Topic 10 · Modelling & Simulation (HL Option)

Reality too DANGEROUS · EXPENSIVE · SLOW · IMPOSSIBLE. Often multiple reasons combined.

All models are wrong; some are useful. The question is 'useful for THIS decision?'

What CHANGES over time. Position, velocity, infected count. The state of the system.

FIXED values you choose. Gravity g, bounce coef e, infection rate β. Tune the dynamics.

Equations or logic relating state at t to t+Δt. v_new = v + g·dt. The dynamics.

Simplifications you've MADE. Air drag = 0. Uniform population mixing. ALWAYS list them.

'Built it RIGHT?' — code matches spec. Tools: unit tests, code review.

'Built the RIGHT thing?' — model matches reality. Tools: hindcasting, held-out data, expert review.

Run model on a KNOWN case first (e.g. analytic answer). If it fails, don't trust complex predictions.

Use the SMALLEST model that answers your question. More parameters = more uncertainty + bugs + slowness.

Advance state by Δt with deterministic rules. For physics, ODEs, predictable dynamics. Satellite orbits, bouncing ball, reactions.

Smaller Δt = more accurate but slower. Too-large Δt can destabilise the simulation.

Random sampling × many runs → average. For stochastic systems or intractable integrals. Pricing, risk, π estimation.

Decreases as 1/√N. To halve error, quadruple samples. Expensive but parallelisable.

Many agents + simple LOCAL rules → global EMERGENCE. For social, traffic, ecology, crowd, spatial systems.

Real systems often combine all three: e.g. Monte Carlo over time-stepped agent-based pandemic runs.

How close predictions are to TRUTH. Measured on held-out data. Watch out for bias.

How CONSISTENT predictions are across runs. Low variance. ≠ accuracy! Precise + biased is dangerous.

Vary one input, plot output. Steep curve = FRAGILE (measure carefully). Flat curve = robust (ignore).

Where the model is reliable. State EXPLICITLY (e.g. '5-year forecast OK; 30-year exploratory only').

Predict the known past as validation. Climate / finance / pandemic models all use this.

Never report a point estimate alone. Always provide uncertainty range + assumptions + validity scope.