Projects

Python notebook for the 2D FitzHugh-Nagumo equation. Explores spiral wave solutions and Turing patterns using finite difference methods.

Python · Direct Simulation

Python notebook for the Allen-Cahn equation. Explores pattern formations using numerical continuation and direct simulation methods.

Python · Numerical Continuation · Direct Simulation

Python notebook for the Bratu equation. Explores pattern formations using numerical continuation methods.

Python · Numerical Continuation · Direct Simulation

Python notebook for the Cahn-Hilliard equation. Explores pattern formations using numerical continuation and direct simulation methods.

Python · Numerical Continuation · Direct Simulation

Python notebook for the FitzHugh-Nagumo equation. Explores pattern formations using numerical continuation methods.

Python · Numerical Continuation · Direct Simulation

Python notebook for the Kuramoto-Sivashinsky equation. Explores pattern formations using numerical continuation and direct simulation methods.

Python · Numerical Continuation · Direct Simulation

Python notebook for the Swift-Hohenberg equation. Explores pattern formations using numerical continuation and direct simulation methods.

Python · Numerical Continuation · Direct Simulation

Minimal Python projects that employs Fourier Neural Networks to learn the solution operator for 2D Darcy Flow and the 1D Kuramoto-Sivashinsky equation.

Python · Machine Learning · Fourier Neural Networks

Python project that employs Fourier Neural Networks to learn the solution operator for the 2D Kuramoto-Sivashinsky equation.

Python · Machine Learning · Fourier Neural Networks

Python project that uses Deep Operator Networks (DeepONet) to learn the solution operator for the advection-diffusion equation.

Python · Machine Learning · DeepONet

Python project that implements a modified Deep Operator Network (DeepONet) to solve the Allen-Cahn equation, approximating its solution operator with neural networks.

Python · Machine Learning · DeepONet

Python project that utilizes Physics Informed Neural Networks (PINN) to learn the solution operator for Burger's equation.

Python · Machine Learning · Physics Informed Neural Networks

Python project that employs Neural Ordinary Differential Equations (NeuralODE) to learn the dynamics of a damped harmonic oscillator.

Python · Machine Learning · NeuralODE

Python project that utilizes Hamiltonian Neural Networks (HNN) to learn the dynamics of a mass-spring system, modeling its energy-dissipation properties.

Python · Machine Learning · Hamiltonian Neural Networks

Python project that utilizes Extended Physics Informed Neural Networks (XPINN) to learn the multiple time scale dynamics for the FitzHugh-Nagumo equation.

Python · Machine Learning · Physics Informed Neural Networks

Python project that utilizes Hamiltonian Neural Networks (HNN) to learn the dynamics of a damped mass-spring system, modeling its energy-conserving properties.

Python · Machine Learning · Hamiltonian Neural Networks

MATLAB project that explores spiral wave solutions in the theta model through a PDE formulation using time stepping and numerical continuation methods.

MATLAB · Numerical Continuation

MATLAB project that simulates 2D spiral waves using geometric flows. The simulation visualizes the formation and evolution of spiral wave patterns in a two-dimensional space.

MATLAB · Shooting Method