Wannier function representation for wave-based neural networks

Elastic systems present very low power dissipation and high nonlinearity. Therefore, they are a promising candidate for low-power internet of things devices. As an example of this potential, we recently demonstrated an elastic neural network that passively distinguishes between spoken commands, without requiring power or batteries. To translate this promise into actual devices, a challenge must be overcame: Designing elastic neural networks is computationally very hard due to the need for large-scale nonlinear simulations. Even model reduction techniques based on eigenmodes struggle in the nonlinear case because the nonlinear interactions between modes grow quadratically with the problem size. In this talk, we will present a model reduction technique based on a quadratic manifold extension of the notion of Wannier functions, that exploits localization to implement linear-time simulation of nonlinear elastic neural networks. We apply our method to phononic computing, the approach works in other wave-based information systems (photonics, microwave, etc.)