Videos and books

Every resource on this page is free to watch or read, from the author's, the university's or the publisher's own page, or from arXiv. Each lesson of the track also ends with a Watch and read section that names the exact video, chapter or paper for that lesson.

How to use it. Watch one short video for the picture, then do the lesson and its notebook, then read the matching chapter or paper from the table at the end of this page. The long lecture series are for a second pass, when you want the same idea from another teacher.

A note on notation. Books and papers in this field use different symbols. Three differences matter most:

• Time direction in generative models. Score-based diffusion (Song et al.; lessons 12–13) puts data at $t = 0$ and noise at $t = T$. Flow matching (Lipman et al., the MIT 6.S184 course; lessons 14–15) puts noise at $t = 0$ and data at $t = 1$. Converting flips the sign of the velocity.
• The sphere. This track uses colatitude $\theta \in [0, \pi]$ and longitude $\phi$ (physics convention, lesson 09). Weather data and lesson 16 use latitude $\pi/2 - \theta$. Some mathematics books swap the names $\theta$ and $\phi$.
• Data assimilation. The track follows the operational notation: background $x^b, B$; forecast $x^f, P^f$; analysis $x^a, P^a$; observations $y = Hx + v$ with $v \sim \mathcal N(0, R)$. Särkkä's book writes the same Kalman filter with $m_k, P_k$ and $H_k, R_k$.

Video courses #

Start here #

• Steve Brunton, Physics Informed Machine Learning (YouTube playlist). Short, clear videos on PINNs, neural ODEs, SINDy, Fourier neural operators and symmetry. Good before lessons 03, 05, 08, 10 and 11.
• ETH Zürich, AI in the Sciences and Engineering (CAMLab, 2025) (YouTube playlist). A full university course: PINNs, neural operators (FNO and more), and ML for weather. Good for lessons 08, 11 and 16.
• Chris Rackauckas, Parallel Computing and Scientific Machine Learning (YouTube playlist, lecture notes). Automatic differentiation, adjoints of ODE solvers, stiffness and neural ODEs from the developer of the Julia SciML tools. Good for lessons 01–03.

Differentiable simulation (lessons 01–04) #

• MIT 18.S096, Matrix Calculus for Machine Learning and Beyond (IAP 2023) (YouTube playlist, course page). Derivatives as linear maps, reverse mode, and adjoint methods. The language of lesson 01.

Chaos, data and uncertainty (lessons 05–07) #

• Steve Brunton, Dynamical Systems (with Machine Learning) (YouTube playlist). Koopman operators, DMD and SINDy in more depth than lesson 05.
• xwu, Short-course on Data Assimilation (ICL and INPE, 2022) (YouTube playlist). A full short course: optimal interpolation, 3D-Var and 4D-Var, the Kalman filter and the EnKF. Good for lesson 06.
• Philipp Hennig, Probabilistic Machine Learning (Tübingen, 2023) (YouTube playlist). Gaussian processes, kernels and Gaussian filtering as one framework. Good for lessons 06 and 07.

Neural operators, symmetry and physics (lessons 08–11) #

• Erik Bekkers, Group Equivariant Deep Learning (UvA, 2022) (YouTube playlist, course page). Groups, representations, steerable and $SE(3)$-equivariant networks. The full course behind lesson 10.

Stochastic and generative models (lessons 12–15) #

• MIT 18.S096, Topics in Mathematics with Applications in Finance (Fall 2013) (YouTube playlist, course page). Lectures 17, 18 and 21 cover Brownian motion, Itô calculus and SDEs. Good for lesson 12.
• MIT 6.S184, Flow Matching and Diffusion Models (Peter Holderrieth, 2026) (YouTube playlist, course page and notes). SDEs, score functions, flow matching and guidance with one notation. The best single course for lessons 12–15.

ML weather and climate models (lesson 16) #

• ECMWF, Learning (learning.ecmwf.int). Free online courses and recorded training from the European weather centre, including numerical weather prediction, data assimilation and machine learning for weather.

Free books #

Short reads #

• Baydin et al., Automatic Differentiation in Machine Learning: a Survey. Forward and reverse mode, with history and examples (lesson 01).
• Steven G. Johnson, Notes on Adjoint Methods. Five pages that derive the adjoint method for linear systems and ODEs (lessons 03–04).
• Kidger, On Neural Differential Equations. A thesis that explains neural ODEs, adjoints and their numerics (lesson 03).
• Gneiting and Raftery, Strictly Proper Scoring Rules, Prediction, and Estimation. The standard reference for CRPS and proper scores (lessons 07 and 16).
• Li et al., Fourier Neural Operator for Parametric PDEs and Bonev et al., Spherical Fourier Neural Operators (lessons 08–09).
• Geiger and Smidt, e3nn: Euclidean Neural Networks. Irreps, tensor products and gates as implemented in e3nn (lesson 10).
• Wang, Sankaran and Perdikaris, Respecting Causality is All You Need for Training PINNs. Causal weighting (lesson 11).
• Yang Song, Generative Modeling by Estimating Gradients of the Data Distribution (blog) and Song et al., Score-Based Generative Modeling through SDEs (lesson 13).
• Lilian Weng, What are Diffusion Models?. A long blog post that connects DDPM, score matching and the SDE view (lesson 13).
• Chen and Lipman, Flow Matching on General Geometries. Riemannian flow matching (lesson 15).
• Lam et al., GraphCast and Rasp et al., WeatherBench 2. One model and one benchmark that every reader of lesson 16 should know.

Tools to explore after the notebooks: PySINDy, PyDMD, DA-tutorials (data assimilation in Python), POT (optimal transport), torch-harmonics (SHT and SFNO), e3nn, and WeatherBench 2.

Which lesson pairs with what #