Swap Week 12/13 content to match GP/PINNs unit swap: Wk12=PINNs (taught 30.06), Wk13=GPs (self-study)

Author: PhilippPelz

index.qmd

@@ -34,8 +34,8 @@ key-points:
   - ML for experimental materials data
   - Vision-based ML for microstructures
   - Time-series ML for processing
-  - Uncertainty-aware regression and optimization
   - Physics-informed and constrained ML
+  - Uncertainty-aware regression and optimization
 date: last-modified
 bibliography: references.bib
 number-sections: true
@@ -372,7 +372,7 @@ Construct a simple ML-based process map; compare constrained vs unconstrained mo
 
 ---
 
-### Unit IV — Characterization, Transformers, and Uncertainty (Weeks 10–12)
+### Unit IV — Characterization, Transformers, and Physics (Weeks 10–12)
 
 #### Week 10 – ML for characterization signals
 
@@ -418,41 +418,41 @@ Apply a small ViT / attention model to a characterization dataset (e.g. 4D-STEM
 
 ---
 
-#### Week 12 – Uncertainty-aware regression & Gaussian Processes
+#### Week 12 – Physics-informed and constrained ML
 
 *Lecture: Tuesday, 30.06.2026, 14:15-15:45 | Exercise: Thursday, 02.07.2026, 16:15-17:45*
 
-**Slides:** [Open](https://pelzlab.science/public_presentations/ml_for_characterization_and_processing/unit11_uncertainty_gp/12_uncertainty_gp.html)
+**Slides:** [Open](https://pelzlab.science/public_presentations/ml_for_characterization_and_processing/unit11_pinns/12_pinns.html)
 
-- Aleatoric vs epistemic uncertainty in experiments.
-- Gaussian Processes as uncertainty-aware surrogates.
-- Exploration vs exploitation in experimental design.
-- Connection to materials acceleration platforms.
+- Embedding physical constraints into ML models.
+- Penalty terms, soft constraints, hybrid approaches.
+- Failure modes of unconstrained models.
 
 **Exercise:**
-Compare GP regression and NN ensembles for a process-parameter problem.
+Train a constrained model for a processing or characterization task.
 
 ---
 
-### Unit V — Physics, Trust, and Synthesis (Weeks 13–14)
+### Unit V — Uncertainty, Trust, and Synthesis (Weeks 13–14)
 
-#### Week 13 – Physics-informed and constrained ML — *self-study (lecture cancelled)*
+#### Week 13 – Uncertainty-aware regression & Gaussian Processes — *self-study (lecture cancelled)*
 
 *Lecture cancelled (Tuesday, 07.07.2026) — delivered as required self-study. Exercise: Thursday, 09.07.2026, 16:15-17:45 takes place as scheduled.*
 
 ::: {.callout-warning}
 ## No lecture on 07.07.2026
-The Tuesday lecture does not take place. This unit — **physics-informed and constrained ML** — is **required self-study** from the slide deck below. It remains examinable and is the unit that delivers the "integrate physical constraints into ML workflows" learning outcome. The Thursday exercise runs as normal.
+The Tuesday lecture does not take place. This unit — **uncertainty-aware regression & Gaussian Processes** — is **required self-study** from the slide deck below. It remains examinable and is the unit that delivers the "quantify and propagate predictive uncertainty" learning outcome. The Thursday exercise runs as normal.
 :::
 
-**Slides (required self-study):** [Open](https://pelzlab.science/public_presentations/ml_for_characterization_and_processing/unit12_pinns/13_pinns.html)
+**Slides (required self-study):** [Open](https://pelzlab.science/public_presentations/ml_for_characterization_and_processing/unit12_uncertainty_gp/13_uncertainty_gp.html)
 
-- Embedding physical constraints into ML models.
-- Penalty terms, soft constraints, hybrid approaches.
-- Failure modes of unconstrained models.
+- Aleatoric vs epistemic uncertainty in experiments.
+- Gaussian Processes as uncertainty-aware surrogates.
+- Exploration vs exploitation in experimental design.
+- Connection to materials acceleration platforms.
 
 **Exercise:**
-Train a constrained model for a processing or characterization task.
+Compare GP regression and NN ensembles for a process-parameter problem.
 
 ---
 

week12_summary.md

@@ -1,47 +1,49 @@
-# Week 12 Summary: Uncertainty-aware regression & Gaussian Processes
+# Week 12 Summary: Physics-informed and constrained ML
 
 ## Cross-Book Summary
 
-### 1. Knowing what you don't know
-- **Aleatoric vs. Epistemic:** Inherent physical noise vs. model ignorance.
-- **Overconfidence Danger:** Point estimates fail safely in unknown regimes; uncertainty metrics are crucial.
+### 1. Physics-Informed Neural Networks (PINNs)
+- **Embedding Laws:** Enforce ODEs/PDEs via the loss function for physical consistency.
+- **Automatic Differentiation:** Exact derivative calculations enable NNs to evaluate physical equations.
+- **Boundary Conditions:** Methods like Lagaris substitution guarantee boundary compliance.
 
-### 2. Gaussian Processes (GPs)
-- **Distribution over Functions:** GP yields posterior mean and variance (uncertainty).
-- **Kernels as Physical Priors:** Encodes assumptions about data smoothness/scale.
-- **Non-Parametric Nature:** Scales with data size, ideal for small, high-quality materials datasets.
+### 2. Governing Equation Discovery
+- **Dictionary-Based Regression:** Build a dictionary of candidate math functions.
+- **Sparse Identification:** Use regularized regression (Lasso) to discover physical laws from noisy data.
+- **Dimensional Reasoning:** Unit analysis ensures physically plausible discoveries.
 
-### 3. GP-Based Process Maps
-- **Confidence Ribbons:** Visualize reliability to guide further experiments.
-- **Kriging:** Interpolates materials property surfaces using GP regression.
+### 3. Constraints in Materials Science
+- **Monotonicity:** Enforce required physical trends (e.g., hardness vs. alloying).
+- **Hybrid Modeling:** Combine physical "White-Box" models with data-driven "Black-Boxes" (Grey-Box).
 
 ## 90-Minute Lecture Strategy
 
-### Part 1: Uncertainty in Science
-- Risk management in materials processing.
-- Visualizing distributions and error bars.
+### Part 1: Why Physics Matters
+- Limits of unconstrained Black-Box models.
+- Accurate but Physical models.
+- PINNs need less data.
 
-### Part 2: GP Fundamentals
-- Function vs. Parameter space.
-- Kernels and "Similarity".
-- Conditional Gaussians and Variance.
+### Part 2: Automatic Differentiation
+- GradientTape mechanics.
+- Derivatives as ML architecture components.
 
-### Part 3: GP Case Studies
-- Predicting tensile strength across parameters.
-- GP for Experimental Design.
-- Multi-Task GPs.
+### Part 3: Solving Physics with NNs
+- PINN Architectures: Data Loss + Physics Loss.
+- Enforcing Boundary Conditions.
+- 3D printing heat transfer case study.
 
-### Part 4: Advanced Probabilistic ML
-- Mixture Density Networks (MDNs).
-- Dropout as Bayesian approximation.
+### Part 4: Equation Discovery
+- Sparse Regression and candidate dictionaries.
+- Damped pendulum equation case study.
+- Unit Analysis search pruning.
 
-### Part 5: Decision Making
-- Safe process windows via confidence intervals.
-- Building trustworthy models.
+### Part 5: The Grey-Box Future
+- Hybrid architectures vs. FEA.
+- Building industrial trust.
 
 ## Quarto Website Update (Summary)
 **Summary for ML-PC Week 12:**  
-- Introduces Probabilistic Machine Learning for uncertainty quantification.
-- Differentiates aleatoric (noise) from epistemic (ignorance) uncertainty.
-- Uses Gaussian Processes (GPs) for uncertainty-aware regression.
-- Applies confidence intervals to map robust process windows.
+- Combines neural networks with physical laws via Physics-Informed ML.
+- Introduces PINNs and automatic differentiation.
+- Details Governing Equation Discovery using sparse regression.
+- Applies physical constraints to build data-efficient Grey-Box models.

week13_summary.md

@@ -1,49 +1,47 @@
-# Week 13 Summary: Physics-informed and constrained ML
+# Week 13 Summary: Uncertainty-aware regression & Gaussian Processes
 
 ## Cross-Book Summary
 
-### 1. Physics-Informed Neural Networks (PINNs)
-- **Embedding Laws:** Enforce ODEs/PDEs via the loss function for physical consistency.
-- **Automatic Differentiation:** Exact derivative calculations enable NNs to evaluate physical equations.
-- **Boundary Conditions:** Methods like Lagaris substitution guarantee boundary compliance.
+### 1. Knowing what you don't know
+- **Aleatoric vs. Epistemic:** Inherent physical noise vs. model ignorance.
+- **Overconfidence Danger:** Point estimates fail safely in unknown regimes; uncertainty metrics are crucial.
 
-### 2. Governing Equation Discovery
-- **Dictionary-Based Regression:** Build a dictionary of candidate math functions.
-- **Sparse Identification:** Use regularized regression (Lasso) to discover physical laws from noisy data.
-- **Dimensional Reasoning:** Unit analysis ensures physically plausible discoveries.
+### 2. Gaussian Processes (GPs)
+- **Distribution over Functions:** GP yields posterior mean and variance (uncertainty).
+- **Kernels as Physical Priors:** Encodes assumptions about data smoothness/scale.
+- **Non-Parametric Nature:** Scales with data size, ideal for small, high-quality materials datasets.
 
-### 3. Constraints in Materials Science
-- **Monotonicity:** Enforce required physical trends (e.g., hardness vs. alloying).
-- **Hybrid Modeling:** Combine physical "White-Box" models with data-driven "Black-Boxes" (Grey-Box).
+### 3. GP-Based Process Maps
+- **Confidence Ribbons:** Visualize reliability to guide further experiments.
+- **Kriging:** Interpolates materials property surfaces using GP regression.
 
 ## 90-Minute Lecture Strategy
 
-### Part 1: Why Physics Matters
-- Limits of unconstrained Black-Box models.
-- Accurate but Physical models.
-- PINNs need less data.
+### Part 1: Uncertainty in Science
+- Risk management in materials processing.
+- Visualizing distributions and error bars.
 
-### Part 2: Automatic Differentiation
-- GradientTape mechanics.
-- Derivatives as ML architecture components.
+### Part 2: GP Fundamentals
+- Function vs. Parameter space.
+- Kernels and "Similarity".
+- Conditional Gaussians and Variance.
 
-### Part 3: Solving Physics with NNs
-- PINN Architectures: Data Loss + Physics Loss.
-- Enforcing Boundary Conditions.
-- 3D printing heat transfer case study.
+### Part 3: GP Case Studies
+- Predicting tensile strength across parameters.
+- GP for Experimental Design.
+- Multi-Task GPs.
 
-### Part 4: Equation Discovery
-- Sparse Regression and candidate dictionaries.
-- Damped pendulum equation case study.
-- Unit Analysis search pruning.
+### Part 4: Advanced Probabilistic ML
+- Mixture Density Networks (MDNs).
+- Dropout as Bayesian approximation.
 
-### Part 5: The Grey-Box Future
-- Hybrid architectures vs. FEA.
-- Building industrial trust.
+### Part 5: Decision Making
+- Safe process windows via confidence intervals.
+- Building trustworthy models.
 
 ## Quarto Website Update (Summary)
 **Summary for ML-PC Week 13:**  
-- Combines neural networks with physical laws via Physics-Informed ML.
-- Introduces PINNs and automatic differentiation.
-- Details Governing Equation Discovery using sparse regression.
-- Applies physical constraints to build data-efficient Grey-Box models.
+- Introduces Probabilistic Machine Learning for uncertainty quantification.
+- Differentiates aleatoric (noise) from epistemic (ignorance) uncertainty.
+- Uses Gaussian Processes (GPs) for uncertainty-aware regression.
+- Applies confidence intervals to map robust process windows.