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Week 4 Summary: From classical microstructure metrics to learned representations
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Week 4 Summary: From classical microstructure metrics to learned representations

Cross-Book Summary

1. Classical Microstructure Metrics (Sandfeld, Domain Knowledge)

  • Stereology: The traditional method of quantifying 3D structure from 2D sections (e.g., grain size, phase fractions).
  • Hand-crafted Descriptors: Features like aspect ratio, tortuosity, and circularity. These are physically interpretable but biased by human intuition.
  • The Information Bottleneck: By reducing a complex micrograph to a few scalar metrics (like “average grain size”), we may discard the very information responsible for rare failure events or subtle property changes.

2. The Foundation of Learned Representations (Neuer Ch 4.5, McClarren Ch 8, Bishop Ch 5)

  • The Artificial Neuron: A mathematical unit that performs a weighted sum of inputs ($ = w_i x_i + b $) followed by a non-linear activation function.
  • Activation Functions: ReLU, Sigmoid, and Tanh introduce the non-linearity required to approximate complex structure-property mappings. ReLU is the current standard for deep learning (Sandfeld Ch 18).
  • Universal Approximation: A network with even one hidden layer can approximate any continuous function, allowing it to “learn” a representation of the data that is optimal for a given task.
  • MLP Topology: Multi-Layer Perceptrons stack these neurons to create increasingly abstract representations of the input data.

90-Minute Lecture Strategy (50 Slides)

Part 1: The Classical Approach (Slides 1-15)

  • How we currently describe materials: Grain size, phase fractions, orientation maps.
  • Quantitative Metallography: Methods and standards.
  • Successes and failures of hand-crafted features.

Part 2: Feature Engineering vs. Feature Learning (Slides 16-25)

  • The concept of a “Representation.”
  • Why “expert” features might be incomplete.
  • The shift from “calculating metrics” to “learning embeddings.”

Part 3: The Building Blocks of ML (Slides 26-40)

  • The Mathematical Neuron (Neuer Ch 4.5.1).
  • Weights and Biases: The “knobs” of the model.
  • Activation Functions: Why we need non-linearity (ReLU, Sigmoid).
  • Forward propagation: From input data to prediction.

Part 4: Multi-Layer Perceptrons (MLP) (Slides 41-45)

  • Stacking layers to build abstraction.
  • The concept of “Hidden” layers.
  • Neural networks as universal function approximators.

Part 5: Outlook: Learning from Microstructures (Slides 46-50)

  • Preview of Week 5: Moving from vectors to images (CNNs).
  • Discussion: Can we trust a “Learned” metric more than an ASTM grain size?

Quarto Website Update (Summary)

Summary for ML-PC Week 4:
This unit marks the transition from classical, hand-crafted microstructure quantification (like grain size and phase fractions) to the modern paradigm of learned representations. We first review traditional stereological metrics and their limitations in capturing complex structural nuances. We then introduce the foundational unit of modern ML: the artificial neuron. By understanding weights, biases, and non-linear activation functions, we build the framework for Multi-Layer Perceptrons (MLPs) that can automatically learn optimal features from materials data.