Models and Simulation - Types of Models

Types of Models:
Three major model types are deterministic model, discrete-event model and stochastic model.

• Deterministic Models: No random variable;
• Lumped Parameter Models: ODE, all spatial distributions are lumped into one variable;
• Distributed Parameter Models: PDE, consisting of spatial derivatives;
• Steady-State/Static Models: No temporal derivative;
• Unsteady-State/Dynamic Models: With temporal derivatives;
• Stochastic Models: Random variables involved (probability distribution function/pseudo-random numbers)
• Population Balanced Models: In multiphase system, discrete/dispersed phases are present as particles, droplets or bubbles. Similar to the "birth and death" of individuals, the particles can agglomerate or break and the bubbles and droplets can break and coalesce. Thus, the number of identities of discrete phases, called population, and the size of the individuals change and form a particle/droplet/bubble-size distribution.
• Agent-Based Models: Each part of the model , called an agent, is capable of making decisions with strong human behavior involved;
• Discrete-Event Models: The states, even time, are considered discrete and NON-continuous;
• Artificial Neural Network-based Models: A black-box approach to correlate various parameters and then predict outcomes from information available. No exact relation between the inputs and outputs is almost possible to establish. No contribution to the understanding of the phenomena.
• Fuzzy Models: based on fuzzy mathematics or fuzzy logic involving fuzzy variables. Fuzzy, not well quantified, such as small, large, very large.

-- The general-purpose language/software can handle various types of models/problems, but require coding of the model equations using the syntax and semantics of the software. While, more dedicated software generates an appropriate set of models of equations for the users to use, but the scope is limited.

-- Stochastic Models:

The random numbers are characterized by their moment. The first moment is known as "average" or "expectation". A model may consider only average properties, thus avoiding the complexity of the process due to the randomness of the properties. Many models consider random behavior of the parameters, although the outputs of the model are average properties. These models also are probabilistic in nature. Various moments of the random variables may be determined analytically (Coulomb's Law?) or by Monte Carlo simulation. The random variables follow a probability distribution function. The choice of the distribution is determined from the assumption involved.

References:

Verma, Ashok Kumar. 2014. Process Modelling and Simulation in Chemical, Biochemical and Environmental Engineering. CRC Press.