Monthly Archives: January 2026

Problem: In one sentence, what is the essence of DFT? Solution: To replace \(\Psi\mapsto n\), where the number density of a system of \(N\) identical quantum particles (usually electrons) \(n(\mathbf x)\) is: \[n(\mathbf x):=N\int d^3\mathbf x_2…d^3\mathbf x_N |\Psi(\mathbf x,\mathbf x_2,…,\mathbf … Continue reading →

Problem: Do an end-to-end walkthrough of the PyTorch machine learning workflow using the most basic univariate linear regression example. In particular, generate some linear data over a normalized feature space (whose slope \(w\) and intercept \(b\) would in practice be … Continue reading →

Problem: Illustrate some of the basic fundamentals involved in using the PyTorch deep learning library. In particular, discuss the attributes of PyTorch tensors (e.g. dtype, CPU/GPU devices, etc.), how to generate random PyTorch tensors with/without seeding, and operations that can … Continue reading →