MFML Lecture

Week	MFML Lecture Focus	MFML Exercise (Python, 90 min)	Pedagogical Purpose
1	Learning vs data analysis; loss functions	NumPy refresher: vectors, dot products, simple loss functions (MSE)	Shift mindset from “data analysis” to “learning”
2	Linear algebra refresher; PCA/SVD (R)	PCA refresher on known dataset; visualize variance directions	Align notation & geometry, no novelty overload
3	Regression as loss minimization	Linear regression from scratch via loss minimization	Bridge known regression → learning viewpoint
4	Neural networks: neuron & activations	Single-neuron model: forward pass + activation functions	First NN contact, zero frameworks
5	Backpropagation & gradients	Manual backprop for 1–2 layer network	Demystify training mechanics early
6	Loss landscapes & optimization behavior	Gradient descent experiments: learning rate, conditioning	Understand why training fails or succeeds
7	Generalization, bias–variance	Overfitting demo: polynomial vs NN models	Make generalization tangible
8	Probabilistic view of learning	Noise injection; likelihood vs MSE comparison	Connect probability to physical data
9	Representation learning	Feature learning vs hand-crafted features (simple NN)	Prepare Materials Genomics concepts
10	Latent spaces & autoencoders	Autoencoder with framework (PyTorch/Keras)	First latent-space construction
11	Unsupervised objectives revisited	Clustering vs autoencoder embeddings	Reframe known clustering methods
12	Uncertainty in predictions	Predictive uncertainty via ensembles / dropout	Teach model trust, not accuracy
13	Physics-informed learning	Simple constrained NN (penalty-based)	Bridge MFML → ML-PC PINNs
14	Explainability & limits	Sensitivity analysis & failure case	Scientific responsibility closure