A neural network is an advanced kind of artificial intelligence mimicking the neurons found in our brains. The strength of connections between neurons affect the strength of the impulse conducted and these connections can be altered by different factors. In a similar fashion, artificial neurons attribute biases and numeric values to certain connections during the training phase.
One drawback of these neural-network systems is that they don't respond well to chaos, this is also referred to as chaos blindness. They cannot predict and cannot adapt in the presence of chaos.
Wrecking ball analogy
Imagine a wrecking ball swinging about. It has both kinetic and potential energy at play. If we take a picture of it mid-swing, we cannot tell for sure where the wrecking ball is headed or at what speed. This is how conventional neural-networks analyze data. If we implement Hamiltonian mechanics into neural-networks' understanding, it can analyze the movement of the ball entirely, meaning it can look at where it was at what time and can determine where it will be headed next.
As John Lindner puts it: “The Hamiltonian is really the ‘special sauce’ that gives neural networks the ability to learn order and chaos.” With this implementation, we can get neural-networks to tackle harder problems and utilize them in novel areas to aid us.