Worked Example Gallery¶
These examples demonstrate the 8-phase workflow: each turns a plain-language idea into an explicit mathematical model, states which perspectives were rejected and why, and closes with falsification criteria. Rows are grouped by primary lens, following the 15 perspective lenses. Most examples also compose secondary lenses.
How to read the numbers¶
Parameter values in these files are illustrative. Each range carries a source class (lit. /
data / est.) so you know how much weight it deserves, but the repository cites no external
source for any of them. Read these as material for learning the workflow, not as
literature-backed models. The one place where numbers are machine-checked is
benchmark results,
which carries its own reproduction command and its own limits.
Full worked examples¶
| Example | Primary lens(es) | Domain | One-line takeaway |
|---|---|---|---|
| Epidemic Spread | Deterministic (+ stochastic check) | Epidemiology | An SIR model exposes an R₀ threshold: whether an outbreak explodes or dies out is decided before any stochastic detail matters. |
| App Adoption Growth | Deterministic (Bass diffusion archetype-first) | Product growth | A single well-chosen archetype, calibrated and gated by BIC, answers ceiling and stall-timing questions. |
| Lake Algae Bloom Tipping Point | Deterministic (+ stochastic validation) | Limnology / ecology | A Monod-coupled algae–zooplankton system has two stable states, so a modest cut in nutrient loading does not clear the bloom. |
| Batch Reactor Scale-Up | Deterministic (+ spatial/transport, thermodynamic, control) | Chemical reaction engineering | Intrinsic selectivity falls with temperature, but internal pellet diffusion can mask the true rate behind the observed one. |
| Damped Pendulum Clock | Deterministic (+ stochastic, thermodynamic, control) | Mechanics | Amplitude, thermal expansion and drag each cost a fraction of a second per day, and the dominant term is the one you can fix. |
| Medical Test Bayes | Bayesian inference (+ CLT validation, decision theory, information) | Diagnostics | A 99%-accurate test on a rare disease produces mostly false positives; only an independent second positive moves the posterior. |
| Drone Hover in Wind | Control (+ stochastic, optimization, SPC) | Control engineering | Feasibility, via thrust margin, decides whether altitude is holdable at all; PID and LQR tuning only matters afterwards. |
| Retail Inventory Under Uncertain Demand | Stochastic (+ optimization, control) | Retail operations | Demand randomness turns a restocking question into an (s,Q) policy built from newsvendor logic plus safety stock. |
| Insurance Ruin Risk | Stochastic | Insurance / risk | For rare-event solvency questions, deterministic averages are useless; ruin probability is a tail property only a stochastic model can price. |
Other lenses¶
| Example | Primary lens(es) | Domain | One-line takeaway |
|---|---|---|---|
| Coffee Shop Staffing | Optimization (+ queueing) | Service operations | An Erlang-C wait cliff embedded in an ILP shows lenses composing: queueing computes the wait, optimization schedules the staff. |
| Two Cafés Pricing War | Game theory | Economics / competition | A price cut looks profitable while rivals are frozen; game theory reveals the rival-response term single-actor optimization cannot see. |
| Rumor Spread in a School | Network | Social dynamics | Contact structure, not just counts, decides how far a rumor travels and whether a public announcement stops it. |
| Greenhouse Night Temperature | Control | Agriculture / building systems | Holding temperature above a setpoint against disturbances is a feedback problem, not a prediction problem. |
| Marketing Attribution | Causal inference | Digital marketing | Users who see retargeting ads buying 3x more is selection, not effect; backdoor adjustment comes before spending decisions. |
| Sensor Placement | Information theory | Data center monitoring | When you cannot measure everything, mutual information tells you which few sensor locations carry the most signal. |
| Delivery Fleet Preventive Maintenance | Reliability | Logistics | Fixed-schedule versus run-to-failure becomes decidable once failure timing is a hazard distribution and costs are renewal-reward. |
Condensed skeletons¶
Two files are 20-line phase outlines rather than full worked examples. They show the report structure, not a validated model; read them after a full-length example.
| Example | Primary lens(es) | Domain | One-line takeaway |
|---|---|---|---|
| Climate-Energy Decarbonization Mix | Optimization (+ deterministic, stochastic) | Energy systems | Condensed skeleton: capacity choice is an optimization problem checked against an energy-balance model, with Monte Carlo wind for reliability. |
| Finance Portfolio Allocation | Optimization (+ stochastic, game theory) | Finance | Condensed skeleton: mean-variance allocation with shrinkage, stress-tested by Monte Carlo and compared against a benchmark. |
The 18 .md reports listed here, plus the runnable quickstart_sir.py, are the 19 files in
/examples.
Domain bundles that say which lenses matter per field are in
packs/domain-packs.md.