Data-Driven Modeling in Science & Engineering

ML for Science

Interactive lectures covering the foundations of scientific modeling, numerical methods, dynamical systems, and machine learning — from first principles to physics-informed neural networks.

Lectures

15 modules

These lectures are incomplete and are being added to as the semester goes on. What is here will keep changing, and slides may appear, move or be rewritten between one week and the next.

From Data to Learning

What data are, the forms they take across science and engineering, and where models come from.

Scientific Modeling Principles and Differential Equations

Conservation laws, dimensional analysis, ODEs, and the art of building models from first principles.

Numerical Computing and Differential Equations

Euler methods, predator-prey, pendulums, chaos, and the Lorenz attractor.

Complex Systems and Probabilistic Modeling

Emergence, self-organization, random variables, and probabilistic reasoning.

Time Series Analysis: Starting from Data

Fourier decomposition, autoregressive models, and ARIMA.

SINDy: Learning Equations from Data

Sparse identification of nonlinear dynamics: from time-series to governing equations.

Introduction to Deep Learning

From McCulloch-Pitts neurons to deep networks: self-organization, universal approximation, and backpropagation.

Symbolic Regression

Discovering symbolic expressions from data using genetic programming and modern methods.

Physics-Informed Neural Networks

Embedding physical laws into neural network training: theory, practice, and limitations.

SVD & PCA: Dimensionality Reduction

Eigenvalues, singular value decomposition, principal component analysis, and low-rank approximation.

Linear Dynamical Systems & DMD

Linear dynamical systems, eigenvalue dynamics, and Dynamic Mode Decomposition.

Deep Learning for Time Series

From Ising models to RNNs: Hopfield networks, Boltzmann machines, LSTMs, and reservoir computing.

Operator Learning & Neural Operators

From separation of variables to Fourier neural operators: DeepONet, FNO, and learning solution maps between function spaces.

Foundation Models & Agentic Science

From self-supervision to autonomous discovery: how LLMs, foundation models, and AI agents are transforming scientific research.

Ethics, Uncertainty, and the Art of Engineering

Tools as means to ends, the intelligence-predictability tradeoff, layers of ethical thinking, acting under uncertainty, and developing taste through failure.