Physical embeddings for AI with the nonlinear Schrödinger equation
Bahram Jalali, Yiming Zhou, Tingyi Zhou, Callen MacPhee · 2025
We introduce the Nonlinear Schrödinger Computing paradigm to address the speed limitations of AI algorithms in ultrafast optical sensing and metrology. This paradigm has two implementations: the Nonlinear Schrödinger Kernel (NSK), and the Nonlinear Schrödinger Network (NSN). NSK is a physical hardware accelerator using femtosecond pulses for data acquisition and computing, leveraging the Nonlinear Schrödinger Equation (NLSE) as an analog computer to enhance data classification accuracy analogous to the kernel method in machine learning. While optimizable via phase encoding, NSK faces limitations due to its rigid physical properties which does not lend itself to easy adaptation and training. To overcome these limitations, our second implementation, the Nonlinear Schrödinger Network (NSN), operates in the numerical domain. NSN is a general-purpose trainable model for learning complex memory and nonlinear behavior in data. Inspired by the NSK, NSN offers a more interpretable and parameter-efficient alternative to traditional black-box neural networks. It achieves comparable or superior accuracy in time series classification tasks with significantly fewer parameters.