This text corresponds to the slides of the Module 1 of the Simulation-based inference workshop held in 2021. Head on to the workshop page for the rest of the content.

🄯 Álvaro Tejero-Cantero for all the text, licensed under a CC-BY-SA license.

ℹ️ Practical parts are indicated in red background. Speaker's notes are under ▸ §.

• Module's learning goals

## Simulators for science

### Models in science

• making models is part of the scientific method
• models capture only some aspects of reality
• when formalized, they enable quantitative, testable hypotheses
• model functionalities
• prediction — to support decisions
• understanding — to select interventions
• the structure that doesn't change is the model
• the malleable part are parameters
• parameters are 'tuned' based on observations
• multiple input parameter sets can lead to the same output prediction
• equifinality, degeneracy are key to resilience, homeostasis of complex systems

### Simple pendulum

$$\frac{{\rm d}^2 \theta}{{\rm d} t^2} + \frac{g}{\ell}\, \sin\theta = 0$$

• Can predict angles $\theta(t)$ given $g/\ell$ and $\theta(0)$.
• Can infer $g/\ell$ from measured $\theta(t)$.
• for small amplitudes $\sin\theta\simeq\theta$ and timing one oscillation $T=2\pi \sqrt{\ell/g}$ approximately suffices to infer $g/\ell$ → $T$ summarises $\theta(t)$ for inference.
• And extract understading wrt. interventions and counterfactuals.
• §