Classical estimation baselines

Learning goals¶

• Set up simulation-based least squares for named parameters with bounds

• Use classical estimators as mandatory baselines before neural inverse methods

• Keep teaching estimands explicit: classical $(H, D)$

Reading¶

• Lab 3 — inertia and damping identification; system identification references Ljung, 1999Brunton & Kutz, 2022

Least squares against a simulator¶

Given measurements $y^{\mathrm{meas}}(t)$ and a simulator $y(t;\theta)$:

with explicit bounds $\Theta$ (e.g. positive $H$, non-negative $D$).

Teaching rule¶

Lab 3 compares simulation-based LS with inverse PINN on the same measurements, windows, and bounds. Do not silently swap in converter GFM $(M_v,D_v,m_p)$ unless the elective says so.

Worked example¶

Fix a load-step experiment. Plot a coarse grid of $\mathcal{L}(H,D)$ and mark the true $(H^\star,D^\star)$ and the LS minimizer.

Lab¶

• Lab 3 — Inertia and damping estimation

Further reading¶

• Lab 3; identifiability chapter next

• Gradient-based version of the same LS problem: differentiable simulation

• Maths background (external, link only): least squares in the EECS 245 notes Rampure, 2026 (CC BY-NC-ND 4.0)

Common misconceptions¶

• Skipping the classical baseline because “PINN is modern”

• Comparing LS and PINN on different noise seeds or windows

• Reporting percent error without stating the true $\theta$ and bounds