Scientific modelling

Scientific modelling is a fundamental activity used to represent empirical objects, phenomena, and physical processes. These models act as simulacra, which are simplified reflections of reality. While they are only approximations, they are extremely useful for making the world easier to understand, define, quantify, or visualize.

Scientists use models to simulate how systems might behave under different conditions. This process is considered one of the three pillars of scientific method, alongside theory building and experimentation. By creating these representations, researchers can gain intuition about complex entities that might otherwise be impossible to study directly.

The process of generating a model begins with a specific task or question. To build it, scientists must use two main techniques: simplification and abstraction. Simplification involves leaving out observed entities and relations that are not important for the specific task at hand. Abstraction involves aggregating information that is important but does not need to be shown in extreme detail.

These choices are shaped by physical, legal, and cognitive constraints. A scientist's perception of reality is itself a model, which is often expressed as a conceptual model. To execute this, the model may be implemented as a computer simulation, which requires making further choices like using numerical approximations.

Different types of models serve different scientific purposes. Conceptual models help researchers better understand a subject through ideas and relations. Mathematical models are used to quantify specific features of a system. Computational models allow for the simulation of complex processes, often referred to as being "in silico" when run on computers.

Other models are "in vivo," meaning they use living models like laboratory rats. There are also "in vitro" models, which are conducted in glassware, such as tissue cultures. Finally, graphical models are used to visualize a subject through images or diagrams.

Systems within these models can be categorized by how they change over time. Discrete models feature variables that change instantaneously at separate points in time. In contrast, continuous models involve state variables that change continuously with respect to time.

A simulation is the method used to implement a model, often when the subject is too complex for a direct analytical solution. A steady-state simulation provides data about a system at a specific instant, usually at equilibrium. A dynamic simulation provides information about how a system behaves and changes over a period of time.

History shows that the study of modelling has long been central to science and philosophy. In 1961, Leo Apostel published work on the formal study of models. John von Neumann also contributed significant ideas regarding methods in the physical sciences. Philosophers such as Nancy Cartwright and Ian Hacking have explored how models represent and intervene in the world.

More recently, scholars like Roman Frigg and Stephan Hartmann have noted that philosophers are paying increasing attention to the various roles models play in scientific practice. This growing interest has led to a larger collection of specialized methods and meta-theories.

Evaluating whether a model is successful is a critical part of the scientific enterprise. A model is evaluated primarily by its consistency with empirical data. Any model that is inconsistent with reproducible observations must be modified or rejected.

Beyond data, scientists look at a model's ability to explain past observations and predict future ones. They also consider the cost of use, the degree of refutability, and the simplicity or aesthetic appeal of the model. Even if a model is not perfectly true, scientists often debate which model is better for a specific task, such as seasonal weather forecasting.

One significant application of these methods is in climate science. Climate models apply knowledge from various sciences to process massive sets of input data. They execute differential equations among grid elements within a three-dimensional model of Earth's climate system.

These models can produce simulated climates that include elements like heatwaves and storms. By describing the intensity and frequency of these events, models support adaptation to projected climate change. They also enable extreme event attribution, which helps explain specific weather events through scientific simulation.