Lab 3 — Inertia and damping estimation

Goals¶

Compare simulation-based least squares with an inverse PINN (or collocation residual estimator) on the same measurements and bounds. Vary noise, window length, and excitation. Plot a two-parameter loss surface or local sensitivity diagnostic. Test fitted $(H,D)$ on another disturbance.

Teaching estimands¶

Classical SMIB inertia and damping $(H, D)$. Do not silently substitute research GFM converter knobs.

Prerequisites¶

• Lab 1 completed

• Chapters: classical estimation, identifiability, inverse PINN, physical vs equivalent

Materials¶

• Starter notebook: lab03_inertia_damping_id.ipynb · Running notebooks

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• Simulator: sciml_ps.simulate_smib (same classical SMIB as Lab 1)

• Optional differentiable rollout: sciml_ps.smib_torch.rollout_smib (needs torch; install with pip install -e ".[torch]" locally)

Local (canonical): conda activate sciml_ps → pip install -e . → open the notebook. Binder/Colab need the public GitHub repo.

Protocol¶

1. Generate a “truth” trajectory with known $(H^\star, D^\star)$ and additive noise on $\omega$

2. Grid or optimize LS loss vs $(H,D)$ with documented bounds

3. Train inverse PINN / residual estimator with the same data contract

   • Optional: fit $(H,D)$ by differentiable simulation (gradient through an RK4 rollout) and add it to the table

4. Plot $\mathcal{L}(H,D)$ or slices; discuss physical vs equivalent

5. Freeze $\hat{\theta}$ and simulate a held-out clearing time; compare to truth

Deliverables¶

• Loss-surface figure

• Table: true $\theta$, LS $\hat{\theta}$, PINN $\hat{\theta}$, held-out trajectory error

• Short paragraph: which parameter was weakly informed, and why

Status¶

Executable notebook provided for the LS + loss-surface path and the optional differentiable-simulation fit; inverse PINN cell is a structured template to complete in class or homework.