Scientific Computing
Three-dimensional Brownian motion trajectory showing random walk behavior

Second-Order Langevin Equation for Field Simulations

Hyperbolic Algorithm adds second-order derivatives to Langevin dynamics, reducing systematic errors to O(ε²) for lattice …

Scientific Computing
Grid of complex molecular structures rendered from SELFIES and SMILES strings

Molecular String Renderer: Robust Visualization Tool

A robust, type-safe Python library for converting chemical strings (SMILES, SELFIES, InChI) into publication-quality …

Scientific Computing
Comparison of exponential sampling methods showing histograms from both inverse transform and von Neumann methods overlaid with the theoretical exponential distribution

Exponential Random Numbers: Two Classic Algorithms

Compare inverse transform sampling and von Neumann's rejection method for exponential random numbers with Python …

Scientific Computing
Velocity Autocorrelation Function showing the signature negative region characteristic of liquid dynamics and the cage effect discovered by Rahman

Modernizing Rahman''s 1964 Argon Simulation

A high-fidelity replication of foundational molecular dynamics using modern software engineering practices: caching, …

Scientific Computing
Velocity Autocorrelation Function showing the signature negative region characteristic of liquid dynamics

Modernizing Rahman's 1964 Argon Simulation

How I used modern software engineering (caching, vectorization, and dependency locking) to reproduce a 60-year-old …

Scientific Computing
Molecular structure alignment showing protein conformations and RMSD calculation

Kabsch Algorithm: NumPy, PyTorch, TensorFlow, and JAX

Learn about the Kabsch algorithm for optimal point alignment with implementations in NumPy, PyTorch, TensorFlow, and JAX …

Scientific Computing
Energy conservation plot showing kinetic, potential, and total energy oscillations for a copper adatom diffusion simulation

Automated Adatom Diffusion Workflow

Python-wrapped reference implementation for surface diffusion simulations using LAMMPS and EAM potentials, with …

Scientific Computing
Comparison of IQCRNN (Our Method) vs standard Policy Gradient showing training curves, phase portraits, and state trajectories for control tasks

IQCRNN: Certified Stability for Neural Networks

PyTorch IQCRNN enforcing stability guarantees on RNNs via Integral Quadratic Constraints and semidefinite programming.

Scientific Computing
Cartesian Genetic Programming graph showing input nodes, function nodes, and output nodes with active and inactive connections

Cartesian Genetic Programming in Julia

An implementation of Cartesian Genetic Programming (CGP) featuring NEAT-like speciation mechanics and novel crossover …

Scientific Computing
Radix-2 DIT butterfly diagram showing the fundamental FFT operation with twiddle factor multiplication

FFTW Compiler in Haskell

Reverse-engineering the genfft logic to generate optimized C kernels for Fast Fourier Transforms using Haskell …

Scientific Computing
Flowchart diagram showing the recursive backtracking algorithm for constraint satisfaction in schedule generation

Term Schedule Optimizer

A constraint satisfaction solver built to generate conflict-free university schedules from web-scraped course data.