Teaching
Teaching
In the ChatGPT era, I think the most valuable part of a classroom is the people in it, the peers and colleagues you get to think alongside. So in the lectures I help teach, I try to lean on participation and discussion rather than one-way delivery. I have mentored seven undergraduate and master's researchers. Three became publication coauthors, and three former mentees subsequently entered graduate programs at ETH Zurich, UC San Diego, and the University of Wisconsin.
Scientific machine learning: a mini lecture series
I taught several lectures within Physics-Informed Machine Learning at UC San Diego, introducing the core ideas of scientific machine learning. The full lectures are on YouTube; here is a quick tour of what each one covers. These are recordings of live classes, so student questions and discussion are woven throughout. In the participation-first spirit above, they are real teaching sessions rather than polished videos.
Watch the full series on YouTubeNeural ODEs
How treating a network's depth as continuous time turns it into a dynamical system that an ODE solver integrates and the adjoint method trains efficiently.
Jump to a highlight
Neural operators
Learning maps between function spaces rather than between fixed vectors, so one model transfers across discretizations. Builds up to DeepONet and the Fourier Neural Operator.
Jump to a highlight
Jump to a highlight
Physics-informed neural networks
Embedding a PDE's residual directly in the training loss so a network can solve or identify differential equations with little or no data, and where the approach tends to break down.
Jump to a highlight
Foundation models
What foundation models are, how pretraining at scale produces general-purpose representations, and what their rise means for scientific computing.
Jump to a highlight