Lectures
Fall 2026 Lectures
Each lecture includes slides, notebooks, and supplementary materials.
Looking for last year? The 2025 semester lectures are still available.
Course Introduction and Logistics
Overview of Data-Driven Modeling and Course Structure
September 01, 2026Learning Examples and Data
The various types of data and examples of modeling them
September 03, 2026From Empirical Laws to Linear Regression
On the early days of science: fitting empirical measurements to linear models
September 08, 2026Generalization
Review of generalization, touching on deep learning, with a Python example on extrapolation in time
September 10, 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.
September 15, 2026Numerical Computing and Scientific Simulation
From differential equations to predictions on a computer. Discretization, error analysis, stability, and chaos.
September 17, 2026Complex Systems and Probabilistic Modeling
Complex systems, chaos, sensitivity to initial conditions, probability theory, uncertainty propagation, and the bridge from randomness to determinism.
October 01, 2026Time Series Analysis: Starting from Data
From Fourier decomposition through autoregressive models to the logistic map and SINDy.
October 06, 2026Sparse Identification of Differential Equations, Part 1
Discovering governing equations from data using sparse regression. Building feature libraries, solving overdetermined systems, and sparsifying with sequential thresholding.
October 08, 2026Project Pre-Proposal Feedback Session
Peer feedback workshop for project pre-proposals. Review guidelines, swap proposals, discuss, and revise.
October 13, 2026Sparse Identification of Differential Equations, Part 2
Extending sparse equation discovery to partial differential equations. Building PDE feature matrices from spatiotemporal data and discovering classical PDEs.
October 15, 2026Symbolic Regression + Quiz
Quiz covering time series, autoregression, and SINDy. Discovering equations as expression trees using genetic algorithms. Selection, crossover, mutation, Pareto-optimal complexity-accuracy tradeoffs, and PySR.
October 20, 2026Introduction to Deep Learning
Building intuition from linear regression to neural networks. Universal approximation, backpropagation, and training deep networks.
October 22, 2026Physics-Informed Neural Networks
From classical residual minimization to PINNs. Basis function expansions, collocation methods, automatic differentiation, forward and inverse problems, training challenges, and PINN variants.
October 27, 2026SVD & PCA: Dimensionality Reduction
Eigenvalues, singular value decomposition, principal component analysis, and low-rank approximation.
October 29, 2026Linear Dynamical Systems & DMD
Linear dynamical systems, eigenvalue dynamics, and Dynamic Mode Decomposition.
November 03, 2026Advanced Deep Learning: Autoencoders & CNNs
Autoencoders for dimensionality reduction and convolutional neural networks for spatial data.
November 05, 2026Deep Learning for Time Series
From Ising models to RNNs: Hopfield networks, Boltzmann machines, LSTMs, echo state networks, and reservoir computing.
November 10, 2026Operator Learning and Neural Operators
From separation of variables to Fourier neural operators: DeepONet, FNO, and learning solution maps between function spaces.
November 12, 2026