Identification pillar overview - Scientific Machine Learning (SciML) for Power Systems (PS)

Engineering question: Which parameters and dynamic relationships explain the measurements?

Focus¶

Identifiability, measurement contracts, excitation, and classical vs physics-informed estimators. Teaching Lab 3 uses classical inertia and damping $(H, D)$ . Converter-parameter electives (GFM/GFL reduced-order knobs) stay optional and must name estimands explicitly.

Learning path¶

Foundations: classical estimation, identifiability, inverse PINN
Measurements and excitation
Physical vs equivalent parameters
Differentiable simulation — gradients through the solver
Lab 3 — Inertia and damping

Honesty rule¶

Low trajectory error does not certify physical parameter recovery. Report bounds, excitation, and a held-out disturbance test.

Discussion: what Identification methods can and cannot claim¶

Can claim (with evidence)	Cannot claim
Recovery of a known $\theta$ in a synthetic test with stated noise and excitation	Recovery on real data without a model-map argument
Held-out disturbance error with frozen $\hat{\theta}$	That $\hat{\theta}$ is a physical constant when the model is mismatched (it may be equivalent)
Which parameter the data inform weakly (loss surface, sensitivity)	That a faster or gradient-based estimator removes weak identifiability

Rule: least squares, differentiable simulation, and inverse PINN are compared on the same data contract, and every estimate is re-simulated with the reference solver.