Physics, not simulation. Or why physics-informed neural networks, such...
Physics, not simulation. Or why physics-informed neural networks, such as ONN's, do not work well on digital GPU's.
The success of current machine learning models are determined almost entirely by the training objective and scale, not by the dynamics engine. Chasing parity with alternative architectures - like oscillatory neural networks - at any scale is a category error. But the bigger picture is important: Nature doesn't backprop through a Kuramoto model on an A100 — it is the oscillators. A coupled-oscillator network settling to phase-lock is solving an optimization by physically rolling downhill, in continuous time, at the speed of the substrate, burning near-zero energy. That's the entire pitch of analog/neuromorphic oscillator hardware: Ising machines, coupled spin-torque or ring oscillators solving combinatorial problems, phase-based associative memory in silicon. The win is femtojoules and nanoseconds. When you run the same dynamics on a GPU you pay full digital cost and keep none of the physical advantage - you're paying to emulate the thing whose only edge was not needing to be emulated.
