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Week 9 Summary: Inverse problems and process maps

Cross-Book Summary

1. Forward vs. Inverse Problems

Causality Gap: Forward problems are unique; inverse are ill-posed/multi-valued.
Non-Gaussianity: Inverse problems require Mixture Density Networks due to multimodality.

2. Physics-Informed Enrichment

Expert in the Loop: Add physical transformations (e.g., FFT) to reduce training effort.
Enrichment: Combine raw data with physics features (PINNs).

3. Process Maps and Corridors

Process Corridors: Identifying stable parameter regions.
ML-Guided Mapping: Interpolating sparse experimental points via surrogates.
Prescriptive ML: Answering "What must I do?" instead of "What will happen?".

90-Minute Lecture Strategy

Part 1: Material Scientist's Dilemma

Inverse problem complexities.
Many-to-one mappings.
Uniqueness in systems.

Part 2: Physics-Informed ML

White vs. Grey vs. Black Box.
Feature Enrichment.
Loss function constraints.

Part 3: Solving the Inverse

Regression failure on inverse tasks.
Regularization and Mixture Models.
Heat treatment parameter case study.

Part 4: Building Process Maps

Continuous maps from points.
Visualizing Safe Corridors.
Laser-material interactions mapping.

Part 5: ML for Material Design

Prescribing processing routes.
Simulation-aided training.
AI vs. human intuition.

Quarto Website Update (Summary)

Summary for ML-PC Week 9:

Explores Inverse Problems for materials design.
Contrasts multi-valued inverse tasks with causal forward problems.
Introduces Physics-Informed Learning and feature enrichment.
Demonstrates building Process Maps and Safe Corridors.