Week 8 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.