Interpreting Neural Operators: How Nonlinear Waves Propagate in Nonreciprocal Solids

Area of Science:

• Physics
• Fluid Dynamics
• Machine Learning

Background:

• Nonlinear dynamics experiments often involve complex systems that are difficult to model using traditional methods.
• Understanding the fundamental principles governing these dynamics is crucial for scientific advancement.

Purpose of the Study:

• To present a novel data-driven pipeline for building interpretable models of nonlinear dynamics.
• To uncover the underlying physical processes responsible for observed phenomena in microfluidic experiments.

Main Methods:

• Combining interpretable machine learning (physics-inspired neural networks/neural operators) with symbolic regression.
• Utilizing hydrodynamic theories and microscopic models.
• Applying the pipeline to data from microfluidic experiments with streaming droplet crystals.

Main Results:

• Successfully inferred the solution and mathematical form of a nonlinear dynamical system accurately modeling experimental data.
• Interpreted the resulting continuum model from fundamental physics principles.
• Discovered that nonreciprocal hydrodynamic interactions stabilize and promote nonlinear wave propagation in droplet crystals.

Conclusions:

• The data-driven pipeline effectively integrates machine learning and physics for uncovering complex dynamics.
• Nonreciprocal hydrodynamic interactions are key to stabilizing and promoting nonlinear wave propagation in this system.
• This work provides a framework for modeling and understanding nonlinear phenomena in various physical systems.