Lectures
Spring 2026 Lectures
Each lecture includes slides, notebooks, and supplementary materials.
Course Introduction and Logistics
Overview of Data-Driven Modeling and Course Structure
January 13, 2026Learning Examples and Data
The various types of data and examples of modeling them
January 15, 2026From Empirical Laws to Linear Regression
On the early days of science: fitting empirical measurements to linear models
January 20, 2026Generalization
Review of generalization, touching on deep learning, with a Python example on extrapolation in time
January 22, 2026Scientific Modeling Principles and Differential Equations
Why differential equations are the language of physics. Inductive biases in scientific modeling: space-time, conservation laws, linearity. From Newton to Navier-Stokes.
January 27, 2026Numerical Computing and Scientific Simulation
From differential equations to predictions on a computer. Discretization, error analysis, stability, and chaos.
January 29, 2026Supervised Learning: MLE, GLMs, Softmax Regression, and SVM
Maximum likelihood estimation, generalized linear models, softmax regression for multi-class classification, and support vector machines.
February 03, 2026