A Monograph Series
Four short, interactive monographs on the same deep question, how to reason about what a machine will not tell you directly. Each builds its methods from scratch, verifies the math, and runs live in the browser. Together they trace a single arc from assuming a model, to learning one, to generating from one.
The four pieces are not alternatives so much as complementary tools, sorted by how much they assume versus how much they learn, and by what they give you back. A rough guide:
What it means to teach a network the laws of physics, built up from a damped oscillator to a live PINN that trains in your browser.
read → 02The same idea put to work: a battery equivalent circuit, IGBT thermal behavior, and a PMSM under field-oriented control, each simulated and identified live.
read → 03How generation-by-denoising works, with real embedded models that synthesize fault signatures on demand, forecast a discharge curve, and flag anomalies.
read → 04The classical answer to hidden state: a predict-correct rhythm that, in four live demos, tracks signals, fuses sensors, estimates charge, and hedges across possibilities.
read →Each method, in the end, measures the same thing: the gap between what is expected and what is observed. The filter calls it the innovation, the residual between prediction and measurement. The PINN calls it the physics residual, how far a candidate solution strays from the governing equation. The diffusion model calls it the denoising error, how unlike the healthy data a signal looks. In every case that gap is both the signal used to correct the estimate and the alarm that announces a fault. Read in order, the series is a tour of four ways to compute it, and four ways to put it to work keeping a vehicle honest about its own health.