A neural operator framework for data-driven discovery of stability and receptivity in physical systems.

A neural operator framework can identify stability and receptivity properties directly from data in complex systems without known equations, even in nonlinear regimes.

• Why it matters: Understanding system responses to perturbations is crucial across science and engineering, but traditional methods depend on known equations and linearization, limiting their applicability to nonlinear or poorly modeled systems.
• What they did: The authors trained a neural network as a dynamics emulator and used automatic differentiation to extract the Jacobian, enabling stability and receptivity analyses from observational data across various systems, including fluid flows and climate datasets.
• The result: The approach successfully identified dominant instability modes and optimal input-output structures, providing a broadly applicable, equation-free tool for analyzing high-dimensional, nonlinear dynamical systems.