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

2024/04/19 by Jonathan Colen, Alexis Poncet, Colen, Jonathan +5
Engineering · #Elasticity and Wave Propagation #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Soft Condensed Matter (cond-mat.soft)

paper · pdf · doi:10.48550/arxiv.2404.12918

openalex publication_date 2024/04/19 · openalex created_date 2024/04/23 · openalex updated_date 2026/07/28

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.

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