeling chaotic epidemic dynamics with seasonal forcing.
Project Overview
A research portfolio demonstrating computational approaches to complex systems across two domains. The first project implements a fractional Physics-Informed Neural Network (fPINN) in PyTorch that solves partial differential equations by encoding physical laws into the loss function. The second develops a seasonally-forced SEIR epidemiological model with nonlinear incidence that exhibits chaotic behavior — both validated with rigorous mathematical benchmarks and animated visualizations.
The Challenge
Traditional numerical methods struggle with fractional-order PDEs and fail to capture the chaotic dynamics of real-world epidemic systems. Standard SEIR models assume constant transmission rates, missing seasonal variation that introduces mathematical complexity. The challenge was implementing computationally robust solutions that could handle these edge cases while producing research-quality outputs demonstrating convergence, chaos, and sensitivity to initial conditions.
The Approach
For the fPINN project, I built a fully connected neural network in PyTorch taking spatiotemporal coordinates as input and outputting solutions. The physics loss encodes the fractional Laplace operator residual, with boundary and initial condition losses enforcing constraints. Trained over 4,000+ epochs with Adam optimizer and validated against exact analytical solutions. For the SEIR model, I implemented the ODE system in SciPy with adaptive step control, added seasonal forcing via sinusoidal transmission rate perturbation, and ran parallel simulations with slightly different initial conditions to demonstrate divergence. Both projects feature extensive Matplotlib visualizations — 2D/3D surface plots, animated phase-space trajectories, and loss convergence curves.
Research Output
Two validated computational models spanning physics and epidemiology — with animated visualizations and rigorous mathematical benchmarking as primary deliverables.
4k+
fPINN Epochs
SEIR+fPINN
Two Models
Validated
vs. Exact Solutions
Animated
Visualizations
Technology Stack
Neural Networks
PyTorchPINN ArchitectureAdam OptimizerPhysics Loss
Scientific Computing
SciPyNumPyODE SolverAdaptive Integration
Visualization
MatplotlibAnimation2D/3D PlotsPhase Space
Process Gallery
SEIR Chaotic Divergence
Neural PDE Solution vs. Exact
Time-Series & Loss Curves
Key Features
Research-grade computational models with mathematical rigor and visual clarity.
Physics-Informed Neural Network
Neural PDE solver encoding fractional Laplace operators directly into the loss function — trained over 4,000+ epochs and validated against exact analytical solutions.
Chaotic Epidemiological Dynamics
SEIR model with seasonal forcing and nonlinear incidence — parallel simulations demonstrating butterfly effect and sensitivity to initial conditions.
Animated Research Visualizations
Matplotlib animations of phase-space trajectories, solution surface evolution, and time-series convergence — exported as video and GIF outputs for presentations.