Topic 10 · Modelling & Simulation (HL Option)

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.