Types of mathematical models

Simulation models mimic a system computationally (weather prediction, traffic flow, manufacturing). Deterministic models have no randomness — the same input always gives the same output (Newton's laws, engineering, fluid dynamics). Stochastic models build in randomness and uncertainty (economics, social sciences, machine learning).

Dynamic models describe how a system evolves over time with differential or difference equations (climate, control systems, population dynamics). Optimisation models look for the best solution under constraints (operations research, supply chains, machine learning). Empirical models are based on observed data rather than theory (environmental science, market analysis).

Game-theoretic models analyse rational agents and their payoffs. Discrete models study systems with separate states (graphs, networks, logistics), continuous models study smooth change (thermodynamics, fluid mechanics), and hybrid models combine approaches (smart grids, cyber-physical systems). Statistical models use data and probability distributions to make inferences — the family most of machine learning belongs to.