Title: Mastering Chaos with Physics Savvy Neural Networks

Abstract:
Newton wrote, “My brain never hurt more than in my studies of the Moon [and Earth and Sun]”, the first hint that the seemingly simple three-body problem was intrinsically intractable. Nonetheless, Hamilton remarkably re-imagined Newton’s laws as an incompressible energy-conserving flow in a phase space of positions and momenta. Today, neural networks at the core of efforts to create artificial intelligence also struggle with nonlinear dynamics, where exponentially diverging trajectories bounded by finite energy repeatedly stretch and fold into complicated self-similar fractals, where ordered and chaotic orbits coexist at the same energy for different initial positions and momenta. Despite deterministic, chaotic systems are practically unpredictable, and therefore creative, making chaos a nonlinear “superpower”, which artificial intelligence should embrace. Indeed, the Nonlinear Artificial Intelligence Lab recently discovered that a new generation of physics-informed neural networks, elegantly constrained by the Hamiltonian phase space flow, can be trained to correctly predict the dynamics of nonlinear systems even as they transition from order to chaos. Examples include the motion of stars, quantum wave packets, and billiards balls. Introspection opens the neural network “black box” to elucidate how Hamiltonian neural networks learn. Physics thereby enhances neural networks, and physics savvy neural networks in turn will help scientists solve hard problems.