February 2026

1. Introduction: What Is Physics-Informed AI? Imagine you are trying to locate your phone inside a large shopping mall using radio signals. In an open field, this would be straightforward: the signal travels in a straight line, and by measuring how long it takes to arrive, you can compute the distance. But inside a building, […]

Figure: Spatial interpolation creates continuous surfaces from scattered data 1. What is Spatial Interpolation? Spatial interpolation is the process of estimating unknown values at unsampled locations based on known values at sampled locations. It transforms sparse, scattered measurements into a continuous surface. Example: You have temperature readings from 10 weather stations. Spatial interpolation lets you

Figure: Kernel Interpolation creates smooth curves through data points Keywords: Kernel Interpolation, Gaussian RBF Kernel, RKHS, Kernel Ridge Regression, Python, Machine Learning, Spatial Interpolation Table of Contents 1. What is Kernel Interpolation? 2. Understanding the Gaussian (RBF) Kernel 3. The Kernel Matrix Explained 4. What is RKHS? (Reproducing Kernel Hilbert Space) 5. Kernel Ridge Regression

From Points to Hyperplanes – How Equations Shape Our Mathematical Universe Introduction: The Hidden Geometry in Every Equation Have you ever wondered why a simple equation like x + y = 5 represents a line? Or why adding more equations changes the shape of the solution from a plane to a line to a single