UML-06: Principal Component Analysis (PCA)
Master PCA: The 'Photographer' of data. Learn how to find the best camera angles (principal components) to capture the most detail (variance) in your data.
UML-05: Gaussian Mixture Models
Master GMM: The 'Explorer in the Fog' of clustering. Learn how to map overlapping 'hills' of data, handle uncertainty with soft clustering, and master the EM algorithm.
UML-04: DBSCAN and Density-Based Clustering
Master DBSCAN: The 'Island Finder' of machine learning. Learn how to map arbitrary cluster shapes, handle noise like an explorer, and tune epsilon without needing to guess 'K' upfront.
UML-03: Hierarchical Clustering
Master Hierarchical Clustering: the 'Digital Librarian' of machine learning. Understand how to organize data into nested trees, interpret dendrograms, and choose the right linkage method without needing to guess 'K' upfront.
UML-02: K-Means Clustering
Unlock the power of clustering. Master Lloyd's Algorithm from scratch, visualize the iterative 'Assignment-Update' loop, and solve the 'How many clusters?' dilemma with the Elbow Method.
UML-01: Introduction to Unsupervised Learning
Unlock the hidden potential of 'Dark Data'. Master Unsupervised Learning fundamentals, explore the 'Student vs. Explorer' analogy, and navigate the taxonomy of Clustering, Dimensionality Reduction, and Anomaly Detection.
Necking of an Elastoplastic Metal Bar: COMSOL vs Abaqus Implementation
A comparative tutorial on simulating necking instability in a tensile metal bar using COMSOL Multiphysics and Abaqus. We explore the modeling approaches, compare stress-strain behavior, and analyze the necking phenomenon from both platforms.
Seeing the Unseen: The Power of Log Scales in Numerical Simulation
Linear plots often obscure the true physics of your simulation. Discover how logarithmic scales reveal hidden details in convergence plots, exponential trends, and field distributions—with real-world COMSOL examples on Solar Cells and Skin Effect.
Metal Fracture Simulation: Comparing Morse and EAM Potentials in LAMMPS
A hands-on tutorial on simulating tensile fracture in copper using LAMMPS. We compare the simplified Morse potential with the accurate EAM potential and analyze stress-strain behavior during crack propagation.
Molecular Dynamics 101: From First Principles to Python, Julia, and LAMMPS
A deep dive into the 'Hello World' of Molecular Dynamics: simulating Lennard-Jones Argon. We derive the physics, build a scratch implementation in Python and Julia, and compare it with production-grade LAMMPS scripts.