Interpreting neural operators: how nonlinear waves propagate in non-reciprocal solids

TL;DR

This paper introduces a data-driven approach combining interpretable machine learning, hydrodynamic theories, and microscopic models to understand nonlinear wave propagation in non-reciprocal solids, exemplified by microfluidic experiments.

Contribution

It develops a novel pipeline integrating neural operators and symbolic regression to uncover and interpret the underlying nonlinear dynamical system from experimental data.

Findings

Non-reciprocal hydrodynamic interactions stabilize nonlinear waves

The method accurately models experimental nonlinear wave data

Microscopic droplet interactions explain wave propagation phenomena

Abstract

We present a data-driven pipeline for model building that combines interpretable machine learning, hydrodynamic theories, and microscopic models. The goal is to uncover the underlying processes governing nonlinear dynamics experiments. We exemplify our method with data from microfluidic experiments where crystals of streaming droplets support the propagation of nonlinear waves absent in passive crystals. By combining physics-inspired neural networks, known as neural operators, with symbolic regression tools, we generate the solution, as well as the mathematical form, of a nonlinear dynamical system that accurately models the experimental data. Finally, we interpret this continuum model from fundamental physics principles. Informed by machine learning, we coarse grain a microscopic model of interacting droplets and discover that non-reciprocal hydrodynamic interactions stabilise and promote nonlinear wave propagation.