Lectures

Date Topics Readings
9/17 Week 1 Course Introduction [slides] [video]
  • Course logistics: no exam, project-based grading, tutorials as the core programming component
  • Scope: physics and engineering (majority of the course) plus a short module on chemistry and biology
  • Scientific method as PDE modeling: from natural phenomena to partial differential equations
  • PDEs as a compact language of nature and a strong prior across physics, engineering, and beyond
  • Why PDEs are hard to solve: few closed-form solutions and costly numerical methods
  • Many-query tasks and the sim-to-real gap as motivation for combining PDE priors with data-driven AI
9/24 Week 2 Introduction to Deep Learning [slides] [video]
  • Learn PDE-modeled physics from data with neural networks
  • From McCulloch–Pitts and the perceptron to MLPs: affine maps, pointwise activations, and stacked layers
  • Universal approximation: an MLP can represent a continuous map, but the parameters still have to be found
  • Supervised learning: labeled data, training loss, and a validation set to check generalization
  • Training by gradient descent, backpropagation, and mini-batch SGD
  • Beyond dense MLPs: CNNs and other structured architectures for high-dimensional inputs

Tutorials

Date Topics Exercise Solutions Materials
9/21 Function Approximation with PyTorch [exercise] [solutions] [pdf]