| 1 |
Data as vectors, models, feature spaces |
What counts as data in processing & characterization |
What counts as data in materials databases |
NumPy arrays, vector operations, plotting simple datasets |
| 2 |
Data types, scales, normalization, units |
Sensors, signals, images as arrays |
Descriptors, compositions, metadata |
Scaling & normalization effects; visual comparison |
| 3 |
Probability, expectation, variance, noise |
Measurement noise in experiments |
Noise & uncertainty in databases |
Monte Carlo sampling, simulate noisy measurements |
| 4 |
Sampling, Nyquist, FFT as representation change |
Signal preprocessing (spectra, time series) |
Property distributions & statistics |
FFT on synthetic signals; filtering |
| 5 |
Linear regression, least squares (geometry) |
Regression for process/property modeling |
Correlation analysis in materials data |
Implement linear regression from scratch |
| 6 |
SVD & PCA (eigenvectors, variance) |
PCA on spectra & micrographs |
PCA & embeddings for materials spaces |
PCA on high-dimensional dataset, visualize components |
| 7 |
Loss functions, gradients, sensitivity |
Model tuning & objective functions |
Descriptor relevance & feature selection |
Manual gradient descent on toy problems |
| 8 |
Optimization, regularization (L1/L2) |
Model robustness & stability |
High-dimensional regression challenges |
Compare regularization strengths |
| 9 |
Neurons, activations, backpropagation |
NN regression/classification for properties |
NN for structure–property mapping |
Tiny neural net: forward + backward pass |
| 10 |
Capacity, overfitting, generalization |
CNNs for images (conceptual math only) |
Representation learning (conceptual) |
Framework NN (PyTorch/Keras), overfitting demo |
| 11 |
Autoencoders & latent variables |
Anomaly detection in processes |
Latent materials spaces & clustering |
Train autoencoder, visualize latent space |
| 12 |
Unsupervised learning & uncertainty intro |
Drift & anomaly detection |
Discovery in latent space |
Clustering + uncertainty estimation |
| 13 |
Physics-informed ML, explainability |
Physics-informed constraints in ML |
Trust, interpretability, causality |
Sensitivity analysis, simple PINN demo |
| 14 |
Integration, limits, outlook |
Integrated case studies |
Discovery limits & ethics |
Mini end-to-end project / synthesis |