Teaching Physics to Neural Networks Enables Predictable Chaos?

Today, we use neural networks, sets of algorithms that have been modeled loosely on the human brain, in many systems applicable worldwide, such as language identification, readability assessments; Grammarly, speech and character recognition, as well as spell checking. The most recent neural networks are able to outperform humans in a variety of tasks, be it complex calculus or a game of Chess. But these super-intelligent artificial neural networks lack the ability to understand chaotic events associated with non-linear dynamics, where fluctuations are aperiodic and are currently impossible to predict indefinitely far into the future; they could not explain irregularities in nature such as clouds, mountains and coastlines.

Researchers at North Carolina State University have discovered that teaching these neural networks Hamiltonian structure allows those networks to more comprehensively digest the mix of order and chaos that shapes our world. They then exposed neural networks, one having been taught Hamiltonian structure, to a known model of stellar and molecular dynamics. The Hamiltonian neural network accurately predicted the dynamics of the system, even as it moved between order and chaos. On a Lyapunov spectrum, an example of one pictured below,

 

Image credits: Researchgate.net available via license: Creative Commons Attribution 3.0 Unported

 

The researchers taught both an untouched neural network and a Hamiltonian neural network trajectories starting in the triangular basin that enables bounded motion. They found that the regular neural network had a large deviation from a true trajectory whereas a Hamiltonian-learnt neural network followed the true patterns closely, therefore one could say that a Hamiltonian neural network is orders of magnitude more accurate when it comes to explaining natural phenomena related to physics. Another example of where Hamiltonian neural networks outperformed regular neural networks is in the predicted and experimented flows of billiard balls’ chaotic changes in momentum around a circular table. Yet again, the Hamiltonian neural networks’ result seemed almost identical to the true path, indicating that it will be extremely accurate in our potential future uses of these networks.

What does this mean for the future? They are also investigating potential applications of these neural networks such as within autonomous drones, where they would need to account for violent changes in wind velocity and atmospheric pressure. These drones would use physics to determine how to navigate and manoeuvre through turbulent air and also during landings. We can further improve these neural networks by incorporating other symmetries, or mathematical systems, in conjunction with “deep learning”, as these Hamiltonian networks are primarily “feed forward” networks, wherein the connections between nodes do not form a cycle, leading to increased training times, and potentially they will be able to understand the order and chaos that rules our existence today.

Thumbnail credits: phys.org