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---
title: Background
order: 0
---

System modeling can be categorized into three broad categories:

## White-box models

In white-box systems, the internal dynamics are evident. The system can be understood in terms of inputs, outputs, and exact internal dynamics. A white-box model assumes perfect knowledge of the system.

## Grey-box models

Grey-box models add some obfuscation to the system dynamics. While the structure or mathematical form of the dynamics may be known, the exact parameter values are not fullt evident. Grey-box models are constrained by the *apriori* knowledge of the system and estimate parameters within those bounds.

An example could be a simple RC circuit with unknown capacitance and resistance. The equations governing the current through the components are known. A physical model can be constructed based off of those equations. The model, in combination with actual measurements from the circuit then estimates the values of parameters in the equations such that the difference between the model's predictions and the actual readings is minimized.

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### State-space equations as grey-boxes

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## Black-box models

A Black-box model foregoes any *apriori* knowledge about the distribution of system parameters. Instead it learns the mechanics from scratch. A neural network used to approximate an RC circuit is a black-box model. The network simply learns the mappings from the inputs to the outputs.

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### LSTM networks as black-boxes

Long short-term memory networks are a variant of recurrent neural networks. They are *stateful* models. An LSTM network is able to memorize earlier states such that it affects later states. This is important when modelling dynamic systems wherre the future states of the system depend on the rate of change of states or other higher order phenomenon.
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### Further reading:

* [System Identification][1]
* [Grey box model][2]

[1]: https://en.wikipedia.org/wiki/System_identification
[2]: https://en.wikipedia.org/wiki/Grey_box_model