Empirical

In the context of scientific or mathematical models, "empirical" refers to an approach or formula based on observation, experimentation, or real world data rather than deriving it from theoretical principles or first principles.  Empirical models are developed by collecting and analyzing data to establish relationships between variables and make predictions or estimates.

Empirical models are often used when the underlying mechanisms or fundamental principles governing a system are not fully understood or are too complex to model directly.  They are based on empirical evidence and statistical analysis of data, allowing researchers to make predictions or draw conclusions based on observed patterns.

Empirical models are commonly used in various fields, including physics, chemistry, biology, social sciences, economics, and engineering.  They provide a practical and efficient way to model and understand complex systems, even when a complete theoretical understanding is lacking.  However, it's important to note that empirical models have limitations and may not always capture the underlying mechanisms accurately or generalize well to new scenarios.