49 lines (38 loc) · 1.91 KB

Week 13 Summary: Physics-informed and constrained ML

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.

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. 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: Why Physics Matters

Limits of unconstrained Black-Box models.
Accurate but Physical models.
PINNs need less data.

Part 2: Automatic Differentiation

GradientTape mechanics.
Derivatives as ML architecture components.

Part 3: Solving Physics with NNs

PINN Architectures: Data Loss + Physics Loss.
Enforcing Boundary Conditions.
3D printing heat transfer case study.

Part 4: Equation Discovery

Sparse Regression and candidate dictionaries.
Damped pendulum equation case study.
Unit Analysis search pruning.

Part 5: The Grey-Box Future

Hybrid architectures vs. FEA.
Building industrial trust.

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.